Eleni Chalkia
email: hchalkia@certh.gr

Beate Mueller
email: mueller@vdivde-it.de3ifsttar

Alain L ' Hostis
email: alain.lhostis@ifsttar.fr

The role of societal resistance in transportation innovation

Keywords: Mobility, societal resistance, megatrend in transport

This paper focuses on the description of societal trends related to mobility and on the way that these trends can be perceived from the society, when implemented. This action represents the starting point of the European project Mobility4EU that focuses on creating an action plan for the coherent implementation of innovative transport and mobility solutions in Europe. In Mobility4EU we have defined a set of possible societal aspects that might lead to societal resistance to the implementation of the future transport megatrends that have been defined. This paper aims to highlight the possibility of societal resistance to a wider implementation of innovative transport solutions, related to foreseen megatrends for the 2030. In consequence the list has not the ambition to be comprehensive, but rather provide a first overview of the societal reaction to widespread diffusion of foreseen solutions.

Introduction

Since the publication of the 'Brundtland report' in 1987 [START_REF] Brundtland | Our Common Future[END_REF], there is a consensus that sustainable development is built around 3 axes: environment, economy and society. Additionally, global socio-economic and environmental megatrends are urging for a paradigm shift in mobility and transport that involves disruptive technologies and multimodal solutions. In all transport developments up to now, the environmental and economic aspects have been broadly viewed and researched. In contrast, the social aspects of sustainable transport, as well as their impacts, are often neglected and remain under-examined in comparison to economic and environmental ones. Thus, the social ramifications of transport developments are unclear and the social factors supporting unsustainable instead of sustainable transport are often forgotten.

The Mobility4EU project aims at producing a roadmap for mobility in 2030, taking into account all modes of transport, as well as a multitude of societal drivers encompassing health, environment and climate protection, public safety and security, demographic change, urbanisation and globalisation, economic development, digitalisation and smart system integration. The overall objective, related also to the current paper, consists in linking present and future societal trends and needs to existing and emerging transport and mobility solutions and providing also possible societal barriers to their implementation.

Since the main domain of study of the project is mobility and logistics, Mobility4EU has provided a comprehensive vision of societal drivers having an impact on mobility, aiming to establish a basis for the understanding of societal trends, in the broad sense, and the baseline for the development of these trends is presented at this paper. Thus, one of the scopes of this paper is to identify the interaction between societal trends and mobility and, the way society might react in future transportation innovative solutions implementation related to those trends and which is the outcome of its resistance in some cases. Most importantly, how this impact is shaping future requirements on transport from an individual and end-user level, will be studied. Thus, the changes in mobility and transport needs related to recent developments, such as e.g. urbanisation, mitigation and also impact of climate change, demographic change, sharing economy etc., will be assessed regarding the way they influence society.

Mobility and Societal challenges

The approach

Global socio-economic and environmental megatrends are urging for a paradigm shift in mobility and transport that involves disruptive technologies and multimodal solutions. The individual transport sectors face diverse technical and non-technical requirements and rather individual, sometimes contradicting challenges. An action plan for the coherent implementation of innovative transport and mobility solutions in Europe is thus urgently needed and should be sustained by a wide range of societal stakeholders. The approach we follow in MOBILITY4EU project is to work towards the development of such a plan taking into account all modes of transport, as well as a multitude of societal drivers encompassing health, environment and climate protection, public safety and security, demographic change, urbanisation and globalisation, economic development, digitalisation and smart system integration. A first step towards the achievement of such an "Action Plan for Future Mobility in Europe", is to identify and assess societal challenges that will influence future transport demand and supply, as well as to find and categorise promising cross-modal technical and organisational transport solutions to address these challenges. In order to achieve these objectives, a thorough methodology has been developed creating a participatory framework that has involved all partners of the consortium (L'Hostis, 2017). The following section describes the basic outcomes of this exercise that takes into account the relevant societal drivers due to current megatrends, such as health, climate and environment protection, safety & security, demographic change, urbanisation, economic development, digitalisation and smart system integration. Additionally, it takes into account in particular the user needs, reflecting the contribution of new mobility concepts to transport efficiency in all modes, highlight the implications of these new concepts on policy, anticipate potential societal resistance to new solutions. The aim is to propose an, as complete as possible, view on the societal factors, in the broad sense, that influence mobility and logistics and categorise them in megatrends clusters.

The Societal megatrends related to mobility

Mobility of passengers and freight is broadly considered as a key feature of modern societies. For this reason many existing and future mobility drivers have roots in societal aspects. Transport refers to technical and organisational solutions to address mobility needs and it involves vehicles, infrastructures, operators and users. Societal aspects will influence all these dimensions of transport, and reciprocally the interaction between transport supply and demand will have direct effects on behaviours, lifestyles and hence deep societal implications.

The acknowledgement that mobility is of crucial importance for our societies represents a broad consensus in scientific literature and in policies. And this trend is not seen as losing importance: according to a study by the International Transport Forum in 2011 [START_REF] Wilson | Transport Outlook 2011: Meeting the Needs of 9 Billion People[END_REF], by 2050 passenger mobility should increase by a staggering 200-300 % and freight activity by as much as 150-250 %.

Society and mobility are so closely linked, that some authors proposed to replace the study of society by the study of mobility [START_REF] Urry | Mobilities[END_REF]. In this spirit, Mobility4EU has chosen not to separate society from mobility and transport but rather consider them in an integrated approach, following the concept depicted at the figure below. That being presented, it makes obvious that almost all societal trends have effects on mobility and logistics demand and supply. In an economical approach, transport is studied as a demand supply paradigm. Nevertheless, a retroactive loop exists where new supply is able to generate a new demand that was not expressed before. In addition, the emphasis on society in our approach allows us to include in the retroaction loop the societal resistance to the implementation of new transport systems.

In Mobility4EU, the term societal drivers, covers an emerging pattern, movement, evolution in society that leads to change and potentially has implications for mobility and transport (e.g. ageing, social networks). Societal trends have impact in transport demand and its evolutions, thus, they can be considered as societal drivers for transport. Societal drivers includes societal trends, political trends, economic trends, technological trends and legal trends.

In Mobility4EU approach, a trend has an unequivocal impact on mobility. In comparison to related exercises in European researches our approach is rooted in the study of societal trends as opposed to a more classical transport demand analysis as for example in TransForum (Anderton, Åkerman, et al., 2015), in TRANSvisions [START_REF] Petersen | Report on Transport Scenarios with a 20 and 40 year Horizon, Final report[END_REF], in FUTRE [START_REF] Bernardino | FUTRE Deliverable 3.1: Factors of Evolution of Demand and Pathways[END_REF], in RACE2050 (Sena e Silva et al., 2013, 20), in EUTransportGHG (Sessa and[START_REF] Petersen | Report on Transport Scenarios with a 20 and 40 year Horizon, Final report[END_REF] or in ORIGAMI (Lemmerer & Pfaffenbichler, 2012). These approaches tend to separate trends along classical transport modes and transport markets, without going one step beyond, in the study of societal trends, as in the Mobility4EU project [START_REF] L'hostis | Mobility4EU project deliverable D2.1 -Societal needs and requirements for future transportation and mobility as well as opportunities and challenges of current solutions[END_REF]. As opposed to these approaches we have started by an analysis of societal dynamics in a broad sense, and in a second stage identifying those trends that have an interaction with mobility and logistics. Societal trends are for us entry points instead of transport solutions and markets. Our approach is hence complementary to these projects. In addition, as opposed to more thematic approaches having also studied societal trends like for instance CITYLAB on freight [START_REF] Dablanc | CITYLAB Observatory of Strategic Developments Impacting Urban Logistics (2016 Version)[END_REF] or TransForum on a few targeted transport sectors (Anderton & Åkerman, et al., 2015), our analysis intends to cover all transport modes, all geographical scales and freight as well as passenger transport.

The outcome of this methodology is a list of trends that depict the present situation and with a temporal horizon of 2030. In consequence, our description of trends aims at capturing the present situation and the dynamics of these trends in the future. This list can be seen as the shortest possible set of trends that allows describing present and emerging societal factors, in a broad sense, that have impacts on mobility, both for freight and passengers' mobility. The list is composed of 29 trends organized in 9 larger megatrend fields. Below the megatrends are described while the detailed trends are going to be presented in a future paper.

Economic megatrend: Lifestyles and economic development

The late modern society (Rosa, 2003) adds to the modern individualism and to the post-modern fluidity, the new dimensions of the social networks and the pervasive use of ICT. The so-called generations Z and Y exemplify these evolutions with a lower use of cars than their predecessors. The theme of the shared economy is strongly favoured by these trends. Direct implications for transport involve e-commerce (and the issue of the last mile) and the impact on the employment in the transport sector. Nevertheless, the trend of universal use of ICT comes with refractory groups, those unable to use them and that must be considered. In addition the trend will develop more carbon-neutral vehicles reduce the dependency of Europe on the import of (expensive) crude oil and as such sustain economic development on a macro-economic scale.

Inclusive society, personalisation, accessibility

The main current and future demographic trends are aging society and migration. The aging issue will have the strongest implications for the organisation of transport systems. The percentage of Europeans aged over 65 is projected to rise from 16% in 2010 to 29% by 2060. The European population aged over 80 is set to rise from 4.1% in 2010 to 11.5% in 2060 (according to an assessment of ILC-UK in 2014). Europe's population is also growing, with the EU population set to increase by 18 million people by 2050. The older European population of the future will have different transport requirements, and current transport and mobility enablers need to adapt to meet these challenges.

Urbanisation

Urban space has become the dominant European geography. As the share of Europeans living in urban areas is expected to increase between now and 2050 from 74% to 84%, transport movements occur increasingly in an urban context (UN, 2010). Growing and extending cities lead to the emerging concept of city-regions, which combines several spatial scales and transport modes. In the context of an artificial land cover increase by 3.4% in Europe between 2000 and 20064, the 50-years lasting car based urban sprawl is more and more seen as an issue by urban and regional planners because of the associated externalities (land consumption, energy, traffic congestion) with proposed alternatives like urban intensification, compact development, Transit Oriented Development (TOD) and, to some extent, smart cities. Regarding urban logistics, it should mentioned5 that freight is an important traffic component in cities (10 to 15% of vehicle equivalent miles), load factors for delivery vehicles in cities are very low (e.g. 38% for vans in London) and urban freight is responsible for 25% of urban transport related CO2 emissions and 30 to 50% of other transport related pollutants.

Environmental protection: climate change, pollution and resource and energy efficiency

Transport has since long time been linked to ecological issues like pollution and noise, with mitigation measures being e.g. ecological corridors. More recently, the impact on climate change raised public concerns and the related mitigation measures became a matter of policies. In 2012, emissions from transport constituted one fifth of all European CO2 emissions and are the only source that is still on the rise (European Parliamentary Research Service Blog). The related countermeasures refer to increasing the energy efficiency of vehicles and reducing the carbon footprint of the energy mix by the use of energy from renewable sources in transport which is enabled by the use of electricity as the energy carrier.

A transition towards the usage of renewable energy in the transport sector will additionally avoid the current depletion rate of fossil fuels and the environmental impacts induced during the sourcing of alternative fossil fuels such as tar sand oil and shale gas. However, when optimising the carbon footprint of transportation, a full system perspective is needed, including other life cycle stages and impact categories in order to avoid shifting the environmental burden (for instance toxicity aspects of mining activities for the production of a specific component should be accounted for.

Furthermore, the growth of transport activities is a serious problem, particularly in freight. The design of sustainable logistic systems depends not only on transport policies and on logistics service providers, but also on decisions made by shippers and manufacturers and even the end customer. Indeed, dematerialisation, 3D-printing, postponement of final product assembly, reshoring and local sourcing may all significantly contribute to transport reduction. Moreover, sustainable supply chains can also be influenced by governmental regulations. In addition, the increasing awareness of society about the operations behind product and services can lead consumers towards more responsible and sustainable choices, with an impact on the sustainability of the whole supply chain.

Digital society and internet of things

Improved environment perception due to advancements in camera and sensor systems as well as methods of sensor data fusion will enable higher degrees of automation in vehicles. Wireless communication among vehicles and between vehicles and the infrastructure add to this trend (V2X). Highly automated functionality, widely applied in aeronautics, is entering the automotive worlds now and will be available in other modes as well. It will increase traffic safety and fleet management significantly, and will sustain traffic control systems. However, new issues arise as well, e.g. related to privacy of data. A major trend for logistics with a 2050 vision is Physical Internet (PI). The aim of PI is to move, store, produce, supply and use physical objects throughout the world in a manner that is economically, environmentally and socially efficient and sustainable. PI aims at extrapolating the way Internet works into the logistics environment, achieving an open global logistic system founded on physical, digital, and operational interconnectivity, enabled through encapsulation of goods, standard interfaces and protocols.

Novel Business models and innovation in transport

The transport sector is witnessing the emergence of new players, new business models interacting with -if not fuelled by -new behaviour. New business models are closely related to the previously mentioned megatrend of Digital Society, Internet of Things and big data. The main issue regards the challenge over the currently dominating individual vehicle ownership model, as well as other cases where new players and new business models emerge, in batteries, in data, in freight. These business models are already here and will emerge greatly by 2030, having the potential overcome typical traditional existing business models in transport.

Safety in transport

No transport mode is exempt of safety issues and many public policies aim at addressing this problem. Road is mainly concerned with traffic safety; despite a continuous reduction of road fatalities, still 26.000 people died from road accidents in 2013 in the EU [START_REF] Paradowska | Comparison of Road Safety Policy Objectives in Poland and in the European Union[END_REF], which makes it a major societal issue. Smart integration and digitalisation of road vehicles implies the development of new safety measures. Despite significant improvement of the levels of safety, especially in the road transport domain, and encouraging perspectives, linked to automation, we perceive no sign that transport safety in general would become less an issue in the future than it is now.

In the perspective of the long term promise of a decrease of road casualty through the introduction of automated cars, a new safety issue emerge with the coexistence of automatic and non-automatic vehicles creating complex networks and environment. Safety will become a far more complex issue than today with insurance and liability necessary adjustment.

Security in transport

Terrorism is a growing concern in our societies and for governments. Attacks often target transportation means and hubs, and hence the interaction between this trend and mobility and freight is straightforward. More security is expected which raises the security/accessibility tension: the provision of more security in transport by introducing controls/barriers reduces accessibility. Urban transit, rail and aviation also have to deal with security and from the operators' point of view resilient operations is a constant objective.

Legislative framework

The legislative dimension translates societal demand by means of the production of laws and rules by public authorities and also by means of jurisprudence. Nevertheless, beyond the mere role of translation of societal demand, it carries a self-dynamic that enlists it as a societal trend in the broad sense. We identify three trends that exert influence in the domains of mobility and logistics.

Societal resistance in mobility

The implementation of the aforementioned megatrends, and then the detailed trends, is closely related with the different social barriers that might occur and from the resistance of the society towards their implementation. Societal resistance refers to the societal opposition to different dominant forms of social norms and values. Societal resistance includes also the opposition to governmental political and social actions and policies, as well as to the adaptation of new technologies or solutions that may implement and support these actions or policies.

Since the publication of the 'Brundtland report' in 1987, there is a consensus that sustainable development is built around 3 axes: environment, economy and society. In transport developments, the environmental and economic aspects have been broadly viewed and been researched. In contrast, the social impacts of sustainable transport are often neglected and remain under-examined in comparison to economic and environmental impacts. Thus, the social ramifications of transport developments are not clearly described and understood and the social/psychological factors supporting unsustainable instead of sustainable transport are often forgotten.

Understanding and defining the social impacts that the implementation of a transport innovative solution might have is not an easy task, since there are a lot of diverse, overlapping and competing ones [START_REF] Geurs | Social Impacts of Transport: Literature Review and the State of the Practice of Transport Appraisal in the Netherlands and the United Kingdom[END_REF]. Since the social impacts of transport have been vigorously neglected, or only been poorly taken into account, the knowledge about the reaction of society to the transport solutions that are proposed and implemented is vague. Thus, sometimes the implemented solutions might merge with the social norms and some other times they might be rejected, since the society cannot incorporate them and resists to its use. This societal resistance to the changes in transport is built upon specific pillars.

Job related resistance

New transportation trends are emerging and new innovative models are implemented to meet the needs of the society. These models always affect in a way the life of the people that live in the area where these models are implemented at. The bigger the change, the greater the resistance; especially in the beginning of the implementation. One of the biggest challenges of all occurs if fear exists that this new transport solution threatens job and especially the own job in any manner.

According to related studies, most unemployed people want full-time employment, even when they disliked the job they previously held [START_REF] Coffield | Learning to live with unemployment: What future for education in a world without jobs?[END_REF]. Thus, feeling threatened from a change at their working routine would make them unwilling to accept this solution. One example of this is the resistance of the society and specifically the taxi drivers to accept UBER (car sharing model). Of course UBER and all the other vehicle-sharing models have the potential to greatly benefit economy (people would buy fewer cars), environment (converting parking spaces to new and environmentally sound uses) and safety (reduce drunk driving and other accidents), but the societal resistance due to the fear of loss of the current employment in some countries, lead to its extinction.

Accessibility

Accessibility is a very important part of mobility, since mobility is the access of people to goods and services. Thus, any new transportation solution should bear in mind to enhance the accessibility of all the people that is targeting to serve. The accessibility features do not only restrain at the physical accessibility, but also expand to accessibility of the design. For example there are lots of bus lines that have been designed and implemented, but neither the vehicles are accessible (without bus ramps), nor the information given (no verbal feedback on the bus stops).

But when referring to accessibility, we do not restrict ourselves only to people with disability or elderly. One of the solutions with the highest market penetration [START_REF] Swapnil | World Advanced Driver Assistance Systems (ADAS) Market -Opportunities and Forecasts[END_REF] is the Advanced Driver Assistance Systems (ADAS). According to most recent reports (Chisult Insight, 2015), in 2014 the largest penetration rates of ADAS market was still in Europe, with a penetration rate of around 9.86%. This solution though excludes most of the car drivers since ADAS are mainly implemented in upper class vehicles, which the average car buyer cannot afford.

Technophobia and personal data protection

New transportation technologies are emerging, to meet the transportation challenges of our times, including connected and autonomous vehicles, keyless fleet management, local zoning, new technology for on-road communications, real-time traffic management, etc. It is clear now that ITS is poised to transform transportation, but as Adams said in 1999 [START_REF] Adams | The social implications of hypermobility[END_REF], "Even if the harmful environmental consequences of current and projected levels of mobility could be eliminated by technological advances, significant social problems would remain". And this problem is twofold. On the one hand there are people who are do not know how to use technology (they are afraid to use it -technophobia) and on the other hand there are people who don't want to use it because despite its impact at the quality of life, it also creates all kinds of problems, including distress, confusion, pathology, and conflict. An example of resistance to technology is the RFID ticketing or the mobile ticketing. This solution has great benefits to the average people, but lacks of benefit to the people who do not possess smart mobile phones or they don't know who to use these specific functionalities.

A consequence of the technology is also the great amount of data gathering in our times. This big data gathering and their treatment is an additional barrier for many. People do not like their personal information to be collected in any way or saved to a Cloud, that most people are not aware of its meaning or existence.

Habit

Ηuman beings usually behave in a sensible manner, meaning that they take account available information and implicitly or explicitly consider the implications of their actions [START_REF] Ajzen | From Intentions to Actions: A Theory of Planned Behavior[END_REF]. Most, of these activities that a person does in order to achieve a task have been designed in advance and their execution occurs as the plan unfolds. As a matter of fact, a certain sequence of these actions can become so habitual or routine that it is performed almost automatically, as in the case of driving from home to work or playing the piano [START_REF] Ajzen | Understanding Attitudes and Predicting Social Behavior[END_REF]. Habit is one of the most persistent human characteristics, since it requires less consciousness thought; the force of habit and social patterns. Once people create a habit over a form of travel behaviour or of organisation, they tend to stick to it. Habits or patterns of behaviour, of either individuals or group of people, are slow to change since, once established, they are extremely resistant to change precisely because of their self-reinforcing loop.

When changing a habit is required, energy consumption is needed and with no extreme extraneous impetus (legislation, death of a friend in a road accident, etc.), it is unlikely that someone who has a strongly developed pattern of car-driving for example, will change behaviour, even if presented with alternatives which are more appealing in terms of cost and more friendly to the environment. This explains heavily the resistance of some people to change, in relation to transportation mode use and this is the most difficult societal resistance bone to break since it is difficult to make counterbalance with specific incentives either economic, or environmental or even societal.

Conclusions

This paper focuses on the description of societal trends related to mobility and on the way that these trends can be perceived from the society, when implemented. This action represents the starting point of the European project Mobility4EU that focuses on creating an action plan for the coherent implementation of innovative transport and mobility solutions in Europe is thus urgently needed and should be sustained by a wide range of societal stakeholders.

During this effort, it has proven difficult to dissociate clearly societal trends from political or technological ones. In order to deal with this difficulty, we have chosen to cluster and categorize the trends in 9 big megatrends that covering multiple detailed mobility trends. These megatrends are the following: 1. Economic trends: wealth and labour market developments 2. Inclusive society, personalisation, accessibility The aforementioned megatrends provide a triggering point to our work on the detailed trends definition that will follow in a future publication. This stepwise and scientifically sound approach has allowed us to involve a large group of stakeholders in the process of identifying, evaluating and prioritising future trends and new transport concepts, implications, as well as potential societal resistance and adoption. This is one critical objective of this paper that has focused on the ways the society resists possible changes on its already established ways of transport.

Despite the widely acknowledged significance of the societal impacts of transport in everyday life, as well as their distributional effects across various segments of society, this issue has received less policy attention relative to respective economic and environmental impacts. That being said, in Mobility4EU we have defined a set of possible societal aspects that might lead to societal resistance to the implementation of the megatrends described. This societal resistance to the changes in transport is built upon four specific pillars: job loss resistance, affordability of technology, technophobia and habits. This paper aims to highlight the possibility of societal resistance to a wider implementation of innovative transport solutions, related to foreseen megatrends for the 2030. In consequence the list has not the ambition to be comprehensive, but rather provide a first overview of the societal reaction to widespread diffusion of foreseen solutions.

Figure 1 :

 1 Figure 1: Relation of societal factors with Mobility4EU project

Figure 2 :

 2 Figure 2: General concept of Mobility4EU project

  protection: climate change, pollution and resource and energy efficiency 5. Digital society and internet of things 6. Novel Business models and innovation in transport 7. Safety in transport 8. Security in transport 9. Legislative framework

Acknowledgements

This work has been developed under the EU funded project Mobility4EU


Mauro Zucchelli

Maxime Descoteaux

Gloria Menegaz

Investigating Diffusion-MRI based neurite density estimation model dependency: an in-vivo study on the HCP dataset

Synthetic data Results (from MICCAI 2017)

Our previous results [START_REF] Zucchelli | A generalized SMT-based framework for Diffusion MRI microstructural model estimation[END_REF] on synthetic data shown that:

• NODDI-SH and BS-SH tend to underestimate the neurite density • MC-MDI tends to overestimate it

HCP Results

HCP Results

Conclusions

• Neurite density has a well defined numerical range and it is stable across healthy subjects • However, its values strongly depend on the choice of the model used to calculate it

• Our results suggest that it could potentially be used as a feature to discriminate between healthy brains and pathological conditions • However, it is extremely important to keep in mind that its values are only proportional to the real underlying neural density and to compare it only with studies that use exactly the same model for its estimation

••

  Neurite density 1,2,3,4,5 is one of the most promising microstructural features that can be estimated from Diffusion-MRI multi-shell data • Recent years have seen a proliferation of Multi-Compartment models developed to estimate the neurite density Multi-Compartment models • Multi-Compartment models represents the diffusion signal as a weighted sum of compartments Neurite Density and Diffusion MRI • Neurite density can be calculated from Multi-Compartment models as the intra-axonal volume fraction ( ia ) • Recent years have seen a proliferation 1,2,3,4,5,6,7,9,10 of Multi-Compartment models • Each of these models makes different assumptions about the values of the diffusivity coefficient and the number of compartments Spherical Mean Technique • This MC representation of the diffusion signal is valid only for fibers aligned in a single direction • We can convolve the single fiber signal to the fiber Orientation Distribution Function (fODF) • With Y l m (v) are the real Spherical Harmonics (SH) functions Aims In this work: • We will compare the neurite density estimated using three different Multi-Compartment models • We evaluate its inter-subject reproducibility • We evaluate the effect of the other model parameters on its estimation We considered 10 subjects of the Human Connectome Project 8 • b-values = [1000, 2000, 3000] s/mm 2 • 90 gradients per shell plus 18 b 0 • ∆ = 43.1ms and δ = 10.6ms Zucchelli, M., Descoteaux, M., Menegaz, G. (2017). Proceedings of MICCAI, Workshop on Computational Diffusion MRI (CDMRI)", Canada.

• The mean of the signal depends only on the microstructural kernel and not on the fiber orientation[START_REF] Zucchelli | A generalized SMT-based framework for Diffusion MRI microstructural model estimation[END_REF][START_REF] Kaden | Multi-compartment microscopic diffusion imaging[END_REF][START_REF] Zucchelli | NODDI-SH: a computational efficient NODDI extension for fODF estimation in diffusion MRI[END_REF]

Aknowledgements

• This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (ERC Advanced Grant agreement No 694665 : CoBCoM -Computational Brain Connectivity Mapping) • Data were provided by the Human Connectome Project, WU-Minn Consortium(Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657)funded by the 16 NIH Institutes and Centers that support the NIH Blueprint forNeuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.


Thibaut Neveux
email: thibaut.neveux@univ-lorraine.fr

Ab-initio process synthesis using evolutionary programming

Keywords: process systems engineering, process synthesis, evolutionary programming, optimization, reaction-separation

published or not. The documents may come

Introduction and motivation

Process synthesis is the procedure of process generation used to select a set of unit operations (transformations of mass and energy), interconnected in a network (process flowsheet) -together with associated design and operating parameters-and optimizing given objectives that could be economic, environmental and/or societal. Such a procedure can be performed by applying various systematic techniques, referred as Process Systems Engineering (PSE) or (global) Process Intensification (PI) methods [START_REF] Grossmann | Research challenges in process systems engineering[END_REF][START_REF] Portha | Local and global process intensification[END_REF]. Possible techniques for process synthesis include heuristics (especially using experience and expertise) and decomposition-based [START_REF] Douglas | Conceptual design of chemical processes[END_REF][START_REF] Smith | The design of separators in the context of overall processes[END_REF][START_REF] Seider | Product and Process Design Principles: Synthesis, Analysis and Design[END_REF] on one hand, and optimization-based [START_REF] Floudas | A review of recent advances in global optimization[END_REF][START_REF] Biegler | Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes[END_REF] methods on the other hand. For details on process synthesis methods, see dedicated books and review articles [START_REF] Douglas | Conceptual design of chemical processes[END_REF][START_REF] Biegler | Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes[END_REF][START_REF] Nishida | A review of process synthesis[END_REF][START_REF] Grossmann | New trends in optimization-based approaches to process synthesis[END_REF][START_REF] Biegler | Systematic Methods of Chemical Process Design[END_REF][START_REF] Floudas | Nonlinear and Mixed-Integer Optimization. Fundamentals and Applications[END_REF][START_REF] Westerberg | A retrospective on design and process synthesis[END_REF], only a short review is provided here to highlight the synthesis challenge addressed in this paper.

Decomposition approaches are able to propose efficient processes, but do not guarantee an optimal process since the interactions between different levels of decomposition (e.g. reaction, separation, heat Superstructure based on process units MILP, MINLP [START_REF] Floudas | Nonlinear and Mixed-Integer Optimization. Fundamentals and Applications[END_REF][START_REF] Biegler | Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes[END_REF] GDP [START_REF] Barttfeld | A decomposition method for synthesizing complex column configurations using tray-by-tray gdp models[END_REF][START_REF] Dowling | A framework for efficient large scale equation-oriented flowsheet optimization[END_REF]] Superstructure based on phenomena or tasks MINLP [START_REF] Demirel | Systematic process intensification using building blocks[END_REF][START_REF] Kuhlmann | Optimization-based approach to process synthesis for process intensification: General approach and application to ethanol dehydration[END_REF] Ab-initio, no superstructure is assumed EP+NLP this study integration) are not considered [START_REF] Cremaschi | A perspective on process synthesis: Challenges and prospects[END_REF]. Optimization-based methods allow to rigorously model and search for an optimal solution within a defined search space, optimizing the selected performance objectives. They rely mainly on mathematical formulations such as generalized disjunctive programming (GDP) [START_REF] Barttfeld | A decomposition method for synthesizing complex column configurations using tray-by-tray gdp models[END_REF][START_REF] Dowling | A framework for efficient large scale equation-oriented flowsheet optimization[END_REF], or mixed integer non-linear programming (MINLP) [START_REF] Biegler | Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes[END_REF][START_REF] Floudas | Nonlinear and Mixed-Integer Optimization. Fundamentals and Applications[END_REF], which can be solved by a large panel of techniques [START_REF] Floudas | Nonlinear and Mixed-Integer Optimization. Fundamentals and Applications[END_REF][START_REF] Dowling | A framework for efficient large scale equation-oriented flowsheet optimization[END_REF][START_REF] Skiborowski | A hybrid evolutionary-deterministic optimization approach for conceptual design[END_REF][START_REF] Adjiman | A global optimization method, αbb, for general twice-differentiable constrained NLPs -I. theoretical advances[END_REF][START_REF] Boozarjomehry | Automatic design of conventional distillation column sequence by genetic algorithm[END_REF][START_REF] Grossmann | Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming[END_REF]. Noticeably, other approaches focusing mainly on Process Intensification explore beyond the concept of unit operations and optimize a process at the phenomenological or functional level rather than at the equipment level [START_REF] Papalexandri | Generalized modular representation framework for process synthesis[END_REF][START_REF] Lutze | Phenomena based methodology for process synthesis incorporating process intensification[END_REF][START_REF] Peschel | Methodology for the design of optimal chemical reactors based on the concept of elementary process functions[END_REF][START_REF] Zivkovic | A method for reactor synthesis based on process intensification principles and optimization of superstructure consisting of phenomenological modules[END_REF][START_REF] Demirel | Systematic process intensification using building blocks[END_REF][START_REF] Kuhlmann | Optimization-based approach to process synthesis for process intensification: General approach and application to ethanol dehydration[END_REF] For a complete overview of optimization-based process synthesis, see for example the recent review of Chen and Grossman [START_REF] Chen | Recent developments and challenges in optimization-based process synthesis[END_REF].

Whatever the mathematical approach in Process Systems Engineering, the first step is to postulate a set of alternatives represented by a process superstructure, including process unit operations of interest and foreseen interconnections [START_REF] Floudas | Nonlinear and Mixed-Integer Optimization. Fundamentals and Applications[END_REF], Chen and Grossman point out that "limitations here arise in our ability to define an appropriate search space" [START_REF] Chen | Recent developments and challenges in optimization-based process synthesis[END_REF]. This initial step could be a difficult task when the number of possible combinations is high due to the process complexity. Counter-intuitive, yet relevant, solutions could also be missed during the process synthesis procedure.

The challenge addressed in this paper is the possibility of performing optimization-based process synthesis without postulating any superstructure (see the Table 1). The ambition is to avoid the subsequent bias due to the restriction of the space search to a set of possibilities. This approach is called here ab-initio process synthesis as a parallel from other fields such as optic [START_REF] Pal | Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming[END_REF] where similar design problems occur; the ab-initio term is also used in chemical engineering for thermodynamic properties calculations [START_REF] Van Speybroeck | The calculation of thermodynamic properties of molecules[END_REF]. This approach could also be referred as "superstructure-free" in building design [START_REF] Boonstra | Super-structure and super-structure free design search space representations for a building spatial design in multi-disciplinary building optimisation[END_REF].

This paper presents a new generic method for process synthesis that does not require the preliminary definition of any set of alternatives, hence mimicking the whole mechanism of process creation and evaluation. The method is presented in section 2; it relies on the combined use of an Evolutionary Programming (EP) algorithm for automatic construction of process flowsheet, and of a Non-Linear Programming (NLP) algorithm for process evaluation. This hybrid optimization strategy works without any superstructure, given a set of available unit operations as elementary blocks assembled through mutation operators by the EP, and an objective function optimized by the NLP. The method is illustrated in section 3 for a reaction-separationrecycle system; the benzene chlorination process from Kokossis and Floudas [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF] is chosen to confront the method presented in this paper to their MINLP optimization of a superstructure. Finally, the possible uses and the challenges of ab-initio process synthesis are discussed in section 4.

Ab-initio process synthesis method

Method overview

The goal of the presented method is to achieve process synthesis without assuming any superstructure, using a set of available unit operations as elementary blocks to build a process flowsheet. The method was developed by trying to transpose the remarkable work of Lipson and Pollack [START_REF] Lipson | Automatic design and manufacture of robotic lifeforms[END_REF] on robotic design in chemical engineering domain. They ab-initio designed robotic lifeforms by evolution from basic building blocks (bars, joints, actuators, artificial neurons) and using a physical simulator for the evaluation of robot fitness (locomotive ability) [START_REF] Lipson | Automatic design and manufacture of robotic lifeforms[END_REF]. In this work, the philosophy is kept whereas the specifics are adapted to the chemical engineering field; instead of bars connected by joints to describe a robot, a process flowsheet is described by unit operations connected by streams.

The process synthesis method is schematized in Figure 1, and is implemented in a newly developed tool called PSEvo (Process Synthesis by Evolution). The method works on two levels combining the use of an Evolutionary Programming (EP) algorithm for automatic construction of process flowsheet, and of a Non-Linear Programming (NLP) algorithm for process evaluation. The EP is applied on the upper level as a construction tool by choosing, assembling and connecting unit operations into a process flowsheet (see section 2.2). Each process is then evaluated by the NLP on the lower level by solving heat and mass balances (see section 2.3) and optimizing an objective function with respect to the process degrees of freedom (e.g. design specifications, operating parameters). The way to define a new process synthesis problem (i.e. application specifics) is described in §2.4, and method implementation in §2.5.

Case set-up

Solution

Definition of process synthesis problem

Task-specific dynamic library

Modules pool

For each module :

•

Evolutionnary synthesis

Automatic construction of process flowsheet

Process evaluation

Objective function calculation

Optimization problem set-up

Evolutionary synthesis

The evolution procedure is responsible for the construction of a process flowsheet given elementary blocks (unit operations), an Evolutionary Programming (EP) method is here employed to do so. Evolutionary Programming [START_REF] Fogel | An Overview of Evolutionary Programming[END_REF] is part of a wider category of nature-inspired methods called Evolution Algorithm (EA) [START_REF] Eiben | Introduction to Evolutionary Computing[END_REF][START_REF] Yu | Introduction to Evolutionary Algorithms[END_REF], which includes: genetic algorithms (GA), evolution strategy (ES), evolutionary programming (EP), and genetic programming (GP) methods. EP differs from other EA methods in that mutation is the only evolution driver. The crossover operators used in other EAs are not used in Evolution Programming, new candidate solutions are generated by exclusively applying mutation operators on existing candidate solutions. Metaphorically speaking, Evolutionary Programming mimics natural selection by focusing on the level of the species (phenotype) and not the level of single individuals (genotype) [START_REF] Fogel | Artificial Intelligence through Simulated Evolution[END_REF].

In chemical engineering, the use of Evolution Algorithms for process synthesis is common [START_REF] Koch | Optimization of combined cycle power plants using evolutionary algorithms[END_REF][START_REF] Boozarjomehry | Automatic design of conventional distillation column sequence by genetic algorithm[END_REF][START_REF] Skiborowski | A hybrid evolutionary-deterministic optimization approach for conceptual design[END_REF][START_REF] Keller | Reactive distillation for multiple-reaction systems: Optimisation study using an evolutionary algorithm[END_REF], mostly by using Genetic Algorithms, and used to optimize a superstructure with the intrinsic bias already mentioned, limiting the search space to a set of alternatives. In this work, by using an Evolutionary Programming method to build a process from elementary blocks (unit operations), the search space is virtually infinite and not restrained by a fixed-size representation. So far, processes have been generated with up to 100 building blocks on dummy cases, such as maximizing the efficiency without limitations on the number of unit operations. For real cases, limitations appear because the number of building blocks is penalized, usually in the form of a capital cost for additional blocks or increased network complexity. These sorts of parsimony principle arising from the definition of the Process Synthesis drivers is discussed on section 4.2.

The general evolution procedure is pictured in Figure 1 Save all data and generate the report with evolution steps, phylogenetic tree and best individuals

The initial population is typically a simple 'empty' flowsheet (a feed connected to an outlet), but could also be any flowsheet defined by the user if required. The stopping criterion can be a maximum number of generations and/or a number of consecutive generations without improvement of the objective function value. Usual selection and replacement methods can be: random uniform, linear or exponential rankings (probability of choice is linearly or exponentially based on process rank), or fitness-proportionate (probability of choice is based on process fitness). The impact on the choice of selection and replacement methods on the convergence is discussed in the case study. Mutation operators are detailed in the next paragraph , and process evaluation (fitness calculation) in §2.3.

Mutation operators

Since the evolution is only driven by mutation, the key aspect is the definition of the mutation operators, so that every process can be obtained from scratch by the application of a sequence of mutation operators. Given a set of elementary building blocks (types of unit operations), mutation operators must be able to assemble them into a flowsheet, while remaining as simple as possible to minimize the inductive bias associated to their definition.

Three elementary mutation operators are used in this work: addition of a block (type of unit operation) between two existing blocks, removal of an existing block, permutation of two streams. See the Figure 2 for details and example.

Using these three simple building rules, any process flowsheet can be created by exploring the possible sets of unit operations (addition and removal operators) and their interconnections (permutation operator). During the mutation step of the evolutionary synthesis, one or several mutation operators are applied with respect to predefined probabilities (see default parameters in §2.5), at least one mutation needs to be applied.

Connectivity rules

During the mutation step, unconnected inlets and outlets can appear. This type of situation occurs if a unit with a different number of inlets and outlets is added or removed. It is particularly illustrated on Figure 2 with the addition of a mixer -a block with two inlets and one outlet-leading an unconnected inlet. Such structures are inconsistent since each connector (inlets and outlets of every block) needs to be linked to another block, which is here circumvented by connectivity rules. Firstly, it is checked if other non-linked connectors exist on another unit operation. If this is the case, a new stream is added to connect them. By security, the outlet of a unit operation can not be linked to one of its inlet, to avoid auto-loops. If several non-linked connectors are available, one of them is randomly selected. Secondly, non-linked connectors could remain. If a block has non-linked outlet connector, it is connected to an additional 'process out' block. Similarly, if a block has a non-linked inlet connector, it is connected to an additional 'Null feed stream' block, i.e. a virtual feed with null stream. A cleanup is also performed to remove useless structures such as a 'Null feed stream' block connected to a 'process out' block.

The first step enables to connect as many unit operations as possible, before adding additional unit operations in the second step to ensure complete process connectivity. These connectivity rules are applied at the end of the mutation step, after the application of mutation operators, and ensure that the process is valid from the connectivity point of view and is suitable for process evaluation.

Process representation (phenotype)

Whereas the evolutionary programming algorithm is generic and resembles to the one of Lipson and Pollack [START_REF] Lipson | Automatic design and manufacture of robotic lifeforms[END_REF], the mode of candidate representation is domain specific and should be able to reproduce the candidate phenotype. Here, a process flowsheet is represented by the following elements: N u the number of unit operations; N s the number of streams connecting the units; IM the incidence matrix (size N s × N u ) detailing the connectivity between units and streams; T a string vector (size N u ) of unit types; and M a logical vector (size N u ), 'true' meaning that the unit is mandatory.

The number and types (e.g. Feed, Reactor) of unit operations are defined by N u and T , their interconnections into a network by N s and IM . The M logical vector indicates if the unit operation is mandatory in the process flowsheet and cannot be removed by the evolutionary synthesis procedure, this vector is particularly useful if the user wishes to impose certain blocks in the process, such as at least a reactant feed and a process outlet. The unit can yet be placed in a different order in the process, particularly by the application of the permutation operator.

During evolution, mutation operators act by simply modifying the process phenotype. For example, a block addition or removal affects the sizes and content of vectors and incidence matrix; stream permutation switches elements in the incidence matrix. The connectivity algorithm also affects the units and/or the unit operations. An example of process representation (phenotype) before and after the application of a mutation operator and the connectivity algorithm is provided in supporting information.

Within this framework, process feeds and outlets must be considered as unit operations, their impact on the process performance (such as reactant consumption, product sales, energy) is taken into account through calculated parameters of each unit operation.

Process evaluation

The role of the process evaluation is to get the flowsheet representation (phenotype) from the evolutionary synthesis procedure, and compute the fitness function (see Figure 1). To do so, the process balances (heat and mass, including possible recycles) need to be solved in order to calculate and optimize the objective function (process fitness). The corresponding mathematical problem is automatically constructed from the process phenotype, and is formulated as a classic Non-Linear Programming (NLP) optimization problem:

           max F obj (z) s.t. g(z) ≤ 0 h(z) = 0 t(z) = s -s(z) = 0 z ∈ [z l , z u ] (1)
with

• z the set of optimization variables z T = [x T , s T ]
• x the set of decision variables (process degrees of freedom, for example the design variables of unit operations such as the volume of a reactor) • s the set of (guessed) tear variables. g and h constraints are (optional) process design inequality and equality constraints, such as limitations on temperature or pressure, minimal production, desired purity and so on • t(z) the set of tear equations ensuring that the recycle equations are satisfied, i.e. the difference between s and the calculated tear stream variables s(z) from the current guess s and decision variables x. s is obtained by sequentially calling the unit operations models.

In case of non-convergence of heat and mass balances, i.e. the t(z) tear equations are not equal to zero, the process is considered non-viable and an arbitrary large negative value (or positive in case of minimization) is affected to F obj . The tearing algorithm of Roach [START_REF] Roach | A new synthetic method for stream tearing in process systems analysis[END_REF] is used here to select a set of tear streams, and hence to determine the calling sequence.

An unfeasible path approach [START_REF] Wolbert | Flowsheet optimization and optimal sensitivity analysis using analytical derivatives[END_REF] is used here since the flowsheet convergence is dealt during the optimization. Such an optimization problem can be solved by a NLP code, for example by using a Sequential Quadratic Programming (such as SLSQP [START_REF] Kraft | Algorithm 733: TOMP-Fortran modules for optimal control calculations[END_REF] or NLPQLP [START_REF] Schittkowski | A Fortran implementation of a sequential quadratic programming algorithm with distributed and nonmonotone line search -user's guide[END_REF]) or an interior-point method such as IPOPT [START_REF] Wächter | On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming[END_REF]. Since the NLP codes are gradient-based method, a typical multistart approach is used to limit the risk of finding a local minimum. A set of different initialization of z is randomly generated in the domain, and the NLP is launched for each of them. The parametric domain is defined by the user, which provides lower and upper values for each optimization parameter (and optionally an initial guess, which is used in addition to the random sampling). The number of sampling points is either fixed by the user, or taken arbitrarily equal to the number of unit operations in the currently evaluated process. In the end, the best solution respecting all constraints is kept So far, it has been observed that the same optimum is found with the various initialization when convergence is reached; this option is still kept for future investigation.

Definition of process synthesis problem

For each process synthesis problem, i.e. for a new application, the user needs to define the following task-specific elements:

• A pool of unit operations, defining for each one:

-the name of unit operation type (e.g. heat exchanger, reactor, reactant feed), -the number of inlet and outlet streams (connectors), -the inlet parameters (i.e. unit operation degrees of freedom such as design specifications), -the calculated parameters (e.g. capital cost, energy), -the relation giving the outlet streams and calculated parameters as a function of inlet parameters and inlet streams (i.e. the unit operation model), -the potential constraints to be respected (e.g. maximum temperature, product purity in the outlet).

• A description of stream: number of variables used to represent a stream (e.g. temperature, pressure, flowrate, composition) • An objective function calculation (e.g. total energy consumption, process annualized cost), computed from the calculated parameters of the different unit operations

The evolutionary synthesis procedure only uses the name of unit operation type, to distinguish the different types of module, and the number of inlet and outlet streams, to connect them into a flowsheet. The process evaluation procedure uses all the elements to define and solve the optimization problem.

In the end, the approach adopted here by field transfer from robotic to chemical engineering, has a similar philosophy than the one developed by Voll et al. [START_REF] Voll | Superstructure-free synthesis and optimization of distributed industrial energy supply systems[END_REF] on energy supplied systems and extended by Wang et al. [START_REF] Wang | Superstructure-free synthesis and optimization of thermal power plants[END_REF] on thermal power plants. In their work, they used six "knowledge-integrated mutation operators" that are application-specific, and the process needs to be hierarchically decomposed into meta, function and technology levels, meaning that mutation operators and process representation needs to be conceptualized for each new synthesis problem. The approach presented here is believed to be more generic since the process description and mutation operators do not depend on the studied system. For a new synthesis problem, the user only needs to define the elementary blocks (pool of unit operations), stream description, and objective function.

Method implementation: PSEvo

The presented method is implemented in a newly developed tool called PSEvo (Process Synthesis by Evolution), coded in Fortran 2008 in an object-oriented way. External libraries are used for specific tasks: the SLSQP optimizer [START_REF] Williams | SLSQP -Modern Fortran Edition of the SLSQP Optimizer[END_REF] as NLP solver, Graphviz [START_REF] Gansner | An open graph visualization system and its applications to software engineering[END_REF] and Gnuplot [START_REF] Williams | Gnuplot 5.0: an interactive plotting program[END_REF] for on-the-fly plotting of process flowsheets and objective function during evolution. Detailed information is generated in a synthetic HTML report to examine the evolution results.

Each new process synthesis problem needs to be compiled into a dynamic library (see Figure 1) using a given template, so that the user does only have to focus on definition of unit operations and objective function. An example of the required data is provided in the case study and in the appendix.

By default, the evolution control parameters are the following: N ind =50 individuals (i.e. population size); a mutation rate of 50% (α); mutation operators probabilities of 5% for module addition and removal (p add and p remove ), 20% for streams permutation (p permut ); random selection (before mutation); replacement based on rank (after mutation); 100 successive iterations without objective function improvement as stopping criterion. These parameters are discussed in section 3.4.

Case study with a reaction-separation-recycle system

The search of an optimal design for reaction-separation-recycle systems can be seen as global (process scale) intensification strategy based on flowsheet architecture improvement [START_REF] Portha | Local and global process intensification[END_REF], and has been dealt in many papers [e.g. [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF][START_REF] Kokossis | Optimization of complex reactor networks -I. isothermal operation[END_REF][START_REF] Esposito | Deterministic global optimization in isothermal reactor network synthesis[END_REF][START_REF] Soltani | Adiabatic reactor network synthesis using coupled genetic algorithm with quasi linear programming method[END_REF][START_REF] Zivkovic | A method for reactor synthesis based on process intensification principles and optimization of superstructure consisting of phenomenological modules[END_REF]. This makes reaction-separation-recycle systems a relevant example to validate the developed method and its implementation.

The benzene chlorination process from Kokossis and Floudas [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF] is chosen as a case study. The idea is to confront their optimization of a given superstructure to the ab-initio process synthesis presented in this work.

The studied reaction is the benzene (A) chlorination to produce monochlorobenzene (B), with dichlorobenzene (C) as a waste product. The mechanisms are simplified into two first-order and irreversible reactions (A → B → C) [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF]. Reactions occur either in Continuous Stirred-Tank Reactors (CSTR) or Plug-Flow Reactors (PFR). The objective being to produce pure B, separators are required. The volatility ranking is A>B>C, ideal distillation columns (100% purity) are used with the following possible separations: A/BC, AB/C, A/B, B/C. [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF] (reproduced with permission of Elsevier), a set of alternatives is defined and a MINLP method selects the optimal flow path and associated degrees of freedom. Right) this work: definition of the ab-initio process synthesis. No superstructure is assumed, the EP constructs the flowsheet from the available unit operations and the NLP determine the optimal degrees of freedom, i.e. the best objective function obtainable for a given flowsheet.

Problem definition

Kokossis and Floudas [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF] defined several superstructures to cover as many process alternatives as possible, combining the use of reactors (CSTR and PFR), ideal distillation columns (A/BC, AB/C, A/B, B/C), mixers and splitters; cf. one of their superstructure on Figure 3 (left).

In this work, the problem definition is quite different. Instead of defining a set of alternatives represented by a process superstructure, only the available unit operations are defined. The evolutionary Synthesis procedure picks into this pool of unit operations to build any process flowsheet; cf. the Figure 3 (right). An 'empty' flowsheet, i.e. a 'Feed' unit (flowrate of pure A) connected to a 'Process Out' unit, is used as an initial population. The objective here is to maximize the annualized profit, which includes capital cost of unit operations, reactant costs, energy costs and product sales. Two cases are investigated to assess the sensitivity of the optimal process to the objective function definition: Case A. Maximize profit for a production of 50 kmol/hr of B, same capital cost for PFR and CSTR.

Case B.

Maximize profit for a production of 50 kmol/hr of B, higher capital cost for PFR than for CSTR Case A is slightly similar to case 2 in [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF] by using the same capital cost for PFR and CSTR, except that the objective function is to maximize profit instead of minimizing the annual cost. Case B is identical to case 4(a) in [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF]. Detailed equations for unit operations and objective functions are reported in Appendix. The default evolution parameters of PSEvo are used (see §2.5).

Process synthesis results

The optimal processes found by PSEvo are displayed on Figure 4 for cases A and B, with associated degrees of freedom (i.e. reactor volumes and reactant feed flowrate). In both cases, the optimized configuration is based on a reaction part (CSTR in series or PFR), a first distillation column A/BC, recycling of unreacted A using a mixer before the reaction part, and a second distillation column B/C to separate the product B from the waste product C. The only difference is that one PFR of 13.01 m 3 is used for case A, whereas three CSTR in series for a total volume of 13.91 m 3 are used for case B (N.B. the three volumes are slightly different due to the evolution of molar volume with composition. If the molar volume would have been constant, the three volumes would be equal to maximize the reaction conversion). Both feed flowrates are also similar: 51.07 kmol/hr for case A and 51.48 kmol/hr for case B.

Not surprisingly, the use of a PFR instead of CSTR in series is chosen if they have the same capital cost (case A), due to the higher conversion achieved with PFR for the same reactive volume. For case B, 3 CSTR in series are used to achieve a similar conversion but at a lower cost. During evolution, processes with up to 5 CSTR in series were produced but not retained by the algorithm since they exhibit a lower profit. Regarding the separation part, the use of A/BC separation before B/C separation is also logical. Separating and recycling A before purification of B leads to a lower flowrate entering the second distillation column, hence a lower cost. Noticeably, both these structures were also obtained by Kokosssis and Floudas based on the superstructure optimization.

Evolution path and convergence

To analyse how processes evolve to produce an optimal solution, the objective function (annual profit) is plotted with generation on Figure 5 for Case B. The dots represents the objective function of the entire population, and the red line the evolution of the best achieved objective function with generations. Objective function rises by steps until convergence, process structures corresponding to notable evolution steps are also displayed on Figure 5. Processes evolved from the initial 'void' structure (a) to the final process (f). Successively, the algorithm added a PFR and a first distillation column (b), then replaced the PFR by a CSTR and added a second distillation column (c), positive profit is then obtained by using 3 CSTR in series (d). On step (e), a mixer is added to recycle unreacted A before the third reactor, leading to a substantial gain in profit. Finally, the A recycle is positioned before the first reactor (f, optimal process). It should be noted that processes (a) to (f) do not necessarily correspond to a mutation from one to another. "Good" processes could emerge by modification of an already interesting process (incremental improvement) or of a non-profitable one.

Due to the stochastic nature of the procedure, several optimizations should be systematically launched to check that the optimal solution is independent of the optimization run. The Figure 6 presents the optimization progress with four different random seeds, using the same problem definition. For the four runs, Optimal process (identical for the 4 runs) the same optimal process is found, but with distinctive evolution paths. Different applications of mutation operators can indeed lead to the same process structure, this non-exclusivity in flowsheet construction is illustrated on the Figure 6.

Sensitivity to evolution control parameters

The evolutionary programming algorithm requires the specification of various evolution parameters, whose sensitivity is assessed here.

Selection and replacement methods

Since evolution is a random process driven by evolutionary pressure, at least one random method must be kept, either for selection or for replacement. Three cases are considered:

1. Selection: random. Replacement: linear ranking 2. Selection; linear ranking. Replacement: random 3. Selection: random. Replacement: random

The third case (random-random) is basically a random search within the search space, both other cases apply a selective pressure (linear ranking) during selection or replacement. An example of optimization progress for three cases is presented in Figure 7, with a high number of generations (up to 1000). For each case, 10 runs are performed with different random seeds, the obtained median and interquartile range is plotted with generations. Both methods applying a selective pressure converged in a limited number of generations (around 50-100 generations for case 1, and 150-200 for case 2), whereas the optimal solution is not found in 1000 generations for pure random search (case 3), illustrating the need for a selective pressure for evolutionary algorithms.

In addition to convergence speed, the population diversity during evolution can be analysed. It is expected that a higher diversity would lead to a higher chance of finding the optimal solution at long-term. To compare diversities, the Shannon entropy [START_REF] Shannon | A mathematical theory of communication[END_REF] is used in this work, which is an extension of the entropy concept in information theory, and is particularly used in biology to quantify biodiversity. For a given population, Shannon entropy H is defined as:

H = - i p i • log 2 (p i ) ( 2
)
where i are the different phenotypes observed in the population, and p i is the probability of observing the phenotype i among the population (i.e. the fraction of population corresponding to the same phenotype). Two individuals belong to the same phenotype if their flowsheet and objective functions are identical. The comparison of flowsheets can be performed by checking if the directed graphs associated to the process structure are isomorphic (i.e. they show exactly the same flowsheet / process structure). The higher the entropy, the higher the biodiversity among the population is. A diverse population has a better long-term viability, meaning a higher chance of finding the optimal solution. A null entropy means that the entire population is uniform with only one phenotype, it only appears during initialization. The maximal entropy is achieved if all individuals are unique in the population. If the number of individuals per generation is 50, the maximal entropy of the system is log 2 (50) ≈ 5.64 (p i = 1/50, ∀i ∈ [START_REF] Grossmann | Research challenges in process systems engineering[END_REF][START_REF] Soltani | Adiabatic reactor network synthesis using coupled genetic algorithm with quasi linear programming method[END_REF]).

Complementary to Shannon entropy, the phylogenetic trees provide visual information on diversity, representing the ancestral relationships with generations. An example of the evolution of Shannon entropy with generations is presented in Figure 8 for the three cases (same random seed), as well as the phylogenetic trees, for the first 100 generations.

No specific pattern appears for the phylogenetic tree of case 3, since it corresponds to a random exploration. For other cases, branches exist in the trees due to selective pressure. A massive extension even appears during the first generations for case 1 (random selection, linear ranking for replacement). Quantitatively, the Shannon entropy for the random exploration (case 3) quickly increases with generations, and stabilizes close to the maximal entropy of 5.64. For case 2, the Shannon entropy also stabilizes after a few generations, but at a lower Shannon entropy value (around 1-2). Yet, the optimal solution is found in less than 200 generations (cf. Figure 7). Interestingly, the case 1 leads to high Shannon entropy, also close to the maximal entropy, reaches a maximum around 60 generations and then decreases. The loss of diversity corresponds to the branch extinction appearing in the phylogenetic tree, and to the generation where an optimal solution is found. After the maximum in entropy, the population evolves with a diversity decrease as more individuals isomorphic to the optimal solution are generated.

From these results, random selection and linear ranking for replacement appear to be the most efficient combination since it leads to a faster convergence fur 10 runs (cf. Figure 7), while leading to a high population diversity (cf. Figure 8). Hence, a higher chance of finding the optimal solution is expected at long-term.

Population size and mutation rate

The sensitivity to mutation rate (α) and population size (N ind , number of individuals per generation) is assessed. More than 200 optimizations were performed to cover the parameters ranges, the number of process evaluation required to find the optimal solution is reported on Figure 9.

The mutation rate represents the fraction of the population that is replaced at each generation. As seen on Figure 9 (top), too low or too high mutation rates lead to a large number of process evaluations. The population size manifests a similar behaviour at high values of number of individuals per generation. A mutation rate between 0.3 and 0.6, and a population size between 30 and 50 seems to be a good compromise of evolution within a generation. The mutation probabilities (p add , p remove , p permut ) were also assessed but no clear trend is observed while variating the mutation probabilities between 0.05 and 0.2.

Choice of evolution parameters

This sensitivity analysis highlights the importance of parameters choices, since the convergence speed can triple depending on the tuning. Other selection/replacement methods could be investigated (e.g. fitnessproportionate, exponential ranking, tournament, age-based), in combination with all other evolution control parameters (population size, mutation rate, probabilities) to cover the entire parameters space, which represents a high number of possibilities. For further tuning, the Shannon entropy could be used to obtain information on the parameters relevance, for example by using the REVAC method [START_REF] Smit | Using Entropy for Parameter Analysis of Evolutionary Algorithms[END_REF].

Case study conclusion

The objective of the case study was to validate the proposed ab-initio process synthesis method on a well-known problem. The same structures have been obtained, without assuming neither the number and types of unit operations nor their interconnections (e.g. reactors before separators, presence of recycle). The proof of concept of the newly proposed process synthesis strategy is therefore considered as validated. The adequacy in terms of solution obtained from two different approaches is remarkable and should be stressed. No previous study addressed, to our knowledge, such a critical comparison. Yet, no new solutions were found compared to the reference paper used for the case study [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF], probably because their superstructure already encompassed a large number of possibilities, using 32 binary variables (~4 billions possibilities).

In this work, the method generally requires fewer than 5000 evaluations to converge (for a number of combinations superior to 10 9 ), which is performed with a CPU time around 2 minutes on a single processor (no parallelization performed yet). This low CPU-time is due to the very simple numerical models used for process units (see the Appendix, no thermodynamic calculations is performed and process units models are mainly composed of analytical expressions) and is not expected to be encountered in real-case applications. The percentage of non-convergence (due to initial values or incoherent structures) observed for the various runs varies between 2 an 20% with an average of 8% on 100 runs.

It should be reminded that this case study remains quite simplified. A higher number of degrees of freedom would be available if non-ideal separations, columns with staged withdrawals and feed, as well as Cl 2 injection and HCl stripping were integrated into the PSE problem, possibly leading to more complex structures.

Discussions and perspectives

On the elementary building blocks

The elementary building blocks include numerical models to calculate outlet streams and parameters from inlet streams and parameters, requiring a certain effort depending on the model complexity. The important question in such process synthesis problem is: where to put the effort?

Types of models

The process designer should put importance into the blocks definition according to the treated problem. Simplified functional or physical models provide relatively few information but are easier to develop and numerically more robust. On the contrary, rigorous models provide detailed information such as a precise link between design and performance, but could be difficult to solve in some cases (internal convergence procedure), hence penalizing the optimization. To circumvent (numerical) complexity, one could use simplified physical models (such as ideal conditions instead of rigorous thermodynamic models, or effective diffusivities instead of Maxwell-Stefan equation for multicomponent mass transfer), but at the -potentially huge-cost of losing accuracy, or missing physical limitations (such as azeotrope in distillation, or diffusion barrier in multicomponent transfer). Depending on the case, a simplified models may not be suited.

The use of surrogate models fitted from a rigorous model may be a good compromise. It requires an additional effort to define a proper numerical design of experiments covering the entire search space (i.e. unit inlets and degrees of freedom) and to perform the model reduction. A large variety of surrogate models can be used (neural networks, polynomial chaos, response surface, kriging etc.). Such models allow to benefit from the information of a complete physical model with the numerical robustness of a simplified one. It should also be noted that this solution allows to use already available models (e.g. former models, using commercial simulator to perform the design of experiments) without requiring informatics coupling between codes.

Internal or external integration

In the case of complex units, numerous degrees of freedom peculiar to the nature of the unit needs to be determined by optimization, including integer values. For example, distillation columns and more specifically heat integrated distillation columns (HIDiC), optimal design requires to determine both continuous (e.g. heat duties, flowrates) and discrete variables (number of stages, withdrawals and injection stages). To deal with such systems, the question is to choose between resolving internally or externally the case of integer decision variables.

If the complexity is dealt internally, a MINLP problem needs to be solved within the unit operation model, while keeping the NLP for convergence and optimization of macroscopic continuous variables at the process level. Such an approach may be long and tedious since the MINLP sub-problem needs to be solve a large number of times, but the overall Process Synthesis problem remains as simple as for a single distillation column. If the complexity is dealt externally, it can be directly integrated in the synthesis problem by decomposing the distillation columns into other elementary building blocks (e.g. theoretical stage / transfer unit, mixers, splitters, reboiler, condenser). This approach complexify the Process Synthesis problem but synergies may be obtained. Intensified units such as reactive distillation could emerge if we consider reaction and separations as elementary building blocks. In the presented method, both approaches would be possible, depending only on the choice of available building blocks by the user.

Beyond unit operations as building blocks

The conceptual method lies on the arrangements of elementary 'black-boxes' building blocks. These blocks could therefore represent more than just unit operations. For instance, one could extend the method using building blocks as phenomenological modules, or an entire existing process (e.g. for retrofitting study), or even a task to be performed (for scheduling optimization). Using building blocks not based on process units have already been explored in literature focused on Process Intensification but few in Process Systems Engineering studies. Such building blocks could for example be based on general heat/mass module [START_REF] Papalexandri | Generalized modular representation framework for process synthesis[END_REF], elementary process functions [START_REF] Peschel | Methodology for the design of optimal chemical reactors based on the concept of elementary process functions[END_REF] or directly involved phenomena [START_REF] Zivkovic | A method for reactor synthesis based on process intensification principles and optimization of superstructure consisting of phenomenological modules[END_REF][START_REF] Demirel | Systematic process intensification using building blocks[END_REF][START_REF] Kuhlmann | Optimization-based approach to process synthesis for process intensification: General approach and application to ethanol dehydration[END_REF]. No further development would be required to the method, the limitations coming essentially from the process designer creativity.

On the synthesis drivers

As in all process synthesis methods, the choice of synthesis drivers is crucial to define appropriate constraints and objective function. Such drivers should reflect the designer's criteria, and commonly need to integrate several design and performance considerations. Some criteria can be integrated as optimization constraints (e.g. security, material temperature limits) while others can be used to define the objective function (e.g. energy, economics, environment).

A key aspect is the introduction of a parsimony principle into the problem formulation to limit the number of equipment and process complexity as much as possible (i.e. when not necessary). This aspect is exacerbated in case of ab-initio process synthesis since the algorithm can generate very complex structures. For the case study, an economic objective function was used. It introduced a sort of parsimony principle: each equipment comes at a certain cost, unit operations inducing no performance improvement are therefore dismissed.

A possibility would be the use of RAM (Reliability, Availability, Maintainability) analysis, allowing to convert process complexity into a loss of operability (e.g. a decreased in annual operation time). Such analysis, if integrated into the objective function, would quantify if an increase in process complexity would imply a sufficient gain compared to the loss of operability.

It should also be noted that working with economic functions comes with certain uncertainties due to the process maturity (Technology Readiness Level from 1 up to 9 such as lab-, pilot and industrial scales) and/or the effort put on the evaluation (e.g. conceptual study, basic design, detailed engineering). These uncertainties needs to be properly evaluated [START_REF] Neveux | Uncertainties in techno-economic evaluation of innovative processes -effect of technology maturity and preparation effort[END_REF], especially when comparing several process alternatives.

On the uses of ab-initio process synthesis

The interest and drawbacks of the proposed approach in comparison with other process synthesis methods are yet to be determined. Global optimization methods used for process synthesis, such as MINLP formulation, provide the optimal solution in a restricted search space; whereas ab-initio approaches intrinsically cannot guarantee the convergence since they freely explore the structure possibilities. The use of evolutionary programming algorithms for process synthesis could show interest to circumvent the bias appearing in new conceptual studies and other problems with a very large number of possible combinations.

In approaches using total connectivity based superstructure, it is possible to be as exhaustive as possible in the interconnections of process units by allowing free connections between the chosen units. However, the same intrinsic bias exists in these approaches since an appropriate set of unit operations needs to be postulated. To increase the chance of finding an optimal solution, the number of unit operations can be increased, potentially leading to technical limitations (e.g. convergence issues, computational time) due to the large size of the system. Compared to the presented approaches, it may not be differences between the results in practice (which is yet to be tested). Still, one potential interest of ab-initio approaches is that the initial time spent to define the problem may be reduced in the proposed approach since the 'process designer' only needs to define the available building blocks (e.g. process unit operation, process function) so that it may focus on the process problem definition, rather trying to include as many alternatives as possible in a mathematical formulation. Further works will try to compare both approaches on a same problem.

Both types of approaches could also be very complementary and used sequentially. An ab-initio approach could be used initially to explore the infinite search space using the defined unit operations; then, the structural results of the best individuals could be analysed to define a superstructure; eventually, a superstructure-based approach would find the optimal solution within this restricted design space.

Conclusion

A new process synthesis approach is proposed which frees from the definition of a set of structure alternatives such as a process superstructure. From a set of unit operations and an objective function defined by the user -i.e. the process designer-, the method systematically constructs process flowsheet structures using an Evolutionary Programming (EP) algorithm and evaluates them using a Non-Linear Programming (NLP) algorithm. The method's implementation, called PSEvo, has been tested on a reactionseparation-problem. Obtained optimal solutions are in compliance with literature [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF], which validates the Future works will include:

• Comparison between several Process Synthesis approaches on the same case study using rigorous models for process units. Candidate problems include separation processes and power cycles in order to evaluate the method performance with multicomponent and highly integrated processes.

• Comparison of different strategies for the definition of integrated process units, to define the best options between integrating the unit complexity within the process unit model and decomposing the unit into elementary functions.

• Definition of appropriate synthesis driver (objective functions and constraints) to consider both process complexity and economic uncertainties during the synthesis procedure. (with a chosen steepness k = 5000 here).

The overall production F prod of pure B (in kmol/hr) is computed from the 'Out' units:

F prod,tot = Out F prod,B,i Out H smooth (x B,i -1) (5)

Available unit operations

The unit operations are detailed in Table 2 and below.

Feed

The 'Feed' has an optimizable flowrate, which is adjusted by the NLP to satisfy the production target of 50 kmol/hr (see §4). The outlet parameter is the purchase of reactants P (in $/hr), which includes benzene (A, cost of 27.87 $/kmol) and chlorine (cost of 19.88 $/kmol) in equimolar quantities: P = (19.88+27.87)F A .

Out

The 'Out' unit is the process outlet. Its calculated parameter is the produced flowrate, which is null if the B purity x B ( x B = F B /(F A + F B + F C )) is lower than 1.

Mixer and splitter

Unlike in [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF], a capital cost of 500$ is considered for mixers and splitters. This value is low compared to capital cost of other unit operations, it is introduced to affect a penalty (even low) to each block.

CSTR

The CSTR outlet streams are calculated by the following equations:

F i,out = F tot • x i,out i = {A, B, C} (6)
with F tot = F A,in + F B,in + F C,in the total molar flowrate (invariant during reaction), and x i,out the molar composition at the outlet, calculated by mass balance:

x A,out = x A,in • F tot F tot + V • k 1 • C tot x B,out = F tot • x B,in + V • x A,out • k 1 • C tot F tot + V • k 2 • C tot (7) x C,out = F tot • x C,in + V • x B,out • k 2 • C tot F tot
with k 1 = 0.412 s -1 , k 2 = 0.055 s -1 , and the molar density C tot = 11.22 • x A + 9.86 • x B + 8.84 • x C (kmol/m 3 ). Since the outlet composition is unknown, a first estimate of C tot is calculated using inlet composition, then an iterative procedure is adopted until convergence. The CSTR CAPEX is calculated respectively for Case A (same cost for PFR and CSTR) and for Case B (higher cost for PFR) from: CAP EX CST R, Case A = 12760.43 + 14059.78 • V CSTR [START_REF] Nishida | A review of process synthesis[END_REF] CAP EX CST R, Case B = 25795.0 + 8178.0 • V CSTR [START_REF] Grossmann | New trends in optimization-based approaches to process synthesis[END_REF]

  No. of stream variables F i,out = F i,in 2 inlets, 1 outlet Cost = ...

Figure 1 :

 1 Figure 1: Overview of PSEvo architecture, see sections 2.2 and 2.3 for details respectively on Evolutionary synthesis and process evaluation procedures

Figure 2 :

 2 Figure 2: The three elementary mutation operators used during evolution for the construction of a process flowsheet

  Superstructure-based process synthesisAb-initio process synthesis (this work) Definition of a superstructure (here fromKokossis & Floudas) Solved by Mixed-Integer Non-Linear Programming (MINLP)Selection of the optimal structure among the predefined alternatives Definition of available unit operations, no superstructure assumed Solved by Evolutionary Programming (EP) and Non-Linear Programming (NLP)Optimal structure generated by choosing, assembling and connecting unit operations (search space is virtually infinite)

Figure 3 :

 3 Figure 3: Differences in problem definition for the benzene chlorination case study. Left) one of the superstructure of Kokossis and Floudas[START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF] (reproduced with permission of Elsevier), a set of alternatives is defined and a MINLP method selects the optimal flow path and associated degrees of freedom. Right) this work: definition of the ab-initio process synthesis. No superstructure is assumed, the EP constructs the flowsheet from the available unit operations and the NLP determine the optimal degrees of freedom, i.e. the best objective function obtainable for a given flowsheet.

Figure 4 :

 4 Figure 4: Process synthesis results for cases A (same cost for CSTR and PFR) and B (higher capital cost for PFR)

Figure 5 :

 5 Figure 5: of optimization progress for the benzene chlorination case, and process flowsheets of notable evolution steps (case B)

Figure 6 :

 6 Figure 6: Optimization progress of four runs with different random seeds (case B)

Figure 7 :

 7 Figure7: Optimization progress for several selection-replacement methods (median in lines, interquartile ranges in gray). See the corresponding phylogenetic trees and Shannon entropy on Figure8. The relative distance to the optimal solution is equal to 1 at initialization (annual profit of the initial population, -1831 k$/yr) and to 0 when convergence is reached (annual profit of the optimal solution, 1283 k$/yr).

Figure

  Figure Example of phylogenetic trees and entropy for several selection-replacement methods during the first 100 generations. The vertical axis of phylogenetic trees represents generations, starting with the initial flowsheet down to the 100 th generation, nodes represent individuals and edges ancestral relationships. The corresponding convergences are plotted on Figure 7

Figure 9 :

 9 Figure 9: Sensitivity to evolution control parameter -median and interquartile range of the number of function evaluations required to find the optimal solution as function of the mutation rate (top) and the number of individuals per generation (bottom) using 10 runs with different random seeds

Table 1 :

 1 Brief overview of process synthesis approaches

	Class of approaches Process synthesis	Methods	Ref.
	Decomposition	Heuristics, expertise and experience	Hierarchical	[3]
			Onion models	[4]
	Optimization

  The product sales S are calculated considering the production target of 50 kmol/hr of pure B (92.67 $/mol). The purity and productivity targets are integrated into the objective function through the product sales, avoiding to define an additional process constraint: H smooth (F prod,tot -50)To ensure continuity, a smooth approximation of the Heaviside function is used: H smooth (x) =

	bottom	bottom of distillation column
	Abbreviations
	CAPEX Capital expenditure ($)
	CSTR	Continuous Stirred-Tank Reactors
	EA EP MINLP Mixed Integer NonLinear Programming Evolutionary Algorithm Evolutionary Programming S = 92.67 • 50 if F prod,tot ≥ 50 0 else NLP NonLinear Programming OPEX Operational expenditure ($/yr) 92.67 • 50 • 1	(4)
	PFR	Plug Flow Reactor	1+exp(-kx)
	PI	Process Intensification
	PSE	Process Systems Engineering
	. PSEvo	Process Synthesis by Evolution
	.
	Nomenclature
	C tot	molar density (kmol/m 3 )
	F i , F tot	partial and total molar flowrate (kmol/hr)
	F obj	objective function
	g	inequality constraints
	h	equality constraints
	H	Shannon entropy index
	k	kinetic constant (s -1 )
	p i	probability of observing an individual (process)
		among the population
	P	purchase of reactants ($/hr)
	r	split ratio
	s	(guessed) tear stream variables
	s	calculated tear stream variables
	S	product sales of B ($/hr)
	t	tear equations
	V	reactor volume (m 3 )
	x	decision variables in the process
	z, z l , z u optimization variables, lower/upper limits
	Greek letters
	α	mutation rate
	Sub-and superscripts
	add	addition of a unit operation (mutation operator)
	in	inlet of a unit operation
	ind	individual
	out	outlet of a unit operation
	permut	permutation of two streams (mutation operator)
	remove	removal of a unit operation (mutation operator)
	top	top of distillation column

Acknowledgements

The author addresses its acknowledgements to Jean-Marc Commenge, Laurent Falk and Eric Favre of the CNRS-LRGP laboratory for their valuable comments and inputs to this work.

Supporting information

An example of process representation (phenotype) before and after the application of a mutation operator and the connectivity algorithm is provided.

Appendix: expressions for the case study

Stream description 3 stream variables: F A , F B , F C (partial molar flowrates, in kmol/hr)

Objective function

The objective function is the annualized profit ($/yr):

with:

• S is the sales of B ($/hr), -see below (4).

• P is the purchase of reactants ($/hr) -see 'Feed' unit operation in Table 2.

• CAP EX is the process capital cost ($) -sum of the CAPEX of all unit operations, CAP EX

• 2.5 is the payout time (yr), • 0.52 is the income tax rate.

• 720 is the annual operation time (hr/yr). The authors [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF] did not report the operation time but it was calculated from one of their example. They obtained a process with a profit of 1224 k$/yr (F obj ), an annual cost of 321 k$/yr ( CAP EX 2.5 + 0.52OP EX), a production of 50 kmol/hr (S = 2481 $/hr), and a fresh feed stream of 51.97 kmol/hr (P = 4634 $/hr). The operation time is therefore 720 hr/yr.

PFR

The PFR outlet streams are calculated by integrating the following ordinary differential equations:

with the initial conditions:

The molar density is recalculated at each integration step.

The PFR CAPEX is calculated respectively for Case A (same cost for PFR and CSTR) and for Case B (higher cost for PFR) from:

Distillation columns

In [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF], four different columns were defined to distinguish ternary (A/BC, AB/C) and binary separations (A/B, B/C). In this work, only two are used (A/BC, AB/C), the different equations between ternary and binary separations are chosen according to feed composition

Dist A/BC . If the feed does not contain C (x C,in = 0), the column is equivalent to a binary A/B distillation (column 4 of [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF]). If not, it is a A/BC distillation (column 1 of [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF]). CAPEX and OPEX are calculated accordingly:

OP EX A/BC = (21.67 + 4.65) • F tot,in • q A/BC [START_REF] Barttfeld | A decomposition method for synthesizing complex column configurations using tray-by-tray gdp models[END_REF] with q A/BC = 10.70 + 28.41

Dist AB/C . If the feed does not contain A (x A,in = 0), the column is equivalent to a binary B/C distillation (column 3 of [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF]). If not, it is a AB/C distillation (column 3 of [START_REF] Kokossis | Synthesis of isothermal reactor-separator-recycle systems[END_REF]). CAPEX and OPEX are calculated accordingly: