Marija Roglić

A network on High Nature Value farming Learning, Innovation, Knowledge LA Dalmatian islands Innovation experiences and needs

Introduction and contents

The challenges facing HNV farming in Dalmatian islands

Contents

This report looks at innovation that supports HNV farming in Dalmatian islands (LAG Brač, LAG Škoji, LAG 5), and identifies the types of innovation that are missing and needed in order to secure a sustainable future for HNV farming (HNVf).

We present examples of innovation existing in this Learning Area (LA) and examples more widely in Croatia (specifically coastal and islander area) that could usefully be transferred to address challenges in the LA.

Types of innovation that seem to be absent in Croatia (specifically coastal and islander area), and that we would like to explore in other countries of the HNV LINK network, are also summarised.

Challenges facing HNV farming in Dalmatian islands

Depopulation of the islands and land abandonment is an ongoing trend with more and more people shifting from agriculture to tourism. Agricultural land cover represents 5,8% of the total LA surface with an average size of cultivated land being 1,7 ha. The majority of the land is used for olive groves (53%), vineyards (21%) and karst pastures (15%). From the overall 57 566 living in the LA total number of domestic animals in households is 32 652 . 45% sheep, 49% poultry, 5% goats and 1% cattle. Data limitations exist with respect to spatial coverage of agriculture.

Before the area had intensive livestock activity on all the islands (mostly goats and sheep) but with the decrease of the population and the abandonment of the agricultural land, the habitats are recolonized by the maquis and then by forest. As a long term result of the agrarian reforms in 1945 and 1953 between 1960 and 1990 the percentage of farms size of 3 ha or less increased from 55% to 70%. The growth of tourism compensated the declining part of agriculture in economy.

Although there is a strong demand for the local products by restaurants that want to offer local menu to the tourists there is a great problem in obtaining local lamb as in the Dubrovnik-Neretva county there is only one slaughter house and it is located on the island of Korčula (Smokvica). On the Pelješac peninsula there is no veterinarian and the breeders need to pay for their arrival from the mainland (Metković). On-farm processing (e.g. cheese) and direct sales cannot develop due to rigid rules and bureaucracy.

The HNV system is under pressure from tourism development and its infrastructure on one hand and land abandonment and the consequent closure of the mosaic landscape on the other. It results in an increasing number of wild fires and loss of biodiversity as the agricultural land and habitats become recolonized by the maquis and then by forest.

Livestock farming is facing a stifling regulatory system (food hygiene, animal health, land ownership and management, land-use planning, inconsistency in policies and subsidies on different governance levels) that closes down most of their options for improving the economics of the system.

Due to fragmented, small parcels and an unreliable land ownership system farms struggle with poor economic viability. They receive very limit limited support from the CAP (Pillar 1) and RDP compared with other sectors and other Member States. what are their strengths and weaknesses for HNV farming?

There is no overall project to support the HNV farmland in the area but there are multiple private, public and civil sector initiatives that aim to promote HNV and HNVf practices. These examples include products from HNVf practices, agro tourism that use HNVf as part of the touristic experience, or activities of a nonprofit organisation that has been working on the protection of the mosaic landscape, its drystone walls and the transfer of is building know-how for the new generations.

Overview of the innovation situation

Learning area of Dalmatian islands is a highly touristic area that covers 7 islands, a peninsula and a coastal municipality. Development is seen as the driver that will meet the needs of the present generation without compromising the ability of future generations to meet their own needs. It is an area of mosaic landscape and low intensity farming activity. There are not a lot of innovation in terms of HNVf as a concept that is being deliberately promoted, but there is broad range of practices and products that have the potential to revitalize HNV farming systems and its natural area. HNV-LINK is a first attempt to create a network aiming to coordinate different actors, actions and projects that will foster HNVf in Croatian islands and link it to sustainable tourism development. Sustainable tourism development as a paradigm that refers to meeting the needs of present tourists and host regions while protecting and enhancing opportunities for the future.

It is envisaged as leading to management of all resources in such a way that economic, social and aesthetic needs can be fulfilled while maintaining cultural integrity, essential ecological processes, biological diversity and life support systems. (Norrby et al., 2003:11)The innovations being presented are the innovation that foster HNV type 2 that is mosaic landscape and the practices of sustainable tourism development in the learning area. LEADER have the funds and the measures to promote and educate local stakeholders on both HNVf and its potential in terms of environmental services and its economic potential in the field of rural tourism. Rural tourism is seen through the paradigm of sustainable development where rural development is seen as a deliberate process of sustained and sustainable economic, social, political, cultural and environmental change, designed to improve the quality of life of the local population of a rural region (Norrby et all., 2003: 4) The area has an example of social and institutional innovations on a local scale through the actions and projects of LEADER organisations and Slow Food movement but they are not supported or transferred on a broader scale. Examples of best practices are actions that are based on private initiative with the help of LAGs or organisations such as 4 grada Dragodid. They are an NGO that is promoting and re-acutalising the dry stone skills and heritage through workshops, field research and media. In 2011 they were awarded Europa Nostra (EU prize for cultural heritage) in training/ raising awareness category. Innovation in the area is slowly increasing as more and more young people come to the islands in a quest for an alternative to the urban turmoil. HNV innovation is closely linked to practices of sustainable tourism development where many local actors see HNVf as way for conserving the landscape features and natural value while securing a necessary income.

Strengths

There are several organisation in the area that support HNV practices There are several producers that are producing in line with HNVf practices

There are multiple initiatives aiming to improve marketing of local products

There is a demand by the local restaurant for local livestock and other HNVf products (honey, olive oil….)

Beekeeeping is increasing and it is fostering the productivity of fruit cultivations

The existing innovations are on an extremely limited scale, compared with the scale of the challenges (that is reconstruction and maintenance of the dry stone walls as one of the main characteristics of the H NV landscape in the islands)

Two innovations are just beginning (Slow food Pelješac and nursery of indigenous species Anemona) and need additional institutional push and subsidies to enhance their HNV impact

There is a problem of specialization (small farmers don't posses bureauratic knowledge needed to apply for subsidies that would foster their HNVf practices)

The existing innovations do not adress the main challenges facing HNV farming that is land abandonment and land stewardship

Social and institutional innovation

Social and Institutional Innovation Needs

In the area there have been several initiatives and projects aiming at promoting and revitalizing mosaic landscape and HNVf but there was no multistakeholders group other then civil society individual projects or small scale farmer initiatives focusing on the issue of long term strategic revitalization of mosaic agriculture. By designing a project that would form an EIP and create a group of designated actors with an action plan that would state concrete actions to be done in the area would mean a significant shift forward in revitalising HNVf as key in protecting both the natural and cultural heritage of the islands that make them so attractive to tourists.

In the island of Korčula and Pelješac peninsula there is an active beekeepers association that has help boost the honey production and has brought many positive side effects in terms of enhanced environmental services. The local community needs to be more involved in the policy making and implementation as the issue of selective law enforcement and complicated policies along with the lack of support for .

On the island of Brač there is an active livestock farmers association whose professionalization would help promote small scale farmers interests from the islands (cheese production especially).

On the national level it is necessary to establish a uniform and transparent system that would speed the process of state land allocation to local farmers and foster giving land to HNVf practices as its environmental services would significantly lover the risk of fires that are quite high in the area.

The different authorities apply their policies without talking to local farmers about best approaches. This creates major problems, and ineffective programmes. A very significant innovation would be for the authorities to engage with local farmers in designing and implementing policies.

Regulatory Framework Innovation Needs

Pilar 1 gives direct support per hectare that is not applicable to HNVf type 2 in the islands. Mosaic agriculture that is characteristic for the area is based on small agricultural parcels that have a wide variety of species. Land management of mosaic landscape is much more work intensive and it is necessary to implement these type of specificities when developing Pillar 1 subsidies. Pillar 1 needs to foster extensive land management and give support to practices that will slow down land abandonment. Republic of Croatia is implementing its 1st Rural development programme that is Pillar 2 and has drafted specific sub measures for reconstruction and maintenance of dry stone walls and terraces as traditional HNV landscape, still there are some inconsistencies in the implementation of policies on different government levels and a discrepancy between the local needs and policy that should be fixed for the next financial perspective through closer communication with the local stakeholders and scientific institutions that have done research on the topic (See Andlar 2002;2007;[START_REF] Andlar | Iznimni kulturni krajobrazi primorske hrvatske[END_REF].

As there is no monitoring of lands given under concession it is necessary to either implement the sustainability criteria for state owned land given up for renting or concession or develop a specific HNVf program for state-owned land that would help farmers with HNVf friendly project to get access to those lands (Abdesater et all, 2017:143).

Regulatory framework -innovation needs

Possible approaches

Solve the severe limitations of Pillar 1 for support to mosaic agriculture Implement sustainability criteria in state-owned land

Monitoring of lands given for concession in order to preserve agricultural landscape patriomony and foster biodiversity

It is necessary to establish an operational group within the National rural network that would draft policy recommendations that are adapt to the realities of mosaic agriculture and insularity

Products and markets innovation Farm techniques and management innovation

Products and Markets Innovation Needs

Innovations identified in this domain are responding to the innovation gap related to branding and promotion of HNVf products and are trying to propose solutions to the identified gap in terms of insufficient labour force and the pressure posed to the environment from the misbalance between tourism and agriculture. In order to answer to the proposed innovation gaps it is necessary to engage a wide range of stakeholders on different scales and sectors. For the viability of the HNVf practices and products in the area it is necessary to have an educational centre who will provide the know-how set and the tools for doing HNVf. It is also necessary to have a support system around certifications that will show to the producers that their label has substance in terms of the services and market position that goes with it. Differentiation on the market through certificate itself isn't enough (as has been shown in the example of the label ''Croatian Island Product'') The issue of land abandonment and consequent lack of labour force could be solved through the promotion of volontourism as a platform for finding people that would help with herd management and restoration/maintenance of terraces (Abdessater et all., 2017).

Farm Techniques and Management Innovation Needs

Learning area of Dalmatian island is are scarce in arable agricultural land and prone to wild fires. Agricultural land is man made through the process of cleaning the land from rocks and building dry stone walls to prevent erosion. The role of dry stonewalls was a way of defining ownership and system for livestock management. These practices with land abandonment and forestation of agricultural land are being ever more forgotten and it is necessary to promote those practices and implement them in the ''modern'' agricultural holdings that are more prone grinding the soil then building dry stone walls. These modern practices foster soil erosion and loss of habitats.

Reintroducment of animals will answer to major problems such as wild fires and los of biodiversity due to the closing dynamics of the abandoned landscape. The area has a potential for breeding to enhance the biodiversity of the are but there are 2 major constraints, lack of funds and lacko of workforce on the other. Following the example of what was done in Bulgaria and Romania to protect traditional forms of breeding (WWF-DCP/EFNCP, 2008), it seems that more could be done by national authorities in Zagreb to create legal and other incentives for the preservation of these practices. In this case, it could take the form of facilitation in use of abandoned land, status for shared herds (as it exists e.g. in France). This would maybe require some lobbying effort from local entities, which could include the LAGs, but also actors involved in these activities, even indirectlylike tourism actors working with animals, in actuality or potentially (Abdessater et all., 2017:145).

Products and markets -innovation needs

Possible approaches

Promote HNVf products and practices Locally-led projects that set objectives for pastoral land with the users, and apply a « payment for results» approach to promote these objectives Flexibility in the application of food hygiene rules to small-scale, on-farm processing units.

Approaches to dealing with animal health controls (TB) in extensive systems on common land with wild fauna vectors.

Land managament system for confused land ownership land

Problems addressed by this example

This project aimed at reinventing the traditional practices that fostered HNVf in the contemporary times. It aimed at tackling the problem of knowledge transfer of traditional practices that stopped due to intensive land abandonment and aging of population.

Story in a nutshell

Maintaining or improving HNV values

The programme was not designed to achieve specifically HNV or conservation objectives, but probably had benefits as a result of maintaining extensive grazing systems and reducing scrub encroachment.

Potentially the programme could have been adapted to give it a more explicit HNV focus, for example, with greater involvement of the nature-conservation authorities.

Economics of HNV farming

Data is not available on the economic impact of the programme for HNV farms.

How does ''Oživi održi otok'' respond to the HNV LINK innovation themes?

The process that made it happen and critical factors for success

Actors and roles:

They key actors were local NGOs and local highly educated youth that wanted to find a way to connect to their heritage but also to be able to ensure its economical viability in the islander area. Murter NGO Argonauta was founded as an answer to the growing demand for an civil society organisation that would look after the environment and nature of the island of Murter and is surrounding area.

(O nama -Udruga Argonauta -Udruga za zaštitu prirode i okoliša te promicanje održivog razvoja.

(n.d.). Retrieved August 1, 2017, from https://www.argonauta.hr/o-nama/). It was this NGO that opened lines of communication with public institutions and with the ''holders of heritage'' using formal and informal acuqaintances to foster a long term multistakeholders, multi islander platform for sustainable development that is still ongoing.

Institutional context that made it possible

The process of acquis harmonization of the Republic of Croatia and access to EU funding for Natura 2000 management plans available to NGO's and other civil society organisations.

Resources

Funding

Processes

The project that drafted the action plan lasted for 18 months but the activities related to its implementation kick started in 2015 and are ongoing.

Critical factors for success:

Major factor was funding availability of EU funds and financial support that came from the Office for NGOs of the Republic of Croatia. Another factor was enthusiasm of all the people involved that created it using solely their own resources and knowledge.

Limiting factors, actual/potential problems, and how could they be overcome?

Project based funding puts constraints on the number of actions that could be done as they are always unexpected opportunities and constraints for the implementation of the vision proposed.

Farming Techniques and Management

This action plan promotes traditional agricultural techniques od mechanical scrub clearance to prevent wild fires and reconstruction of dry stone walls for preventing erosion and also as a livestock management system.

Regulations and Policy

This action plan holds in itself concrete project proposals that aim at using RDP funds for implementing policies designated for HNV and Natura 2000 sites.

Products and Markets

Drafts and kick starts pilot projects for promotion and direct sales such as ''Not all sheep are black'' that aims at branding traditional wool products that are treated as waste and not as a resource. For HNV preservation of traditional landscapes and revitalization of agricultural practices in a way that it answers to the contemporary needs of the locals (incorporation of nature protection, revitalisation of landscapes and sustainable tourism).

Is the innovation unique to its territory and its characteristics, or is it replicable in other areas?

It is an innovation that is replicable and that has been in some extent implemented in other areas (such is the Strategic development framework of the National Park of Mljet that functions both as a baseline assessment of the territory and an action plan with a set of project proposals to ensure its implementation).

Could it be rolled out on a bigger territorial scale?

Existing examples that have been mapped were focused on small to medium scales such is the territory of National park, Nature park and plans and projects that were developed as part of a wider international programme such was the COAST project (Conservation and Sustainable Use of Biodiversity in the Dalmatian Coast through Greening Coastal Development -COAST).

What would be needed to do this successfully?

For implementation of HNVf as a concept that will secure livelihood for the local stakeholders it is necessary to secure overheads for organizations that are local key holders of the concept in order to have long term education and collaboration in both implementing and promoting HNVf practices as well as branding its products.

Problems addressed by this example

Institutional support and promotion of HNVf practices and products.

Story in a nutshell

In the area of Dalmatian islands there are several LEADER organizations and other multistakeholder organizations that indirectly promote HNV friendly practices and its products. They represent partnership of public, private and civil sector established in order to get EU funding for local projects that foster rural development and benefit their agro-eco system. These multistakeholder organizations comprising representatives from public, private and civil sector serve as knowledge brokers and catalysts for the implementation of HNV values in local communities. Movements such as Slow Food Convivum also contribute to international promotion and branding of such products. Slow Food Pelješac Convivium aims to encourage and promote local food production and consumption on principles of being good, clean and fair . Its main activities are encouraging nutrition based and seasonal produce, protection of biodiversity in their focused territory, documenting and reviving local recipes and foods that are endangered or forgotten, bringing the producers and consumers closely together, promoting organic farming that doesn't involve harmful herbicides and pesticides.

Location: Dalmatian islands

Economics of HNV farming

Administrative support for 20 HNVf friendly projects. Several workshops and manifestations regarding the promotion of HNVf products and the Slow Food Concept.

Maintaining or improving HNV values

The organizations and its projects and work programmes weren0t designed to achieve specifically HNV or conservation objectives, but probably had benefits as a result of maintaining extensive grazing systems and reducing scrub encroachment.

Potentially their work could have been more adapted to give it a more explicit HNV focus, for example, with greater involvement of the nature-conservation authorities.

Social and institutional

Multistakeholder organizations of different forms represent an important social innovation as they are a first step in creating institutional structures and avoiding a short-term project culture. These social innovations that are par of either international movements or rural development programmes are grounded in the social processes of the community and can best help create social value for that community.

Products and Markets

Multistakeholder organisations, both LEADER organizations work on developing new projects that will brand the territory (such as Active Adriatic South project of LAG 5 that connects local cuisine to cyclo tourism) and the products such is the initiative of the Slow Food Presidium ''Pelješki varenik''.

Not the case

Not the case NGOs reached out to local community and authorities. Emphasis on dialogue with local farmers and helping to address their problems.

The process that made it happen and critical factors for success

Lessons learnt from this innovation example, and its potential replication

Actors and roles:

As a process of harmonization with the EU norms LEADER project was implemented in Croatia and as a process of implementing this EU rural development programme regional authorities have drafted the outlines and gathered local stakeholders into LAGs. The role of the stakeholders and organizations themselves was defined by their local members from the private, public and the civil sector. The establishment of the Slow Food Pelješac came as part of a LAG 5 project (LAG 5 Green Agenda) where the local stakeholders met and exchanged practices with the civil sector activists from Slow FooD Liburna.

Institutional context that made it possible

The process of acquis harmonization of the Republic of Croatia and access to EU funding that fostered more field trips, exchange of best practices and networking.

Resources

Funding was available through EU funds.

Processes

The funding came from EU funds and the major factor was the process of harmonization with the EU acquis that put an emphasis on nature protection and bottom-up development.

Critical factors for success:

Major factor was funding availability of EU funds and enthusiasm of all the people involved that trhey will be able to kick-start projects that will truly improve the life of their rural communities and their own businesses.

Limiting factors, actual/potential problems, and how could they be overcome?

Project based funding puts constraints on the number of actions that could be done as they are always unexpected opportunities and constraints for the implementation of the vision proposed. For HNV preservation of traditional landscapes and revitalization of agricultural practices in a way that it answers to the contemporary needs of the locals (incorporation of nature protection, revitalisation of landscapes and sustainable tourism) key is territoral approach to development that foster multistakeholder integrated engagement towards the realization of a unified vision.

Is the innovation unique to its territory and its characteristics, or is it replicable in other areas?

It is an innovation that is replicable and that has been in some extent implemented in other areas.

Could it be rolled out on a bigger territorial scale?

Existing examples that have been mapped were focused on small to medium scales, in those terms the innovation is replicable on various scales.

What would be needed to do this successfully?

For implementation of HNVf as a concept that will secure livelihood for the local stakeholders it is necessary to secure overheads for organizations that are local key holders of the concept in order to have long term education and collaboration in both implementing and promoting HNVf practices as well as branding its products.

Croatia -innovation example 2)Multistakeholder organizations LAGs and Slow Food: fostering HNV products and practices

Problems addressed by this example

Branding and promotion of HNVf products. Economic sustainability of HNVf.

Story in a nutshell

This innovation examples gather different stakeholder that have several things in comon: they have all return to the cultivate agricultural lands of their ancestor and revitalize their heritage and their biggest shopper are tourists visiting the area. Kruno Cukrov who is the owner of th Olive Oil Museum decided to renovate the old family mill and turn it in a museum. Museum presents the story of his family, visitor that came can participate in the work on the olive fields, sight see or buy and taste local food. Diana Marović, owner of Eko Škoj together with her husband left the capital of Croatia, Zagreb where they both lived and work to open an SMS that is today one of the best rated in the country. Vlaho Komparak, a student of Agronomy during his studies decided to come back to the island and translate all the theory in a practice of his own making. What does HNVf as a tourist activity achieve for HNV farming

Achievements

Linking HNVf to tourism ensures the economic viability of these practices beyond subsidies and ensure its long term endurance. Presenting HNVf as a tourist activity helps increase its popularity and becomes a ''in thing'' both in tourism and agriculture.

Economics of HNV farming

Data is not available on the economic impact of the programme for HNV farms.

Maintaining or improving HNV values

These activities didn't come as an output of pro HNV measures but probably had benefits as a result of maintaining extensive grazing systems and reducing scrub encroachment. The activities could have been adapted to give it a more explicit HNV focus, for example in terms of branding and HNVf labelling.

Products and Markets

Tourist demand and the biodiversity on the agricultural holdings helps in the creation of an array of diverse and unique local products that have and added value with the labels such as PDO and ECO label. Additional support is necessary as there is a high unit cost in certification of these products as there are small number of units per product but a great variety of products. The existing administrative and fiscal burden is stopping additional certification that is necessary for creating and added value for these products.

The process that made it happen and critical factors for successt

Actors and roles:

Key actors were enthusiasts and entrepreneurs that after a life in the city or schooling in a big city decided to come back to their island and cultivate their agricultural and cultural heritage.

Institutional context that made it possible

Opening of Croatia to tourism that is based on local products and local tradition helped create a market niche that would economically valorise the added value of their agricultural products.

Resources

Major resources was their heritage, their own savings or a credit loan and a lot of their own hard work in the field, in the sphere of marketing and promotion and in dealing with bureaucracy.

Processes

These processes were kick-started in different times in the 2000s and are all still ongoing and improving.

Critical factors for success:

Their success is a result of years and years of hard work with the sole support of their enthusiasm and their families. Critical factor being enthusiasm and will to persevere are the initial obstacles.

Limiting factors, actual/potential problems, and how could they be overcome?

The administrative burden that has no flexibility for micro scale agribusiness in the islands is a major limiting factor. Lack of organised institutional support and national legislation in different sector (legislation for tourism, business and agriculture differ and there is a need of having different legal entities in order to have low cost legal entities) block a lot of integrate entrepreneurial ideas that would foster viability and promotion of HNVf. Coordinate action of institutional stakeholder on different levels and sphere of government is necessary in order to produce an administrative ease in doing this type of businesses. For HNV preservation of traditional landscapes and revitalization of agricultural practices in a way that it answers to the contemporary needs of the locals (incorporation of nature protection, revitalisation of landscapes and sustainable tourism).

Is the innovation unique to its territory and its characteristics, or is it replicable in other areas?

It is an innovation that is replicable and that has been in some extent implemented in other areas such as it has been presented in this example.

Could it be rolled out on a bigger territorial scale?

Existing examples that have been mapped were focused on small to medium scales such is the scale of an SMS.

What would be needed to do this successfully?

Administrative and fiscal easing of these type of HNVf friendly entrepreneurial activities.

Croatia -innovation example 4)Drystone walls: keystone for mosaic HNVt

Problems addressed by this example

Preservation and restoration of HNV habitats and grasslands. Protection from soil erosion and actions to prevent landscape closure. Transgenerational knowledge transfer and promotion of HNVf friendly land management practices.

Respecting the knowledge and skill of our ancestor to manage natural resources in this vast and often arid carst area, making the best of it, we aim to promote sustainable ways of managing land and water resources. The aim is to re-establish dry-stone techniques as an efficient, aesthetic, humane and sustainable alternative to concrete in construction of simple buildings and objects in the Mediterranean, especially in areas such as national/natural parks and protected heritage sites. [START_REF] Bubalo | Innovation fiche Dragodid 4 Grada[END_REF]. In the communities where the continuity of agricultural production was broken by the abandonment of the agricultural land during the 20th century, there is a noticeable generation gap between the elder, who are, if still alive, mostly retired, and the younger generations of agriculturists, who are revitalizing the agricultural practices in the new circumstances. Recently, this gap has begun to fill in with the activities of various organisations and enthusiasts that organize workshops and issue printed and digital handbooks and newsletters. Often such actions bring the elder masters "from oblivion", giving them the opportunity to show their skill and share their knowledge. Promoting the valorisation and protection of vernacular heritage as a growth asset in the region lead us to trans-national partnership with similar organizations, and interdisciplinary collaborations (home and abroad) resulted in UNESCO nomination for dry stone walling on representative list of the intangible cultural heritage of humanity. [START_REF] Bubalo | Innovation fiche Dragodid 4 Grada[END_REF] Economics of HNV farming

Story in a nutshell

Data is not available on the economic impact of the programme for HNV farms but the overall mosaic agriculture in the learning area is fenced and managed through the system om several hundreds of kilometres of dry stone walls.

Maintaining or improving HNV values

The programme was not designed to achieve specifically HNV or conservation objectives, but probably had benefits as a result of maintaining extensive grazing systems and reducing scrub encroachment. Potentially the programme could have been adapted to give it a more explicit HNV focus, for example, with greater involvement of the nature-conservation authorities.

Regulations and Policy

The activities of this NGO that has been working on the promotion of dry stone walls have resulted in policy recommendations and have translated in concrete measures (4.4.1. and measure 10 of the Croatian RDP.

Farming Techniques and Management

Dry stone walls are one of the oldest and most effective ways of land management in the LA of Dalmatian islands. Promotion of this techniques and its transgenerational skill transfer is a key innovation in maintaining mosaic landscape.

Not the case

Not the case

Maintenance of dry stone walls and grazing in the eumediterranean pastures

The process that made it happen and critical factors for successt

Actors and roles:

They key actors were local NGOs and local highly educated youth that wanted to find a way to connect to their heritage but also to be able to ensure its economical viability in the islander area.

It was this NGO that opened lines of communication with public institutions and with the ''holders of heritage'' using formal and informal acuqaintances to foster a long term multistakeholders, multi islander platform for sustainable development that is still ongoing.

Institutional context that made it possible

The process of acquis harmonization of the Republic of Croatia and access to EU funding.

Resources

Volunteer work and funding avaliable through different EU programmes.

Processes

The initiative started in 2002 and is still ongoing.

Critical factors for success:

For us as an association, the enabling factors were basically set of circumstances. First of all we all participated in international workshop on the island Of Vis were we we introduced to abandon village of Dragodid and the owner Mr. Andrija Suić, who teached us traditional skills of dry stone walling.

Although funding was and still is a problem, our commitment for preservation and DIY aesthetics slowly led us to forming national network of partners (heritage professionals, institutions, local NGOs) and local stake holders. With few national and one international award, it all fell into perfect timing and we were able to create momentum with numerous workshops throughout Croatia and abroad, making this traditional skill very popular on numerous events especially in rural areas. However, there is a need to establish some formal or semi-formal courses in order to make the knowledge and skills available to those who wish to acquire them so as to cultivate their own estates or do it professionally for other, especially now that new measures for rural development (maintaining dry stone walls) have been approved. [START_REF] Bubalo | Innovation fiche Dragodid 4 Grada[END_REF] Limiting factors, actual/potential problems, and how could they be overcome?

Project based funding puts constraints on the number of actions that could be done as they are always unexpected opportunities and constraints for the implementation of the vision proposed.

Enthusiasm Volunteer work

Main practitioners of dry stone walls: shepherds, vine and olive

Lessons learnt from this innovation example, and its potential replication Overall lessons from this example, especially from point of view of HNV farming?

For HNV preservation of traditional landscapes and revitalization of agricultural practices in a way that it answers to the contemporary needs of the locals (incorporation of nature protection, revitalisation of landscapes and sustainable tourism).

Is the innovation unique to its territory and its characteristics, or is it replicable in other areas?

It is an innovation that is replicable and that has been in some extent implemented in other areas.

Could it be rolled out on a bigger territorial scale?

The innovation itself is already being implemented on different scales.

What would be needed to do this successfully?

Ensuring long term financial support as these activities are time consuimg and require a lot of man power both in terms of research, education, mapping and reconstruction itself.

The dry stone as intangible cultural heritage of humanity is from the start the result of a dialogue among communities, groups and individuals that see the element as something they have in common and wish to cooperate in order to promote its significance and value, and therefore is applicable to every country included in project. By creating a platform for the future cooperation, except being a centre for distributing traditional knowledge, it would create attention to local, regional and national stakeholders of the importance of dry stone walls both as cultural and natural (biodiversity) heritage, and raising awareness of importance of using sustainable and traditional way of maintaining agricultural landscape.

Croatia -innovation example 5)Nursery of indigenous species ''Anemona''

What does nursery of indigenous species ''Anemona'' achieve for HNV farming?

Problems addressed by this example

Traditional practices and agricultural seedling that are indigenous to the area and foster HNV (not invasive.

Story in a nutshell

Anemona is a plan nursery and garden center that is constantly investing time and resources to research and monitor nature of island of Korčula. Lavandula from pupnat, rosemary, olives, tomato from Lumbarda, island cabbage, different products from Myrtus communis, Arbutus unedo, Salvia and a lot of other plants are the stories and products that Anemona holds. They are monitoring ascomycetes, dragonflies, fallow deer, Kočje natural reserve, island of Badija protected habitat, Kamenjak, Donje Blato habitats, protected forest Hober together with other partners and institutions.

The gathered data and knowledge is shared with the local community and specially among children through collaboration with schools and the local radio station. One of the educational points is also the garden centre whose aim is to educate and to raise awareness among the islanders on the high nature value of the area.

Location: island of Korčula

Economics of HNV farming

Data is not available on the economic impact of the programme for HNV farms.

Maintaining or improving HNV values

The plantation house is improving HNV values of the area by producing seedlings for HNVf and raising awareness on the HNV of the area through education and promotion of mosaic agriculture.

The process that made it happen and critical factors for success

Actors and roles:

Project started in 1988 by a teams of researchers Milan Vujinović, ing of forestry and Roman Ozimec, mag. biology with goal to achieve integration of human activity into nature. Since then Anemona has researched, produced and offered plants valuable for local markets and final production.

Institutional context that made it possible

There was no institutional support or structured support for the activities of Anemona plantation house although they participated in several EU projects as an example of good practices and held workshops presenting their work.

Resources

Bank loans and own resources.

Processes

Started in 1998 and ongoing.

Limiting factors, actual/potential problems, and how could they be overcome?

Problems with waste management and high prices of resources needed for production. A lot of problem have been solved using renewables and recycling. Farming Techniques and Management Nursery plan ''Anemona'' provides resilient islander seedlings and education on how to plant them and manage the mosaic landscape of islander agricultural fields.

Page 2 :

 2 Introduction and contents Page 3: The challenges facing HNV farming in LA Dalmatian islands Page 4: Overview of innovation in LA Dalmatian islands Page 5: Innovation examples in LA Dalmatian islands: what are their strengths and weaknesses for HNV farming Page 6: What are the main innovation needs in LA Dalmatian islands and how could they be addressed: social and institutional innovation Page 7: What are the main innovation needs in LA Dalmatian islands and how could they be addressed: regulatory framework innovation Page 8: What are the main innovation needs in LA Dalmatian islands and how could they be addressed: products and markets innovation Page 9: What are the main innovation needs in LA Dalmatian islands and how could they be addressed: farm techniques and management innovation Page 10: Innovations from outside the LA that could help adress LA needs Page 11: Innovation examples for which LA Dalmatian islands is looking to other Member States Page 31-36: Croatia innovation example 5 Page 38: Photo credit Page 39: Bibliography Overview of innovation in LA Dalmatian islands Innovation examples in LA Dalmatian islands:

  LEADER as a tool to foster HNV: LAG 5 Slow Food Pelješac: fostering HNV products and practices Dry stone walls: keystone for mosaic HNV Doing agriculture as a tourist activity Nursery of indigenous species: Anemona

  Creation and implementation of a local brand Creation of formal local value chains Oživi održi otok -Action plan for sustainable use of resources of Murter region Multistakeholder organizations: fostering HNV products and practices HNVf as a tourist activity: SMS Vlaho Komparak, SMS Eko Škoji, Olive oil museum Drystone walls: keystone for mosaic HNV Nursery of indigenous species ''Anemona'' for sustainable use of resources of Murter region Location: island of Murter, National park Kornati, Nature park Vransko lake HNV system: mosaic agriculture and extensive grazing, mainly sheep on eumediteraneean grassland Scale of operation: Natura 2000 sites of Vransko lake, islands of Murter and National park Kornati Timespan: 18 months (2014/2015) Keys to success: Partnership of civil and private sector, EU funding, creation of a local multistakeholders platform to promote and implement the concept

  knowledge on nature protection and sustainable use of its resources. Incorporation of nature protection in development of island of Murter through sustainable tourism. Creation of a platform of people from the islands and their Parks for sstrengthened capacities of stakeholders on the topic ecosystem services; sstrengthened capacities of stakeholders for development of participative management of Natura 2000 areas; explored practices of participative management policies in protected areas on the model of French eco-museums; revived local traditional practices of sustainable use f natural resources.

  sustainable development Overall lessons from this example, especially from point of view of HNV farming?

  an important role in educating the farmers on available subsidies and helping them receive and administer those subsidies by implementing HNVf friendly projects such as buying livestock, building shelters for livestock, restoring extensive oil grove, restoring one-year crops on mosaic farmland and opening landscapes and planting local medicinal herbs. Slow Food Pelješac Convivum has organized several workshops and gatherings with the aim of promoting and educating the local stakeholders on the importance of local cuisine, on what we eat and how its linked to biodiversity.

  Overall lessons from this example, especially from point of view of HNV farming?

Location

  : a broad spectar of products, tourism as product placement

  Tourism as a boost for HNVf productsHNVf as an unique tourist experience Tourism as a marketing tool for HNVf Overall lessons from this example, especially from point of view of HNV farming?

NGO 4

 4 Grada Dragodid is a group of enthusiasts who have established and organization that is promoting and re-actualising the dry stone skill and heritage thrugh workshops, field research and media. They are making links between the bearers of knowledge and the audience: young professionals (agriculture, architecture, construction, tourism, etc.), heritage enthusiasts, tourists. Location: Croatian coast and islands HNV system: mosaic agriculture and extensive grazing, mainly sheep on eumediteraneean grassland Scale of operation: islands, coast, coastal hinterland of Croatia Timespan: The origins of the initiative go back to 2002 and is ongoing. Dry stone walls as a farming technique in the islands are over 2000 years old Keys to success: enthusiasm, EU funding, EU recognition (Europa Nostra award) What do drystone walls and NGO 4 grada Dragodid achieve for HNV farming? Achievements Revival of local knowledge on nature protection and sustainable use of its resources. Creation of a platform for reviving local traditional practices of sustainable use of natural resources and land management.

  HNV system: mosaic agriculture and extensive grazing, mainly sheep on eumediteraneean grassland Scale of operation: island of Korčula and the sourrounding area Timespan: Founded in 2010. and is still runing Keys to success: service of knowledge and hard work. Constant listening to customers and knowledge on nature protection and sustainable use of its resources.

What are the main innovation needs in LA Dalmatian islands, and how could they be addressed? Regulatory framework innovation Social and institutional -innovation needs Possible approaches

	Establish long-term HNV "animation" project for LA Dalmatian islands	Design a project for RDP measure 16.1.1.	SMS Vlaho Komparak
			SMS Eko Škoji
	Integrate the approach of government departments towards mosaic agriculture	Regional authorities develop a strategy and a cross-departmental working group with island LAGs	Olive oil musem
	Create an online and transparent platform	National authorities establish dialogue with
	for acquiring state land for stewardship	local actors for development of approaches
	Sharing of good farming practices	Capacity building in the form of exchange of
		good practices should be provided associated
		to subsidies for HNV farming.
			Weaknesses
	6		7

Innovations from outside the LA that could help address LA needs Innovation examples for which LA Dalmatian islands is looking to other Member States Innovation Fitches from Croatia

		Establish a centre for agrobiodiversity of the
		islands: educational, economical and tourist CAP measures that foster HNV development centre for preservation of agrobiodiversity and the promotion of elements Agricultural advisory services
		of traditional agricultural cultures
	Develop certifications	Design a certification for the islander HNVf products and specific support marketing
		and distribution measures for the holders
		of the certificate
	Laboratory for HNVf fostering tourism	Create a collaborative platform of multistakeholders from the islands that will
		develop HNVf friendly tourist products and
		services and create an overarching marketing
		strategy for the area
	Developing volunteering tourism	Introduce volontourism as a way to battle lack of labour force
	for sustinable use of resources
	of Murter region

Zagreb webshops of HNVproducts ''Island of Pag lamb'' certificate of origin Cadaster of dry stone walls of Croatia

  This was a project ''Revival of local traditional practices of sustainable use of resources of the island of Murter and its natural region'' funded through the pre-accesion funds of the European Union (Supporting CSOs in Development of Partnerships for Sustainable Use of Protected Areas in Croatia, Including Potential NATURA 2000 Sites) as a result of a partnership collaboration of NGOs Argonauta, 4 Grada Dragodid, Feniks Arbor, Modrave Murter-Betina and public institutions National park Kornati and Nature park Vransko lake. One of the outputs of the workshops was the action plan that documented local resources in terms of natural resources and biodiversity friendly practices and innovations linked to it. It underlined the key elements for revitalization and sustainable use of local resources ''open eco museum'' of the Murter region. Publication was to serve as a document to future generations as it holds the memories of 20 engaged local stakeholders that are holders of the vision of sustanable use o natural resources. Additionally it has 7 concrete project proposals that were developed as a next step in the implementation process: Archaeologicalrecreational park Colentum -tourist valorisation of the cultural and historical heritage of the island of Murter; Modrave gardens -Fostering ecological olive growing with a combination of

tradition and innovation; Not all sheeps are black -The revitalization of traditional cattle breeding for the protection of the eumediterranean lawns; Dry stone walls as a the bond of social capital and sustainability -A register of local dry stone walls heritage and knowledge holders; Wooden shipbuilding tomorrow-revitalization of traditional knowledge of wooden shipbuilding; Laboratory for innovative and sustainable tourism -development of tourist offer outside of the tourist season of the Murter region; Cooperative for the 21st century-founding of the integral cooperative Murter.

  was avaliable through EU funds, specifically IPA -Supporting CSOs in Development of Partnerships for Sustainable Use of Protected Areas in Croatia, Including Potential NATURA 2000 Sites. Knowledge came from the local community and outer EU community.

This project has received funding from the European Union Horizon 2020 research and innovations program under Grant Agreement No. 696391

The process that made it happen and critical factors for successt

Local knowledge and skills to answer to the local problems in HNVf Overall lessons from this example, especially from point of view of HNV farming?

For HNV preservation of traditional landscapes and revitalization of agricultural practices in a way that it answers to the contemporary needs of the locals (incorporation of nature protection, revitalisation of landscapes and sustainable tourism).

Is the innovation unique to its territory and its characteristics, or is it replicable in other areas?

It is an innovation that is replicable and that has potential for replication into other areas.

Could it be rolled out on a bigger territorial scale?

It is possible to manage such a project on the level of an island or a region, depending on the agrobioenvironmental characteristics of the area.

What would be needed to do this successfully?

Additional financial support for finalisation of the project called ''Center for agrobiodiversity of the island of Korčula''.


Jenny L Diaz

Senior Member IEEE Carlos Ocampo-Martinez

A comparison of modelling approaches for closed-loop decision making over discrete domains in manufacturing systems

The manufacturing industry is transforming towards smart, flexible, and energy-efficient systems. In this regard, control strategies based on optimisation have been proposed to improve the energy efficiency of manufacturing systems. Usually, the optimisation problem behind the controller design involves decision variables constrained to binary and discrete domains resulting in Mixed-Integer Linear Programming (MILP) problems and require a high computational burden to find their optimal solution. In this paper, three different approaches are proposed for the closed-loop decision making over discrete domains in manufacturing systems, including the constraints and limitations to their implementation. Thus, the number and nature of required variables as well as the additional constraints needed to represent the discrete domains of the decision variables are established. These approaches are tested and compared to solve the optimisation problem behind a predictive-like controller designed to minimise the energy consumption of a manufacturing process line.

I. INTRODUCTION

In many industrial processes, both the optimal design and the implementation of optimisation-based control techniques often require variables constrained to a discrete set of admissible values. Some relevant applications of the use of discrete input signals can be found in chemical processes [START_REF] Ning | Data-driven robust MILP model for scheduling of multipurpose batch processes under uncertainty[END_REF], process planning and scheduling [START_REF] Lu | Energy-efficient permutation flow shop scheduling problem using a hybrid multi-objective backtracking search algorithm[END_REF], smart grids [START_REF] Hans | Hierarchical distributed model predictive control of interconnected microgrids[END_REF], and on-off systems [START_REF] Goodwin | Opportunities and challenges in the application of advanced control to power electronics and drives[END_REF]. For the particular case of manufacturing systems, system actuators can be of on-off nature of having different activation levels or status [START_REF] Diaz | Energy efficiency in discretemanufacturing systems: Insights, trends, and control strategies[END_REF]. Thus, both the problem formulation and discrete optimisation method are crucial to solve these optimisation problems in a reliable and fast way. This last fact is quite important in control applications subject to real-time implementation constraints [START_REF] Rawlings | Model Predictive Control: Theory and Design[END_REF].

The use of discrete decision variables would imply a high computational burden for the optimisation routines. In most of the control applications, decisions involving discrete actuators are removed from the control layer and dealt with logic rules, precomputed control laws, or heuristic approximations [START_REF] Rawlings | Model predictive control with discrete actuators: Theory and application[END_REF], [START_REF] Prodan | Enhancements on the hyperplanes arrangements in mixed-integer programming techniques[END_REF], [START_REF] Diamond | A general system for heuristic minimization of convex functions over non-convex sets[END_REF]. However, most of these approaches are not able to respond effectively to disturbances or changes in the system since they are predefined considering specific operational conditions. For the case of flexible manufacturing systems, in which their operational conditions can change, these Jenny L. Diaz C. and Carlos Ocampo-Martinez are with Automatic Control Department, Universitat Politècnica de Catalunya, Institut de Robòtica i Informàtica Industrial (CSIC-UPC), Llorens i Artigas 4-6, 08028 Barcelona, Spain. (e-mail: {jenny.lorena.diaz, carlos.ocampo}@upc.edu) Sorin Olaru is with the Laboratory of Signals and Systems (L2S, UMR CNRS 8506), Centrale Supélec-CNRS Université Paris Sud, Université Paris-Saclay, 91190 Gif-sur-Yvette, France. (e-mail: sorin.olaru@centralesupelec.fr) approaches could be not suitable. Thus, with advances in computer performance and optimisation software, the common way to solve such problems is by transforming them into Mixed-Integer Programming (MIP) problems and solving them by using branch-and-bound-based MILP solvers such as those available in packages like cplex and gurobi. Based on this approach, to choose among n discrete values in an MIP problem, n binary variables that sum up to one are required [START_REF] Yıldız | Incremental and encoding formulations for mixed integer programming[END_REF]. Nonetheless, if the optimisation problem is not properly formulated and the decision variables are not restricted effectively to the feasible alternative, this approach could lead to unbalanced branch-and-bound trees and may result in long solution times [START_REF] An | Enhanced linear reformulation for engineering optimization models with discrete and bounded continuous variables[END_REF].

Different approaches have been proposed in the literature to reduce the number of decision variables and the computational time to solve the related problem [START_REF] Prodan | Mixed-Integer Representations[END_REF]. However, in more complex cases, these approaches imply the product of some polynomial terms, thus losing the linearity. In [START_REF] Li | Linear reformulation of polynomial discrete programming for fast computation[END_REF], a set of equations for linearising discrete cross-product terms that can be incorporated into conventional MILP reformulations is proposed. Similarly, a framework for reformulating Mixed-Integer Non-Linear Programming (MINLP) problems to a convex relaxed form is discussed in [START_REF] Lundell | Solving global optimization problems using reformulations and signomial transformations[END_REF]. As common ideas, trying to avoid both bi-linear and non-linear terms into the problem reformulation is linked to the reduction of the number of decision variables and simplifying the nature of the proposed constraints from the definition stage of the optimisation problem.

Thus, the main contribution of this work is to provide three different ways of representing discrete feasible sets for control applications based on optimisation as well as to present a comparison of such approaches concerning the required computational burden for their implementation. In this regard, mathematical tools and representations such as rounding error and polyhedrons [START_REF] Bemporad | Convexity recognition of the union of polyhedra[END_REF], [START_REF] Lubin | Polyhedral approximation in mixed-integer convex optimization[END_REF] have been employed to constrain the discrete sets and to reduce the number of binary variables required when the optimisation problem is reformulated as a compact 0-1 MILP problem. The main idea is to reformulate the optimisation problem effectively and efficiently to simplify the input to optimisation routines such that the controllers can be suitable for their implementation in real time without the use of precomputed control laws. Other strategies have been excluded from this proposed comparative assessment due to their computational burden, a fact that does not allow their use in real time according to the field of application considered in this paper.

Then, to test the performance of the proposed approaches, an optimisation-based controller proposed in [START_REF] Diaz | An optimization-based control strategy for energy efficiency of discrete manufacturing systems[END_REF] to min-imise the energy consumption of a manufacturing process line will be considered. In this case, the optimal activation instants of binary and discrete actuators should be determined considering the operating constraints on both the process line and the system actuators. Thus, the optimisation problem is reformulated as an MILP problem using the proposed approaches, and the closed-loop performance for the controller is compared in terms of the control objective and the computational burden required to find an optimal solution.

The rest of the paper is organised as follows. The energy efficiency control strategy for manufacturing systems and the problem statement are introduced in Section II. Then, in Section III, the proposed approaches to model the discrete sets are presented. Next, the case study and the related decision models are introduced in Section IV. Later, the simulations results and the comparative assessment for the proposed approaches are presented and discussed in Section V. Finally, conclusions from the obtained results are presented in Section VI.

II. ENERGY EFFICIENCY OF MANUFACTURING SYSTEMS

A. Energy Efficiency Control Strategy

A process line is a complex system including several machine tools and peripheral devices that work sequentially and logically, as shown in Figure 1. Machines refer to a set of devices that are directly related to the machining processes (e.g., milling, cutting, turning), while the peripheral devices are those elements that provide the resources required to machines for their proper operation. Thus, there exist several functional relationships between machines and peripheral devices that determine the productivity of the process line.

Machine tools are characterised by periodic behaviour according to the time required to process a piece, which is denoted by T Mi . Besides, due to the different operations performed by machine devices, there are high and low energy consumption stages along T Mi . Then, since peripheral devices supply resources to machines in the process line, such devices might or might not show a periodic behaviour, which may match with T Mi . Thus, to improve the energy efficiency of manufacturing system, a predictive-like controller to manage the activation instants of the peripheral devices in a process line without affecting its productivity has been proposed in [START_REF] Diaz | An optimization-based control strategy for energy efficiency of discrete manufacturing systems[END_REF]. In this case, the activation/deactivation of the machine devices along T Mi , i.e., the machining sequence of the i-th machine (Λ M i ), is considered as fixed and periodic over time. Thus, T Mi are kept the same and machines can handle the same number of pieces as when the control strategy is not implemented. The energy consumption for Λ M i , i.e., β M i = T M i k=1 S Mi (k), will also be constant over any interval T Mi and periodic over time, being S Mi the instantaneous power consumption of the machine.

The control strategy proposed in [START_REF] Diaz | An optimization-based control strategy for energy efficiency of discrete manufacturing systems[END_REF] focuses on the management of peripheral devices to minimise the total energy consumption and guarantee the supply of the resources required by the machines. Then, considering a fixed number of both machines and peripheral devices in a process line, their activation sequences can be defined as

Λ M i (k) = {u Mi,1 (k), u Mi,2 (k), . . . , u Mi,v (k)}, (1a) Λ P (k) = {u 1 (k), u 2 (k), . . . , u m (k)}, (1b)
being k ∈ Z ≥0 the discrete-time index, and u M i,l (k) and u j (k) the activation signals of machining devices of the i-th machine and the peripheral devices in the process line. Then, considering a prediction horizon H p , the sequence1 for Λ P along H p is defined as

Γ(k) {Λ P (k|k), . . . , Λ P (k + H p -1|k)}, (2)
and an MPC controller is designed based on the following open-loop optimisation problem:

min Γ(k) Hp k=1 S(k)∆k (3a)
subject to

ξ(k + r + 1|k) = f (ξ(k + r|k), Λ M i (k + r|k), . . . uj(k + r|k)), (3b) S(k + r|k) = g (ξ(k + r|k)) , (3c) Qj(k + r + 1|k) = qj(Qj(k + r|k), uj(k + r|k), . . . Λ M i (k + r|k)), (3d) uj(k + r|k) ∈ Ωj = {sj 1 , sj 2 , • • • , sj n }, (3e)
Q h (k + r + 1|k) ∈ Q h Q h , (3f)
for r ∈ {0, 1, 2, .., H p -1}, being S ∈ R the instantaneous power consumption of the whole process line given by

S(k) = b i=1 S Mi (k) +   m j=1 S j (k)   , (4)
with S Mi ∈ R and S j ∈ R the power consumption of the machines and peripheral devices, respectively. Besides, in

, ξ ∈ R n1 is the state vector of the energy consumption model of the process line, while f : R n1 × Ω j → R n1 and h : R n1 → R ≥0 are the maps for such a model. Moreover, Q j corresponds to states of the process dynamics related to the operation of peripheral devices with q j : Ω j × R → R ≥0 the maps that consider the operational relationships between machines and peripheral devices. According to Figure 1, the q-relations in (3) correspond to the process dynamics for the supply systems of compressed air and coolant.

B. Problem Statement

It is worth noting that (3e) and (3f) refer to the constraints for the domain of decision variables and process variables Q j , respectively. In this case, Ω j ⊂ R is the discrete and countable finite set of cardinality n j describing the feasible domain of u j , with s jn the values (or symbols) that form such discrete (or alphabet) set. In the most simple case, u j will be constrained to a binary set, which represents the on/off status of a device with nominal power consumption. Taking into account the admissible domain for the decision variables in (3), the problem addressed in this paper is to determine suitable ways of modelling these domains, fact that contributes to reducing the computational burden required to solve (3). This last fact is important for the real-time implementation of closed-loop control strategies based on optimisation, in which the optimisation problem should be solved fast enough at every instant k. Therefore, to get suitable representations of discrete sets such as Ω j , the nature of the decision variables and corresponding mathematical expressions to represent the admissible values should be determined and added to the optimisation problem.

III. MODELLING OF DISCRETE SETS

Due to the nature of the decision variables in (3), three different ways to represent the discrete sets are presented below to formulate the optimisation problem as a compact 0-1 MILP problem. Although there are some optimisation routines that model directly such sets, the idea behind the proposed approaches is to further simplify the problem before to use the optimisation solver.

Approach 1: Rounding-error based strategy: In this case, to model Ω j the following statement is assumed:

Assumption 1: A discrete set Ω j = {s j1 , s j2 , • • • , s jn } with s jn ∈ R is an set in which all its elements have a regular spacing ρ.

Under this assumption, to model the discrete feasible set Ω j , one decision variable, i.e., ũj ∈ [ε, ε] with ε = max(Ω j ) and ε = min(Ω j ) is required. Besides, to ensure that only the admissible values of Ω j in [ε, ε] could be selected, the rounding error should be added as a constraint into the optimisation problem in (3) as follows:

ρ ũj ρ -ũj ≤ 0, (5)
with [•] the round operator and ρ the regular spacing among the elements of Ω. Based on the previous inequality, only the values in [ε, ε] that satisfy (x mod ρ) ≡ 0 can be chosen. Remark 1: If zero belongs to Ω j and its distance to the next element in Ω j does not satisfy the spacing regularity of the rest of the elements, a new variable and a constraint should be introduced, e.g., when zero represents the off status and the rest of the elements refer to different activation levels. Thus, zero is considered separately by its nilpotent properties within Ω j , and an extra binary variable φ j and a new constraint are added as follows:

ε φ j ≤ ũj ≤ ε φ j , (6)
with φ j ∈ {0, 1} and ũj ∈ [ε, ε]. Besides, this approach could be extended to the case in which ρ for the elements of Ω j is not regular. The original set is split into subsets with regular spacing, which are associated with one binary variable, rounding error equation, and extra constraints on binary variables to ensure the selection of only one set. Approach 2: Direct binary approach encoding: Given a set Ω j = {s j1 , s j2 , • • • , s jn } with s jn ∈ R, one can associate n decision variables, i.e., γ 1 , γ 2 , • • • , γ n ∈ {0, 1}, and reinforce the alternative of decision with the constraint

γ 1 + γ 2 + • • • + γ p = 1. (7)
Indeed, to guarantee the selection of only one of the values in Ω j , the decision variable u j is computed according to

u j = s j1 γ 1 + s j2 γ 2 + • • • + s jn γ n . (8)
Remark 2: It should be noted that if zero belongs to Ω j , n -1 binary variables are needed, and the constraint in [START_REF] Rawlings | Model predictive control with discrete actuators: Theory and application[END_REF] should be relaxed as

γ 1 + γ 2 + • • • + γ n-1 ≤ 1.
Approach 3: Geometrical representation of the feasible domain: In this case, the discrete set will be modelled by means of a polyhedron given as the intersection of inequalities and equalities (referred to as H-representation). To get a polyhedral representation of a discrete set, auxiliary variables are defined to fit the vertices of the polyhedron. For instance, considering a discrete set Ω j = {s j1 , s j2 , s j3 , s j4 }, two binary variables and one real variable, i.e., δ 1 , δ 2 ∈ {0, 1}, and u j ∈ R, are required. Next, the discrete values of Ω j will be associated to the combinations of variables δ 1 and δ 2 , which define the vertices set V of the polyhedron as

V = {[0, 0, s j1 ]; [0, 1, s j2 ]; [1, 0, s j3 ]; [1, 1, s j4 ]} .
Then, using suitable tools, such as the MPT Toolbox [START_REF] Kvasnica | Multi-Parametric Toolbox (MPT)[END_REF], the H-representation of the polyhedron P v = {v|A v ≤ b, A e v = b e }, which corresponds to the convex hull of V , can be determined. These expressions should be added as constraints in the optimisation problem such that [δ 1 , δ 2 , u j ]

T ∈ P v . Based on this formulation, for any combination of the binary variables only the values in Ω j satisfy the inequality and equality matrices added as constraints.

IV. BENCHMARK SYSTEM According to Figure 1, the process line is formed by n subsystems, which consists of three machines and two shared peripheral devices. Thus, the process description presented below for the one sub-system is straightforwardly extended to the other sub-systems without lost of generality. It is assumed that all machines in each sub-system have the same period, i.e., T Mi = 28s ∀ i = 1, 2, 3, and that the peripheral devices P 1 and P 2 are shared among these machines. In this case, P 1 is associated to a supply system of compressed air with nominal energy consumption, i.e., u 1 ∈ Ω 1 {0, 1}. Thus, the q-relations in (3d) related to P G1 refer to the dynamics for the total change of mass M T1 and pressure P T1 inside a storage tank T 1 , which are expressed as follows:

MT 1 (k + r + 1|k) = MT 1 (k + r|k) + τs σ(k + r|k), (9a)
σ(k + r|k) = min uG 1 (k + r|k) - b i=1 mout M i (k + r|k), (9b) PT 1 (k + r|k) = MT 1 (k + r|k) R T VT 1 Wair , ( 9c
)
with τ s the sampling time, m out M i the air consumption from M i , m in the air flow pumped by P G1 towards the tank T 1 , and, R, T, V T1 , and W air the gas constant, air temperature, volume of T 1 , and the molecular weight of the air, respectively. Besides, P T1 must belong to P T1 , P T1 .

Besides, P 2 is related to a coolant supply system for the cutting operations at each machine, and its activation can be modulated at different levels, i.e., u 2 ∈ Ω 2 {0, 100, 120, 140}. According to Figure 1, a flow of coolant m c is pumped by P 2 from T 3 towards T 2 , passing through a filter in which the gross particles are separated. The coolant flows required by the machines are pumped from T 2 . The level dynamics in both tanks are given by

L2(k + r + |k) = L2(k + r|k) + τs γ(k + r|k) 1 ρc AT 2 , (10a)
γ(k + r|k) = mc(k + r|k) - b i=1 mout,c M i (k + r|k), (10b)
L3(k + r + 1|k) = L3(k + r|k) + τs θ(k + r|k) 1 ρc AT 3 , (10c)
θ(k + r|k) = b i=1 min,c M i (k + r|k) -mc(k + r|k), (10d)
Pout(k + r|k) = Pin(k + r|k) + ρch f 1→2 (k + r) -η W (k + r|k) mc(k + r|k) , (10e)
with m out,c M i the coolant flow required by the i-th machine, and m in,c M i the flow of the dirty coolant recovered. Besides, P in and P out correspond to the input and output pressure in the pipe system from T 3 towards T 2 , while, ρ c , η, W and h f1→2 are the coolant density, the pump efficiency, the work supply to P G2 , and the energy losses by friction, respectively.

A. Discrete domain for the decision variables

Given the nature of the discrete sets Ω 1 and Ω 2 , the decision variables and constraints required by each one of the approaches proposed in Section III are presented below.

Approach 1: If zero is removed from the set Ω 2 and an extra variable is added for the switching off of P 2 , i.e. u 2 = 0, it is possible to fix ρ = 20 for the elements of Ω 2 . Thus, three decision variables are required to model Ω 1 and Ω 2 , i.e., u 1 (k), φ 2 (k) ∈ {0, 1}, and ũ2 (k) ∈ [100, 140] , with u 1 related to P 1 and, φ 2 and ũ2 associated to Ω 2 . Then, considering ε = 100 and ε = 140, constraints in ( 5) and ( 6) should be adapted and added to (3).

Approach 2: In this "full" binary encoding, four binary variables are required to represent the domain of decision variables, i.e., u 1 (k), γ 1 (k), γ 2 (k), γ 3 (k) ∈ {0, 1} , with u 1 related to the device P 1 , and according to Remark 2, three binary variables γ 1 , γ 2 and γ 3 are required to model the discrete set Ω 2 together with the following constraint:

γ 1 (k) + γ 2 (k) + γ 3 (k) ≤ 1. (11)
Finally, u 2 is given by

u 2 (k) = 100γ 1 (k) + 120γ 2 (k) + 140γ 3 (k). (12)
Approach 3: In this case, one binary variable for the activation/deactivation of P 1 is required, i.e., u 1 (k) ∈ {0, 1}, while two binary variables, i.e., δ 1 (k), δ 2 (k) ∈ {0, 1} , and one real variable, i.e., ũ2 (k) ∈ R, are needed to model Ω 2 . Then, each combination of δ 1 and δ 2 will be related to one element in the set Ω 2 , and a polyhedron with vertices

V P G 2 = {[0, 0, 0] [0, 1, 100] [1, 0, 120] [1, 1, 140]}
is defined and shown in Figure 2. Next, using the MPT toolbox, the H-representation of the polyhedron was obtained and, the following inequality matrix is added to (3):

   -0.
      δ 1 δ 2 ũ2 -1    ≤    0 0 0 0    .

B. Energy consumption models

Data-driven models were used to identify the power consumption models of machines and peripheral devices. In this case, Subspace Identification (SI) methods were used since they allow identifying the matrices of a state-space realisation of linear time-invariant systems based on inputoutput data [START_REF] Qin | An overview of subspace identification[END_REF]. According to [START_REF] Diaz | An optimization-based control strategy for energy efficiency of discrete manufacturing systems[END_REF], different sequences of Λ M i along T Mi were designed and tested in a test bench that emulates the energy consumption of machine tools to collect the data of S Mi . Besides, different sequences of Λ P were tested to obtain a rich range of the outputs S Pj . From the obtained input-output data sets, energy consumption models were identified by using the n4sid routine of the System Identification Toolbox TM provided by Matlab R . Thus, different values of N were tested to identify the matrices that allow the highest fitting degree between the real and modelled outputs. The energy consumption models are detailed in [START_REF] Diaz | An optimization-based control strategy for energy efficiency of discrete manufacturing systems[END_REF].

V. SIMULATION RESULTS

The control strategy was tested using each one of the proposed approaches to compare their performance and computational burden. All simulations were performed using an Intel Core i7-55000U 2.4 GHz processor with 8G RAM and considering a sampling time equal τ s = 0.1 s. The simulation results were obtained in Matlab by using the software IBM ILOG CPLEX Optimisation Studio integrated to YALMIP toolbox [START_REF] Löfberg | Yalmip : A toolbox for modeling and optimization in Matlab[END_REF]. Since the controller was designed to make decisions every second along H p = 28s, a faster internal loop (blocking) for both the process and energy consumption models are implemented [START_REF] Maciejowski | Predictive Control with Constraints[END_REF].

The resulting energy consumption profile and the optimal activation/deactivation sequence of peripheral devices are presented in Figures 3a and3b for the case in which n = 1. Besides, in Figure 3c the process dynamics related to both P G1 and P G2 are shown. From these results, some differences can be observed for the peripheral device with a discrete domain, i.e., P G2 , for which even when the device was turned on at the same time instant, the activation value was different according to the approach tested. Thus, although the stopping criteria of optimisation routine were the same for all approaches, these differences could be related to the solver ability to test all possible combinations for each approach before to reach the stopping criteria. This is due to the fact that, for each modelling approach, the nature and the total number of decision variables are different and, therefore, the number of the possible combinations could differ although the feasible domain is similar.

Next, to compare the computational burden when more decision variables are considered, a process line adding subsystems as shown in Figure 1 is studied. It should be noted that for each one of the sub-systems added, the operating conditions, machine cycles, energy consumption models, and dynamics of peripheral devices are assumed to be the same that for the first subsystem with three machines and two peripheral devices. In Table I, a comparison of the proposed approaches concerning both the computational burden and the control objective is presented when several sub-systems are considered as the process line. In this regard, the decision variables (DV) along H p , their classification, the number of equality and inequality constraints, the CPU time and the value of the cost function are presented in Table I.

In Table I, the auxiliary variables (AV) refers to the variables added to model the non-linear operators involved in the rounding error expression. Thus, the total number of decision variables considered by each approach corresponds to the set of both the decision and auxiliary variables. Besides, for Approach 1 all the auxiliary variables added to the decision model were defined as integer variables and by the optimisation routine internally. Finally, the total number of continuous variables (CV) for Approaches 1 and 3 are summarised in the seventh column. From these results, it should be noted that the equality constraints are the same for all approaches since they correspond to the initial conditions for both the process model and the machining sequences.

Based on the results in Table I, it is possible to observe that even when the optimal activation sequences of peripheral devices obtained from each approach are different, the total energy consumption is similar for each one of the approaches tested. However, higher differences can be observed in the CPU time spent to solve the optimisation problem at each iteration. Thus, although the Approach 1 has a higher number of total decision variables, the solution is obtained faster than for the rest of cases. This behavior is related to the fact that Approach 1 has a lower number of binary variables, and therefore, fewer combinations should be tested and the completion conditions are achieved faster. Therefore, when the branch-and-bound algorithms are employed, the computational burden to evaluate all (or most of) the combinations is increased as the binary variables increase. In this regard, by implementing the proposed Approach 1 with fewer number of binary variables, the computational burden can be reduced even when auxiliary variables are required. However, although both Approaches 2 and 3 require more binary variables to model Ω 2 than Approach 1, the latter is more restrictive than the other approaches. Thus, when more complex discrete sets with no regular spacing are analysed, Approach 1 could require more binary variables than Approaches 2 and 3, in addition to the auxiliary variables due to both the rounding operator and absolute value.

VI. CONCLUSIONS

In this paper, three different approaches to reformulate optimisation problems involving discrete and continuous variables into a mixed-integer MILP problem have been presented. Based on the proposed formulations, ordered and non-ordered discrete sets could be modelled by using rounding error, binary variables or polyhedral approximations. Besides, the necessary constraints to guarantee the selection of the discrete admissible values according to each approach as well as the conditions for their implementation were presented and discussed. Based on the obtained results, it is possible to conclude that the total amount of binary variables is a crucial factor regarding the computational burden even when the total number of decision variables is lower. However, despite the computational cost, the binary variables lead to optimisation problems that involve non-ordered and nonregularly distributed symbol sets can be solved in an efficient manner and with a manageable computational burden.

Fig. 1 :

 1 Fig. 1: A b-stage serial process line with its corresponding peripheral devices.

Fig. 2 :

 2 Fig. 2: Polyhedron for the discrete set Ω 2 .

Here, z(k + r|k) denotes the prediction of the variable z at time instant k + r performed at k. The index r will cover the finite prediction window of length Hp.

ACKNOWLEDGEMENT

This work has been partially funded by the project IKER-CON (ref. C10683) and and the FI-AGAUR scholarship of the Catalan government.