Djamal Eddine Ghersi

Meriem Amoura

Khaled Loubar

Umberto Desideri

Mohand Tazerout

Multi-objective optimization of CCHP system with hybrid chiller under new electric load following operation strategy

Keywords: Combined cooling, heating and power system, Electric load following strategy, Hybrid chiller, Multi-objective optimization

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

grid power generation efficiency (%) ! grid distribution efficiency (%) ! heat recovery system efficiency (%)

Introduction

During the past century, fossil fuels (natural gas, oil, and coal) were the major primary source of energy in the world, and provided 85-93% of all energy production from 1950 to 2005 [START_REF] Nehring | Traversing the mountaintop: world fossil fuel production to 2050[END_REF]. According to International Energy Agency (IEA), the global energy demand will continue to rise by 30% from 2015 to 2040 [START_REF]World Energy Outlook 2017[END_REF]. If this growth is covered by conventional power plants, it may cause negative economic and environmental implications.

In conventional power plants, the electricity conversion efficiency ranges from 30 to 50% [START_REF] Ahmadi | Thermodynamic and economic analysis of performance evaluation of all the thermal power plants: A review[END_REF].

Conventional thermal power plants discharge large amounts of heat in the atmosphere.

Recovering all or part of this heat can increase the overall energy efficiency of power plants.

Additional energy losses also appear in the transmission and distribution of electric energy [START_REF] Fumo | Analysis of cooling, heating, and power systems based on site energy consumption[END_REF]. Distributed generation, described as power generation near to final consumer, can minimize the transmission losses [START_REF] Ghaebi | Thermodynamic modeling and optimization of a combined biogas steam reforming system and organic Rankine cycle for coproduction of power and hydrogen[END_REF]. Thus, the combined production of cold, heat and electricity (CCHP) from a primary source of energy, which is called too as trigeneration, is seen as a promising solution for satisfying and solving energy-related problems with high technical, economic and environmental benefits [START_REF] Wang | Optimization of capacity and operation for CCHP system by genetic algorithm[END_REF]. CCHP systems generated more than 11% of national electric power for the G8 countries in 2006 recovering exhaust heat for both heating and cooling of buildings and in industrial processes. This share is expected to reach 24% by 2030 [START_REF] Kerr | Combined heat and power: evaluating the benefits of greater global investment[END_REF].

The CCHP system concept is simple: electricity is produced via a power generation unit (PGU). The heat rejected by the PGU can be recovered by another integrated system to provide the primary energy for the cooling and heating load in buildings and in industrial processes. Generally, a simple CCHP system is composed of PGU, heat recovery system, absorption chiller units (AC) and a heat exchanger. The absorption chiller can be driven by the rejected heat of the PGU to meet cooling demand [START_REF] Moussawi | Selection based on differences between cogeneration and trigeneration in various prime mover technologies[END_REF]; the heat recovery system is installed to recover the rejected heat to be able to satisfy the heating demand.

Compared to conventional separated energy production system (SP), in which the electricity demand is satisfied by the electricity purchased from the grid and/or the thermal demand is satisfied by burning a fuel in a boiler, the CCHP system benefits of higher energy efficiency and lower pollutant emissions [START_REF] Zhang | Comparison of combined cooling, heating and power (CCHP) systems with different cooling modes based on energetic, environmental and economic criteria[END_REF]. Therefore, the objective of designing CCHP systems aims to minimize primary energy consumption, annual cost, and greenhouse gas emissions as much as possible. To attain this, the following issues should be taken into consideration in the design of such system: the operating strategy of the system, the efficiency of each component and the requirements of building for electricity, heat and cold [START_REF] Cho | Evaluation of CCHP systems performance based on operational cost, primary energy consumption, and carbon dioxide emission by utilizing an optimal operation scheme[END_REF].

In general, there are two fundamental operation strategies for CCHP system: electric load following (ELF) and thermal load following (TLF). The evaluations and analyses of each of these two strategies are examined in [START_REF] Wang | Performance comparison of combined cooling heating and power system in different operation modes[END_REF][START_REF] Mago | Evaluation of a turbine driven CCHP system for large office buildings under different operating strategies[END_REF][START_REF] Smith | Analysis of a combined cooling, heating, and power system model under different operating strategies with input and model data uncertainty[END_REF][START_REF] Jing | Life cycle assessment of a solar combined cooling heating and power system in different operation strategies[END_REF], where the major previous studies found that ELF strategy can achieve better energetic and environmental performance compared to TLF strategy.

When the CCHP system operates under ELF strategy, the system delivers sufficient electricity for the building first and takes advantage of the by-product heat to meet all the thermal demand. If the by-product cannot satisfy the thermal needs, an auxiliary boiler should be implemented. When the CCHP system operates under TLF strategy, the system meets all the thermal demand of building first. If the electrical power generated by the PGU cannot meet all the electric demand, additional electric power should be imported from the national grid.

However, if electrical power generated by the PGU exceeds the demand, excess electricity could be transferred to the electric grid.

In addition to the researches in operation strategies of CCHP systems, there are also some studies on the cooling methods. Typically, CCHP system uses absorption chiller to meet the cooling demand. Therefore, in such systems, owing to the relatively low coefficient of performance (COP) of the absorption chillers machine, the energy consumption of CCHP systems can be higher than conventional systems [START_REF] Afzali | Optimal design, operation and analytical criteria for determining optimal operating modes of a CCHP with fired HRSG, boiler, electric chiller and absorption chiller[END_REF]. However, a hybrid system with absorption chiller and electric chiller (EC) can be an attractive method to satisfy the cooling demand, that may help matching the ratio of the power and heat provided by PGU with user loads considerably better [START_REF] Wang | Life cycle assessment (LCA) optimization of solarassisted hybrid CCHP system[END_REF]. Nevertheless, taking into account the high rates of the electricity, an operation strategy requires to be designed to identify the optimal electric/absorption cooling ratio. To increase the performance of this strategy, other researchers have suggested to use optimal electric/absorption cooling ratio that may improve energy, economic, and environmental performance of the hybrid chiller CCHP system. Wang et al. [START_REF] Wang | Particle swarm optimization for redundant building cooling heating and power system[END_REF] applied the particle swarm optimization algorithm (PSOA) to the design and operation of the CCHP system by optimizing the capacity of the PGU, the storage tank and, the rate of electric cooling to total cooling load in order to achieve the highest energy, economy and environment performances of the CCHP system. Hajabdollahi et al. [START_REF] Hajabdollahi | Assessment of new operational strategy in optimization of CCHP plant for different climates using evolutionary algorithms[END_REF] examined the variable electric/absorption cooling ratio strategy with the constant electric/absorption cooling ratio strategy for several climates, where they found that the variable electric/absorption cooling ratio strategy provided more benefit in the all studied climates. Li et al. [START_REF] Li | Optimal design and operation strategy for integrated evaluation of CCHP (combined cooling heating and power) system[END_REF] optimized the energic, economic and environmental performance of CCHP system with hybrid chiller. The authors found that if the CCHP system couples with thermal storage and renewable energies systems, the performance of the CCHP system increases significantly. Li et al. [START_REF] Li | Exergy-analysis based comparative study of absorption refrigeration and electric compression refrigeration in CCHP systems[END_REF] performed energetic and exergetic comparison between absorption chiller and electric chiller in CCHP system which functions with a combined cycle of gas turbine and steam turbine as prime mover. It has been shown that the choice between these two types of cooling is strongly dependent on the distance between the power plant and the cooling device, in a way that when the distance is less than 5 km, absorption cooling system is more effective. Hyeunguk et al. [START_REF] Ahn | Performance assessment of hybrid chiller systems for combined cooling, heating and power production[END_REF] proposed the modified electric load following strategy (MELF) for CCHP system which uses a hybrid chiller which combines electric chillers and absorption chillers based on two U.S. Department of Energy reference buildings located in two different climates. Their results showed that the hybrid chiller based CCHP systems with new MELF strategy achieves lower energy consumption and carbon dioxide emissions than the absorption chiller based CCHP systems.

The economic aspect is one of the main concerns in CCHP system design. Different techniques must be investigated and the one that satisfies utility demands with the lowest annual cost is usually adopted [START_REF] Lai | Feasibility and flexibility for a trigeneration system[END_REF]. Ziher et al. [START_REF] Ziher | Economics of a trigeneration system in a hospital[END_REF] examined economic feasibility of CCHP implemented in one of the largest hospitals in Slovenia. The trigeneration system consisted of a natural gas turbine and steam absorption along with compression chillers with cold storage. The pay-back period of this system was 5.8 years. Pagliarini et al. [START_REF] Pagliarini | Hospital CHCP system optimization assisted by TRNSYS building simulation tool[END_REF] optimized and analyzed the feasibility of a CCHP system for a hospital in Parma, Italy, by minimizing the total operational and maintenance cost. The economic analysis showed that the suggested CCHP system can be paid back in a period of about 15 months. Gu et al. [START_REF] Gu | Integrated assessment of combined cooling heating and power systems under different design and management options for residential buildings in Shanghai[END_REF] studied the performance of CCHP systems for residential buildings in Shanghai, China, using several management options and designs. The most advantageous option was a CCHP system with gas engine under energy island mode. Moreover, the CCHP system has the ability to decrease primary energy consumption and carbon dioxide emission by 17% and 40%, respectively. However, the net present value is -0.5 million USD. This shows that CCHP systems are not always suitable to be introduced in residential buildings in Shanghai. Chua et al. [START_REF] Chua | Sustainable energy systems for a remote island community[END_REF] evaluated several CCHP system configurations by combining various prime mover technologies. The systems had been designed for the tourist island of Pulau Ubin, Singapore.

Amongst all combinations of the different primary mover technologies, the economically optimum combination can contribute to 20% renewable energy integration into the CCHP system with a gain of 0.15 million USD per year. Abbasi et al. [START_REF] Abbasi | Energy, exergy, and economic evaluations of a CCHP system by using the internal combustion engines and gas turbine as prime movers[END_REF] designed and analyzed a CCHP system with gas turbine (GT) and IC engine for a residential complex located in Shahrood, Iran. It was shown that the combination of diesel engine and gas engine under ELF strategy is the best option producing 87, 62.8 and 80% of energy efficiency, exergy efficiency and cost saving, respectively. Hyeunguk et al. [START_REF] Ahn | Economic feasibility of combined cooling, heating, and power (CCHP) systems considering electricity standby tariffs[END_REF] studied the economic performance of hybrid chiller CCHP systems, under MELF strategy, applied for a large office building in three different regions in the United States. The authors reported that CCHP systems can decrease the annual operation cost by up to 0.4 million USD per year (38%) compared to the conventional system in the best case. In any case, the economic feasibility of CCHP systems is considerably affected by the energy prices that vary from one region to another.

As described above, a good CCHP system should generate economic savings, energy savings as well as reductions in pollutant emissions. The performance of the CCHP system depends closely on its operation strategy and configuration. In order to maximize the benefit of the CCHP system, it is important to optimize the design parameters of the CCHP systems such as the capacity of the facilities. In the case of SP system, this capacity is easy to specify because the size depends directly on the energy load of the building [START_REF] Wang | Optimization of capacity and operation for CCHP system by genetic algorithm[END_REF]. On the other hand, as a result of the complexity of operation strategies, the capacity of facilities is hard to be determined in the CCHP systems [START_REF] Wang | Optimization of capacity and operation for CCHP system by genetic algorithm[END_REF]. Considering the prices of facilities, grid electricity cost and fuel rates, some multi-objective optimization approaches have been adopted to determine the optimal capacity of facilities in order to maximize the energetic, economic and environmental benefits of CCHP system [START_REF] Gao | An overview of optimization technologies applied in combined cooling, heating and power systems[END_REF].

Some researchers have adopted conventional multi-objective optimization methods such as weight method [START_REF] Mohammadkhani | Energy and emission management of CCHPs with electric and thermal energy storage and electric vehicle[END_REF][START_REF] Khaloie | Co-optimized bidding strategy of an integrated wind-thermal-photovoltaic system in deregulated electricity market under uncertainties[END_REF][START_REF] Khaloie | Coordinated wind-thermal-energy storage offering strategy in energy and spinning reserve markets using a multi-stage model[END_REF] and ε-constrain method [START_REF] Jing | Economic and environmental multi-optimal design and dispatch of solid oxide fuel cell based CCHP system[END_REF][START_REF] Cao | Optimal operation of CCHP and renewable generation-based energy hub considering environmental perspective: An epsilon constraint and fuzzy methods[END_REF][START_REF] Hou | Distributed energy systems: Multi-objective optimization and evaluation under different operational strategies[END_REF]. The weight method is widely used due to its simple procedure. However, it is not easy to determine the weight of each objective and an insufficient number of Pareto solutions would be generated with a weight method, which makes it difficult to exactly reach the Pareto front [START_REF] Gao | An overview of optimization technologies applied in combined cooling, heating and power systems[END_REF]. On the other hand, the ε-constraint method suffers from its computational complexity which is considerably higher than the weight method, and only a local optimum is obtained by using this method.

This means that the global optimum relies on the initial guess [START_REF] Gao | An overview of optimization technologies applied in combined cooling, heating and power systems[END_REF].

In order to deal with the limitations of classical methods, evolution-based algorithms have been adopted for CCHP system optimization. The most common evolution-based algorithm used in CCHP system is the non-dominated sorting genetic algorithm-II (NSGA-II) [START_REF] Abbasi | A methodology to obtain the foremost type and optimal size of the prime mover of a CCHP system for a large-scale residential application[END_REF][START_REF] Yan | An integrated design for hybrid combined cooling, heating and power system with compressed air energy storage[END_REF][START_REF] Chen | Multi-criteria assessment and optimization study on 5 kW PEMFC based residential CCHP system[END_REF][START_REF] Song | Multi-objective optimization of a solar hybrid CCHP system based on different operation modes[END_REF],

which has been proved to be one of the most effective multi-objective optimization algorithms capable of seeking a much better solution range and better convergence close the Pareto-optimal front relative to other multi-objective evolution-based algorithms [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: NSGA-II[END_REF].

Therefore, the NSGA-II is adopted in the present study to determine the optimal capacity of facilities.

In view of this, energetic, economic, and environmental optimization of a new proposed electric load-following strategy for CCHP systems equipped with hybrid chillers has been carried out in this study. The new strategy, proposed by the authors, was investigated and compared with the existing electric load following strategies for a Mosque complex located in the north of Algeria. The new strategy for CCHP systems with hybrid chillers was examined with consideration to the primary energy consumption, annual total cost and carbon dioxide emission. Multi-objective optimization method using NSGA-II algorithm was employed to obtain the Pareto front. The final optimal solutions among the possible solutions located on the Pareto fronts are chosen by using decision-making methods with the aim of choosing the best capacity of the power generation unit, absorption chiller, and electrical chiller to maximize the performance of each system and strategy. The primary energy saving, annual total cost saving and carbon dioxide emission reduction obtained with the new strategy, under the optimized parameters, are assessed and compared with those of the other electric load following strategies. Finally, the effect of the chiller type and the operation strategy, to support the building load, on the performance of the systems are discussed and compared based on the integrated analysis. The paper is structured in the following manner. First, the case study and its heating, cooling, and power requirements are described in Section 2.

Section 3 presents the description of CCHP systems and the conventional SP system, where the mathematical models of the strategies based on energy flow were established. Section 4

focuses on the suggested approach for solving the multi-objective optimization problem, where the NSGA-II algorithm and decision-making approaches are described. Section 5 discusses the optimization results and compares the performance of the new suggested strategy with the other strategies. Finally, the related conclusions are drawn in Section 6.

Case study

The Algerian state has launched the construction of a new national landmark "Great Mosque of Algeria", 500 meters away from Algiers Bay, in the Mohamadia province. The Mosque is the third-largest in the world (Fig. 1) with a floor area of about 400,000 m 2 , and is expected to host more than 120,000 visitors daily. The minaret of the Mosque will be the world's tallest at a height of 265 meters (the highest building in Africa), and will include a museum, research facilities and a visitor's platform (Fig. 2). The Mosque complex will also include a convention center, a library and a university. A passage will ensure the transport connection between the underground car park in the basement of the Mosque, which is designed to accommodate more than 4,000 parking spaces, and the city highway, from which two passages provide an urban connection to the Mediterranean coast. A CCHP system is being designed for this Mosque complex. The design is based on the estimated monthly energy requirements. As shown in Fig. 3, the monthly electricity requirement is quite constant throughout the year. Although requirements for heating and cooling vary with weather conditions in different months. The cooling demand is higher in summer (from May to October) while the heat demand is higher in winter (from November to April). The CCHP system ought to be designed considering the capability to meet all these expected demands of the building for electricity, heat, and cold.

Fig. 3.

Expected peak monthly utility demand [41].

In addition to the monthly loads, the hourly expected cooling demand profile is presented in The CCHP plant can be sized to import electricity from the grid when the site demand is higher than the generation capacity of the PGU. Based on the operating strategy used, the heat available from the CCHP plant, if not enough to fulfill the heat needs of the building, can be provided by a standby gas boiler.

The CCHP system can operate following two different strategies, electrical load following and heat load following. For the electrical load following strategy, the electrical output of PGU should be controlled to meet the building electrical load, any deficiency in heat production must be generated by a gas boiler and any excess heat production should be rejected to the environment. In the heat load following strategy, the output of the PGU unit should be controlled to meet the building heat demand first. This means that the electrical power output of the PGU will also vary and any deficiency will be made up from the national grid. In case that the electric power generation is greater than the building electrical demand, the surplus of electricity should be exported to the national grid.

Previous studies have demonstrated that the ELF strategy is capable of achieving higher energy and environmental performance compared to the TLF strategy. Therefore, we will be interested by the ELF and modified ELF strategies.

System design and strategy description

Separated production system

Heating demand can be satisfied by using the natural gas provided from the national grid as a source of thermal energy. Also, the cooling demand could be satisfied by using the electricity provided from the national grid in compression chillers. In this design, a compression chiller and heat boiler are used to provide heating and cooling demands as showed in Fig. 5. In order to meet all expected demand conditions, these components are sized according to the annual maximum thermal demands. The total electrical energy consumed by SP system from the grid [START_REF] Wang | Particle swarm optimization for redundant building cooling heating and power system[END_REF], E $%&' () , is

" * + (1)
Where is the building electric energy consumption the and is the electric energy consumed by the electrical chiller, which can be calculated as follows [START_REF] Wang | Particle swarm optimization for redundant building cooling heating and power system[END_REF] *

Where is the coefficient of performance ( ) of the electrical chiller.

The total electricity consumption from grid can be converted to fuel consumption as follows [START_REF] Wang | Particle swarm optimization for redundant building cooling heating and power system[END_REF] *

" ! " ! (3)
Where ! " and ! are the grid power generation efficiency and the grid distribution efficiency, respectively.

The fuel consumption from the heating system is calculated by

* ! (4)
Where is the heat demand, and η . is the boiler efficiency. Therefore, the total fuel consumption can be calculated as

" * ! " • ! + • ! " • ! + ! (5)

Absorption chiller-only CCHP system under ELF strategy

Under ELF, the PGU generates electricity as much possible . If the electrical load ( ) is higher than the maximum power generation capacity of PGU, the electric deficiency of the building is covered by the grid. The PGU uses natural gas as fuel and generates electricity to the building. The high-temperature waste heat of PGU is recovered to support the thermal load for cooling and heating. For the absorption chiller-only CCHP system (Fig. 6), a boiler is used to generate additional heat ( ) when the recovered heat ( ) is not able to meet the cooling load ( ) and the heating load ( ). In this case, the absorption chiller provides the totality of cooling load by consuming more heat from the boiler [START_REF] Wang | Performance comparison of combined cooling heating and power system in different operation modes[END_REF]. The electrical energy balance in System I is [START_REF] Wang | Performance comparison of combined cooling heating and power system in different operation modes[END_REF]:

Where is the building electric demand, is the electricity supplied by the national grid to the CCHP system, is the generated electricity by power generation unit (PGU) and is the maximum capacity of power generation unit.

It is possible to calculate the PGU fuel consumption ( ) as follow [START_REF] Wang | Performance comparison of combined cooling heating and power system in different operation modes[END_REF]:

* ! ( 8
)
Where ! is the PGU electrical efficiency.

The recovered heat can be calculated as

* × ! × 11 -! 4 ( 9
)
Where ! is the heat recovery system efficiency.

The heat balance between the cooling and the heating systems is

* 5 , < , ≥ (6)
* 5 0 - , < , ≥ (7)
+ * + (10)
Where is the boiler's additional heat, and respectively are the heats supplied to the absorption chiller and the heating system.

The heat consumed by the absorption chiller can be calculated by

* ( 11
)
Where is the absorption chiller .

The supplementary fuel consumed by the boiler, , can be calculated as [START_REF] Wang | Performance comparison of combined cooling heating and power system in different operation modes[END_REF]:

* + - ! (12)
Therefore, the fuel consumption, 9 , is calculated as

9 * + + * ! + ! " • ! + ! (13)

Hybrid chiller CCHP system

The arrangement of the hybrid chiller CCHP system is illustrated in Fig. 7. Under ELF, the PGU generates electricity as much possible if the electrical charge ( ) is higher than the maximum power generation capacity of PGU, while the missing electric energy of the building is covered by the grid. The electrical output of the PGU ( ) and the grid electricity consumption ( ) depend on the amount of electricity required for the building ( ) and also the electric chiller ( ).

To provide supplementary electric cooling, the PGU must increase the power generation. As the PGU power output increases, so does the heat output, leading to additional heat available to be used in absorption cooling and building heating. This causes lower demand for electric cooling and boilers heating [START_REF] Wang | Optimization of capacity and operation for CCHP system by genetic algorithm[END_REF]. Fig. 7. Schematic of the hybrid chiller CCHP system (System II).

The electric load following (ELF)

If the recovered heat ( ) does not completely satisfy the building needs, i.e. the heating load ( ) and the additional heat required for the absorption chillers ( ), a boiler should be used to produce more heat ( ). Moreover, when the absorption chiller does not satisfy cooling requirements, supplementary cold is generated from the electric chiller by consuming more electricity. The detailed model of this strategy is described as follows [START_REF] Wang | Optimization of capacity and operation for CCHP system by genetic algorithm[END_REF]:

* 5 + , + < , + ≥ (14)
* 5 0 + - , + < , + ≥ (15) * ! (16)
And the recovered heat is calculated as

* × ! × 11 -! 4 (17)
The heat consumed by the absorption chiller can be calculated as

: ; , < , (18)
, ≥ ,

Where , is the absorption chiller capacity.

And the heat produced by the boiler is calculated as

* 5 0 + - , , ≥ + , < + (19)
And the cold produced by the electric chiller is calculated as

, * 5 0 -, , < , , ≥ , (20)
And the electric energy consumed by the electric chiller is expressed as

* , (21)
In this configuration the fuel consumption of the system is calculated as

9 * + + * ! + ! " • ! + ! (22)

The modified electric load following (MELF)

In this strategy to satisfy the heating and cooling requirements in the building, the recovered heat ( ) is used primarily for heating ( ) and, secondly, for absorption cooling ( ). If the recovered heat is unable to satisfy the heating load ( ), additional heat should be produced by an auxiliary boiler. In this case, the electric chiller delivers the whole cooling load by consuming more electric power [START_REF] Ahn | Performance assessment of hybrid chiller systems for combined cooling, heating and power production[END_REF][START_REF] Ahn | Economic feasibility of combined cooling, heating, and power (CCHP) systems considering electricity standby tariffs[END_REF] :

The electrical energy balance is expressed as

* 5 + , + < , + ≥ (23)
* 5 0 + - , + < , + ≥ (24)
the PGU fuel consumption ( ) is calculated as follow

* ! (25)
And the recovered heat is calculated as

* × ! × 11 -! 4 (26)
The recovered heat ( ) is used primarily for heating ( ) and then for absorption cooling ( ) in order to meet the heating and cooling loads in the building. As a result, the relationship between , and can be expressed as

* < - 0 , > , ≤ (27)
If the recovered heat is not sufficient to satisfy the heating load ( ), the gas boiler produces additional heat. In this case, the electric chiller supplies the entire cooling load.

* 5 0 - , > , ≤ (28)
We introduce new parameter ?, which is the maximum cold that can be produced by absorption, using the residual heat that we get from the recovered heat after the subtraction of the required heat for heating ( -).

? * < 1 -4 × 0 , > , ≤ (29)
Then if ? is less than absorption chiller capacity, the cold produced by absorption is equal to ?. Instead, if ? is bigger than the absorption chiller capacity, the cold produced by absorption chiller is equal to the maximum capacity of this latter.

If the absorption cooling cannot meet the cooling load, all the residual cooling load should be provided by the electrical chiller. In this case, the cold produced by the electric chiller is expressed as

, * -, (31)
And the electric energy consumed by the electric chiller is expressed as

* , (32)
And the fuel consumption of the system is calculated as follow

9 * + + * ! + ! " • ! + ! (33)
More details regarding the MELF strategy are described in references [START_REF] Ahn | Performance assessment of hybrid chiller systems for combined cooling, heating and power production[END_REF][START_REF] Ahn | Economic feasibility of combined cooling, heating, and power (CCHP) systems considering electricity standby tariffs[END_REF].

The new modified electric load following (NELF)

In the new suggested strategy, the boiler is only operated if the recovered heat does not satisfy the heating demand or if the electric chiller does not fulfill the cooling requirements of the building. Therefore, If the electric chiller is unable to fully satisfy the cooling requirements ( ), the absorption chiller provides additional cooling (Q A,BC ) by using supplementary heat from the boiler.

* 5 + , + < , + ≥ (34)
* 5 0 + - , + < , + ≥ (35)
* × ! × 11 -! 4 (37)
• In case that the recovered heat is less than or equal to heat load ( ≤ 4, the cooling load should be covered by the electric chiller first , *

And if the cooling load is higher than electric chiller capacity ( , ), the absorption chiller should provide the residual cooling load. In this case, the heat required for cooling is expressed as

• In case the recovered heat is larger than heat load ( > ), the cooling load should be provided first by the absorption chiller, by using the residual thermal energy that we get from the recovered heat after the subtraction of the required energy for heating. The expression of ?, which is the maximum cold that can be produced by absorption, will be

? * 1 -4 × (40)
If ? is greater or equal to absorption chiller capacity ( , ≤ ?), then the cold produced by the electric chiller is expressed as

, * 5 0 -, , ≤ , , > , (41)
* ! (36) * -, (39)
If ? is less than absorption chiller capacity ( , > ?), then the cold produced by the electric chiller is expressed as , * D 0 -? , , ≤ ? , ? < < , + ?

, , + ? ≤

In case the cold produced by the absorption chiller, based on the residual heat (?), and by the electric chiller ( , ) is less than cooling load, the absorption chiller provides additional cooling ( , ) by consuming supplementary heat from the boiler.

The heat consumed by the cooling system can be calculated as

* -, (43)
And the thermal energy produced by the boiler can be expressed as

* + - (44)
In addition, the electric energy consumed by the electric chiller is expressed as

* , (45)
And the fuel consumption of the system is calculated as follow

9 * + + * ! + ! " • ! + ! (46)

Multi-objective optimization

In multi-objective optimization problems, there is usually no viable solution capable of maximizing or minimizing all objective functions at the same time. Therefore, attention is then given to Pareto's optimal solutions, that are not dominated by any other solutions and cannot be improved with regard to any objective without weakening at least one objective.

The Pareto optimal set is defined as the set of all non-dominated solutions, and the associated objective function values are called the Pareto frontier. The Pareto frontier is limited by a nadir objective vector z nadir , and an ideal objective vector z ideal , which define the lower and the upper bounds of the optimum Pareto solution's objective function [START_REF] Konak | Multi-objective optimization using genetic algorithms: A tutorial[END_REF],

respectively. All the elements mentioned above are illustrated in fig. 8, which shows the Pareto front of the multi-objective optimization of the two objective functions f1 and f2. Genetic and evolutionary algorithms (GEAs) were proposed by John Holland in his pioneering work on the field, as a repetitive, stochastic search method to find optimal solutions by mimicking in a simplified way the theory of biological evolution [START_REF] Holland | Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence[END_REF]. Multi-objective optimization using a genetic algorithm is employed in this study, based on the well-known NSGA-II algorithm of Deb et al [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: NSGA-II[END_REF], to achieve the Pareto optimal set by the seven steps described in Fig. 9. In the NSGA-II evolutionary process, the initial parent population is first created and sorted on the basis of two criteria which are rank and crowding distance. Next, the chosen individuals by a tournament selection would be deposited in an intermediate mating pool, crossover, and mutation processes will be used to produce the child populations. Then, the old set of solutions and the newly generated solutions are combined to make a larger size of population, and fitness values are attributed to all individuals by non-dominated sorting. Finally, individuals with the best fitness values are chosen by elitist sorting, and they become the parent population. These steps are reproduced until the maximum number of generations is reached. Once NSGA-II finishes processing, the approximate Pareto front of multi-objective space would be generated by the nondominated solutions of the final population.

Therefore, to optimize the CCHP systems, the technical and economic parameters are listed in Tables 1,2, and 3, respectively. Table 4 lists the input parameters of the algorithm NSGA-II [START_REF] Chen | Multi-criteria assessment and optimization study on 5 kW PEMFC based residential CCHP system[END_REF]. The population and the maximum number of generations were set to 500 and 600, respectively, to balance between more accurate optimal results and less optimization time.

Selecting the mutation probability and crossover probability is crucial to find the global optimal solutions. The mutation operators are used mainly to provide exploration and crossover operators are usually used to guide the population to converge on the good solutions. In addition, a high crossover probability value can improve the search process for complicated search spaces. on the other hand, the probability of mutations normally must be maintained very low. Alternatively, convergence can be delayed needlessly [START_REF] Ren | Multi-objective optimization of combined cooling, heating and power system integrated with solar and geothermal energies[END_REF].

Table 1

The variables of SP system and CCHP system.

Definition of objective functions

In this multi-objective optimization, three objective functions are considered [START_REF] Wang | Optimization of capacity and operation for CCHP system by genetic algorithm[END_REF][START_REF] Fang | Complementary configuration and operation of a CCHP-ORC system[END_REF]: primary energy consumption (to be minimized), annual total cost (to be minimized) and carbon dioxide emissions (to be minimized). Therefore, the objective functions have been formulated as follows:

Energetic criterion

Primary energy consumption ( ) is the most important and consistent indicator reflecting the CCHP system's operational efficiency. In addition, has a strong relationship with environmental and economic performance. So, this criterion is used first.

* + + (47)

Economic criterion

The annual total cost ( ), including the annual cost of capital, the annual cost of operation and maintenance, and the annual cost of energy is determined as follows:

* EFG + H& + J + (48)
* × K L L + M × K L L + K KN O, × O, + O,P × O,J Q RS OTU VWX TU Y U Y U ( 49
)
Where EFG , H& , J and are the annual equipment investment cost, operation & maintenance cost, natural gas cost, and grid electricity cost, respectively. While and are the installed power of the equipment and the initial capital cost of each type of equipment in euro (1 € = 132 DA), respectively. Z is the number of equipment, O, and O,J are the hourly energy tariffs of electricity and natural gas, respectively. The annual operation and maintenance cost of equipment is considered to be as 6% (ԑ=0.06) of their investment cost [START_REF] Zhang | Exergetic and exergoeconomic evaluation of co-firing biomass gas with natural gas in CCHP system integrated with ground source heat pump[END_REF].

The capital recovery factor, , is defined as:

* [11 + [4 F 11 + [4 F -1 ( 50
)
Where [ is the rate of interest and n is the equipment's service life (i=6% and n=20 years).

while the values of [ and \ are considered to be equal to all types of equipment.

Environmental criterion

The emission conversion factors can be used to determine the amount of carbon dioxide emissions (CDE) as follows:

* 1 + 4 × ] H ^,J + × ] H ^, (51)
where ] H ^,J and ] H ^, are the natural gas and grid emission conversion factors respectively.

Decision-making in multi-objective optimization

The decision-making process is necessary for multi-objective optimization problems to choose a final optimal solution from the possible solutions. The decision-making process usually depends on engineering experience, the preferences and criteria taken by the decision-maker on which objective function would be of more importance. There are many methods for decision-making process in decision problems. For instance, Fuzzy, TOPSIS and LINMAP decision-making methods. These methods are usually used for selection of a final optimal solution from the Pareto frontier [START_REF] Ahmadi | Designing a solar powered Stirling heat engine based on multiple criteria: maximized thermal efficiency and power[END_REF]. Decision-making has been applied in two phases in this paper. Firstly, as with multi-objective optimization, we get a set of optimal solutions, called the Pareto front. Consequently, there is not a single final optimal solution, like in the single-objective optimization problems. In the next phase of decision-making, one configuration should be chosen from all the feasible optimal configurations of the CCHP system located in the Pareto frontier. For this reason, three most recognized and common approaches of decision-making, namely Bellman-Zadeh fuzzy [START_REF] Kahraman | Fuzzy multi-criteria decision making: theory and applications with recent developments[END_REF], LINMAP [START_REF] Xia | Fuzzy LINMAP method for multiattribute decision making under fuzzy environments[END_REF], and TOPSIS [START_REF] Krohling | Fuzzy TOPSIS for group decision making: A case study for accidents with oil spill in the sea[END_REF] decision methods were used. A brief description of these three methods is reported in [START_REF] Sayyaadi | Efficiency enhancement of a gas turbine cycle using an optimized tubular recuperative heat exchanger[END_REF]. Nevertheless, in this study, one strategy for the conventional CCHP system and three strategies for the CCHP system with hybrid chiller were optimized and for each, Pareto frontier has been obtained. Consequently, three optimal solutions were picked up from the Pareto frontier by using the three decision-making approaches, and a decision-making was needed to determine the final configuration of each CCHP system under the different strategies. Therefore, in this stage of decision-making the most economical optimal solution was adopted.

Performance indicators

To evaluate the energetic, economic and environmental performance of CCHP system in comparison to SP system, the following evaluation criteria are utilized.

Primary energy saving ratio

* " - 9 " * 1 - 9 " (54)
PES is generally utilized to assess the fuel energy saving attained by CCHP system over SP system.

Annual Total Cost Saving Ratio

The ratio between the annual CCHP system total cost and the annual SP system total cost is defined as the ATCS ratio.

Carbon dioxide emission reduction ratio

* " - 9 " * 1 - 9 " (56)
CDERR illustrates the environmental benefits gained through the use of CCHP system compared to SP system.

Results and discussion

The multi-objective optimization of the four CCHP systems resulted into four sets of Pareto fronts as shown in Fig. 10. The Pareto fronts of the CCHP systems have the same shape and the three objectives showed an interrelated relationship. When the PEC shows a decreasing trend and the CDE follows the same trend, while the ATC shows an upward trend. Tab. 5

summarizes the results and design parameters for all candidate solutions on Pareto fronts curves.

Fig. 10a and respectively.

In the hybrid chiller CCHP based ELF strategy, when PESR and CDERR are at their optimal solutions 22.53% and 24.45% respectively, ATCSR is at its lowest value -2.14% (Fig. 10b and Table 5). On the contrary, when ATCSR is at its optimal solution with 19.74%, PESR and CDERR are at their lowest values 20.00% and 21.60% respectively.

For the hybrid chiller CCHP based MELF strategy, when PESR and CDERR achieve their best values of 23.65% and 25.55% respectively, ATCSR reaches its lowest value of -9.98% (Fig. 10c and Table 5). Alternatively, when ATCSR hits its best value of 13.80%, PESR and CDERR are at their lowest values of 18.36% and 19.92% respectively.

In the same way, with the hybrid chiller CCHP based NELF, when the system hits its highest PESR and CDERR values of 23.65% and 25.55% respectively, the ACSR of the system is at its lowest value of 2.02% (Fig. 10d and Table 5). While, when the ACSR is at its highest value of 20.34%, both the PESR and CDERR drop to 21.1% and 22.65% respectively.

In addition, Fig. 10 shows that in the hybrid chiller CCHP based ELF and MELF strategies, if the CCHP system is optimized to save energy, there are no economic benefits in this case (ATCS is negative).

As illustrated in Fig. 10, it is not possible to obtain the maximum energetic and environmental performance simultaneously with the maximum economic performance.

Consequently, in order to select the best feasible solutions on the Pareto fronts, a decisionmaking approach should be employed. In this fact, three most recognized and common approaches of decision-making, Bellman-Zadeh fuzzy, LINMAP, and TOPSIS decision methods were used in this study. Table 5 shows the characteristics of CCHP systems suggested by Fuzzy, LINMAP and TOPSIS decision-making approaches. The issue now is which decisionmaking optimal solution should be adopted. Table 5 and Fig. 10 are presented here to help us to decide between various decision-making methods. Fig. 10 shows that, LINMAP decision-making method lead to the highest ATCSR for all the CCHP systems followed by Fuzzy and TOPSIS decision-making methods, respectively. Consequently, the optimal solutions of LINMAP method appeared to be a more desirable final solutions in our case study. It should be mentioning that in general there is no decision-making method having superiority over other methods in all cases. In fact, different decision-making approaches are used to help decision-makers who choose the final solution based on their priority and experience. In this study, three decision-making approaches have been implemented and it was found that the LINMAP decision-making approach selects the final optimum solution that is more suitable to our criteria and preferences. From the technical viewpoint, the CCHP system with hybrid chiller is recognized to be the most suitable technique for the Mosque complex application, with satisfying energy savings.

On the other hand, from the viewpoint of design and management, all examined CCHP systems have higher PESR than that SP System.

Nevertheless, the PESR value of the NELF hybrid chiller CCHP system is higher than those of MELF and ELF. The reason for this difference is caused not only by the mode of operation but also by the prime mover size. It can be mentioned that the capacity of PGU in the system-II following NELF strategy is bigger than those of ELF and MELF strategies, respectively. This leads to less electricity consumption from the grid and more heat production to feed the building requirement in the NELF strategy than other strategies. In general, from an energetic point of view, NELF, MELF, and ELF based CCHP systems are suitable strategies for the Mosque complex examined in the current case study. Among the examined four design and management options, the hybrid chiller CCHP system based NELF strategy achieve the best energy performance, followed by the hybrid chiller CCHP system based MELF strategy, the hybrid chiller CCHP system based ELF and absorption chiller CCHP system based ELF strategy. In this study, economic parameters for comparing the CCHP systems are annual investment cost, operating and maintenance cost, natural gas cost and grid electricity cost. Fig. 12 shows these four parameters. As shown in Fig. 12, the lowest annual investment and operation costs are obtained for system II based ELF strategy and system II based NELF strategy, due to the low size and investment cost of the boiler. On the other hand, the highest annual investment and operation costs are observed for system II based MELF strategy and system I based ELF strategy. This can be explained by the over sizing of the electric chiller and boiler in the system II based MELF strategy and the high capacities of the absorption chiller and the boiler in the system I based ELF strategy. In different types of chillers, the COP of the electric chiller is higher than the absorption chiller, so system II have the lowest natural gas consumption costs due to the higher impact of electric chiller COP. In addition, system I presents the lowest grid electricity consumption cost due to the high capacity of PGU and the absence of an electric chiller in this strategy.

Moreover, Fig. 12 shows the ATC and ATCSR for various optimized options. Typically, all CCHP systems reach positive ATCSR under different designs and strategies. This implies that from an economic point of view, it is possible to implement the CCHP system for the studied Mosque complex. As for the relative comparison, with different management strategies, the hybrid chiller CCHP system under the NELF strategy offers better economic performance than the other systems, due to its low investment and fuel consumption costs. Although the hybrid chiller CCHP system under MELF has relatively high investment cost, its ATC is larger than other CCHP systems. This is mainly due to the relatively high annual investment cost caused by the oversizing of the CCHP system devices under this strategy. Therefore, from an economic point of view, the CCHP system can be considered as an attractive energy supply system, especially under hybrid chiller design, for the Mosque complex in the current situation. This is mainly the result of the relatively low capital cost of the CCHP system devices and the relatively high electricity price compared to natural gas price. Fig. 13 shows the CDE and CDERR of the optimized CCHP systems. Generally speaking, in the Mosque complex, the introduction of the CCHP system leads to better environmental performance than the energy and economic performance discussed above. As can be seen, all of the CCHP systems can significantly reduce CDE and achieve satisfying CDERR. For all the CCHP systems, the majority of carbon dioxide emissions come from PGU, due to its high consumption of natural gas to meet the electricity demand. On the other hand, the design of CCHP system with hybrid chiller results in larger CDERR than absorption chiller only based CCHP system. This is due to the high boiler gas consumption in system I to meet the heat demand for cold production in absorption chiller only based CCHP system and to the high COP of the electric chiller which reduce the energy consumption for cold production in the hybrid chiller based CCHP systems. As a result, the order of magnitude of the CDERRs for each system is the same as that of the PESRs. This is attributable to the fact that all energy requirements fulfilled by the CCHP systems are essentially generated by the consumption of natural gas. The more primary energy consumption is required, the more carbon dioxide is emitted. Thus, the hybrid chiller CCHP system based NELF strategy enjoys the best environmental performance with a CDERR close to 24%, followed by the MELF strategy and ELF strategy. Therefore, the hybrid chiller CCHP system is considered to be the most suitable choice for the Mosque complex. Otherwise, due to the size of the prime mover, the hybrid chiller CCHP system based NELF strategy is the best option with the highest CDERR compared to the other design and management modes. Furthermore, irrespective of the design or strategy employed, the performance of the CCHP system are superior to that of the separate system. While, the variation of CDERR is the largest, followed by the variation of PESR and the smallest variation is related to ATCSR.

Figures also reveal that for all CCHP designs and strategies in the cold winter and hot summers such as January, August, and December the values of CDERR and PESR are low, while in the transition seasons such as May, June, and October, the values are high.

Conversely, the trend of the ATCSR is opposite to that of the PESR and CDERR, in hot summer and transition season, the values of ATCSR are large, while in winter the values are small.

The main reason is in the transition season, the thermal load is lower and the heat/electric ratio is therefore lower. In this situation, the heat to power demand rate becomes closer to the rate of heat to power generated by PGU, which results in a better use of the PGU recovered heat and thus an increase in the energetic and environmental performances. In hot summer, the heating and cooling demand are higher, and the recovered heat is often unable to meet the required thermal demand. The remaining heat is supplied by the boiler and the remaining cold is supplied by the electrical chiller. The increased natural gas and electrical demand are imported from the grid. Therefore, the energetic and environmental performance are less than that in the transition season. In the cold winter, the heat/electricity ratio is low and the heat recovered from the PGU can meet the whole thermal requirement. In this situation, the excess heat is rejected in the environment, which decreases the energetic and environmental performance in the winter compared to the transition season.

Compared to the other seasons, absorption chiller only CCHP system in summer has no significant advantage over SP systems, since absorption chiller has a relatively low COP, which decreases the energy consumption performance of the system and affects the economical and the environmental performance.

For the hybrid chiller CCHP system, which also meets some of the cooling needs in summer by the combination of the absorption chiller and the gas boiler, the use of the gas boiler is much less than that of an absorption chiller only CCHP system. However, the electric chiller meets the largest part of the cooling demand with a high COP compared to the COP of an absorption chiller. Therefore, System II still has good performance in summer.

For the monthly ATCSR, CCHP systems may reduce monthly costs for all the examined CCHP systems compared to the SP system, especially in summer (Fig. 15), despite the energy consumption increase in this season (see Fig. 17). This is mainly due to the reduction of the electricity consumption in CCHP systems compared to SP system and to the high electricity/natural gas price ratio (Fig. 18 and Tab. 3).

The monthly energy costs dramatically increase during the summer caused by the high energy demand during the summer months compared to other months, and the increase of the electricity consumption. However, in winter and transition seasons, the variations of the monthly electricity costs are relatively small due to the small energy demand variation compared to energy demand variation in summer season.

Our results highlight that the economic performances of CCHP systems are extremely sensitive to electricity and natural gas tariffs. However, according to current economic parameters, the economic performances of the hybrid chiller CCHP system under NELF and ELF strategies are quite close, and they are the most recommended systems for the Mosque among all the systems proposed from an economic point of view.

Conclusion

In this paper, a new electric load following (NELF) strategy for CCHP system with hybrid chiller was proposed to supply the cooling, heating and electricity demands of a Mosque complex located in Algiers, Algeria. The NELF for CCHP system with hybrid chiller was analyzed and compared with separated production system (SP), CCHP system with absorption chiller only under ELF strategy and with hybrid chiller under ELF and MELF strategies. The systems configurations were optimized by using multi-objective optimization method, based on primary energy consumption, annual total cost and carbon dioxide emission criteria, and by using decision-making approach. As the results show, the CCHP system with hybrid chiller under NELF, in addition to its economic feasibility, has a significant capacity to reduce fuel consumption and pollutant emissions. The main study results can be summed up as follows:

• From an energetic, economic and environmental point of view, the introduction of CCHP systems is a viable option to be applied in the Mosque complex with high benefits due to the higher electricity price and the lower price of natural gas.

• During the summer months, the performance of the absorption chiller only CCHP system under ELF strategy decreases due to the high heat to power ratio and the relatively low COP of the absorption chiller.

• The hybrid chiller CCHP System is the most suitable configuration for the mosque application. Where the performance of all the operational strategies for this configuration show a similar trend.

• The MELF strategy for the CCHP system with a hybrid chiller is not a recommended strategy due to its high initial investment cost which leads to low economic benefits.

• Considering the overall performance, the NELF strategy provided more benefits in comparison with other strategies in all studied criteria. The NELF strategy showed 22.19%, 19.03% and 23.88% improvement in PESR, ATCSR and CDERR respectively, in comparison to the conventional system.

Future works could be directed towards exploring and comparing the performance of the new strategy with other CCHP systems using different prime mover technologies and integrating other energy sources such as bioenergy and solar energy. This would allow interested researchers to efficiently select the right design parameters and strategies for their CCHP systems.

Fig. 1 .

 1 Fig. 1. The Great Mosque of Algiers [41].

Fig. 2 .

 2 Fig. 2. The Great Mosque of Algiers minaret [41].

Fig. 4 .

 4 Fig. 4. As can be observed, the demand for cooling is high between 8 a.m. and 9 p.m. while it is low from 9 p.m. to 8 a.m. The hourly consumption of electricity and heat, which are not presented in the figure, are estimated to have a similar trend as the cooling load during the day [42].

Fig. 4 .

 4 Fig. 4. Expected hourly cooling load [41].

Fig. 5 .

 5 Fig. 5. Schematic of the SP system.

Fig. 6 .

 6 Fig.6. Schematic of the Absorption chiller-only CCHP system (System I).

Fig. 8 .

 8 Fig. 8. Pareto frontier of a multi-objective optimization.

Fig. 9 .

 9 Fig. 9. Flow chart of NSGA-II algorithm.

Fig. 10 .

 10 Fig. 10. Pareto frontier for triple objective (PEC,ATC,CDE) optimization of CCHP systems.

Fig. 11 .

 11 Fig. 11. Annual PEC and PESR of the reference and CCHP systems.

Fig. 12 .

 12 Fig. 12. Annual ATC and ATCSR of the reference and CCHP systems.

Fig. 13 .

 13 Fig. 13. Annual CDE and CDERR of the reference and CCHP systems.

Figs. 14 -

 14 Figs.[START_REF] Jing | Life cycle assessment of a solar combined cooling heating and power system in different operation strategies[END_REF][START_REF] Afzali | Optimal design, operation and analytical criteria for determining optimal operating modes of a CCHP with fired HRSG, boiler, electric chiller and absorption chiller[END_REF][START_REF] Wang | Life cycle assessment (LCA) optimization of solarassisted hybrid CCHP system[END_REF] show the monthly PESR, CDERR, and ATCSR compared with the SP system for the different systems. It can be seen that all variations in all CCHP systems are positive.

Fig. 14 .

 14 Fig. 14. Monthly PESR of the CCHP systems.

Fig. 15 .

 15 Fig. 15. Monthly TCSR of the CCHP systems.

Fig. 16 .

 16 Fig. 16. Monthly CDERR of the CCHP systems.

Fig. 17 .

 17 Fig. 17. Monthly grid electricity and natural gas consumption.

Fig. 18 .

 18 Fig. 18. Monthly grid electricity and natural gas cost.

Table 2

 2 Unit cost of the equipment in CCHP and SP systems.

	Component

Table 3

 3 Natural gas and electricity prices under time-of-use tariff in Algeria.

		Natural gas Electricity	Electricity	Electricity
			(6:00-17:00,21:00-22:30)	(17:00-21:00)	(22:30-6 :00)
	Unit price (€/kWh)	0.0018	0.0156	0.0703	0.0083

Table 4

 4 Parameter values used in NSGA-II algorithm.

	Tuning parameter

  Table 5 show that, for absorption chiller CCHP based ELF, the maximum value of PESR and CDERR are 21.35% and 23.30% respectively, while the ATCSR is at its lowest value in this point with 2.79%. Conversely, while the ATCSR is at its highest value with 16.06%, the PESR and CDERR are at their lowest values in this point with 17.59% and 19.27%

Table 5

 5 Results and design parameters for the optimized systems selected from Pareto fronts. Fig.11illustrates the primary energy consumption structures and primary energy saving ratio (PESR) of the optimized CCHP systems and SP system. According to the figure, the energy consumption is reduced for all examined CCHP systems. Moreover, the hybrid chiller CCHP system based NELF, the hybrid chiller CCHP system based MELF strategy and the hybrid chiller CCHP system based ELF have lower primary energy consumption than absorption chiller CCHP system based ELF strategy respectively.The gas boilers in the systems II based MELF, systems II based NELF and systems II based ELF consume less natural gas and produce less thermal energy than that in System I, respectively. Thus, systems II based MELF, based ELF and based NELF, consume extra grid electricity for electric chiller and extra natural gas for PGU to compensate the thermal energy. However, system II following MELF seems to consume a bit more grid electricity than others strategies, because of its high demand of electricity for its electric chiller. Comparing all the CCHP systems, Hybrid chiller CCHP systems have a higher PESR compared to CCHP system with absorption chiller only due to the high COP of electric chiller (5.2) and the low COP of the absorption chiller (0.76) that requires undesirably high boiler gas consumption to serve large cooling and heating loads.

		PGU	AC	EC	B	PEC	ATC	CDE	PESR	ACTSR	CDERR
		(MW)	(MW)	(MW)	(MW)	(10 7	(10 5 €	(10 6 kg	(%)	(%)	(%)
						kWh	/year)	/year)
						/year)
	SP System
		-	-	11.173 4.0476 15.525 16.566 35.025	-	-	-
	CCHP system under ELF
	Bellman-Zadeh Fuzzy Solution	8.342	11.173	-	6.471	12.376 14.540 27.265	20.28	12.23	22.15
	LINMAP Solution	7.790	11.173	-	7.299	12.478 14.240 27.511	19.63	14.16	21.45
	TOPSIS Solution	10.178 11.173	-	4.613	12.210 16.104 26.862	21.35	2.79	23.30
	Single objective based on minimum PEC	10.178 11.173	-	4.613	12.210 16.104 26.862	17.59	16.05	19.27
	Single objective based on minimum ATC	6.522	11.173	-	8.725	12.795 13.906 28.274	17.59	16.05	19.27
	Single objective based on minimum CDE 10.178 11.173	-	4.613	12.210 16.104 26.862	21.35	2.79	23.30
	Bellman-Zadeh Fuzzy Solution	-	-	-	-	12.210 13.906 26.862	21.35	16.05	23.30
	Hybrid CCHP system under ELF
	Bellman-Zadeh Fuzzy Solution	8.303	5.855	5.318	1.499	12.106 14.038 26.681	22.02	15.26	23.82
	LINMAP Solution	7.403	5.289	5.884	1.304	12.197 13.515 26.923	21.43	18.53	23.13
	TOPSIS Solution	11.217	6.077	5.096	1.689	12.026 16.921 26.459	22.53	-2.14	24.45
	Single objective based on minimum PEC	11.218	6.077	5.096	1.689	12.027 16.921 26.459	22.53	-2.14	24.45
	Single objective based on minimum ATC	6.591	5.438	5.735	1.397	12.420 13.296 27.457	20.00	19.74	21.60
	Single objective based on minimum CDE 11.218	6.077	5.096	1.689	12.027 16.921 26.459	22.53	-2.14	24.45
	Ideal Solution	-	-	-	-	12.027 13.396 26.459	22.53	19.74	24.45
	Hybrid CCHP system under MELF
	Bellman-Zadeh Fuzzy Solution	7.887	5.790	11.173	4.048	12.030 15.127 26.531	22.51	8.69	24.25
	LINMAP Solution	7.136	5.117	11.173	4.048	12.138 14.672 26.808	21.82	11.55	23.46
	TOPSIS Solution	10.764	8.172	11.173	4.048	11.853 18.220 26.076	23.65	-9.98	25.55
	Single objective based on minimum PEC	10.764	8.172	11.173	4.048	11.853 18.220 26.076	23.65	-9.98	25.55
	Single objective based on minimum ATC	6.561	1.404	11.173	4.048	12.675 14.280 28.047	18.36	13.80	19.92
	Single objective based on minimum CDE 10.764	8.172	11.173	4.048	11.853 18.220 26.076	23.65	-9.98	25.55
	Ideal Solution	-	-	-	-	11.853 14.280 26.076	23.65	13.80	25.55
	Hybrid CCHP system under NELF
	Bellman-Zadeh Fuzzy Solution	8.487	6.378	4.795	0.205	11.962 14.028 26.355	22.95	15.32	24.75
	LINMAP Solution	7.508	5.483	5.690	0.129	120.80 13.432 26.660	22.19	19.03	23.88
	TOPSIS Solution	10.757	8.162	3.011	0	11.853 16.232 26.076	23.65	2.02	25.55
	Single objective based on minimum PEC	10.757	8.162	3.011	0	11.853 16.232 26.076	23.65	2.02	25.55
	Single objective based on minimum ATC	6.526	4.546	6.627	0	12.249 13.196 27.089	21.10	20.34	22.65
	Single objective based on minimum CDE 10.757	8.162	3.011	0	11.853 16.232 26.076	23.65	2.02	25.55
	Ideal Solution	-	-	-	-	11.853 13.196 26.076	23,65	20.34	25.55


Nicolas Maubeuge

PhD Mathilde S A Deloire

Professor Bruno Brochet
email: bruno.brochet@u-bordeaux.fr

PhD Nathalie Ehrlé

Julie Charré-Morin

Msc Aurore Saubusse

MD Aurélie Ruet

Msc

Pr Moreau

Dijon Mme Quaglio

Dr Mme Nkendjuo

Dunkerque Leclercq

Pr Hautecoeur

M Lenne

Pr Vermersch

Mme Jougleux

Pr Pelletier

Marseille Mme Reuter

Pr Labauge

Montpellier; Pr M Trauchessec

Mme Debouverie

Nancy ; Morele

Mme Pr Lebrun-Frenay

Nice; Dr Joly

Mme Heinzhef

Tissier

Validation of the French version of the minimal assessment of cognitive function in multiple sclerosis (MACFIMS)

Keywords: MULTIPLE SCLEROSIS, COGNITION, NEUROPSYCHOLOGY

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Despite the influence of cognitive impairment (CI) on activities of daily living in patients with multiple sclerosis (MS) (Ruet et al.,2012[START_REF] Langdon | Cognition in multiple sclerosis[END_REF], its detection and assessment remain limited in clinical practice [START_REF] Langdon | Cognition in multiple sclerosis[END_REF][START_REF] Deloire | How to detect cognitive dysfunction at early stages of multiple sclerosis?[END_REF]. The frequency of CI has been reported to be between 30% and 70% of persons with MS (PwMS) [START_REF] Langdon | Cognition in multiple sclerosis[END_REF][START_REF] Brochet | Cognitive Impairment in Multiple Sclerosis With Regards to Disease Duration and Clinical Phenotypes[END_REF]. Considering its negative impact on several aspects of the lives of PwMS, including working retention (Ruet et al., 2012;[START_REF] Morrow | Predicting loss of employment over three years in multiple sclerosis: clinically meaningful cognitive decline[END_REF], the detection of CI is important. Moreover, as CI has been shown to predict subsequent physical disability, probably because it is an indicator of the on-going neurodegenerative process [START_REF] Deloire | Early cognitive impairment in multiple sclerosis predicts disability outcome several years later[END_REF], its early detection should be part of the clinical work-up in PwMS. Over the last several decades, several internationally recognised batteries of neuropsychological (NP) tests for MS have been validated in English, including the Brief Repeatable Battery of neuropsychological tests [START_REF] Rao | Cognitive Function Study Group, National Multiple Sclerosis Society. A manual for the Brief Repeatable Battery of neuropsychological tests in multiple sclerosis[END_REF]) and the Minimal Assessment of Cognitive Function in MS (MACFIMS) [START_REF] Benedict | Minimal neuropsychological assessment of MS patients: a consensus approach[END_REF].

The MACFIMS battery was proposed by a panel of experts in the field who met in April 2001, based on scientific literature published at that time [START_REF] Benedict | Minimal neuropsychological assessment of MS patients: a consensus approach[END_REF]. It includes seven NP tests covering the main cognitive domains or functions affected by the disease. The NP tests had to fulfil several criteria for inclusion in the battery, i.e. standardisation, normative data, adequate range (absence of ceiling or floor effects), reliability, validity (i.e. able to discriminate PwMS from healthy subjects [HS]), existence of alternate forms and practicality (easy to administer) [START_REF] Benedict | Minimal neuropsychological assessment of MS patients: a consensus approach[END_REF]. The seven NP tests assess working memory (WM), information processing speed (IPS), verbal and visual learning and memory, executive function (EF), visual perception, spatial processing and verbal fluency. MACFIMS has been validated for English-speaking subjects ( [START_REF] Benedict | Validity of the minimal assessment of cognitive function in multiple sclerosis (MACFIMS)[END_REF] as well as some other languages [START_REF] Dusankova | Cross cultural validation of the Minimal Assessment of Cognitive Function in Multiple Sclerosis (MACFIMS) and the Brief International Cognitive Assessment for Multiple Sclerosis (BICAMS)[END_REF]Eshagi et al., 2012;[START_REF] Argento | The Italian validation of the minimal assessment of cognitive function in multiple sclerosis (MACFIMS) and the application of the Cognitive Impairment Index scoring procedure in MS patients[END_REF] but not for French-speaking subjects, and there are no normative data for most of the individual tests for French-speaking subjects.

This study was performed to validate the MACFIMS in France, including the establishment of normative data in a sample of HS and its validation for detecting CI in a sample of PwMS.

SUBJECTS AND METHODS

Study design

This study was approved by the institutional review board for human subject research of

Subjects

All participants provided written informed consent and were registered in the French Social Security system. They were native French speakers and not under 18 or over 64 years old.

Control population

Normative data were established in a sample of HS recruited in one centre, by advertising, who were paid to participate in the study. Exclusion criteria were history of neurological disease or psychiatric illness, on-going psychotropic drug use, other significant chronic disease, abuse of alcohol or drugs, on-going pregnancy, cognitive complaints or having participated in a cognitive study in the last year. HCs were recruited and divided into 16 groups according to age (18-34, 35-44, 45-54, 55-64), sex, and education level (secondary education [usually 12 years of schooling] and graduated [at least baccalaureate]).

Patients

PwMS fulfilling the MS diagnostic criteria [START_REF] Polman | Diagnostic criteria for multiple sclerosis: 2010 revisions to the McDonald criteria[END_REF] were recruited from 15 MS centres in France between February 2015 and June 2017. Exclusion criteria were similar to those for HS with the addition that PwMS had not started, changed dosage or stopped taking psychotropic drugs in the previous 2 months, nor had they started, changed dosage or stopped disease-modifying therapy (DMT) or received steroids in the previous 1 month. They did not have neurological motor, visual or sensory impairment that could preclude their ability to perform cognitive tests. There was no limitation regarding MS phenotype, i.e. relapsingremitting, primary progressive or secondary progressive MS (RRMS, SPMS or PPMS, respectively) [START_REF] Lublin | Defining the clinical course of multiple sclerosis: the 2013 revisions[END_REF].

Methods

Neuropsychological assessment

PwMS and HS were evaluated by qualified senior neuropsychologists. At baseline, the assessment included all of the tests in the MACFIMS battery. At 1 month for all patients and 50% of HS the assessment included the same cognitive evaluation as applied at baseline.

The MACFIMS battery has been described in detail previously [START_REF] Benedict | Minimal neuropsychological assessment of MS patients: a consensus approach[END_REF]2006).

The battery included the Symbol Digit Modalities Test, oral version (SDMT) [START_REF] Smith | Symbol digit modalities test: Manual[END_REF], which mainly reflects IPS; the Paced Auditory Serial Addition Test with 3.0-s interstimulus interval, PASAT-3) [START_REF] Gronwall | Paced auditory serial-addition task: a measure of recovery from concussion[END_REF] [START_REF] Benton | Multilingual aplasia examination[END_REF] for phonemic verbal fluency (letters P, R and S). The edited CVLT French version [START_REF] Poitrenaud | CVLT -Test d'apprentissage et de mémoire verbale[END_REF] did not include an alternative form. We used the recently developed FLT [START_REF] Maubeuge | French Validation of the Brief International Cognitive Assessment for Multiple Sclerosis[END_REF] at the baseline visit and the published CVLT form at the follow-up visit. The Reims group created this alternate form of the French version following the same methodology. This version (courtesy of Dr Ehrlé) was pretested in a group of 20 HS. The ECCC is a measure of conceptual reasoning that permits the differentiation of concept formation from conceptual flexibility and is used to assess higher executive function. This test is a French adaptation of the DKEFS Sorting test. The cards are different but the structure of the test and the scoring are similar. The goal of this executive test is to isolate and measure specific components of problem-solving capabilities. The test has two conditions. In the first, the subject must classify six cards spontaneously in two columns of three cards each according to the most possible different rules (maximum eight) and indicate the rule after each ranking. The cards are varied in many ways, allowing conceptual sorting in accordance with at least eight different principles (e.g. card shape, card colour, semantic associations among words). The ECCC is a timed test with 4 minutes allowed for each of two card sets. The dependent variable considered here was the total number of correct sorts (CS). In the second condition, the subject was required to verbalise the rankings made by the examiner with a maximum duration of 45 s per classification (eight classifications per package). The dependent variable considered here was the verbal description score (DS). We used the Total Learning (TL) and Delayed Recall (DR) indices from the FLT and BVMT-R and both the Total Correct Sorts (CS) and the Description Score (DS) from the ECCC Sorting Test. Alternative forms were use at 1 month for the SDMT, the CVLT, the BVMT and the ECCC.

Statistical analysis

All statistical analyses were carried out using SPSS version 23 (SPSS Inc., Chicago, IL, USA). Between-group differences were examined with Student's t test and the χ 2 test for continuous and categorical variables, respectively. Effect size was calculated with Cohen's D statistic. The results were considered significant at an α-level of < 0.05. Regression-based norms were created according to the procedures of Parmenter et al. (2010) but with the adjustment described by [START_REF] Berrigan | Reliability of regression-based normative data for the oral symbol digit modalities test: an evaluation of demographic influences, construct validity, and impairment classification rates in multiple sclerosis samples[END_REF] for centring the age variable (age minus the mean age) to prevent multicollinearity and for ease of interpretation. First, the raw scores of the HS were converted to a scaled score metric (mean 10, SD 3) based on the cumulative frequency distribution of each measure presented in Table 2. This served to normalise all of the test score distributions. The percentile range encompassed by each scaled score was set such that the resultant distribution of scaled scores was as normal as possible. We adopted the data analysis and presentation approach of the Wechsler Intelligence Scale for Childrenrevised [START_REF] Ivnik | Mayo's Older Americans Normative Studies: WAIS-R norms for ages 56 to 97[END_REF]. Next, the resulting scaled scores were regressed on four demographic variables: centred age (agec = age -agemean (43.83)), agec 2 , sex (female vs. male) and educational attainment. The factor agec 2 was added to account for possible nonlinear effects of age on test performance.

The participants were divided into four groups according to educational level: low educational level (LEL) group, individuals who did not complete secondary education, which usually requires 12 years of schooling; high educational level (HEL) group, individuals who completed secondary education or graduated with a 'baccalauréat' level (equivalent to A levels in the UK) or higher. The HEL group was further divided into three subgroups: HEL-BAC, subjects who graduated with a 'baccalauréat' degree; HEL-BAC+2-4, subjects with ≥ 2 years but < 5 years of secondary education; and HEL-BAC+5, subjects with ≥ 5 years of secondary education.

Next, predicted scores were calculated by multiple regression analysis based on β weight values for all four demographic variables and their predictive constants:

Scaled score predicted = constant + βagec (agec) + βagec 2 (agec 2 ) + βsex (sex) + βeducation (education)
The predicted scaled scores were subtracted from each participant's actual obtained scaled score and the difference was divided by the root mean squared error (RMSE) of the HS: Tests with z-score ≤ -1.5 were considered 'impaired'.

None of the assumptions of regression analysis were violated (no influential cases, normality of the residuals or homoscedasticity).

For the BDI-FS, which was not normally distributed in the MS sample, the following cut-off scores were used, consistent with the test manual: Normal = BDI-FS < 3; Borderline = BDI-FS 3 -8; Depressed = BDI-FS > 8.

RESULTS

Clinical and demographic characteristics of participants

The clinical characteristics of the 276 HS and 134 PwMS participating in the study are presented in Table 1.

The PwMS population consisted of 43 with RRMS, 46 with SPMS and 45 with PPMS.

Comparison of demographic characteristics indicated no significant between-group differences in education or sex but age was significantly different between the groups (p < 0.001). Self-reported questionnaires for depression, anxiety and fatigue showed higher scores in PwMS (p < 0.001) than in HS.

MACFIMS impairment rates using regression-based norms

Table 2 shows scale conversion and Table 3 shows the regression model for each test used to derive demographically adjusted z-scores for the PwMS, including agec (age -43.84), agec 2 , sex and education as predictive variables.

Using this formula and the coefficients from Table 3, Bachelor's degree, 2: 2 to 4 years of secondary education, 3: > 4 years of secondary education. We can then convert the patient's actual score on the SDMT (e.g. 59) to a scaled score (10) using Table 2, which allows us to calculate the difference between the predicted and actual scores. The z-score can be calculated by dividing the difference between the actual scaled score and the predicted scaled score by the relative standard error (RSE) of the regression model (Table 3).

In our example: z-score = (10 -10.73) / 2.56 = -0.28 Regression analyses (Table 3) indicated that agec was a significant predictor of performance for all tests in HS except PASAT and COWAT. Sex was a significant predictor of performance in FLT, SDMT, PASAT, JLOT and ECCC. Finally, educational level was a significant predictor of performance in all tests except BVMT-R. The proportions of CI patients in all subtypes are shown in Figure 1. There were significant differences in the frequency of impairment on COWAT between RRMS and PPMS (p < 0.05). With a CI rate of 42.90%, patients with SPMS showed a significantly higher rate of CI on the MACFIMS than patients with RRMS (p < 0.05). CI was detected in 35.3% of patients with PPMS and 18.8% of patients with RRMS, but the difference was not significant (p = 0.13).

Test-retest reliability

The Pearson's correlation coefficients between the first and second tests in 147 HS and in PwMS, 1 month apart, are presented in Table 5.

Effects of confounding factors

Level of fatigue (EMIF-SEP), level of anxiety (STAI A and B), depression status (BDI-FS)

and mood (EHD-PRO) were not significantly associated with any of the outcome measures in our study for PwMS (Pearson's correlation).

Vocational status and MACFIMS

Unemployment was present in 58.8% of CI patients and 53.7% of non-impaired (p=0.63).

Impairment on the MACFIMS was not significantly associated with an increased risk of unemployment (OR= 1.2 (0.5-2.8); p= 0.63).

DISCUSSION

The main objectives of this study were to evaluate cognitive assessment using the MACFIMS The domains with more frequent impairment were learning (FLT-TL, BVMT-R-TL) followed by IPS (SDMT), delayed memory (FLT-DR, BVMT-DR), verbal fluency and working memory (PASAT). We did not observe significant differences between PwMS and HS in the JLOT test, as reported in some other studies [START_REF] Argento | The Italian validation of the minimal assessment of cognitive function in multiple sclerosis (MACFIMS) and the application of the Cognitive Impairment Index scoring procedure in MS patients[END_REF]Migliore et al., 2017). The mean scores of the ECCC were not different between PwMS and HS. The absence of significant results for these tests may have been due to a lack of power, small number of patients with SPMS in our population, clinical phenotype associated with more frequent EF involvement 1 or to low sensitivity of these tests.

However, unlike the original validation study [START_REF] Benedict | Validity of the minimal assessment of cognitive function in multiple sclerosis (MACFIMS)[END_REF] in which significant differences were observed for all tests between PwMS and HS, other studies showed the absence of significant differences for some tests, e. Recently, an abbreviated form of the MACFIMS has been proposed as a short assessment [START_REF] Gromisch | Comparison of the abbreviated minimal assessment of cognitive function in multiple sclerosis (aMACFIMS) and the brief international cognitive assessment for multiple sclerosis (BICAMS)[END_REF].

The effect size of the tests was assessed by the Cohen's D showing a larger effect for IPS (SDMT) followed by episodic memory. This was consistent with the MS literature (Ruet et al., 2012;[START_REF] Langdon | Cognition in multiple sclerosis[END_REF].

The validity of the battery was confirmed by the capacity of the MACFIMS to distinguish PwMS from HS.

Only the SDMT shows good test-retest reliability (>0.8), the test-retest reliability is acceptable for FLT and COWAT (>0.7). The BVMTR reliability is particularly poor in comparison with literature.It is a limitation of the study.. The use of alternative forms for the memory tests and the ECCC may explain the lower reliability observed for these tests. The results of the tests were unaffected by confounding factors, as determined using self-reported questionnaires concerning mood, depressive symptoms, anxiety and fatigue, although the scores for these scales were significantly different between PwMS and HS. Another limitation of the study is the lack of good external criterion for validity. Risk of unemployment was not associated with CI on the MACFIMS. Other standards to judge the adequacy of the testing could have been added to the study such as assessment of activities of daily living.

In conclusion, this study established the norms of the MACFIMS battery for the Frenchspeaking population and provided evidence for the validity of the MACFIMS as a large battery for assessment of cognition in MS. PwMS HS (n = 276) P (1) Effect size n z-score Impaired (2) z-score Impaired (2) SDMT

  Bordeaux (Comité de Protection des Personnes (CPP) Sud-Ouest et Outre-Mer; No. 2014/95). This study was part of the BICAFMS study (Clinical Trial.gov NCT02391064) (Maubeuge et al., 2020).

2. 3 . 2

 32 Neurological evaluation Neurological disability was measured using the French version of the Expanded Disability Status Scale (EDSS) (Brochet et al., 2009). 2.3.3 Patient-related outcome (PRO) All subjects completed patient-related outcome (PRO) questionnaires concerning depressive symptoms (Beck Depression Inventory-Fast Screen [BDI-FS]) (Benedict et al.,, 2003), anxiety (State Trait Anxiety Inventory [STAI]) (Spielberger et al., 1993), mood (Echelle d'Humeur Dépressive [EHD-PRO]) (Lamargue-Hamel et al., 2015) and subjective fatigue (French version of the Fatigue Impact Scale [EMIF-SEP]) ( Debouverie et al., 2007).

  2.3.5 z-score = (scaled score predictedscaled score actual)/RMSE.

  we can for example calculate the predicted SDMT score of a 42-year-old female (male: sex = 1; female: sex = 2) PwMS with a 'baccalauréat' degree (1): 8.91 -0.09 × (42-43.84) -0.002 × (42-43.84) 2 + 0.65 × 2 + 0.36 × 1 = 10.73 Values for participants' educational level in the calculation are 0: Low education level, 1:

  The proportion of PwMS with impairments in each test applying these norms and effect sizes are summarised in Table4. Only 101 PwMS performed all tests of the battery. Compared to HS, PwMS had lower z-scores on the FLT-TL, SDMT, BVMT-R-TL, FLT-DR and BVMT-R-DR (all, p < 0.001), COWAT (p < 0.01) and PASAT-3 (p < 0.05). There were no differences in JLOT and ECCC.Performance on each measure of the MACFIMS was classified as impaired or intact based on the z-score. The MACFIMS battery was able to identify CI (at least two abnormal tests in different domains) in 32.7% of PwMS. A short version of the MACFIMS, including only tests significantly lower in PwMS than in HC (SDMT, memory tests, COWAT and PASAT, excluding ECCC and JLOT) identified 29.7% of patients with CI (three patients were not classified as CI in the short version but were classified CI by the whole battery).

  g. in recent Italian studies, with regard to the SDMT (Argento et al., 2018; Migliore et al., 2017), CVLT TL (Argento et al., 2018), BVMT TL (Migliore et al., 2017) and the PASAT 3 (Migliore et al., 2017).. Thesediscrepancies may be explained by differences between the groups in these studies. Indeed, in the first validation study[START_REF] Benedict | Validity of the minimal assessment of cognitive function in multiple sclerosis (MACFIMS)[END_REF], a large proportion of the PwMS were referred due to suspicion of cognitive difficulties, unlike in the present study. Considering these results, we evaluated the sensitivity of a shorter form of the MACFIMS battery not including the JLOT and the ECCC. This short battery identified 29.7% of patients with CI. The usefulness of this shorter battery must be assessed in other samples in future studies.

  3%) and then RRMS (18.8%). These results were consistent with those in the literature, in different countries and languages(Ruet et al., 2012; Benedict et al., 2006; Dusankova et al., 2012; Eshagi et al., 2012 ; Argento et al., 2018 ; Migliore et al., 2017).

	The second objective was to study the test-retest reliability. Finally, the effects of
	confounding factors, such as depression, anxiety and fatigue, were examined.
	Using these norms, the MACFIMS battery was able to identify CI (at least two abnormal tests

in a French-speaking sample of PwMS and HS and establish its validity by determining whether it can discriminate between PwMS and HS. This is the first study to validate a French version of the MACFIMS. We aimed to establish formally the norms of the MACFIMS battery for the French-speaking population, utilising the regression-based norms adjusted for age, sex and education in a large sample of HS. The regression-based approach to norms development enables us to account for the influences of demographic factors on test performance and use the entire normative sample rather than divide it into smaller subgroups for the computation of age-or education-stratified means and standard deviations. The sample of PwMS was recruited from multiple centres. in different domains) in 33.7% of PwMS. The proportion of CI varied according to the disease subtype. The most affected patients were those with SPMS (42.9%) followed by PPMS (35.

  Beck Depression Index-Fast Screen; EDSS, Expanded Disability Status Scale; EHD-PRO, Echelle d'Humeur Dépressive-patient reported outcome; EMIF-SEP, French adaptation of the modified fatigue Impact Scale; HEL, high education level (see Methods); HS, healthy subjects; LEL,

	Patients (n = 134) 49.62 (9.34) BDI-FS, low education level; not significant; ns, PP, primary progressive; RR, relapsing remitting; SD, HS (n = 276) p Age 43.84 (12.42) < 0.001
	Sex standard deviation; SP, secondary progressive; STAI, State-Trait Anxiety Inventory (A = trait, B = ns
	state).	Female (%)	85 (63.4%)	158 (57.3%)
	Education			ns
		LEL (%)	60 (44.8%)	114 (41.3%)
	HEL-BAC (%)	23 (17.2%)	22 (8.0%)
	HEL-BAC+2-4 (%)	42 (31.3%)	105 (38.0%)
	HEL-BAC+5 (%)	9 (6.7%)	35 (12.7%)
	Disease duration (years)	15.23 (9.62)
	EDSS (median)	4.0 [0 -8]
	Disease subtype
		RR (n)	43
		SP (n)	46
		PP (n)	45
	BDI-FS	3.64 (3.2)	1.47 (2.1)	< 0.001
	EHD-PRO	20.00 (5.25)	16.03 (3.92)	< 0.001
	STAI A	39.35 (11.74)	29.07 (8.13)	< 0.001
	STAI B	42.44 (9.03)	34.53 (9.56)	< 0.001
	EMIF-SEP-physical	23.56 (8.71)	9.09 (8.42)	< 0.001
	EMIF-SEP cognitive	15.85 (9.57)	9.28 (8.43)	< 0.001
	EMIF-SEP-social	3.85 (2.57)	2 (2.18)	< 0.001
	Employment (%)	60 (44.8%)
	Results are expressed as means unless otherwise specified.

Table 2 :

 2 Raw score to scaled score conversions

	Raw score

Table 3 :

 3 Final regression models for MACFIMS measures

				Standard				Total R
	Measure	Predictor	B		Standardised B	t	p		RMSE
				error B				square
		(constant)	8.91	0.603		14.761 < 0.001
		agec	-0.09	0.013	-0.397	-7.169 < 0.001
	SDMT	agec 2	-0.002	0.001	-0.097	-1.746	0.082
		Sex	0.65	0.317	0.113	2.049	0.041
		Education	0.36	0.14	0.143	2.586	0.01	0.185	2.56
		(constant)	7.52	0.608		12.354 < 0.001
		agec	-0.05	0.013	-0.219	-3.932 < 0.001
	FLT-TL	agec 2	-0.003	0.001	-0.132	-2.348	0.02
		Sex	1.33	0.319	0.231	4.151	< 0.001
		Education	0.68	0.141	0.27	4.832	< 0.001	0.173	2.58
		(constant)	10.26	0.617		16.637 < 0.001
		agec	-0.08	0.013	-0.333	-5.798 < 0.001
	BVMT-
		agec 2	-0.002	0.001	-0.09	-1.567	0.118
	R-TL
		Sex	-0.17	0.324	-0.03	-0.517	0.605
		Education	0.25	0.143	0.098	1.712	0.088	0.122	2.62
		(constant)	7.57	0.604		12.546 < 0.001
		agec	-0.04	0.013	-0.194	-3.357	0.001
	FLT-DR	agec 2	-0.001	0.001	-0.033	-0.566	0.572
		Sex	1.24	0.317	0.227	3.921	< 0.001
		Education	0.46	0.14	0.191	3.291	0.001	0.113	2.56
	BVMT-	(constant)	10.48	0.56		18.694 < 0.001
	R-	agec	-0.06	0.012	-0.28	-4.816 < 0.001
	DR	agec 2	-0.002	0.001	-0.125	-2.139	0.033

Table 4 :

 4 Comparison between PwMS and HS in each metric using individual z-scores derived from regression-based model Judgment of Line Orientation Test; PASAT-3, Paced Auditory Serial Addition Test with 3.0-s interstimulus interval; SDMT, Symbol Digit Modalities Test.

(1): p values between PwMS and HS. (2): Subjects were considered impaired if z-score ≤ -1; BVMT-R, Brief Visuospatial Memory Test-revised; COWAT, Controlled Oral Word Association Test; CS, correct sorts; D, description score; DR, Delayed recall; ECC, épreuve de classement de cartes de Champagne. TL, total learning; FLT, French Learning Test; JLOT,

Table 5 :

 5 Correlation between the two sessions All correlations were significant (p < 0.001). BVMT-R, Brief Visuospatial Memory Testrevised; COWAT, Controlled Oral Word Association Test; D, description score; CS, correct sorts; DR, Delayed recall; ECC, épreuve de classement de cartes de Champagne. TL, total learning; FLT, French Learning Test; JLOT, Judgment of Line Orientation Test; PASAT-3, Paced Auditory Serial Addition Test with 3.0-s interstimulus interval; SDMT, Symbol Digit

		125	-0.77 (1.20)	28.5%	0.01 (1.00)	6.9%	p < 0.001	0.73
	FLT (TL)	134	-1.14 (1.44)	38.1%	-0.33 (1.05)	13.4%	p < 0.001	0.68
	FLT (DR)	134	-0.58 (1.15)	21.6%	0.02 (1.00)	6.9%	p < 0.001	0.57
	BVMT-R (TL)	134	-0.68 (1.18)	29.1%	-0.22 (1.02)	12.3%	p < 0.001	0.43
	BVMT-R (DR)	133	-0.53 (1.15)	19.5%	-0.01 (1.00)	7.2%	p < 0.001	0.49
	PASAT-3	119	-0.22 (1.15)	10.9%	0.03 (1.00)	6.6%	p < 0.05	0.24
	JLOT	134	-0.07 (1.00)	9.7%	-0.04 (1.00)	6.9%	p = 0.770
	ECCC (CS)	125	-0.05 (1.34)	12.0%	-0.03 (1.00)	10.6%	p = 0.858
	ECCC (D)	121	-0.13 (1.21)	9.9%	-0.001(1.00)	5.5%	p = 0.299
	COWAT	134	-0.40 (1.32)	17.2%	-0.01 (1.00)	5.8%	p < 0.01	0.40

Acknowledgements:

Funding: The study was sponsored by the Bordeaux University Hospital CHU de Bordeaux.

The study was funded by an unrestricted grant from Bayer Healthcare Pharma. The funder did not contribute to the study design, data collection, analysis or reporting of the study.

grants and other from teva, grants from bayer, personal fees and non-financial support from medday, grants, non-financial support and other from ROCHE, personal fees, non-financial support and other from biogen, personal fees, non-financial support and other from NOVARTIS, nonfinancial support from merck, outside the submitted work .

Dr. Brochet reports grants, research support, personal fees or non-financial support from Genzyme, Bayer, Medday, Actelion, Roche, Biogen, Celgene, Novartis, and Merck outside the submitted work.

Conflict of Interest Statement/ The authors did not report any conflict of interest in relation to the study.