Thomas Laloix
email: thomas.laloix@renault.com

Methodological framework for global performance control of manufacturing system in automotive sector

Keywords: machining centre performance, product performance, part quality, functional modelling, health monitoring, maintenance decision making

come

Methodological framework for global performance control of manufacturing system in automotive sector

1

Problem statement

In the field of industrial systems, the continuous control of system performances is one of the major key to ensure enterprise competitiveness and to face economic issues, particularly in automotive sector, context of this Ph.D. work. In manufacturing industry, system performances can be related both to the production system itself through its feature and operating condition and the product/service it is delivering. This respectively correspond to the effectiveness/efficiency of the machining centre (e.g. productivity, availability) and the quality of the machined part (e.g. dimensional variation, surface roughness).

According to Renault postulate, degradation at component level can considerably affect the quality of the machined part, in spite of periodic maintenance policy. Health state of each component (individual view) could be seen not critical for the component itself but combination of these degradations could lead to deviation of the product parameter. Moreover, product quality deviation is often resulting from the combination of degradation of several system components [START_REF] Cocheteux | System performance prognostic: Context, issues and requirements[END_REF]. Then, to preserve quality of machined part, operators have to reconsider machining parameters. In automotive sector, machining centre plays a central role in the production systems and are the target of the proposed study. Hence, the development of an anticipating strategy based on the control of the quality of machined part from the machining centre degradation constitutes a real challenge. Currently product quality control is performed by statistical approaches, such statistical process control (SPC) policy. These techniques are performed after the part machining (without anticipating strategy). The insufficiency of machined part quality produced a loss of production time in reconfiguration of the machining parameters, tool change and treatment of the non-conformed machined part. It is resulting an important direct and indirect costs.

In addition, even if maintenance plans deployed are solving the degradation or failure that may occur (machine point of view), maintenance actions are not optimal regarding to the impact they have directly on the product features.

Research question

To face the integration of these two types of performances, considered usually as isolated, few approaches are proposed. For example, [START_REF] Colledani | Performance evaluation of production systems monitored by statistical process control and off-line inspections[END_REF] search to estimate machine performance through SPC techniques, but do not tackle the limit caused by sampling inspections. [START_REF] Bhuiyan | Monitoring the tool wear, surface roughness and chip formation occurrences using multiple sensors in turning[END_REF]) demonstrate a relationship between acoustic emission and surface roughness, then vibration emission and tool wear, during machining. [START_REF] Jain | Quality Control Based Tool Condition Monitoring[END_REF] consider the relation between wear of the cutting tool and the machined surface roughness. Nevertheless, most of the resulting models proposed are component-oriented with difficulties to obtain performance at the machine level, i.e. considering the interaction of several components. Moreover, they are usually specific to an application case [START_REF] Lee | Prognostics and health management design for rotary machinery systems-Reviews, methodology and applications[END_REF], [START_REF] Lu | Study on prediction of surface quality in machining process[END_REF]). Thus, current integrated approaches underline limitations in terms of (a) the consideration of the performance at the system level and not only at component one, and (b) the maintenance plan optimization to keep acceptable product performances from maintenance action on a component and to enhance machine availability before non-quality occurred.

Consequently, the research question addressed to our study is the following: Is it possible to develop a formalized and efficient approach to control the performances (and their deviations) of the machined part directly from the control of machining centre performances (and its degradations)?

Proposed framework methodology

The main result expected by using such approach is to be able to obtain a good product as output by controlling the machine performances. To face this issue, contribution of this first year of Ph.D. work is to consider an integrated approach of these both types of performance leading to a proactive strategy by the monitoring of component degradation (thus machine performance) to anticipate product performance evolution. Main steps of a methodology emerge (i) functional and dysfunctional analysis, (ii) development of health state and performance indicatorscurrent and forecast trend, allowing (iii) decision making aid suggested to operators. The context of this work is centred on a machining centre but in order to extend this approach to other machines diversity in manufacturing process, the developed methodology have to be generic. First step consists in the formalisation of the interactions and causal relationships between functions performed by machining centre (at the component and system abstraction level) and the flows produced and consumed by each of these functions. The interesting flows are product, energy, information, knowing that each flow is composed by objects (e.g. part occurrence for the product flow) and each flow/object is defined by properties (e.g. geometry). The relationship between functions (supported by components at field level) and flow modification is the key concept on which the approach is based. The formalisation step can be supported by SADT analysis coupled with system theory rules [START_REF] Iung | Using probabilistic relational models for knowledge representation of production systems: A new approach to assessing maintenance strategies[END_REF]. Moreover, some pattern can be developed regarding generic function classes (e.g. linear displacement, rotation movement, clamping) and be instantiated by each system through their own specific organizational context (e.g. environmental, structural, maintenance policy, production policy).

Then, consequences identification of deviations of each property related to flows/functions or component degradation need to be described. Potential cause of the deviation of output flows properties is the deviation of input flow and/or the degradation of the component. For example, deviation of displacement properties produced by a linear axis can be caused either by the degradation of the component / system supporting the function such as rolling element bearing or ball screw, or by the deterioration of electrical energy (input flow). Deviation of an output flow will become the cause of the deviation of the next output flow function [START_REF] Medina-Oliva | Root cause analysis to identify physical causes[END_REF]. The trend of the deviation is influenced by the environmental context (e.g. temperature, humidity) and organizational context (e.g. maintenance and production policy, competencies of the operator) of the system. Identification of the causal relationship between different abstraction levels of the system leads to the definition of the main performances indicators of the machine components and the machine itself which influence the part performances (e.g. vibration of bearing spindle as performance indicator of spindle that impact the surface quality or the form of the machined cylinder block). It also contributes to associate performances indicators with key levers of performance (impact definition). This analysis is necessarily oriented on items involved in cylinder block quality (help by the use of maintenance and SPC reports). Such analysis can be performed by a coupling between FMECA, FTA and HAZOP studies [START_REF] Medina-Oliva | Root cause analysis to identify physical causes[END_REF].

The second step consists in the formalization of the relationships between component degradation on the others at the same abstraction level (horizontal consideration), or component degradation to the subsystem and machine performances (vertical consideration). Each of these relationships can be supported by semantic rules. Then, influences of performances indicators of different abstraction levels of machining centre (e.g. bearing of feeding axis or displacement of cutting tool, on the dimensional deviation or surface roughness of the machined cylinder block) can be assessed by means of aggregation techniques [START_REF] Rizzolo | Aggregation of Health Assessment Indicators of Industrial Systems[END_REF]. Instantiation of this model by data acquisition allow to assess the current health state of the system and so the system and the product performances.

Finally, the forecast of the trend of performance indicators on machine allows to propose to the operators a window of opportunities/actions to perform the tuning of machine parameters e.g. feed rate, cutting speed, or to replace a component for anticipating deviation of cylinder block quality (proactive strategy). Assessment of the impacts of such proposed actions concludes an optimisation phase (multi-criteria decision). Optimisation is guided on the manufacturing business model through direct and indirect costs of maintenance, product cost and/or production time, safety …

Developments of the methodology on the case of GROB machining centre

We propose, in the following section, to illustrate the first steps of this methodology on an application case. The framework of this study is on the machining process of engine cylinder block (Fig. 1). A major element of a machining centre corresponds to the electro spindle (Fig. 2), particularly regarding our application case oriented through two-spindle machine type, machining centres GROB BZ560 and GROB G520 (Fig. 3). Also, electro spindle is directly involved in the machining process by the holding of the cutting tool and thus involved in the product quality. Electro spindle corresponds to a complex system composed by electromechanical elements. It consumes energy (e.g. electrical, hydraulic and pneumatic) and material (e.g. lubricant, part) flows. These flows can be characterised by attributes representative of the performance of the function. Functions performed by electro spindle can be designated as To rotate cutting tool (supported by an electrical motor system), To clamp cutting tool (supported by a clamping system). These functions are involved in machining process and play a central role in the product quality.

Regarding especially To rotate cutting tool function, input flows can be the cutting tool itself, characterized by length, material properties and useful time, and electrical energy, characterized by current and voltage. Output flow can correspond to the generated rotary movement which properties are torque, speed and spatial location conditioned by the machining process requirements and cutting tool wear, with geometry properties. Deviation of an input flow such as inopportune shutdown of electrical energy will lead to the deviation of the output flowdecrease of torque and speed -and directly have an impact on the machined part quality through the dimensional aspect and the surface roughness. In the same way, abnormal vibrations on the rolling element bearing (failure mode) will affect radial amplitude of cutting tool position (deviation of spatial location) and cause cutting tool wear and surface roughness on the machined part. A consequence of the degradation of the rolling element bearing is an increase of the electric motor torque and thus, electric current. This latter is then able to represent an early indicator of rolling element bearing degradation. Detection of deviation or degradation mechanism shall be realized by relevant indicators at element and/or system level. Then, it can be necessary to build indicator at higher abstraction level to identify the root causes of abnormal functioning. System indicator can be the result of fusion or aggregation of lower abstraction level indicators. The choice of relevant indicators is motivated by two factors: availability of the information, generally obtained from direct or indirect observations, and relevance regarding the need of the maintenance operators, i.e. there is no interest to propose an obscure indicator the operators will not understand and then not use.

Conclusion and perspectives

The research proposal, resulting from the first year of a Ph.D. work, examines an integrated consideration of the machining performances and product performances. It allows to isolate some issues and limits for achieving real integration as requested by the RENAULT context (Cléon factory). So, to face some of these issues, main phases of an integrated methodology are investigated in the frame of GROB machining centre manufacturing RENAULT cylinder block. Next action is to finalise all the models and algorithms required to support each phase, and to deploy them on a tool usable by the operator on site. Finally, due to its important cost impact and its interactions with the machine, another challenge is to consider the cutting tool as a product of the machine centre, leading to control its performances e.g. wear, breakage, from the control of machine centre performances.

Fig. 1 :

 1 Fig. 1: Renault cylinder block Fig. 2: Electro spindle


Asma Ben-Said
email: asma.ben-said@hds.utc.fr

Racha El-Hajj
email: racha.el-hajj@hds.utc.fr

Aziz Moukrim
email: aziz.moukrim@hds.utc.fr

An adaptive heuristic for the Capacitated Team Orienteering Problem

Keywords: Capacitated Team Orienteering Problem, iterative local search, adaptive destruction/construction heuristic

The Capacitated Team Orienteering Problem (CTOP) is a new variant of the wellknown Team Orienteering Problem (TOP) where an additional constraint is imposed on the vehicles capacities. By associating a profit and a demand to each customer, the objective of solving CTOP is to select the set of customers to be served in such a way that the total amount of profits collected from the visited customers is maximized, while respecting all the resource limitations, i.e., maximum length limit and maximum capacity of each vehicle. We present in this paper a new adaptive heuristic to solve CTOP. Our method is based on an adaptive iterative destructive constructive heuristic, which adjusts its parameters according to the solution progress. Computational experiments applied on the benchmark of CTOP show the effectiveness of our proposed method, which provided some results of high quality with a competitive computational time. Moreover, an improvement was found in the score of one of the hardest instances of the benchmark.

INTRODUCTION

The Capacitated Team Orienteering Problem (CTOP) is a variant of the Vehicle Routing Problems (VRP) where not all customers can be visited due to some resource limitations. In this problem, a profit is associated with each customer, which is collected when the customer is served. A demand is also associated with customers and is provided from the vehicle's capacity. Each vehicle must start its route from a specified point called the departure depot and returns to the arrival one while not exceeding its maximum travel time limit. In addition, each customer must be served at most once by the fleet of vehicles only if the overall provided demands respects the maximum capacity of the vehicle. The objective of solving CTOP is to maximize the total collected profits from the visited customers while respecting all the resource limitations.

CTOP arises in many real life applications. It mainly appears in the truck-load transportation industry, where shippers often look to outsource the transportation of goods to carriers. In some cases, due to the increasing demands of the customers and the limited resources, i.e. number of available vehicles, capacity of each vehicle, the carriers must choose the most convenient customers to serve in order to maximize the collected profit. Therefore, it is recommended to model these problems with CTOP to choose the best itinerary of visits for the available vehicles.

CTOP was first introduced by [START_REF] Archetti | The capacitated team orienteering and profitable tour problems[END_REF]. Despite its importance in many real life applications, few researchers had focused on providing solution techniques for this problem. To the best of our knowledge, only two exact methods have been developed to solve CTOP. The first method was based on the branch-and-price algorithm and was proposed by [START_REF] Archetti | The capacitated team orienteering and profitable tour problems[END_REF]. The authors adapted the branch-and-price algorithm proposed by [START_REF] Boussier | An exact algorithm for team orienteering problems[END_REF] for TOP, by taking into consideration the capacity constraints while solving the subproblems. Recently, [START_REF] Archetti | Optimal solutions for routing problems with profits[END_REF] proposed a new exact algorithm based on the branch-and-price technique, where a restricted heuristic is used to provide primal bound values for each node of the enumeration tree. Beside the exact algorithms, some heuristic approaches were developed to provide solutions for CTOP in a short computational time. Three heuristic methods were proposed by [START_REF] Archetti | The capacitated team orienteering and profitable tour problems[END_REF]. First, a tabu search algorithm, which just explores feasible solutions was presented as the Tabu Search T SF , then another tabu search algorithm called T SA, which considers feasible and admissible solutions was developed. Finally, a variable neighborhood search (V N S) that iteratively uses the two heuristics T SF and T SA was proposed. [START_REF] Tarantilis | The capacitated team orienteering problem: a bi-level filter-and-fan method[END_REF] then proposed a Bi-level search method, which seems to be more efficient for CTOP. Many neighborhood solutions are explored at each iteration by applying a local search technique randomly chosen between three local searches that focus on the replacement movement and the insertion. These local searches are followed by an adjustment procedure used to reduce the traveled distance in the best solution found. Moreover, [START_REF] Luo | An adaptive ejection pool with toggle-rule diversification approach for the capacitated team orienteering problem[END_REF] had recently proposed a new heuristic method named Adaptive Ejection Pool with Toggle-rule diversification (ADEP T ). Their approach uses a list of unrouted customers sorted according to a certain priority rule chosen between two: The first rule uses a decreasing order of a valuation associated to each customer and the second one uses the first-in-first-out policy. At each iteration, the highest priority customer is randomly inserted in the current solution. Then, a local search is applied to improve the solution, where the feasibility of the obtained solution is restored by removing minimumvaluation customers. So far, ADEP T seems to be the best method for CTOP since it is able to outperform all the existing methods in the literature.

In this paper we propose a new Heuristic method to solve CTOP. Our algorithm is mainly based on an Adaptive Iterative Destruction/Construction Heuristic (AIDCH), which is composed of an adaptive construction phase based on a Best Insertion algorithm, followed by an adaptive diversification phase with some local search techniques. Our algorithm is initialized with several parameters and then adjusts them by itself according to the solution progress throughout the resolution process. The remainder of the paper is organized as follows. Section 2 provides a formal formulation of CTOP, then our proposed method is described in Section 3. Computational experiments performed on the standard benchmark of CTOP are reported in Section 4 followed by some conclusions and futur works in Section 5.

PROBLEM DESCRIPTION AND NOTATION

CTOP is modeled with a complete undirected graph G = (V ∪ {0}, E), where V = {1, . . . , n} is the set of vertices representing customers with vertex 0 the depot and E = {(i, j) : i, j ∈ V ∪ {0}} the set of edges interconnecting the vertices. A profit p i and a demand d i are associated with each customer i ∈ V . Each edge (i, j) ∈ E is valued with a cost l ij which is assumed to be symmetric and verifying the triangle inequality. A fleet F of m homogeneous vehicles with a maximum capacity Q is available to serve customers, where each vehicle cannot travel more than L max time units. We define a route r k as a sequence of q r k customers assigned to vehicle k in the fleet F. Each route starts and ends with the depot vertex 0:

r k = (0, r k [1], . . . r k [q r k ], 0), ∀k ∈ F .
The total demand of all customers served in route r k , denoted by D(r k ), cannot exceed the vehicle capacity Q and the total length of route r k , denoted by L(r k ), must respect the travel time limit L max . A solution S of CTOP represents a set of m routes in which each customer is served at most once by the fleet of vehicles. We denote the total profit of a solution S by P (S) = i∈S p i and the total demand provided to the served customers by D(S) = i∈S d i . The objective of solving CTOP is to find a solution S such that the total profit collected in all its routes is maximized.

ADAPTIVE ITERATIVE DESTRUCTION/CONSTRUCTION HEURISTIC

In order to provide feasible solutions for CTOP with good quality, we propose an adaptive iterative destruction/construction heuristic. The global scheme of our proposed approach is described in Algorithm 1.

Starting with an empty solution, we use an adaptive construction procedure to build an initial solution. Then, at each iteration, a part of the solution is destroyed by removing from the routes a limited random number of customers, bounded by dmax. Therefore, we define dmax as the degree of diversification. This value is initialized to 3 and then incremented after each non-improving iteration. As soon as an improvement is found, we reset dmax to 3 in order to entirely explore the neighborhood of the new solution. A 2-opt operator is next applied to the solution to reduce the length of the routes. Finally, we perform an adaptive construction procedure to complete the solution. This process is reiterated and stops when all customers are served or when a certain number of consecutive iterations have failed to improve the quality of the solution. The final result is the best solution found over all iterations. Based on the previous work of [START_REF] Dang | An effective pso-inspired algorithm for the team orienteering problem[END_REF] Our algorithm makes use of an adaptive diversification mechanism to avoid its stuck in a local optimum. The idea is to explore the neighborhood of the new solution as soon as an improvement is found and to explore more distant zones whenever the search is trapped in a local optimum.

The main component of our proposed algorithm is the adaptive construction heuristic based on a Best insertion algorithm (BIA). This algorithm considers a partial solution S, which might be an empty solution, and tries to insert unrouted customers one by one in the solution. The objective of BIA is to evaluate, at each iteration, all feasible insertions that respect the length and the capacity constraints of all the routes in the resulting solution. The best insertion is then performed. This process is iterated until either all customers are served or no further feasible insertions are available.

To evaluate the insertion of customer c between vertices i and i + in route r, many experiments pointed out the insertion criterion denoted by CI ci . Let P max be the profit of the most profitable customer, and ∆L ci = l i,c + l c,i + -l i,i + , the difference in length caused by inserting customer c between i and i + . The insertion criterion is then calculated as follows:

(r) + d c ≤ Q then foreach couple of consecutive customers (i, i + ) do calculate ∆L ci ; if L(r) + ∆L ci ≤ L max then calculate CI ci ; F I := F I ∪ {(c,
CI ci = ( 1+∆Lci 1+Lmax ) β * ( dc Q ) γ ( pc Pmax ) α (1)
Our proposed criterion aims to maximize the profit, and minimize the total traveled distance and the used load.

We note that we added a unit to the length factor in order to equally study the insertion criteria, even if the inserted customer c is aligned with the two customers i and i + between which it should be inserted or coincide with one of them. A normalized value is considered for each factor in order to evaluate them in the same manner. Beside that, each factor is weighted with a certain parameter, denoted by α, β and γ as shown in Expression (1) in order to control their relative importance.

Algorithm 2 illustrates the Best Insertion Procedure, where we use the notation (c, r, (i, i + )) to denote the insertion of customer c between customers i and i + in route r. The insertion operation is denoted by ⊕.

At each iteration i of the AIDCH, the proposed construction procedure operates as follows. Five constructive heuristics CM j,j∈{1,...,5} launch separately BIA with different triplets (α, β, γ) on the current solution. During each launch, α, β and γ are chosen randomly in the cube having the center (α i-1 , β i-1 , γ i-1 ) and the side length ϕ, where α i-1 , β i-1 and γ i-1 represent the best parameters obtained by the method at iteration i -1. At the end of each method applied CM j,j∈{1,...,5} , the parameters leading to the best solution found by CM j are saved to be used to calculate the BIA parameters of the next iteration.

Finally, the best solution obtained among the five methods is retained as the current solution. The purpose of this procedure is to perform parallel independent searches in the solutions space and choose the best track to follow in order to converge faster toward a good solution.

COMPUTATIONAL EXPERIMENTS

To evaluate our AIDCH, we used the standard benchmark of CTOP generated by [START_REF] Archetti | The capacitated team orienteering and profitable tour problems[END_REF]. Our algorithm is coded in C++ using the Standard Template Library (STL) for data structures, where we used the GNU GCC to compile our program. All tests are carried out on a linux server with an Intel Xeon X7542 CPU clocked at 2.66 GHz.

In order to evaluate the proposed methods, [START_REF] Archetti | The capacitated team orienteering and profitable tour problems[END_REF] proposed a new benchmark of CTOP composed of 130 instances which are classified into 13 sets according to the number of vehicles available, to the vehicle capacity and to the maximum length.

In what follows, we analyze the impact of various components in our AIDCH and we provide some experiments to tune the needed parameters.

We use the best known score in the literature, denoted by BK, which represents the best score obtained by the heuristic and the exact methods proposed in the literature for CTOP. We tested our approach with the same protocol used in [START_REF] Dang | An effective pso-inspired algorithm for the team orienteering problem[END_REF] and [START_REF] Ke | Ants can solve the team orienteering problem[END_REF]. For each instance, our algorithm is executed 10 times from which we recorded the relative percentage error (RPE), which is defined as the relative error between the best score obtained by the heuristic and the exact methods proposed in the literature for CTOP (BK) and the maximal score obtained among the 10 runs.

Impact of the adaptive construction mechanism

In order to evaluate the performance of our adaptive mechanism, we carried out several experiments to choose the best value of the step ϕ and to compare the behavior of our algorithm with and without the adaptive mechanism.

The value of the step ϕ affects significantly the resulting performance of our method. Various experiments with different values of ϕ are tested. For these tests, we performed a fast version of our algorithm where iter max is set to n instead of n 2 . Figure 1 shows the evolution of RPE in terms of ϕ. Based on the graphic of Figure 1, we notice that our algorithm provides the best RPE with ϕ = 0.1. Hence, we have chosen the parameter ϕ to be equal to 0.1 in our next experiments.

On the other hand, we examined the ability of the adaptive construction mechanism to guide the search toward finding, at each time, the best trade-off between the profit, the distance and the demand. Therefore, we test two versions of our algorithm, the first one by considering the overall approach and the second one where the adaptive mechanism is disabled and the parameters (β, γ) are chosen randomply in [0,1] at each iteration. In these experiments, for each instance, the algorithm is launched only once and the best solution for the first 15000 iterations is recorded.

The RPE values obtained in each iteration are reported in Figure 2. These experiments show that with the use of the adaptive construction mechanism, the search procedure converges quickly toward good solutions. In contrast, the convergence to the best solution is very slow in the case treated without adaptive construction mechanism. Therefore, based on the obtained results, it is recommended to fix parameter α to 1, and to vary β and γ in [0, 1].

Impact of the diversification mechanism

To evaluate the effectiveness of our adaptive perturbation component, we implemented an alternative version of AIDCH where the perturbation procedure is used as in the approach of [START_REF] Dang | An effective pso-inspired algorithm for the team orienteering problem[END_REF], which was developed to solve the vehicle routing problems with profits. In their studies, they limited the maximum number of removed customers dmax to 3. Figure 3 illustrates the average RPE recorded against the number of iterations to show the evolution of the two versions: with and without the adaptive diversification mechanism. Based on these two graphs, we can easily notice that the average RPE with the adaptive perturbation component is always below the average RPE with the standard perturbation of [START_REF] Dang | An effective pso-inspired algorithm for the team orienteering problem[END_REF] at each iteration, which shows the effectiveness of our proposed technique.

Comparison with the literature

We compared the results of our AIDCH on the benchmark of CTOP with the state-of-the-art heuristic methods available in the literature:

• T SF , T SA and V N S proposed by [START_REF] Archetti | The capacitated team orienteering and profitable tour problems[END_REF], tested on a Pentium 4 2.80 GHz CPU. • BiF proposed by [START_REF] Tarantilis | The capacitated team orienteering problem: a bi-level filter-and-fan method[END_REF], tested on an Intel Core2 Quad 2.83 GHz CPU. • ADEP T proposed by [START_REF] Luo | An adaptive ejection pool with toggle-rule diversification approach for the capacitated team orienteering problem[END_REF], tested on an Intel Xeon E5430 2.66 GHz CPU.

To compare the cpu times between different machines, it is recommended to use the Super PI protocol, which estimates the CPU speed. By performing these tests to the four machines, we noticed that our machine and those used by [START_REF] Tarantilis | The capacitated team orienteering problem: a bi-level filter-and-fan method[END_REF] and [START_REF] Luo | An adaptive ejection pool with toggle-rule diversification approach for the capacitated team orienteering problem[END_REF] have almost similar computational power and are about three times faster than the machine used by [START_REF] Archetti | The capacitated team orienteering and profitable tour problems[END_REF].

The performance of all methods is evaluated according to the quality of the solutions and the computational times. Table 1 reports the averages RPE obtained for the 13 sets of the benchmark, while the average TTB is summarized in Table 2. The dash mark '-' indicates that the algorithm is not tested on the corresponding set of instances. In the line best, we count the number of best solutions found, while in the bottom of each table we report the average RPE and TTB on all CTOP instances.

The results obtained in these tables show that our proposed algorithm was able to find the best solutions for 127 instances of the benchmark of CTOP with a much lower computational time compared to In addition, ADEP T was not tested on the instances of the first set of instances. In their survey [START_REF] Luo | An adaptive ejection pool with toggle-rule diversification approach for the capacitated team orienteering problem[END_REF], the authors didn't give the result of their ADEP T algorithm in the first set of instances. By comparing the average computational time of the common treated sets i.e. from g2 to g13, we found that our AIDCH consumed 3.3 sec which is much smaller than the TTB of ADEP T , which reached 33.2 sec. We note that our AIDCH makes a greater computational time in the first set which contains large scale instances. This result pointed out the ability of our method to deal with difficult instances.

On the other hand, our AIDCH was able to improve one new best solution for an instance from the first set with m = 15, Q = 200 and L max = 200. It is worth to mention that [START_REF] Tarantilis | The capacitated team orienteering problem: a bi-level filter-and-fan method[END_REF] showed that their BiF algorithm was able to serve all customers in this instance which is impossible in terms of capacity constraint with the use of only 15 vehicles, where at least 16 vehicles are needed to cover the demand of all customers.

CONCLUSION AND FUTURE WORK

We presented in this paper an adaptive iterative destruction construction heuristic for the Capacitated Team Orienteering Problem. Two main adaptive mechanisms high-light our approach and had proven to be very efficient for the case of CTOP. The adaptive construction procedure based on the best insertion algorithm manages the insertion of customers in the solution according to the progress of our algorithm, while the adaptive perturbation mechanism controls the number of removed customers according to the search efficiency and to the status of the solution obtained so far.

Computational experiments performed on the benchmark of CTOP show the effectiveness of our algorithm compared to the other heuristic methods performed for CTOP. Our AIDCH reached a relative error of 0.008% and improved the quality of one of the hardest instances with a small computational time.

As for future work, we will perform several ameliorations for our AIDCH to improve its performance in terms of RPE and computational time. By applying some modifications to the problem, we will be able to solve other variants of CTOP in order to respond to new needs, as CTOP with time windows and/or resource synchronization.

Algorithm 2

 2 Best Insertion Algorithm Input : S 0 : partial solution UR: unrouted customers (α, β, γ): criterion parameters Output : Solution S Variables: F I : list of feasible insertions insert : boolean (one customer inserted) S := S 0 ; insert := true; while (U R not empty) and (insert = true) do F I := ∅; insert := false; foreach customer c do foreach Tour r do if D

Fig. 1 .

 1 Fig. 1. Performance of AIDCH in terms of ϕ

Fig. 2 .

 2 Fig. 2. Impact of the adaptive construction mechanism

Fig. 3 .

 3 Fig. 3. Impact of the adaptive diversification mechanism

  for the vehicle routing problem with profits, the maximum number of consecutive iterations without improving the best result is set to n 2 .

	Algorithm 1 General structure of AIDCH
	Input	: An instance of CTOP
	Output : S best solution found
	Variables: dmax : diversification degree
		S i : current solution
		U R : unrouted customers
	dmax := 3;
	iter max := n 2 ;
	AdaptiveConstruction(S);
	S iter := 0;
	end
	end
	else
	dmax = min(dmax+1, n);
	end
	end

i := S; while (iter < iter max ) and (U R not empty) do d := rand(1, dmax); AdaptiveDestruction(S i , d); Apply2-Opt(S i ); AdaptiveConstruction(S i ); iter++; if (P (S i ) > P (S)) or (P (S i ) = P (S) and D(S i ) ≤ D(S)) then dmax := 3; if (P (S i ) > P (S)) or (P (S i ) = P (S) and D(S i ) < D(S)) then S := S i ;

  T SF , T SA and V N S methods which have solved, respectively, 87, 69 and 101 instances. Moreover, these results show that AIDCH and BiF methods are very competitive in terms of computation time. In contrast, we obtained best solutions for

	Set	T SF	T SA	V N S	BiF	ADEP T	AIDCH
	g1	0.029 0.018	0.005	0	-	-0.003
	g2	0	0.075	0	0.081	0	0.075
	g3	0	0.05	0	0	0	0
	g4	0	0.079	0	0	0	0
	g5	0	0	0.047	0	0	0
	g6	0.096 0.096	0.096	0	0	0
	g7	0.102 0.299	0.196	0	0	0
	g8	0.107 0.253	0.035	0	0	0
	g9	0.143 0.540	0.240	0.049	0	0
	g10	0.348 0.739	0.332	0	0	0.037
	g11	0.266 0.212	0.018	0	0	0
	g12	0.469 0.278	0.049	0	0	0
	g13	0.189 0.226	0	0	0	0
	best	87	69	101	126	120	127
	average	0.135 0.220	0.078	0.010	0	0.008
	Table 1. Comparison of the average RPE be-
	tween our AIDCH and the other heuristic
			methods in the literature
	Set	T SF	T SA	V N S	BiF	ADEP T	AIDCH
	g1	43.3	50.4	720.0	0.2	-	121.2
	g2	98.7	150.9	138.4	0.2	3.5	0.0
	g3	97.9	168.8	182.4	0.2	9.4	0.1
	g4	97.4	163.6	243.7	1.0	11.6	0.1
	g5	594.1 723.3	892.9	5.7	13.2	0.1
	g6	630.2 692.0 1151.2	6.0	33.1	0.4
	g7	740.2 426.1 1325.0	29.3	39.4	4.7
	g8	706.7 765.1 1147.1	13.7	35.7	0.6
	g9	848.6 747.4 1353.1	54.3	125.9	9.7
	g10	738.9 999.3 1621.4	65.3	98.5	13.3
	g11	382.1 275.1	714.7	1.3	2.0	1.9
	g12	381.7 264.2 1244.2	8.2	10.2	35.0
	g13	400.1 241.7 1640.8	1.3	15.4	14.0
	average	443.1 436.0	951.9	14.4	33.2	15.5
	Table 2. Comparison of the average RPE be-
	tween our AIDCH and the other heuristic
			methods in the literature
	127 instances while BiF obtained 126 best solutions.

ACKNOWLEDGEMENTS

This work is carried out in the framework of the Labex MS2T, which was funded by the French Government, through the program "Investments for the future" managed by the National Agency for Research (Reference ANR-11-IDEX-0004-02). It is also partially supported by the TCDU project (Collaborative Transportation in Urban Distribution, ANR-14-CE22-0017).


MD; Psychiatrist Paul Brunault
email: paul.brunault@univ-tours.fr

MD Ephrem Salamé

MD; Nematollah Jaafari

MD Robert Courtois

PhD ; Psychiatrist

Christian Réveillère

MD; Christine Silvain

MD Amine Benyamina

MD; Addictologist Lisa Blecha

David Belin

MD Nicolas Ballon

Why do liver transplant patients so often become obese? The addiction transfer hypothesis

Keywords: liver transplantation, liver disease, food addiction, obesity, binge eating disorder, compulsive eating behaviour, alcohol dependence, alcohol addiction, alcohol abuse, alcohol use disorder, alcoholism, addiction transfer, switch, insight, psychiatric disorders

In patients who receive transplantation for alcohol liver disease, obesity and metabolic syndrome are highly prevalent after transplantation and both contribute to a significant proportion of cardiovascular complications, late morbidity and mortality in this population. Although immunosuppressive medications have been hypothesised to explain some of these post-liver-transplantation (LT) metabolic complications, they cannot be considered the sole cause of obesity and metabolic syndrome, and the high prevalence of these illnesses remains unexplained. Given the significant overlap between the neurobiological, psychiatric and psychological factors that underlie alcohol addiction and reward-related behavioural dyscontrol disorders such as food addiction (FA), we hypothesised that the high prevalence of obesity and metabolic syndrome reported in patients who receive transplantation for alcohol liver disease could be explained at least partially by a switch in some individuals from a previous alcohol addiction to post-transplantation FA (i.e., addiction transfer = addiction switch). In our integrative model, we also speculate that an increased prevalence of FA or alcohol addiction may occur in patients with both specific psychobiological profiles and shared risk factors. We further hypothesise that in the subpopulation of patients who develop either alcohol addiction or FA after LT, those with high insight with regard to the consequences of alcohol use could be at higher risk for FA, whereas those with low insight could be at higher risk for alcohol addiction. We discuss here evidence for and against this hypothesis and discuss which patients could be more vulnerable to these two addictions after LT. Because it will not be either possible or ethical to test some of our hypotheses in humans, future studies should test these hypotheses using a translational strategy, using both clinical and preclinical approaches. If our hypotheses could account for the significant increase in obesity and metabolic syndrome after LT, this would lead to new avenues for research and preventive as well as therapeutic interventions for alcohol-related LT patients. All patients with previous or current alcohol addiction should be systematically screened for FA and followed up for subsequent risk of obesity and metabolic syndrome. Such strategies might be effective in improving survival, outcomes and quality of life after LT and also in the overall population of patients with alcohol addiction. By determining common risk factors for both alcohol addiction and FA using a translational approach, our model could help to find novel psychopharmacological and psychological strategies that might be effective in both FA and alcohol addiction.

INTRODUCTION

Alcohol use disorders are defined by a cluster of cognitive, behavioural, and physiological symptoms that indicate persistent use of a substance despite significant substance-related problems [START_REF]American Psychiatric Association. Diagnostic and Statistical Manual of mental disorders[END_REF]. These disorders are a major public health problem worldwide, with a lifetime prevalence rate in the United States estimated at 17.8% (0.5) and 12.5% (0.4) for alcohol abuse and dependence [START_REF] Merikangas | Epidemiology of substance use disorders[END_REF], thereby representing a health, social and economical burden to western societies [START_REF] Rehm | Global burden of disease and injury and economic cost attributable to alcohol use and alcohol-use disorders[END_REF]. Approximately 3.8% of all global deaths and 4.6% of global disability-adjusted life-years are attributable to alcohol [START_REF] Rehm | Global burden of disease and injury and economic cost attributable to alcohol use and alcohol-use disorders[END_REF]. In France, in 2009, 36,500 deaths in men were attributable to alcohol (13% of total mortality) versus 12,500 in women (5% of total mortality) [START_REF] Guérin | Alcohol-attributable mortality in France[END_REF]. One of the somatic consequences of protracted alcohol addiction is liver cirrhosis or liver failure, for which liver transplantation (LT) has progressively become the best, and sometimes the only therapeutic alternative for patients with end-stage liver failure [START_REF] Matesanz | Global Education Initiatives[END_REF].

However, the success rate of LT in patients suffering from alcohol addiction remains relatively poor. It is critical to better identify the factors that contribute to poorer post-transplant outcomes in former alcohol addicts not only because alcohol use disorders are currently the leading cause for LT [START_REF] Dew | Meta-analysis of risk for relapse to substance use after transplantation of the liver or other solid organs[END_REF] but also because these factors lead, when untreated, to lower quality of life and lower survival rates [START_REF] Iruzubieta | Long-term survival after liver transplantation for alcoholic liver disease[END_REF]. This is a major public health issue not only for these patients but also because of the economic and social costs associated with liver transplantation and the limited number of organ donors, which prevents other patients with potentially better outcomes from benefiting from this treatment [START_REF] Matesanz | Global Education Initiatives[END_REF].

Obesity and metabolic syndrome are among the main factors that contribute to a significant part of cardiovascular complications and late morbidity and mortality after LT [START_REF] Pagadala | Posttransplant metabolic syndrome: an epidemic waiting to happen[END_REF]. Some factors such as use of immunosuppressive medications, donor characteristics (e.g., body mass index), and pre-transplant nutritional and metabolic status have been hypothesised to account for some of these post-LT metabolic complications (see for review [START_REF] Anastácio | Metabolic syndrome and its components after liver transplantation: incidence, prevalence, risk factors, and implications[END_REF]). However, these hypotheses cannot explain why and how patients with a pre-transplant alcohol use disorder are at higher risk than other liver-transplanted patients for developing post-transplant metabolic syndrome [START_REF] Pagadala | Posttransplant metabolic syndrome: an epidemic waiting to happen[END_REF][START_REF] Anastácio | Metabolic syndrome after liver transplantation: prevalence and predictive factors[END_REF] and obesity [START_REF] Yeomans | Alcohol, appetite and energy balance: is alcohol intake a risk factor for obesity?[END_REF]. According to a study conducted by Anastácio et al. in 148 liver transplanted patients with a mean follow-up of 3.5 years [START_REF] Anastácio | Metabolic syndrome after liver transplantation: prevalence and predictive factors[END_REF], prevalence for metabolic syndrome was 84% higher in patient transplanted for an alcohol liver disease when compared to patients transplanted for a non-alcohol liver disease (prevalence rate for metabolic syndrome were respectively 71.7% and 38.9%; OR=3.88; 95% CI=1.43-10.51; p<0.001).

The elevated rate of metabolic syndrome observed in patients with alcohol use disorder after LT is all the more surprising given that the risk of relapsing to alcohol use after LT, a classic risk factor for post-LT metabolic complications, is lower in these patients than in control populations that are treated for alcohol abuse [START_REF] Beresford | Probabilities of relapse and abstinence among liver transplant recipients[END_REF]. During the five years following LT, one out of four and one out of eight patients, respectively, will relapse to any alcohol use or to heavy alcohol use [START_REF] Dew | Meta-analysis of risk for relapse to substance use after transplantation of the liver or other solid organs[END_REF], whereas in primary care, more than four patients out of five will relapse to alcohol use in any given 18-month period [START_REF] Malet | Outcomes from primary care management of alcohol dependence in France[END_REF]. We currently don't know whether it is the amount of alcohol intake an/or the duration of alcohol intake that are associated with higher risk for post-transplant metabolic complications, and we alsolack an understanding of why patients who receive transplantation for alcohol liver disease show both an increased risk of metabolic syndrome and obesity and a lower risk of relapse to alcohol addiction after LT.

Although excessive and compulsive food intake may be a prominent contributor to the high incidence of overweight and obesity after LT and in patients with a preoperative alcohol use disorder, data on food intake in patients who receive transplantation for an alcohol use disorder are very scarce [START_REF] Anastácio | Metabolic syndrome and its components after liver transplantation: incidence, prevalence, risk factors, and implications[END_REF]. Only Correia et al. mentioned that "non-healthy habits' might be a risk factor for post-transplant obesity [START_REF] Correia | Post-liver transplant obesity and diabetes[END_REF], but no studies have so far explicitly assessed whether an increased propensity to develop food addiction could be a potential risk factor for later obesity or metabolic syndrome in patients who receive transplantation for an alcohol use disorder. Food addiction, a concept that has been recently proposed by applying the DSM-IV-TR criteria for substance dependence to eating behaviour in order to describe patients who exhibit eating patterns that are similar to the behaviours classically seen in drug-addicted patients [START_REF] Brunault | Validation of the French version of the Yale Food Addiction Scale: an examination of its factor structure, reliability, and construct validity in a nonclinical sample[END_REF][START_REF] Gearhardt | Food addiction: an examination of the diagnostic criteria for dependence[END_REF][START_REF] Ifland | Refined food addiction: a classic substance use disorder[END_REF], is indeed strongly associated with obesity [START_REF] Gearhardt | An examination of food addiction in a racially diverse sample of obese patients with binge eating disorder in primary care settings[END_REF][START_REF] Meule | Food addiction and body-mass-index: A non-linear relationship[END_REF], and it has been hypothesised to play a major role in the recent increase in obesity prevalence in the overall population [START_REF] Corsica | Food addiction: true or false?[END_REF].

Finally, it is noteworthy that studies in the field of bariatric surgery have demonstrated that when previous eating behaviour was restricted by bariatric surgery, alcohol use disorders increased [START_REF] King | Prevalence of alcohol use disorders before and after bariatric surgery[END_REF].

HYPOTHESIS

Our main hypothesis is that the high rates of obesity and metabolic syndrome reported in post-LT patients could be attributable to a switch from a previous alcohol addiction to a post-LT food addiction (i.e., addiction transfer = addiction switch) in a subpopulation of vulnerable individuals who share certain specific psychobiological risk factors and who also share coping strategies under the peer and moral pressure associated with LT. More specifically, we hypothesise that low insight with regard to the somatic and psychological consequences of alcohol addiction could predict higher risk of alcohol relapse after LT whereas high insight could predict higher risk of developing a food addiction after LT.

We will present a correlational model in which food addiction could partially account for the variance in obesity and metabolic syndrome observed post LT in former alcohol addicts, in addition to other factors such as pre-transplant nutritional status, use of medications and donor's nutritional status.

HYPOTHESIS EVALUATION

Our hypothesis is based on four different assumptions regarding the population of patients who receive transplantation for alcohol liver disease:

1) The prevalence of alcohol addiction decreases, while the prevalence of food addiction increases, after LT.

2) A significant part of the weight gain, obesity and metabolic syndrome after LT is attributable to the increased prevalence of food addiction after LT.

3) The increased prevalence of food addiction or alcohol relapse after LT occurs in patients with specific psychobiological risk factors.

4) In patients who display addictive behaviours post-LT, the level of insight with regard to the somatic and psychological consequences of alcohol use before LT predicts either the development of a food addiction or the resuming of their former alcohol addiction after LT.

We will review here the pros and cons in support of each of these assumptions before addressing the added value of our hypothesis to the theoretical framework of post-LT complications and potentially refined treatment strategies. We will also describe the potential operationalisations that will be necessary to test our hypothesis. 1) In the specific population of patients transplanted for alcohol-induced liver disease, the prevalence of alcohol addiction decreases, while the prevalence of food addiction increases, after LT.

To explain the fact that the risk of relapsing to alcohol use after LT is lower than it is in control populations that are treated for alcohol abuse [START_REF] Beresford | Probabilities of relapse and abstinence among liver transplant recipients[END_REF], a number of hypotheses might be proposed. First, these patients do face a lifethreatening illness, and they receive better social support through improved medical follow-up. Additionally, and perhaps even more importantly, patients benefit from the sustained support of peers and health professionals. Both factors may interact to greatly contribute to subsequently diminishing the risk of alcohol relapse through improved motivation to stop alcohol use, improved perceived social support and improved insight with regard to the somatic and psychological consequences of alcohol addiction. Third, alcohol use after LT might be restricted by heavy social pressure because LT is a rare and costly procedure. Considering this hypothesis, former alcohol addicts who crave alcohol after LT might cope by switching to a more socially accepted or less stigmatised substance or behaviour that could produce similar rewarding effects, thereby increasing the risk for a potential addiction to another reinforcer.

In that context, highly palatable food might be a reinforcerof choice because it is widely available and not yet socially stigmatised or associated with liver cirrhosis in the way that alcohol or illicit drugs are, and it has similar neurobiological properties to alcohol and other drugs [START_REF] Ifland | Refined food addiction: a classic substance use disorder[END_REF][START_REF] Blum | Neuro-Genetics of Reward Deficiency Syndrome (RDS) as the Root Cause of "Addiction Transfer": A New Phenomenon Common after Bariatric Surgery[END_REF][START_REF] Gearhardt | Neural correlates of food addiction[END_REF][START_REF] Deneen | Addictions -From pathophysiology to treatment[END_REF]. Both drug use and the intake of certain foods (e.g., sugar) have been associated with alterations to the brain's reward systems, including dopamineergic, opioidergic, cholinergic, serotoninergic, and GABAergic systems [START_REF] Corsica | Food addiction: true or false?[END_REF][START_REF] Corwin | Feeding and reward: perspectives from three rat models of binge eating[END_REF], an observation that, along with other neuro-imaging studies, has yielded to the concept of overlapping processes between food and drug cravings [START_REF] Blum | Neuro-Genetics of Reward Deficiency Syndrome (RDS) as the Root Cause of "Addiction Transfer": A New Phenomenon Common after Bariatric Surgery[END_REF]. Multiple lines of research have also demonstrated that food-addicted and drug-addicted individuals share common alterations in brain circuitry, including impaired dopaminergic pathways [START_REF] Belin | Parallel and interactive learning processes within the basal ganglia: relevance for the understanding of addiction[END_REF][START_REF] Smith | The Neurobiological Underpinnings of Obesity and Binge Eating: A Rationale for Adopting the Food Addiction Model[END_REF][START_REF] Volkow | Food and drug reward: overlapping circuits in human obesity and addiction[END_REF] such as those that regulate the neuronal systems associated not only with reward sensitivity and incentive motivation but also with conditioning (memory/learning), impulse control (behavioural inhibition), stress reactivity, and interoceptive awareness [START_REF] Volkow | Food and drug reward: overlapping circuits in human obesity and addiction[END_REF]. More specifically, both ventral striatal (predominantly associated with reward and motivation) and dorsal striatal (associated with habits or stimulus response learning) networks were found to be involved in both drug addiction and food addiction [START_REF] Volkow | Food and drug reward: overlapping circuits in human obesity and addiction[END_REF]. Recent studies have reported similar patterns of neural activation in addiction-like eating behaviours and substance dependence [START_REF] Gearhardt | Neural correlates of food addiction[END_REF][START_REF] Volkow | The addictive dimensionality of obesity[END_REF]. Studies have found elevated activation of the reward circuitry (the amygdala, anterior cingulate cortex, medial orbitofrontal cortex, dorsolateral prefrontal cortex and caudate) in response to food-related cues associated with the reduced activation of inhibitory regions (lateral orbitofrontal cortex) in response to food intake [START_REF] Gearhardt | Neural correlates of food addiction[END_REF]; these regions are the same neural substrates that are hypothesized to underlie drug addiction [START_REF] Gearhardt | Neural correlates of food addiction[END_REF][START_REF] Volkow | The addictive dimensionality of obesity[END_REF]. These results have been confirmed in animal studies, in which the consumption of sugar-rich foods or drinks is associated with the release of endorphins and dopamine within the nucleus accumbens, akin to some drugs of abuse such as alcohol [START_REF] Fortuna | Sweet preference, sugar addiction and the familial history of alcohol dependence: shared neural pathways and genes[END_REF]. Not only does exposure to highly palatable food trigger neurobiological responses that are, at least qualitatively, similar to those of addictive drugs but both preclinical and clinical research has demonstrated that sugary and salty foods both induce withdrawal [START_REF] Ifland | Refined food addiction: a classic substance use disorder[END_REF], which, at least for sugar, is associated with an imbalance in the acetylcholine and dopamine systems in the same manner as has been shown for opiate withdrawal [START_REF] Blum | Neuro-Genetics of Reward Deficiency Syndrome (RDS) as the Root Cause of "Addiction Transfer": A New Phenomenon Common after Bariatric Surgery[END_REF].

Our hypothesis of an increased risk of food addiction in former alcohol addicts also stems from the clinical observation that former drug addicts who maintain abstinence display an increased preference for sweetness and tend to develop sugar addiction [START_REF] Fortuna | Sweet preference, sugar addiction and the familial history of alcohol dependence: shared neural pathways and genes[END_REF][START_REF] Krahn | Sweet intake, sweet-liking, urges to eat, and weight change: relationship to alcohol dependence and abstinence[END_REF]. Former drug addicts also report significant weight gain during abstinence [START_REF] Krahn | Sweet intake, sweet-liking, urges to eat, and weight change: relationship to alcohol dependence and abstinence[END_REF][START_REF] Hodgkins | Weight gain during substance abuse treatment[END_REF]. Some other studies conducted in patients treated for a substance use disorder found that abstinence from alcohol use was associated with significant weight gain, increase in BMI [START_REF] Hodgkins | Adolescent drug addiction treatment and weight Gain[END_REF] and incidence of bulimia [START_REF] Walfish | Incidence of bulimia in substance misusing women in residential treatment[END_REF], suggesting higher food intake and potentially higher risk for food addiction after alcohol abstinence. In addition, when previous eating behaviour was restricted by bariatric surgery in patients who were obesewhich is highly comorbid with food addiction [START_REF] Meule | Food addiction and body-mass-index: A non-linear relationship[END_REF] alcohol use disorders increased [START_REF] King | Prevalence of alcohol use disorders before and after bariatric surgery[END_REF]. Because this latter study suggests that a transfer from preoperative food addiction to postoperative alcohol addiction is possible, we can also assume that a transfer is also possible from preoperative alcohol addiction to postoperative food addiction in a subpopulation of vulnerable individuals.

Altogether, these data suggest close inter-relationships between food and alcohol addiction in that a decrease in one addiction is frequently associated with an increase in the other. However, the mechanisms by which the switch from one to the other occurs and the potential risk factors that might account for the switch remain to be established. Future studies should also take into account potential confounding factors to determine that these two observations are causally related.

2) A significant part of the weight gain, obesity and metabolic syndrome after LT is attributable to the increased prevalence of food addiction after LT.

We also hypothesise that significant proportions of the weight gain, obesity and metabolic syndrome that follow LT could be causally explained by the increased prevalence of food addiction after LT. Although no longitudinal studies have demonstrated that food addiction directly causes weight gain and obesity, perhaps because the clinical definition of food addiction is very recent, cross-sectional studies have demonstrated that food addiction is highly prevalent among obese patients [START_REF] Gearhardt | An examination of food addiction in a racially diverse sample of obese patients with binge eating disorder in primary care settings[END_REF][START_REF] Meule | Food addiction and body-mass-index: A non-linear relationship[END_REF]. Similarly, loss of control over eatingwhich is a key symptom of food addictionpredicted subsequent excessive weight gain among children and adolescents [START_REF] Tanofsky-Kraff | Binge eating disorder: The next generation of research[END_REF]. There is also some evidence that loss of control over eating in childhood is associated with both the subsequent development of components of metabolic syndrome and later overweight and obesity [START_REF] Tanofsky-Kraff | Binge eating disorder: The next generation of research[END_REF][START_REF] Sonneville | Longitudinal associations between binge eating and overeating and adverse outcomes among adolescents and young adults: Does loss of control matter?[END_REF].

Because obesity is a complex, multifactorial disease [START_REF] Loos | Obesityis it a genetic disorder?[END_REF], other factors in addition to preoperative alcohol addiction could explain part of its increased prevalence following LT in former alcohol addicts. In liver-transplanted patients, intake of specific foods might also be facilitated by some of the medications that are frequently used after LT, such as steroids, which contribute to weight gain either through enhanced appetite (direct effect on food intake) or by stimulating the intake of sweet and high-fat foods (which could have an indirect effect on food intake through compulsive eating behaviour) [START_REF] Anastácio | Metabolic syndrome and its components after liver transplantation: incidence, prevalence, risk factors, and implications[END_REF]. Tobacco withdrawal is another factor that has often been associated with weight gain [START_REF] Farley | Interventions for preventing weight gain after smoking cessation[END_REF], but no studies have investigated this hypothesis in the specific population of liver-transplanted patients.

To explain the higher risk of obesity and metabolic syndrome after LT in former alcohol addicts, the impact of altering some metabolic functions consecutive to alcohol consumption could also be considered. Continuous or transient effects of alcohol on the autonomic nervous system and on the transport and metabolism of glucose might indeed be related to an increased concentration of glucose and triglycerides and high blood pressure, leading to higher risk of metabolic syndrome [START_REF] Kahl | Prevalence of the metabolic syndrome in men and women with alcohol dependence: results from a cross-sectional study during behavioural treatment in a controlled environment[END_REF]. Leptin, a hormone implicated in regulating appetite, body weight and energy homeostasis, was found to be elevated in alcohol-dependent patients, and LT-associated alcohol abstinence may alter the function of this peptide thereby influencing the development of metabolic syndrome [START_REF] Kahl | Prevalence of the metabolic syndrome in men and women with alcohol dependence: results from a cross-sectional study during behavioural treatment in a controlled environment[END_REF]. Although none of these factors alone can explain the higher risk of metabolic syndrome in this population, future studies should assess all of these possible risk factors for obesity in addition to those mentioned in our food addiction hypothesis.

3) The increased prevalence of food addiction or alcohol relapse after LT occurs in patients with specific psychobiological risk factors.

To explain the increased risk of these addictions, we will first discuss the risk factors that are typically shared among a wide range of addictions, including alcohol and food addiction, and then the factors that are more specific to a given addiction. Among these shared risk factors, some psychobiological factors might be associated with both food and alcohol addiction given that overlaps between binge eating and binge drinking have been demonstrated. These risk factors might include certain executive dysfunctions that are shared between binge eating and binge drinking, such as impaired cognitive flexibility or shifting attention [START_REF] Kelly | Executive functioning and behavioral impulsivity of young women who binge eat[END_REF][START_REF] Van Holst | Drug-related decrease in neuropsychological functions of abstinent drug users[END_REF] and some psychiatric comorbidities such as mood disorders, anxiety disorders [START_REF] Conway | Lifetime comorbidity of DSM-IV mood and anxiety disorders and specific drug use disorders: results from the National Epidemiologic Survey on Alcohol and Related Conditions[END_REF][START_REF] Gearhardt | An examination of the food addiction construct in obese patients with binge eating disorder[END_REF], and attention deficit hyperactivity disorder [START_REF] Cortese | Attention-deficit/hyperactivity disorder (ADHD) and binge eating[END_REF][START_REF] Wilens | The intersection of attention-deficit/hyperactivity disorder and substance abuse[END_REF]. Shared risk factors also include some stable personality features such as high neuroticism, low agreeableness, and low conscientiousness [START_REF] Ferriter | Binge eating and binge drinking: an integrative review[END_REF] (as well as high impulsivity [START_REF] Ferriter | Binge eating and binge drinking: an integrative review[END_REF][START_REF] Meule | Women with elevated food addiction symptoms show accelerated reactions, but no impaired inhibitory control, in response to pictures of high-calorie food-cues[END_REF]) that binge eating and binge drinking also share. We can thus assume that having such a personality and/or psychiatric profile would lead to a higher risk of post-transplant food/alcohol addiction. To our knowledge, no studies to date have assessed these dimensions in an integrative framework as potential risk factors for alcohol or food addiction in livertransplanted patients as well as in the overall population. Among the potential genetic risk factors, variants of the D2 dopamine receptor gene could be considered following the fact that Blum et al. hypothesised that the substitution of food addiction for other dependencies such as alcohol might be attributable to a specific reward deficiency syndrome (indeed, a core component of addiction) that has common genetic determinants such as variants of the D2 dopamine receptor gene, especially the DRD2 A1 allele [START_REF] Blum | Neuro-Genetics of Reward Deficiency Syndrome (RDS) as the Root Cause of "Addiction Transfer": A New Phenomenon Common after Bariatric Surgery[END_REF].

Although food addiction and alcohol addiction do share some common risk factors, different risk factors might also be implicated specifically in the development of either food or alcohol addiction. Not all patients who abstain from alcohol use will eventually develop food addiction, and we might also assume that some factors may play a protective role against one addiction or the other. As demonstrated by Volkow, although eating craved foods and drug addiction both activate the reward circuitry that involves dopaminergic pathways, these actions activate these pathways in different ways [START_REF] Volkow | Overlapping neuronal circuits in addiction and obesity: evidence of systems pathology[END_REF]. Food addiction affects the reward circuitry through endogenous opioids and cannabinoids, whereas drugs affect the same circuitry through direct effects on dopaminergic neurons or indirectly via other neurotransmitters [START_REF] Volkow | How can drug addiction help us understand obesity?[END_REF]. In addition, the neurobiological regulation of feeding is much more complex than the regulation of drug intake because food consumption is controlled not only by reward but also by multiple peripheral, endocrine and central factors beyond those that participate in reward [START_REF] Volkow | Overlapping neuronal circuits in addiction and obesity: evidence of systems pathology[END_REF]. In line with this hypothesis, current studies indicate more widespread abnormalities in obesity and eating disorders than in drug addictions.

One interesting hypothesis comes from animal research, which has demonstrated that orexins are involved in motivation for drug use as well as natural rewards [START_REF] Brown | Ascending orexinergic pathways and alcohol-seeking[END_REF][START_REF] Cason | Role of orexin/hypocretin in rewardseeking and addiction: implications for obesity[END_REF][START_REF] Chen | Glutamatergic input to the lateral hypothalamus stimulates ethanol intake: role of orexin and melanin-concentrating hormone[END_REF][START_REF] Sebastiano | Orexin and natural reward: feeding, maternal, and male sexual behavior[END_REF], providing an interesting theoretical framework whereby the underpinnings of compulsive alcohol use may facilitate the emergence of compulsive food intake in previously alcohol-dependent patients after LT. Indeed, administration of orexins has been shown to stimulate food consumption [START_REF] Sakurai | Orexins and orexin receptors: a family of hypothalamic neuropeptides and G Protein-coupled receptors that regulate feeding behavior[END_REF]. In self-administration studies, the orexin 1 receptor antagonist SB-334867 attenuated instrumental responses for high-fat pellets, sucrose pellets and ethanol but not cocaine, demonstrating that signalling at orexin receptors is necessary for mediating the reinforcing properties of specific rewards [START_REF] Cason | Role of orexin/hypocretin in rewardseeking and addiction: implications for obesity[END_REF]. If altering the orexinergic system and orexin-dependent plasticity processes that sub-serve alcohol intake may facilitate the development of aberrant food intake under abstinence [START_REF] Cason | Role of orexin/hypocretin in rewardseeking and addiction: implications for obesity[END_REF], further investigation is warranted to determine whether the function or dysfunction of the orexin system may contribute to the overeating associated with obesity in former alcoholics with LT. Similarly, alcohol-associated recruitment of the stress system in rats, including the activation of corticotropin releasing factor receptor 1 (CRF-R1) within the cortico-striatal circuitry may provide a long-lasting substrate to individual vulnerability to relapse to compulsive behaviours after stress [START_REF] Bossert | Neurobiology of relapse to heroin and cocaine seeking: an update and clinical implications[END_REF][START_REF] Shalev | Role of CRF and other neuropeptides in stress-induced reinstatement of drug seeking[END_REF].

As another example of a potential difference in terms of risk factors, alterations in the medial temporal and superior frontal regions that are functionally connected with the dorsal striatum could also be studied further given that they are associated with a greater vulnerability to obesity and eating disorders than to drug addictions [START_REF] Tomasi | Striatocortical pathway dysfunction in addiction and obesity: differences and similarities[END_REF]. Future studies should assess factors that could play either a protective or a vulnerability role in influencing relapse to either alcohol intake or food addiction.

4) In patients who display addictive behaviours post-LT, the level of insight with regard to the somatic and psychological consequences of alcohol use before LT predicts either the development of a food addiction or the resuming of their former alcohol addiction after LT

In addition to the risk factors that are either common to both food and alcohol addiction or specific to a given addiction, the dimension of insight should also be considered. In patients who do either relapse to alcohol use or develop food addiction after LT, we hypothesise here that an increased prevalence of alcohol addiction after LT occurs more frequently in a specific subpopulation that is characterised by little insight into the cause of the liver failure, namely, alcohol addiction (see Figure 1).

The concept of insight refers here to the ability to recognise one's own mental illness, with its causes and consequences [START_REF] Marková | Insight in psychiatry[END_REF], and refers to patients' awareness and understanding of their attitudes, feelings, behaviours, and symptoms. Insight encompasses two different dimensions: symptom insight, the patient's awareness of his symptoms, and attribution, which refers to how the patient causally attributes his illness [START_REF] Paillot | French translation and validation of the Scale to assess Unawareness of Mental Disorder (SUMD) in patients with schizophrenics[END_REF]. Because lower insight into alcohol addiction has been associated with poorer outcomes following treatment [START_REF] Lacoste | Insight and motivational interviewing effectiveness on relapse prevention in alcohol dependent patients[END_REF], we assume that in patients who develop either food or alcohol addiction after LT, those who attribute their liver disease to a cause other than alcohol (low attribution) are at higher risk of relapsing to alcohol addiction than are patients with non-impaired insight (Figure 1). More specifically, patients who receive transplantation for alcohol liver disease may be at higher risk than other patients of developing a post-transplant food addiction because they may, under the peer and moral pressure associated with LT, manage their addiction by displacing the object of their craving from alcohol to food, the latter being considered a non-dangerous source of reward relative to the former (i.e., addiction transfer). We suggest here that insight with regard to the somatic and psychological consequences of alcohol should be addressed specifically in addition to the other well-known post-LT risk factors for alcohol relapse that we have previously discussed.

HOW SHOULD WE TEST OUR HYPOTHESES?

The best approach to testing this model appears to be one that relies on a translational design. Indeed, in addition to the clinical usefulness of human models, animal models allow for a direct causal understanding of the neurobiological and pharmacological factors that cannot be assessed in humans for obvious ethical reasons. Additionally, preclinical studies allow for a complete longitudinal approach that gives insights into the contribution of premorbid risk factors to the switch from alcohol addiction to food addiction, as illustrated in the addiction field [START_REF] Belin | High impulsivity predicts the switch to compulsive cocaine-taking[END_REF][START_REF] Belin-Rauscent | Intrastriatal shifts mediate the transition from drug-seeking actions to habits[END_REF].

In human studies, we will first investigate, within a longitudinal study, both pre-and post-LT alcohol addiction and food addiction over a period of at least three years to screen for a sufficient number of patients who have developed an addiction after LT. To test the hypothesis that both decreases in alcohol use disorders and increases in food addiction are causally related, we will regularly (once a year) assess both disorders using appropriate and reliable measures: food addiction will be assessed using the Yale Food Addiction Scale, the gold standard for such assessments [START_REF] Brunault | Validation of the French version of the Yale Food Addiction Scale: an examination of its factor structure, reliability, and construct validity in a nonclinical sample[END_REF][START_REF] Gearhardt | Preliminary validation of the Yale Food Addiction Scale[END_REF]; alcohol addiction will be assessed using semi-structured interviews based on DSM-5 criteria. Because it is often difficult for patients to tell the transplantation team that they have relapsed [START_REF] Tome | Addictive behavior after solid organ transplantation: what do we know already and what do we need to know?[END_REF] and because medical record reviews alone greatly underestimate alcohol relapse rates [START_REF] Dew | Meta-analysis of risk for relapse to substance use after transplantation of the liver or other solid organs[END_REF], we will establish whether relapse indeed occurred using repeated measurements with complementary methods, including a patient self-report, a collateral report, and biological measures [START_REF] Dew | Meta-analysis of risk for relapse to substance use after transplantation of the liver or other solid organs[END_REF][START_REF] Mccallum | Liver transplantation for alcoholic liver disease: a systematic review of psychosocial selection criteria[END_REF]. We will also separate the study staff from the transplantation staff to keep notifications of alcohol or drug use confidential within the study [START_REF] Tome | Addictive behavior after solid organ transplantation: what do we know already and what do we need to know?[END_REF].

To demonstrate that the increased prevalence of obesity, weight gain and metabolic syndrome after LT could be causally related to food addiction, we will assess not only body mass index but also the prevalence of diabetes, dyslipidemia and hypertension. If this association is confirmed, we will then search for explanations that might account for this significant association. To demonstrate that this switch occurs in a vulnerable subpopulation, we will jointly investigate the neurobiological, psychiatric and psychological factors that are typically associated with both food addiction and alcohol addiction, at both the clinical and preclinical levels. These factors include personality dimensions (which we will measure using the Big Five Inventory, a brief and reliable measure of the five common personality dimensions) [START_REF] John | The Big Five Inventory--Versions 4a and 54[END_REF][START_REF] Plaisant | Factor structure and internal reliability of the French Big Five Inventory (BFI-Fr). Convergent and discriminant validation with the NEO-PI-R][END_REF], personality traits (such as impulsivity, which can be measured for example using the Barratt Impulsiveness Scale) [START_REF] Stanford | Fifty years of the Barratt Impulsiveness Scale: An update and review[END_REF] and psychiatric disorders (attention deficit hyperactivity disorder, major depression, anxiety disorders, personality disorders, which can be measured using clinical interviews based on DSM criteria) [START_REF]American Psychiatric Association. Diagnostic and Statistical Manual of mental disorders[END_REF].

However, in human studies, for obvious ethical reasons, it is difficult to disentangle LT's contribution to metabolic regulation from the processes that depend on the pharmacological treatments that are associated with LT, namely, immunosuppressive drugs such as cyclosporine. Indeed, the latter have been suggested to potentially contribute to post-LT obesity, MS and lower rates of alcohol relapse [START_REF] Pagadala | Posttransplant metabolic syndrome: an epidemic waiting to happen[END_REF][START_REF] Correia | Post-liver transplant obesity and diabetes[END_REF][START_REF] Beresford | Cyclosporine-A discourages ethanol intake in C57bl/6j mice: a preliminary study[END_REF]. We will therefore use preclinical models in rats with great heuristic value with regard to habitual and compulsive alcohol [START_REF] Vanhille | 20 -Differential effect of environmental enrichment on the acquisition of drug use and the transition to addiction[END_REF] and food seeking and taking [START_REF] Giuliano | Inhibition of opioid transmission at the μ-opioid receptor prevents both food seeking and binge-like eating[END_REF] to identify the neurobiological substrates of the effect of cyclosporine treatment on relapse to alcohol or food-seeking behaviour and the potential switch from alcohol. Thus, we propose to address these issues in a preclinical model of habitual and compulsive alcohol and food seeking. Animal studies will also be helpful in studying the polymorphisms in orexin genes that could contribute to alcohol relapse or food addiction after LT.

Finally, we will also implement longitudinal studies in rats that aim at identifying whether specific behavioural markers such as novelty seeking, impulsivity, decision making, sweetness preference, sign tracking, behavioural flexibility and anxiety [START_REF] Belin | High impulsivity predicts the switch to compulsive cocaine-taking[END_REF][START_REF] Vanhille | High Locomotor Reactivity to Novelty Is Associated with an Increased Propensity to Choose Saccharin Over Cocaine: New Insights into the Vulnerability to Addiction[END_REF][START_REF] Murray | Increased impulsivity retards the transition to dorsolateral striatal dopamine control of cocaine seeking[END_REF][START_REF] Dilleen | High anxiety is a predisposing endophenotype for loss of control over cocaine, but not heroin, self-administration in rats[END_REF][START_REF] Molander | High impulsivity predicting vulnerability to cocaine addiction in rats: some relationship with novelty preference but not novelty reactivity, anxiety or stress[END_REF] contribute to an increased propensity to switch from alcohol to compulsive food seeking with or without cyclosporine treatment following self-abstinence triggered by repeated adverse consequences related to alcohol seeking [START_REF] Marchant | Context-induced relapse to alcohol seeking after punishment in a rat model[END_REF]. This combination of a clinical and preclinical model will provide the scientific community with a new post-LT prognostic approach, thereby unlocking both a scientific and technical barrier: better insight into the psychological and biological dimensions that are associated with post-transplant food addiction, metabolic syndrome and obesity and a preclinical model of the switch from a previous addiction to food addiction. The model has clear medical and translational implications because it should provide new avenues for treating the primary post-LT impairments, namely obesity, metabolic syndrome, food addiction and alcohol addiction.

CONSEQUENCES OF THE HYPOTHESIS: DISCUSSION

Provided that it is confirmed, the present hypothesis may yield to a novel treatment strategy for helping some patients benefit from LT, as well as to new avenues for future research not only in liver-transplanted patients but also in patients who are followed up for alcohol addiction.

Implications for liver-transplanted patients include the fact that patients with a history of pre-transplant alcohol addiction should be systematically screened after LT for food addiction and followed up for subsequent risk of obesity and metabolic syndrome. These patients should also be screened for psychiatric disorders both pre and post LT. A subpopulation of vulnerable individuals who develop post-LT obesity or metabolic syndrome could also be referred to addiction units in order to screen for and treat food addiction. Interventions that target risk factors for both alcohol and food addiction in the pre-and post-transplant periods could also reduce the prevalence of these two disorders after LT. Such interventions are critical because they could not only improve survival, comorbidities and health-related quality of life after LT but also help to address the critical shortage of donor organs and increase public willingness to donate. Such an integrative assessment would enable the early recognition of food addiction and alcohol addiction and their risk factors, as well as early screening for psychiatric comorbidities that could potentially diminish quality of life if left untreated. These studies could help to build a simple and practical tool for clinicians that could include assessing the specific pre-and post-LT psychiatric and personality dimensions that are associated with post-LT food and alcohol addiction and poorer outcomes. This assessment is also a preliminary step before effective psychopharmacological and psychotherapeutic strategies that target these specific risk factors can be tested. Given that the drugs used to treat both of these disorders are primarily metabolised by the liver, studies that focus on the efficacy and side effects of psychopharmacological strategies should take into account the prominent concern about safety and overdosing in this population.

Finally, the dimension of insight should be systematically assessed after LT so that psychotherapeutic interventions that target insight itself or the psychopathological factors associated with it might be undertaken. If low insight is confirmed to be a risk factor for subsequent alcohol addiction, psychotherapeutic strategies such as motivational interviewing could be effective and should be tested in these populations. Such an approach finally aims to improve patients' survival, outcomes and quality of life following LT.

Our addiction transfer model could also be tested and generalised for patients in the overall population who are treated for alcohol addiction because current studies suggest that patients who stop alcohol use are at higher risk of developing food addiction, thereby leading to an increased risk of obesity and metabolic syndrome. Investigation of our model might also help discover neurobiological, psychiatric and psychological risk factors for both alcohol addiction and food addiction. These studies would help us improve our understanding of the links between alcohol addiction, food addiction and obesity and, ultimately, to developing more efficient therapeutic strategies for these patients. Future studies should also determine whether our addiction transfer model could also be extrapolated to other patients; it could, for example, explain why some patients who are treated for food addiction develop alcohol addiction after treatment (i.e., in a subpopulation of bariatric surgery patients), why patients who are treated for alcohol addiction may be at higher risk of switching, and this model could even explain addiction transfers between alcohol and other addictions (i.e., other drug and behavioural addictions). In patients who develop addiction after LT (top of the figure), we hypothesise that the level of insight with regard to the somatic and psychological consequences of alcohol might predict either alcohol relapse or the development of food addiction after LT. In this population and after LT, we hypothesise that patients with low insight (e.g., "my liver failure has nothing to do with my drinking behaviour") are at higher risk for relapsing to alcohol addiction, whereas patients with high insight (e.g., "I recognise that my drinking behaviour is responsible for my liver failure") are at higher risk for developing food addiction. Before the diagnosis of liver failure (LF) and LT, these patients might have experienced a different type of insight that was more difficult to assess because it was affected by LF-induced cognitive deficits. LF: Liver Failure.

LT: Liver Transplantation.

Figure 1 .

 1 Figure 1. In patients who either relapse to alcohol or develop food addiction after LT, low insight predicts an increased propensity to relapse to alcohol addiction, whereas high insight relapse predicts an increased propensity to develop food addiction.

  FIGURE LEGEND: This figure differentiates between (1) patients who relapse to alcohol or develop food addiction after LT (top of the figure) and (2) patients who do not (bottom of the figure). As illustrated in the left part of the figure, the first population is more likely to have a high risk of relapse (as assessed by the combination of psychobiological factors that we have previously discussed in the paper), whereas the second population is more likely to have a low risk of relapse (as assessed by the same combination of psychobiological factors).

Sources of support: this study was conducted without specific funding. DB is supported by the University of Cambridge and the Agence Nationale de la Recherche (ANR) grant ANR12 SAMA00201.

Conflicts of interest statement

DB is supported by the University of Cambridge and the Agence Nationale de la Recherche (ANR) grant ANR12 SAMA00201. PB has received financial support from Lundbeck to participate in two sessions of continuing medical education at the Lundbeck Institute (2012 and 2013) and to attend three medical meetings (2013 and 2014); from DNA Pharma in 2014 for participating in a clinical trial as an associated investigator; and from Astra Zeneca to attend two medical meetings (2014). NB received financial support as chairman for medical meetings from Astra Zeneca in 2010 and Lundbeck in 2013 and 2014 and as co-investigator in a study sponsored by DNA Pharma in 2012-2013.