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Multi-Objective Optimization

Description

Aucune description disponible pour cet axe de recherche.

Membres

Slim Bechikh Slim Bechikh
Moez Hammami Moez Hammami
Abir Chaabani Abir Chaabani
Imen Oueslati Imen Oueslati
Ahmed Yosreddin Samti Ahmed Yosreddin Samti
Ines Ben Jaafar Ines Ben Jaafar
Amel ZIDI Amel ZIDI
Maha Elarbi Maha Elarbi
Rihab Said Rihab Said

Publications

  • 2025
    Maha Elarbi, Slim Bechikh, Carlos Artemio Coello Coello

    Adaptive Normal-Boundary Intersection Directions for Evolutionary Many-Objective Optimization with Complex Pareto Fronts

    In International Conference on Evolutionary Multi-Criterion Optimization (pp. 132-147). Singapore: Springer Nature Singapore., 2025

    Résumé

    Decomposition-based Many-Objective Evolutionary Algorithms (MaOEAs) usually adopt a set of pre-defined distributed weight vectors to guide the solutions towards the Pareto optimal Front (PF). However, when solving Many-objective Optimization Problems (MaOPs) with complex PFs, the effectiveness of MaOEAs with a fixed set of weight vectors may deteriorate which will lead to an imbalance between convergence and diversity of the solution set. To address this issue, we propose here an Adaptive Normal-Boundary Intersection Directions Decomposition-based Evolutionary Algorithm (ANBID-DEA), which adaptively updates the Normal-Boundary Intersection (NBI) directions used in MP-DEA. In our work, we assist the selection mechanism by progressively adjusting the NBI directions according to the distribution of the population to uniformly cover all the parts of the complex PFs (i.e., those that are disconnected, strongly convex, degenerate, etc.). Our proposed ANBID-DEA is compared with respect to five state-of-the-art MaOEAs on a variety of unconstrained benchmark problems with up to 15 objectives. Our results indicate that ANBID-DEA has a competitive performance on most of the considered MaOPs.

  • Nabil Morri, Sameh Morri, Hadouaj, Lamjed Ben Said

    Fuzzy logic based multi-objective optimization of a multi-agent transit control system.

    Memetic Comp. 15, 71–87 (2023)., 2023

    Résumé

    This paper models a transit control system for the management of traffic perturbations of public transport. The transit system data is voluminous and highly dynamic. Moreover, the transit domain has a remarkable lack of intelligent systems to monitor and maintain better performance. Consequently, realizing an intelligent transit control system has become a consistent need. The modeling of the system addresses a problem of optimizing performance measures based on key performance indicators. Its objective is to find the optimal control action in disturbance cases. The solution consists in combining all performance measures in a single measure by using fuzzification without neglecting the space and time requirements of the traffic. To model and implement our system we used a multi-agent approach. The experiments performed were based on real network traffic data. The obtained results demonstrate the relevance of the proposed fuzzy approach in our optimization problem and show the advantage of the multi-agent system in the modeling of our control system. We prove that the proposed control system achieves better results than certain existing fuzzy approaches and is able to manage disturbances with a better performance than the existing solutions.

    Abir Chaabani, Mouna Karaja, Lamjed Ben Said

    An Efficient Non-Dominated Sorting Genetic Algorithm for Multi-objective Optimization

    International Conference on Control Decision and Information Technology Codit’9, Rome, 1565-1570, 2023

    Résumé

    Multi-Objective Evolutionary Algorithms (MOEAs) is actually one of the most attractive and active research field in computer science. Significant research has been conducted in handling complex multi-objective optimization problems within this research area. The Non-Dominated Sorting Genetic Algorithm (NSGA-II) has garnered significant attention in various domains, emphasizing its specific popularity. However, the complexity of this algorithm is found to be O(MN2) with M objectives and N solutions, which is considered computationally demanding. In this paper, we are proposing a new variant of NSGA-II termed (Efficient-NSGA-II) based on our recently proposed quick non-dominated sorting algorithm with quasi-linear average time complexity; thereby making the NSGA-II algorithm efficient from a computational cost viewpoint. Experiments demonstrate that the improved version of the algorithm is indeed much faster than the previous one. Moreover, comparisons results against other multi-objective algorithms on a variety of benchmark problems show the effectiveness and the efficiency of this multi-objective version

    Abir Chaabani, Mouna Karaja, Lamjed Ben Said

    An Efficient Non-dominated Sorting Genetic Algorithm For Multi-objective Optimization.

    9th International Conference on Control, Decision and Information Technologies, CoDIT 2023, Rome, Italy., 2023

    Résumé

    Multi-Objective Evolutionary Algorithms (MOEAs) is actually one of the most attractive and active research field in computer science. Significant research has been conducted in handling complex multi-objective optimization problems within this research area. The Non-Dominated Sorting Genetic Algorithm (NSGA-II) has garnered significant attention in various domains, emphasizing its specific popularity. However, the complexity of this algorithm is found to be O(MN2) with M objectives and N solutions, which is considered computationally demanding. In this paper, we are proposing a new variant of NSGA-II termed (Efficient-NSGA-II) based on our recently proposed quick non-dominated sorting algorithm with quasi-linear average time complexity; thereby making the NSGA-II algorithm efficient from a computational cost viewpoint. Experiments demonstrate that the improved version of the algorithm is indeed much faster than the previous one. Moreover, comparisons results against other multi-objective algorithms on a variety of benchmark problems show the effectiveness and the efficiency of this multi-objective version.

  • Mouna Karaja, Abir Chaabani, Ameni Azzouz, Lamjed Ben Said

    Efficient bilevel multi-objective approach for budget-constrained dynamic Bag-of-Tasks scheduling problem in heterogeneous multi-cloud environment

    Applied Intelligence, 1-29, 2022

    Résumé

    Bag-of-Tasks is a well-known model that processes big-data applications supporting embarrassingly parallel jobs with independent tasks. Scheduling Bag-of-Tasks in a dynamic multi-cloud environment is an NP-hard problem that has attracted a lot of attention in the last years. Such a problem can be modeled using a bi-level optimization framework due to its hierarchical scheme. Motivated by this issue, in this paper, an efficient bi-level multi-follower algorithm, based on hybrid metaheuristics, is proposed to solve the multi-objective budget-constrained dynamic Bag-of-Tasks scheduling problem in a heterogeneous multi-cloud environment. In our proposed model, the objective function differs depending on the scheduling level: The upper level aims to minimize the makespan of the whole Bag-of-Tasks under budget constraints; while each follower aims to minimize the makespan and the execution cost of tasks belonging to the Bag-of-Tasks. Since multiple conflicting objectives exist in the lower level, we propose an improved variant of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) called Efficient NSGA-II (E-NSGA-II), applying a recently proposed quick non-dominated sorting algorithm (QNDSA) with quasi-linear average time complexity. By performing experiments on proposed synthetic datasets, our algorithm demonstrates high performance in terms of makespan and execution cost while respecting budget constraints. Statistical analysis validates the outperformance of our proposal regarding the considering metrics.

    Malek Abbassi, Abir Chaabani, Lamjed Ben Said

    An efficient chemical reaction algorithm for multi-objective combinatorial bi-level optimization

    Engineering Optimization, 54(4), 665-686, 2022

    Résumé

    The Bi-Level Optimization Problem (BLOP) is defined as a mathematical program with two nested optimization tasks. Although many applications fit the bi-level framework, however, existing resolution methods were most proposed to solve single-objective bi-level problems. Regarding Multi-objective BLOPs (MBLOPs), there do not exist too many previous studies because of the difficulties associated with solving these complex problems. Additionally, a recently proposed metaheuristic, called Non-dominated sorting Chemical Reaction Optimization (NCRO), has been successfully applied to solve single-level Multi-Objective Problems (MOPs). NCRO applies a quick-non-dominated sorting technique that makes it one of the most powerful search algorithms in solving MOPs. Based on these observations, a new Bi-level Multi-objective CRO method, called BMCRO, is proposed in this article for solving MBLOPs. The main idea behind BMCRO is to come up with good solutions in an acceptable execution time within the bi-level framework. Experimental results on well-established benchmarks reveal the outperformance of the proposed algorithm against a bi-level variant of the Non-dominated Sorting Genetic Algorithm (NSGA-II) which is developed for this purpose.

    Malek Abbassi, Abir Chaabani, Lamjed Ben Said

    An elitist cooperative evolutionary bi-level multi-objective decomposition-based algorithm for sustainable supply chain

    International Journal of Production Research, 60(23), 7013-7032, 2022

    Résumé

    Many real-life applications are modelled using hierarchical decision-making in which: an upper-level optimisation task is constrained by a lower-level one. Such class of optimisation problems is referred in the literature as Bi-Level Optimisation Problems (BLOPs). Most of the proposed methods tackled the single-objective continuous case adhering to some regularity assumptions. This is at odds with real-world problems which involve mainly discrete variables and expensive objective function evaluations. Besides, the optimisation process becomes exorbitantly time-consuming, especially when optimising several objectives at each level. For this reason, the Multi-objective variant (MBLOP) remains relatively less explored and the number of methods tackling the combinatorial case is much reduced. Motivated by these observations, we propose in this work an elitist decomposition-based evolutionary algorithm to solve MBLOPs, called ECODBEMA. The basic idea of our proposal is to handle, decomposition, elitism and multithreading mechanisms to cope with the MBLOP's high complexity. ECODBEMA is applied to the production–distribution problem and to a sustainable end-of-life products disassembly case-study based on real-data of Aix-en-Provence French city. We compared the optimal solutions of an exact method using CPLEX solver with near-optimal solutions obtained by ECODBEMA. The statistical results show the significant outperformance of ECODBEMA against other multi-objective bi-level optimisation algorithms.

    Syrine Ben Abbes, Lilia Rejeb, Lassaad Baati

    Route planning for electric vehicles

    IET Intell. Transp. Syst. 16, 875–889 (2022). https://doi.org/10.1049/itr2.12182, 2022

    Résumé

    This work addresses the multi-objective route planning and charging problem for Battery Electric Vehicles (BEVs). The proposed solution is based on the NSGA-II algorithm to derive the Pareto-optimal set of eco-routes with the minimum travel and charging time, distance, energy consumption and charging costs while complying with the constraints related to the battery State of Charge (SoC) and the status of charging stations. Influencing factors, such as, vehicle and battery parameters, weather conditions, driver behaviour, road grade, Time Of Use (TOU) electricity cost, and Charging Stations (CS) status and type, are taken into account. The final results of the proposed method are compared with the well-established simulator SUMO.

    Maha Elarbi, Chaima Elwadi, Slim Bechikh, Zied Bahroun, Lamjed Ben Said

    An Evolutionary Multi-objective Approach for Coordinating Supplier–Producer Conflict in Lot Sizing

    International Journal of Information Technology & Decision Making, 21(02), 541-575, 2022

    Résumé

    Context. This paper deals with bilateral joint decision making in supply chains, and more specifically focuses on coordinating the decisions taken by the supplier and the producer in lot sizing. Research gap. Previous existing works in lot sizing have modeled the coordination task as a bi-level optimization problem. Unfortunately, the bi-level model causes a hierarchy between the two actors by making the leader imposing the decisions that suits his/her interests to the follower. This induces a significant conflict of interest between the two stakeholders because the leaders benefit is always greater than the follower’s one. Objective. The main goal of this work is to attenuate the conflict of interest issue between both actors by proposing a multi-objective model that alleviates the hierarchy and creates a win–win situation. Method. We propose an effective multi-objective lot sizing model, called Supplier-Producer Multi-Objective Lot Sizing (SP-MOLS); that alleviates the hierarchy between the actors’ objectives by assigning them the same importance degree and hence optimizing them simultaneously. The resolution of our SP-MOLS model using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), as an effective meta-heuristic search engine, provides a set of trade-off solutions, each expressing a compromise degree between the two actors: the supplier and the producer. Results. To validate our approach, we use five test problems each containing 100 instances with a planning horizon of 10 periods and we analyze the obtained trade-off solutions using the compromise degree and the gap between costs as main consensus metrics. The obtained results reveal that a small sacrifice in the leader’s benefit could produce a significant improvement in the follower’s one. For instance, a 10% increase of the producer’s cost may generate a 42% decrease in the supplier’s one. Reciprocally, a 0.4% increase of the supplier’s cost may generate a 49% decrease in the producer’s cost. Method algorithmic improvement. As solutions of interests for both stakeholders are usually located within the extreme regions of the Pareto front, we propose NSGA-II with Focus on Extreme Regions (NSGA-II-FER) as a new variant of NSGA-II that focuses the search in the extreme regions of the Pareto front thanks to a modified crowding measure that is adaptively managed during the evolution process. This variant has shown its ability to eliminate dominance-resistant solutions and thus to come up with better extreme regions. Based on the experimental results, NSGA-II-FER is shown to have the ability to provide the decision makers with more convergent and more diversified extreme non-dominated solutions, expressing better trade-off degrees between both actors’ costs. Managerial implications. The promising results obtained by our proposal encourage decision makers’ to adopt a multi-objective approach rather than a bi-level one. From our personal perspective, we recommend running the three models (the multi-objective model and the two bi-levels ones); then analyzing the solutions of all models in terms of compromise degrees and logistic costs. This would allow both actors to observe how the hierarchy incurred by the bi-level models increases conflicts, while the multi-objective one generates solutions with much improved consensus degrees. Such observations will convince the supply chain stakeholders to adopt our multi-objective approach, while keeping an eye on the bi-level models’ solutions and the consensus degrees. Finally, we also recommend focusing on the extreme regions of the Pareto front since they contain rich solutions in terms of consensus. Such solutions are more convincing in the negotiation process and thus could lead to better win–win situations.

  • Malek Abbassi, Abir Chaabani, Lamjed Ben Said, Nabil Absi

    An Approximation-based Chemical Reaction Algorithm for Combinatorial Multi-Objective Bi-level Optimization Problems

    IEEE Congress on Evolutionary Computation, 1627-1634, 2021

    Résumé

    Multi-objective Bi-Level Optimization Problem (MBLOP) is defined as a mathematical program where one multi-objective optimization task is constrained with another one. In this way, the evaluation of a single upper level solution necessitates the evaluation of the whole lower level problem. This fact brings new complexities to the bi-level framework, added to the conflicting objectives and their evaluation which need a large number of Function Evaluations (FEs). Despite the number of works dedicated to solve bi-level optimization problems, the number of methods applied to the multi-objective combinatorial case is much reduced. Motivated by these observations, we propose in this paper an approximation-based version of our recently proposed Bi-level Multi-objective Chemical Reaction Optimization (BMCRO), which we called BMCROII. The approximation technique is adopted here as a surrogate to the lower level leading then to generate efficiently the lower level optimality. Our choice is justified by two main arguments. First, BMCRO applies a Quick Non-Dominated Sorting Algorithm (Q-NDSA) with quasi-linear computational time complexity. Second, the number of FEs savings gained by the approximation technique can hugely improve the whole efficiency of the method. The proposed algorithm is applied to a new multi-objective formulation of the well-known Bi-level Multi Depot Vehicle Routing Problem (BMDVRP). The statistical analysis demonstrates the outperformance of our algorithm compared to prominent baseline algorithms available in literature. Indeed, a large number of savings are detected which confirms the merits of our proposal for solving such type of NP-hard problems.

  • Malek Abbassi, Abir Chaabani, Lamjed Ben Said, Nabil Absi

    Bi-level multi-objective combinatorial optimization using reference approximation of the lower-level reaction.

    International conference on Knowledge Based and Intelligent information and Engineering Systems (On Line), 2098-2107, 2020

    Résumé

    Bi-level optimization has gained a lot of interest during the last decade. This framework is suitable to model several real-life situations. Bi-level optimization problems refer to two related optimization tasks, each one is assigned to a decision level (i.e., upper and lower levels). In this way, the evaluation of an upper level solution requires the evaluation of the lower level. This hierarchical decision making necessitates the execution of a significant number of Function Evaluations (FEs). When dealing with a multi-objective optimization context, new complexities are added and imposed by the conflicting objectives and their evaluation techniques. In this paper, we aim to reduce the induced complexity using approximation techniques in order to obtain the lower level optimality. To this end, ideas from multi-objective optimization have been extracted, improved, and hybridized with evolutionary methods to build an efficient approach for Multi-objective Bi-Level Optimization Problems (MBLOPs). In this work, three techniques are suggested: (1) a complete lower level approximation Pareto front procedure, (2) a reference-based approximation selection procedure, and (3) a sub-set reference-based approximation selection one. The proposed variants are applied to a new multi-objective formulation of a well-known combinatorial problem integrating two systems in the supply chain management, namely, the Bi-level Multi Depot Vehicle Routing Problem (Bi-MDVRP). The statistical analysis demonstrates the efficiency of each algorithm according to a set of metrics. Indeed, a large number of savings are detected which confirms the efficiency of our proposals for solving combinatorial optimization problems.

    Malek Abbassi, Abir Chaabani, Lamjed Ben Said, Nabil Absi

    An improved bi-level multi-objective evolutionary algorithm for the production distribution planning system

    In International Conference on Modeling Decisions for Artificial Intelligence, MDAI’20,, 2020

    Résumé

    Bi-level Optimization Problem (BOP) presents a special class of challenging problems that contains two optimization tasks. This nested structure has been adopted extensively during recent years to solve many real-world applications. Besides, a number of solution methodologies are proposed in the literature to handle both single and multi-objective BOPs. Among the well-cited algorithms solving the multi-objective case, we find the Bi-Level Evolutionary Multi-objective Optimization algorithm (BLEMO). This method uses the elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) with the bi-level framework to solve Multi-objective Bi-level Optimization Problems (MBOPs). BLEMO has proved its efficiency and effectiveness in solving such kind of NP-hard problem over the last decade. To this end, we aim in this paper to investigate the performance of this method on a new proposed multi-objective variant of the Bi-level Multi Depot Vehicle Routing Problem (Bi-MDVRP) which is a well-known problem in combinatorial optimization. The proposed BLEMO adaptation is further improved combining jointly three techniques in order to accelerate the convergence rate of the whole algorithm. Experimental results on well-established benchmarks reveal a good performance of the proposed algorithm against the baseline version.

    Rihab Said, Slim Bechikh, Ali Louati, Abdulaziz Aldaej, Lamjed Ben Said

    Solving Combinatorial Multi-Objective Bi-Level Optimization Problems Using Multiple Populations and Migration Schemes

    IEEE Access, vol. 8, pp. 141674-141695, 2020

    Résumé

    Many decision making situations are characterized by a hierarchical structure where a lower-level (follower) optimization problem appears as a constraint of the upper-level (leader) one. Such kind of situations is usually modeled as a BLOP (Bi-Level Optimization Problem). The resolution of the latter usually has a heavy computational cost because the evaluation of a single upper-level solution requires finding its corresponding (near) optimal lower-level one. When several objectives are optimized in each level, the BLOP becomes a multi-objective task and more computationally costly as the optimum corresponds to a whole non-dominated solution set, called the PF (Pareto Front). Despite the considerable number of recent works in multi-objective evolutionary bi-level optimization, the number of methods that could be applied to the combinatorial (discrete) case is much reduced. Motivated by this observation, we propose in this paper an Indicator-Based version of our recently proposed Co-Evolutionary Migration-Based Algorithm (CEMBA), that we name IB-CEMBA, to solve combinatorial multi-objective BLOPs. The indicator-based search choice is justified by two arguments. On the one hand, it allows selecting the solution having the maximal marginal contribution in terms of the performance indicator from the lower-level PF. On the other hand, it encourages both convergence and diversity at the upper-level. The comparative experimental study reveals the outperformance of IB-CEMBA on a multi-objective bi-level production-distribution problem. From the effectiveness viewpoint, the upper-level hyper-volume values and inverted generational distance ones vary in the intervals [0.8500, 0.9710] and [0.0072, 0.2420], respectively. From the efficiency viewpoint, IB-CEMBA has a good reduction rate of the Number of Function Evaluations (NFEs), lying in the interval [30.13%, 54.09%]. To further show the versatility of our algorithm, we have developed a case study in machine learning, and more specifically we have addressed the bi-level multi-objective feature construction problem.

  • Malek Abbassi, Abir Chaabani, Lamjed Ben Said

    An investigation of a bi-level non-dominated sorting algorithm for production-distribution planning system

    In International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems IEA AIE’19, china, 819- 826, 2019

    Résumé

    Bi-Level Optimization Problems (BLOPs) belong to a class of challenging problems where one optimization problem acts as a constraint to another optimization level. These problems commonly appear in many real-life applications including: transportation, game-playing, chemical engineering, etc. Indeed, multi-objective BLOP is a natural extension of the single objective BLOP that bring more computational challenges related to the multi-objective hierarchical decision making. In this context, a well-known algorithm called NSGA-II was presented in the literature among the most cited Multi-Objective Evolutionary Algorithm (MOEA) in this research area. The most prominent features of NSGA-II are its simplicity, elitist approach and a non-parametric method for diversity. For this reason, in this work, we propose a bi-level version of NSGA-II, called Bi-NSGA-II, in an attempt to exploit NSGA-II features in tackling problems involving bi-level multiple conflicting criteria. The main motivation of this paper is to investigate the performance of the proposed variant on a bi-level production distribution problem in supply chain management formulated as a Multi-objective Bi-level MDVRP (M-Bi-MDVRP). The paper reveals three Bi-NSGA-II variants for solving the M-Bi-MDVRP basing on different variation operators (M-VMX, VMX, SBX and RBX). The experimental results showed the remarkable ability of our adopted algorithm for solving such NP-hard problem.

  • Maha Elarbi, Slim Bechikh, Abhishek Gupta Computational Intelligence Laboratory, School of Computer Engineering, Nanyang Technological University, Singapore, Lamjed Ben Said, Yew-Soon Ong

    A new decomposition-based NSGA-II for many-objective optimization

    IEEE transactions on systems, man, and cybernetics: systems, 48(7), 1191-1210, 2017

    Résumé

    Multi-objective evolutionary algorithms (MOEAs) have proven their effectiveness and efficiency in solving problems with two or three objectives. However, recent studies show that MOEAs face many difficulties when tackling problems involving a larger number of objectives as their behavior becomes similar to a random walk in the search space since most individuals are nondominated with respect to each other. Motivated by the interesting results of decomposition-based approaches and preference-based ones, we propose in this paper a new decomposition-based dominance relation to deal with many-objective optimization problems and a new diversity factor based on the penalty-based boundary intersection method. Our reference point-based dominance (RP-dominance), has the ability to create a strict partial order on the set of nondominated solutions using a set of well-distributed reference points. The RP-dominance is subsequently used to substitute the Pareto dominance in nondominated sorting genetic algorithm-II (NSGA-II). The augmented MOEA, labeled as RP-dominance-based NSGA-II, has been statistically demonstrated to provide competitive and oftentimes better results when compared against four recently proposed decomposition-based MOEAs on commonly-used benchmark problems involving up to 20 objectives. In addition, the efficacy of the algorithm on a realistic water management problem is showcased.

  • Slim Bechikh, Abir Chaabani, Lamjed Ben Said

    An efficient chemical reaction optimization algorithm for multi-objective optimization

    IEEE transactions on cybernetics, 45(10), 2051-2064, 2015

    Résumé

    Recently, a new metaheuristic called chemical reaction optimization was proposed. This search algorithm, inspired by chemical reactions launched during collisions, inherits several features from other metaheuristics such as simulated annealing and particle swarm optimization. This fact has made it, nowadays, one of the most powerful search algorithms in solving mono-objective optimization problems. In this paper, we propose a multiobjective variant of chemical reaction optimization, called nondominated sorting chemical reaction optimization, in an attempt to exploit chemical reaction optimization features in tackling problems involving multiple conflicting criteria. Since our approach is based on nondominated sorting, one of the main contributions of this paper is the proposal of a new quasi-linear average time complexity quick nondominated sorting algorithm; thereby making our multiobjective algorithm efficient from a computational cost viewpoint. The experimental comparisons against several other multiobjective algorithms on a variety of benchmark problems involving various difficulties show the effectiveness and the efficiency of this multiobjective version in providing a well-converged and well-diversified approximation of the Pareto front.

    Abir Chaabani, Slim Bechikh, Lamjed Ben Said, Radhia Azzouz

    An improved co-evolutionary decomposition-based algorithm for bi-level combinatorial optimization

    Conference on Genetic and Evolutionary Computation GECCO’15, Spain, 1363-1364,, 2015

    Résumé

    Several real world problems have two levels of optimization instead of a single one. These problems are said to be bi-level and are so computationally expensive to solve since the evaluation of each upper level solution requires finding an optimal solution at the lower level. Most existing works in this direction have focused on continuous problems. Motivated by this observation, we propose in this paper an improved version of our recently proposed algorithm CODBA (CO-evolutionary Decomposition-Based Algorithm), called CODBA-II, to tackle bi-level combinatorial problems. Differently to CODBA, CODBA-II incorporates decomposition, parallelism, and co-evolution within both levels: (1) the upper level and (2) the lower one, with the aim to further cope with the high computational cost of the over-all bi-level search process. The performance of CODBA-II is assessed on a set of instances of the MDVRP (Multi-Depot Vehicle Routing Problem) and is compared against three recently proposed bi-level algorithms. The statistical analysis of the obtained results shows the merits of CODBA-II from effectiveness viewpoint.

  • Nabil Belgasmi, Lamjed Ben Said, Khaled Ghédira

    Multiobjective Analysis of the Multi-Location Newsvendor and Transshipment Models

    International Journal of Information Systems and Supply Chain Management (IJISSCM), 6(4), 42-60., 2013

    Résumé

    Unlike the Newsvendor model, a system based on lateral transshipments allows the unsold inventories to be moved from locations with surplus inventory to fulfill more unmet demands at stocked out locations. Both models were thoroughly studied and researches were usually confined to cost minimization or profit maximization. In this paper, the authors proposed a more realistic multiobjective study of both multi-location Transshipment and Newsvendor inventory models. The aggregate cost, the fill rate, and the shared inventory quantity are formulated as conflicting objectives and solved using two reference multiobjective evolutionary algorithms (SPEA2 and NSGA-II). The proposed models take into account the presence of storage capacity constraints. The obtained Pareto fronts revealed interesting information. When transshipments are allowed, both low aggregate cost and high fill rate levels are ensured. The required shared inventory may have an important variability. The considered objective functions are conflicting and very sensitive to local storage capacities.

  • Nabil Belgasmi, Lamjed Ben Said, Khaled Ghedira

    Greedy local improvement of SPEA2 algorithm to solve the multiobjective capacitated transshipment problem

    In: Coello, C.A.C. (eds) Learning and Intelligent Optimization. LION 2011. Lecture Notes in Computer Science, vol 6683. Springer, Berlin, Heidelberg., 2011

    Résumé

    We consider a multi-location inventory system where inventory choices at each location are centrally coordinated through the use of lateral Transshipments. This cooperation between different locations of the same echelon level often leads to cost reduction and service level improvement. However, when some locations face embarrassing storage capacity limits, inventory sharing through transshipment may cause undesirable lead time. In this paper, we propose a more realistic multiobjective transshipment model which optimizes three conflicting objectives: (1) minimizing the aggregate cost, (2) maximizing the fill rate and (3) minimizing the transshipment lead time, in the presence of different storage capacity constraints. We improve the performance of the well-known evolutionary multiobjective algorithm SPEA2 by adequately applying a multiobjective quasi-gradient local search to some candidate solutions that have lower density estimation. The resulting hybrid evolutionary algorithm outperforms NSGA-II and the original SPEA2 in both spread and convergence. It is also shown that lateral transshipments constitute an efficient inventory repairing mechanism in a wide range of system configurations.

  • Nabil Belgasmi, Lamjed Ben Said, Khaled Ghedira

    Evolutionary optimization of the multiobjective transshipment problem with limited storage capacity

    In Winter Simulation Conference (pp. 2375-2383)., 2009

    Résumé

    In situations where some sellers have surplus stock while others, belonging to the same firm, are stocked out, it may be desirable to share the unsold units to fulfill more unmet demands and avoid holding costs. Such practice is named Transshipment. It ensures cost reduction and service level improvement. In this paper, we present a multiobjective study of a multi-location transshipment inventory which optimizes three objectives: (1) the aggregate cost, (2) the fill rate, and (3) the shared inventory quantity (SIQ), in the presence of different storage capacity constraints. Simulation is needed to evaluate the expected value of the problem stochastic objective functions. Two reference evolutionary multiobjective algorithms (SPEA2 and NSGA-II) are used to solve instances of the problem. Based on the obtained Pareto fronts, it is shown that both low aggregate cost and high fill rate levels could be ensured, while the shared inventory quantity is considerably increased.

  • Nabil Belgasmi, Lamjed Ben Said, Khaled Ghédira

    Evolutionary multiobjective optimization of the multi-location transshipment problem

    Operational Research International Journal 8, 167–183, 2008

    Résumé

    We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However, this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the strength Pareto evolutionary algorithm (SPEA2), to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives.