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Malek Abbassi

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Malek Abbassi
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  • 2022
    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.

  • 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.

  • 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.