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The 0/1 Multidimensional Knapsack Problem and Its Variants: A Survey of Practical Models and Heuristic Approaches

American Journal of Operations Research 2018年第5期8卷 395-439页

作者： Soukaina Laabadi Mohamed Naimi Hassan El Amri boujemaa achchab ENS-Hassan II University Laboratory of Mathematics and Applications Casablanca Morocco EST-Hassan I University Laboratory of Analysis Modeling Systems and Decision Support Berrechid Morocco

The 0/1 Multidimensional Knapsack Problem (0/1 MKP) is an interesting NP-hard combinatorial optimization problem that can model a number of challenging applications in logistics, finance, telecommunications and other fields. In the 0/1 MKP, a set of items is given, each with a size and value, which has to be placed into a knapsack that has a certain number of dimensions having each a limited capacity. The goal is to find a subset of items leading to the maximum total profit while respecting the capacity constraints. Even though the 0/1 MKP is well studied in the literature, we can just find a little number of recent review papers on this problem. Furthermore, the existing reviews focus particularly on some specific issues. This paper aims to give a general and comprehensive survey of the considered problem so that it can be useful for both researchers and practitioners. Indeed, we first describe the 0/1 MKP and its relevant variants. Then, we present the detailed models of some important real-world applications of this problem. Moreover, an important collection of recently published heuristics and metaheuristics is categorized and briefly reviewed. These approaches are then quantitatively compared through some indicative statistics. Finally, some synthetic remarks and research directions are highlighted in the conclusion.

关键词： 0/1 Multidimensional Knapsack Problem Survey Real-World Applications Heuristics Metaheuristics

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PARAMETER IDENTIFICATION BY OPTIMIZATION METHOD FOR A POLLUTION PROBLEM IN POROUS MEDIA

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Acta Mathematica Scientia 2018年第4期38卷 1345-1360页

作者： R. ABOULAICH B. achchab A. DAROUICHI LERMA Ecole Mohammadia d'Ingénieurs Université de Mohammed V-Agdal Avenue Ibn Sina B.P 765 Agdal Rabat Maroc Universite Hassan 1 Ecde Superieure de Technologic Berrechi and LAMSAD ESTB B.P 218 Berrechid Maroc Universite Cadi Ayyad Ecole Superieure de Technologie B.P 383 Essaouira Maroc

In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is given. We use the optimal control framework to establish both the existence and necessary condition of the minimizer for the cost func- tional. Furthermore, we prove the stability and the local uniqueness of the minimizer. Some numerical results will be presented and discussed.

关键词： inverse problem coefficient identification optimization method pollutionproblem porous media

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