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The multiobjective multidimensional knapsack problem: a survey and a new approach
Author(s) -
Lust Thibaut,
Teghem Jacques
Publication year - 2012
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.2011.00840.x
Subject(s) - knapsack problem , heuristics , extension (predicate logic) , mathematical optimization , metaheuristic , pareto principle , continuous knapsack problem , computer science , set (abstract data type) , combinatorial optimization , local search (optimization) , mathematics , programming language
The knapsack problem (KP) and its multidimensional version (MKP) are basic problems in combinatorial optimization. In this paper, we consider their multiobjective extension (MOKP and MOMKP), for which the aim is to obtain or approximate the set of efficient solutions. In the first step, we classify and briefly describe the existing works that are essentially based on the use of metaheuristics. In the second step, we propose the adaptation of the two‐phase Pareto local search (2PPLS) to the resolution of the MOMKP. With this aim, we use a very large scale neighborhood in the second phase of the method, that is the PLS. We compare our results with state‐of‐the‐art results and show that the results we obtained were never reached before by heuristics for biobjective instances. Finally, we consider the extension to three‐objective instances.