MOTGA: A multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem

MOTGA: A multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem

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Article ID: iaor20084150
Country: United Kingdom
Volume: 34
Issue: 11
Start Page Number: 3458
End Page Number: 3470
Publication Date: Nov 2007
Journal: Computers and Operations Research
Authors: ,
Keywords: heuristics: genetic algorithms, programming: integer
Abstract:

This paper presents a new multiobjective genetic algorithm based on the Tchebycheff scalarizing function, which aims to generate a good approximation of the nondominated solution set of the multiobjective problem. The algorithm performs several stages, each one intended for searching potentially nondominated solutions in a different part of the Pareto front. Pre-defined weight vectors act as pivots to define the weighted-Tchebycheff scalarizing functions used in each stage. Therefore, each stage focuses the search on a specific region, leading to an iterative approximation of the entire nondominated set. This algorithm, called MOTGA (Multiple objective Tchebycheff based Genetic Algorithm) has been designed to the multiobjective multidimensional 0/1 knapsack problem, for which a dedicated routine to repair infeasible solutions was implemented. Computational results are presented and compared with the outcomes of other evolutionary algorithms.

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