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

This paper presents a newmultiobjective 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, calledMOTGA (Multiple objectiveTchebycheff basedGeneticAlgorithm) has been designed to themultiobjective multidimensional 0/1 knapsack problem, forwhich a dedicated routine to repair infeasible solutionswas implemented.Computational results are presented and compared with the outcomes of other evolutionary algorithms. 2006 Elsevier Ltd. All rights reserved.