Bicriteria Knapsack Problem with GUB Structure by Hybrid Genetic Algorithm

Abstract

In this paper, a hybridized genetic algorithm-based method for solving bicriteria knapsack problem with GUB (generalized upper bounding) structure is introduced. In this hybridized genetic algorithm, we propose the new chromosome representation which represents the GUB structure simply and effectively at a time. The proposed chromosome representation can hold the GUB structure in spite of carrying out the genetic operations. Further, the number of gene necessary to represent is much smaller than the chromosome representation based on 0-1 variables, so the proposed chromosome representation is advantageous over computation efficiency and memory required especially for large scale real world problems. Also, by introducing the hybrid genetic algorithm that makes use of the peculiarity of the GUB structure, the proposed approach is efficient in finding solution. That is, in each GUB constraint, the decision variables are ranked based on efficiency index and integrated into the process which improves the solution by ranking in genetic algorithm. Therefore, by the proposed approach, the solution can search solution efficiently. Further, to demonstrate the effectiveness of the proposed approach, a large scale reliability optimization problem is introduced for a numerical example.