Improvement of genetic algorithms with decomposition procedures for large-scale multiobjective multidimensional 0-1 knapsack problems incorporating fuzzy goals

For a 0-1 knapsack problem, if it is small in size, a strict optimal solution can be obtained by the branch-and-bound method or dynamic programming. As the size of the problem grows larger, however, it rapidly becomes harder to find a strict optimal solution to it based on these methods because of the exponential increase of computational load. As a result, various approximate algorithms have been proposed to obtain approximate optimal solutions. For a large-scale 0-1 knapsack problem, the authors have proposed a genetic algorithm using triple string representation and decomposition procedures to make use of the special structure of the problem. However, in this genetic algorithm, in decoding procedures in which an individual S in the individual space is mapped to a solution x in the solution space, since only constraints are considered, improvements of search efficiency are being sought by taking consideration of objective functions. Therefore, in this paper we propose a new genetic algorithm with decomposition procedures using individual representation on the basis of an optimal solution to the corresponding continuous relaxation problem.