Interactive fuzzy programming for decentralized two-level multidimensional 0-1 knapsack problems through genetic algorithms with decomposition procedures

In this paper, we focus on a decentralized two-level multidimensional 0-1 knapsack problem with a block angular structure involving a single decision maker (DM) at the upper level and multiple DMs at the lower level, and we apply interactive fuzzy programming to derive a satisfactory solution in consideration of the balance between the satisfactory level of the DM at the upper level and those of the DMs at the lower level. Since it is shown that all of the problems solved by the interactive fuzzy programming have block angular structures, we propose the introduction of a genetic algorithm with decomposition procedures for the purpose of utilizing the special structure of the problems.