An interactive fuzzy satisficing method for multiobjective multidimensional 0-1 knapsack problems through genetic algorithms

In this paper, an interactive fuzzy satisficing method for multiobjective multidimensional 0-1 knapsack problems is proposed by incorporating the desirable features of both the interactive fuzzy programming methods and genetic algorithms. By considering the vague nature of human judgements, fuzzy goals of the decision maker (DM) for objective functions are quantified by eliciting linear membership functions. If the DM specifies a reference membership level for each of the membership functions, the corresponding (local) Pareto optimal solution can be obtained by solving the formulated minimax problem through a genetic algorithm with double strings. For obtaining an optimal solution not dominated by the solutions before interaction, the algorithm is revised by introducing some new mechanism for forming an initial population. Illustrative numerical examples demonstrate both feasibility and effectiveness of the proposed method.