Fuzzy programming for general multiobjective 0-1 programming problems through genetic algorithms with double strings

In this paper, for general multiobjective 0-1 programming problems involving positive and negative coefficients, considering fuzzy goals to represent the ambiguous nature of the decision maker's judgment for objective functions, we propose a fuzzy satisficing method through genetic algorithms which is an extension of genetic algorithms with double strings for multidimensional 0-1 knapsack problems. In the extended genetic algorithms, a new decoding algorithm for individuals represented by double strings which maps an each individual to a feasible solution is proposed through the incorporation of a reference solution and its renewal. The efficiency and effectiveness of the proposed method are investigated by several numerical examples.