A genetic algorithm‐based fuzzy goal programming approach for solving fractional bilevel programming problems

This paper presents a genetic algorithm (GA) based fuzzy goal programming procedure for modelling and solving bilevel programming problems having fractional objectives in a hierarchical decision system. In the proposed approach, the concept of tolerance membership functions in fuzzy sets for measuring the degree of satisfactions of the decision‐makers (DMs) regarding achievements of fuzzily described objective goals as well as the degree of optimality of the decision vector controlled by the upper‐level DM are considered in the decision‐making context. The proposed approach leads to achieve the highest membership value (unity) of each of the defined fuzzy goals to the extent possible in the decision‐making situation. In the GA search process, the fitter codon selection scheme, two‐point crossover and random mutation are adopted to reach a satisfactory solution in the decision‐making environment. To illustrate the potential use of the approach, a numerical example is solved.