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

Abstract

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.