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

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  • Bijay Baran Pal
  • Somsubhra Gupta

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.

Suggested Citation

  • Bijay Baran Pal & Somsubhra Gupta, 2012. "A genetic algorithm-based fuzzy goal programming approach for solving fractional bilevel programming problems," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 14(4), pages 453-471.
    • Handle: RePEc:ids:ijores:v:14:y:2012:i:4:p:453-471
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    Cited by:

    1. Ritu Arora & Kavita Gupta, 2018. "Branch and bound algorithm for discrete multi- level linear fractional programming problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 5-21.

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