Mixed 0−1 Goal Programming Approach to Interval-Valued Bilevel Programming Problems Via Bio-Inspired Computational Algorithm

Abstract

This paper presents how the mixed 0-1 programming in the framework of goal programming (GP) can be used to solve interval-valued fractional bilevel programming (IVFBLP) problems by employing genetic algorithm (GA) in a hierarchical decision making system. In the model formulation of the problem, a goal achievement function for minimizing the lower-bounds of the necessary regret intervals defined for the target intervals of achieving the goals and thereby arriving at a compromise decision is constructed by using both the aspects of 'minsum ' and 'minmax' approaches in GP. In the decision process, an GA scheme is employed for execution of the problems at the two stages, target interval specification and optimal decision determination, for distribution of decision powers to the decision makers (DMs) in the order of hierarchy. A numerical example is provided to illustrate the potential use of the approach.