A genetic algorithm based goal programming approach to Interval-valued multilevel programming problems

This article presents a goal programming (GP) procedure for solving Interval-valued multilevel programming (IVMLP) problems by using genetic algorithm (GA) in a large hierarchical decision making and planning organization. In the proposed approach, first the individual best and least solutions of the objectives of the decision makers (DMs) located at different hierarchical decision levels are determined by using an GA method. Then, the target interval for achievement of each of the objectives as well as the target interval of the decision vector controlled by the upper-level DM is defined in the inexact decision making environment. In the model formulation of the problem, first the interval valued objectives and control vectors are transformed into the conventional form of goal by using interval arithmetic technique and then introducing under- and over-deviational variables to each of them. In the solution process, both the aspects of minsum and minmax GP formulation are adopted to minimize the lower bounds of the regret intervals for goal achievement within the specified interval from the optimistic point of view and thereby distribution of proper decision powers to the DMs of the hierarchical levels. The potential use of the approach is illustrated by a numerical example.