Evolutionary technique based goal programming approach to chance constrained interval valued bilevel programming problems

The real world multiobjective decision environment involves great complexity and uncertainity. Many decision making problems often need to be modelled as a class of bilevel programming problems with inexact coefficients and chance constraints. To deal with these problems, a genetic algorithm (GA) based goal programming (GP) procedure for solving interval valued bilevel programming (BLP) problems in a large hierarchical decision making and planning organization is proposed. In the model formulation of the problem the chance constraints are converted to their deterministic equivalent using the notion of mean and variance. Further, the individual best and least solutions of the objectives of the decision makers (DMs) located at different hierarchical levels are determined by using GA method. The target intervals for achievement of each of the objectives as well as the target interval of the decision vector controlled by the upper-level DM are defined. Then, using interval arithmetic technique the interval valued objectives and control vectors are transformed into the conventional form of goal by introducing under- and over-deviational variables to each of them. In the solution process, both the aspects of minsum and minmax GP formulations are adopted to minimize the lower bounds of the regret intervals for goal achievement within the specified interval from the optimistic point of view. The potential use of the approach is illustrated by a numerical example