Using Fuzzy Goal Programming with Penalty Functions for Solving EEPGD Problem via Genetic Algorithm

Abstract

This chapter presents how the concept of penalty functions is incorporated within the framework of Fuzzy Goal Programming (FGP) for modelling and solving Economic-Environmental Power Generation and Dispatch (EEPGD) problems by employing genetic algorithms. In model formulation, first penalty functions to measuring membership values of defined fuzzy goals are presented. Then, minsum FGP method is used to obtain rank based solution in imprecise environment. In the process of solving the problem, a GA scheme is implemented at two different stages. At the first stage, optimal solutions of objective functions are determined for fuzzy representation of each of them. At the second stage, evaluation of achievement function to arrive at the highest membership value of fuzzily described objective goals is taken into account. The standard IEEE 6-Generator 30-Bus test system is considered to illustrate the approach. A comparison of model solution with the solutions of conventional approaches is also made to highlight the potential use of the approach.