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What is Fuzzy Mathematical Programming

Chapter 15

Handbook of Research on Novel Soft Computing Intelligent Algorithms: Theory and Practical Applications

It has been applied firstly by Bellman and Zadeh in 1970s when they established the basic concepts of fuzzy goals, fuzzy constraints, and fuzzy decisions to the mathematical programming problem.

Published in Chapter:

Multi-Objective Generation Scheduling Using Genetic-Based Fuzzy Mathematical Programming Technique

Abdellah Derghal (Oum el Bouaghi University, Algeria) and Noureddine Goléa (Oum el Bouaghi University, Algeria)

Source Title: Handbook of Research on Novel Soft Computing Intelligent Algorithms: Theory and Practical Applications

DOI: 10.4018/978-1-4666-4450-2.ch015

Abstract

This chapter presents a solution for multi-objective Optimal Power Flow (OPF) problem via a genetic fuzzy formulation algorithm (GA-FMOPF). The OPF problem is formulated as a multiple objective problem subject to physical constraints. The objectives and constraints are modelled as fuzzy mathematical programming problems involving the minimization of the objective function with fuzzy parameters and uncertainties in set of constraints. So the method is capable of representing practical situations in power system operation where the limits on specific variables are soft and the small violations of these limits may be tolerable. Then, genetic algorithm is used in order to seek a feasible optimal solution to the environmental/economic dispatch problem. Illustrative examples are given to clarify the proposed method developed in this manuscript and the performance of this solution approach is evaluated by comparing its results with that of their existing methods.

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