Hookes-Jeeves-Based Variant of Memetic Algorithm

Hookes-Jeeves-Based Variant of Memetic Algorithm

Dipti Singh (Gautam Buddha University, India) and Kusum Deep (Department of Mathematics, Indian Institute of Technology, Roorkee, India)
DOI: 10.4018/978-1-5225-0788-8.ch018
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Abstract

Due to their wide applicability and easy implementation, Genetic algorithms (GAs) are preferred to solve many optimization problems over other techniques. When a local search (LS) has been included in Genetic algorithms, it is known as Memetic algorithms. In this chapter, a new variant of single-meme Memetic Algorithm is proposed to improve the efficiency of GA. Though GAs are efficient at finding the global optimum solution of nonlinear optimization problems but usually converge slow and sometimes arrive at premature convergence. On the other hand, LS algorithms are fast but are poor global searchers. To exploit the good qualities of both techniques, they are combined in a way that maximum benefits of both the approaches are reaped. It lets the population of individuals evolve using GA and then applies LS to get the optimal solution. To validate our claims, it is tested on five benchmark problems of dimension 10, 30 and 50 and a comparison between GA and MA has been made.
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Mathematical Form Of Optimization Problems

Different types of practical problems lead to different types of mathematical models for which optimal solutions have to be obtained. The general mathematical formulation of single objective optimization problem is:

  • Minimize (or maximize)

  • Subject to usually defined by

and
where
are functions defined on

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