Serdar Carbas1,* and Mehmet Polat Saka 2

1 Department of Engineering Sciences, Middle East Technical University, Ankara, Turkey * Corresponding Author. Tel: +90 312 210 2396; Fax: +90 312 210 4462; E-mail address: carbas@metu.edu.tr

2 Civil Engineering Department, University of Bahrain, Isa Town, Bahrain

ABSTRACT

Many optimization techniques have been proposed since the inception of engineering optimization in 1960s. Traditional mathematical modeling-based approaches are incompetent to solve the engineering optimization problems, as these problems have complex system that involves large number of design variables as well as equality or inequality constraints. In order to overcome the various difficulties encountered in obtaining the solution of these problems, new techniques called metaheuristic algorithms are suggested. These techniques are numerical optimization algorithms that are based on a natural phenomenon. In this study, a state-of-art improved harmony search method with a new adaptive error strategy is proposed to handle the design constraints. Number of numerical examples is presented to demonstrate the efficiency of the proposed algorithm in solving engineering optimization problems.

KEYWORDS: Improved Harmony Search Algorithm, Metaheuristic Techniques, Optimization Problems, Engineering Design

1. INTRODUCTION

The improvements in the performance of high-speed computing systems and the progress taken place in computational methods of optimization, the meta-heuristic techniques which are computationally intensive have become practical and used widely in obtaining the solution of engineering design optimization problems in recent years. These techniques simulate the paradigm of a biological, chemical or social system to develop a numerical optimizations method. Depending on what they simulate they are named accordingly such as evolutionary algorithms that mimic survival of the fittest, ant colony or particle swarm optimizations which are based on swarm intelligence or simulated annealing that imitates the cooling of molten metals through annealing [1-6]. It is generally accepted that stochastic approaches can handle engineering optimization problems more efficiently and easily than deterministic algorithms. In addition to their robustness with respect to the growth of problem size, other significant advantages of these methods are related to their relative simplicity and suitability for problems where the implementation of the optimization process is complicated by complexity and differentiability of design domain [7]. These heuristic algorithms are now becoming very popular in many disciplines of science and engineering [8-13].

In this study an improved harmony search optimum design algorithm is proposed for solving engineering design optimization problems. The classical harmony search method is improved by including some new strategies and then used to determine the solution of optimum design problem. The benchmark design examples taken from literature and the structural design examples are considered to demonstrate the effectiveness and robustness of the improvements suggested in the harmony search technique. The novelty of this study not only lies in the improvement suggested for the classical harmony search method, but also in the new error adaptive strategy suggested for constraint handling.

2. STATEMENT OF AN OPTIMIZATION PROBLEM

A general engineering optimization problem can be defined as follows [14];

Minimize;

f(X), X={X1, X2,…,XNd} (1)

which is subjected to

gi(X)≤0, i=1,2,…,p (2)

and

hj(X)=0, j=1,2,…,m...