Harmony Search Methods for Multi-modal and Constrained Optimization - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 38

Harmony Search Methods for Multi-modal and
Constrained Optimization
X.Z. Gao, X. Wang, and S.J. Ovaska
Department of Electrical Engineering, Helsinki University of Technology,
Otakaari 5 A, FI-02150 Espoo, Finland
{gao,xiaolei}@cc.hut.fi, [e-mail]
Abstract. The Harmony Search (HS) method is an emerging meta-heuristic optimization algo-
rithm. In this chapter, we propose two modified HS methods to handle the multi-modal and
constrained optimization problems. The first modified HS method employs a novel HS memory
management approach to handle the multi-modal problems. The second modified HS method util-
izes the Pareto-dominance technique, and it targets at the constrained problems. Several simula-
tion examples are used to demonstrate and verify the effectiveness of our new HS methods.
Keywords: Harmony Search, Multi-Modal Optimization, Constrained Optimization, Artificial
Fish Swarm, Pareto Dominance.
1 Introduction
Firstly proposed by Geem et al. in 2001 [1], the HS method is inspired by the underlying
principles of the musicians' improvisation of the harmony. During the recent years, it has
been successfully applied to the areas of function optimization [2], mechanical structure
design [3], pipe network optimization [4] and Sudoku puzzle [5]. However, empirical
study has shown that the original HS method has a limitation in dealing with the multi-
modal and constrained optimization problems. To overcome these drawbacks, we pro-
pose two modified HS methods in this chapter. The first modified HS method employs
an efficient diversity maintenance policy for the members of the HS memory. The second
modified HS method is based on the direct handling of the given constraints. Extensive
simulations have demonstrated that our two modified HS methods can outperform the
original HS method in attacking the multi-modal and constrained problems.
The rest of this chapter is organized as follows. We briefly introduce the essential
principles of the HS method in Section 2. The two new HS methods are presented and
discussed in Sections 3 and 4, respectively. Simulation examples of the multi-modal
and constrained optimization are demonstrated in Section 5. Finally, in Section 6, we
conclude our chapter with some remarks and conclusions.
2 Harmony Search Method
When musicians improvise a harmony, they usually try various possible combinations
of the music pitches stored in their memory. This kind of effective search for a perfect
harmony is analogous to the procedure of finding an optimal solution in engineering
problems. The HS method is inspired by the working principles of the harmony im-
provisation [1]. Figure 1 shows the flowchart of the basic HS method, in which there
are four principal steps involved.