Overview of Applications and Developments in the Harmony Search Algorithm - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 15

Overview of Applications and Developments in the
Harmony Search Algorithm

Gordon Ingram and Tonghua Zhang

Department of Chemical Engineering, Curtin University of Technology,
Perth, Australia
{g.ingram,t.zhang}@curtin.edu.au

Abstract. The Harmony Search (HS) algorithm appeared around the year 2000 and it now has a
substantial literature. The aim of this chapter is to inform the reader of the diversity of HS ap-
plications and the range of modified and hybrid HS methods that have been developed. The
chapter contains five sections. In the first, the different types of optimisation problem are de-
scribed. Section two provides an overview of the growth in the literature, a chronology of some
HS highlights and a breakdown of HS work by discipline. In the third section, HS applications in
nine discipline areas are reported. The fourth section classifies the types of modifications that have
been made to the original HS method and summarises the innovations in many of the modified
algorithms. Lastly, we take a step back and reflect on the current state of the HS literature.

Keywords: Harmony Search, Literature Review, Chronology, Industrial Application, Algorithm
Development.

1 Introduction

Since the initial development of the Harmony Search (HS) algorithm by Zong Woo
Geem in 2000 [1], HS methods have been applied to a diverse range of problems—
from structural design to solving Sudoku puzzles, from musical composition to medi-
cal imaging, from heat exchanger design to course timetabling. This chapter presents
an extensive, though not exhaustive, summary of HS applications and associated de-
velopments in the HS method itself.
After some preliminaries in Section 1.1 and 1.2, we treat the HS literature in three
ways to cater for readers with different interests. For those wishing to see the broad
view of HS, Section 2 provides an overview of HS activities, including the historical
growth in the HS literature, a chronology of selected HS 'highlights', and a summary
of its application areas. For readers interested in a particular field, such as water dis-
tribution or information technology, we summarise HS applications by discipline area
in Section 3. For researchers concerned with the methods of metaheuristic optimisa-
tion, Section 4 outlines the many modifications that have been proposed to the origi-
nal HS method. Section 5 briefly reflects on the body of HS work to date.

1.1 Mathematical Description of Optimisation Problems

HS is an optimisation method, and it is worthwhile clarifying at the outset the nature
of the problem being addressed. The unconstrained , single objective , multivariable
optimisation problem may be written as

min f ( x )

(1)

x