Zong Woo Geem

A New Heuristic Optimization Algorithm: Harmony Search

Many optimization problems in various fields have been solved using diverse optimization al gorithms. Traditional optimization techniques such as linear programming (LP), non-linear programming (NLP), and dynamic program ming (DP) have had major roles in solving these problems. However, their drawbacks generate demand for other types of algorithms, such as heuristic optimization approaches (simulated annealing, tabu search, and evolutionary algo rithms). However, there are still some possibili ties of devising new heuristic algorithms based on analogies with natural or artificial phenom ena. A new heuristic algorithm, mimicking the improvisation of music players, has been devel oped and named Harmony Search (HS). The performance of the algorithm is illustrated with a traveling salesman problem (TSP), a specific academic optimization problem, and a least-cost pipe network design problem.

Optimal cost design of water distribution networks using harmony search

This study presents a cost minimization model for the design of water distribution networks. The model uses a recently developed harmony search optimization algorithm while satisfying all the design constraints. The harmony search algorithm mimics a jazz improvisation process in order to find better design solutions, in this case pipe diameters in a water distribution network. The model also interfaces with a popular hydraulic simulator, EPANET, to check the hydraulic constraints. If the design solution vector violates the hydraulic constraints, the amount of violation is considered in the cost function as a penalty. The model was applied to five water distribution networks, and obtained designs that were either the same or cost 0.28–10.26% less than those of competitive meta-heuristic algorithms, such as the genetic algorithm, simulated annealing and tabu search under similar or less favorable conditions. The results show that the harmony search-based model is suitable for water network design.

Harmony search optimization: Application to pipe network design

Abstract The Pipe network design problem is considered by choosing least-cost diameter pipes to satisfy flow demands and minimum head restrictions. Harmony and innovation are brought together as in music to devise a search pattern that can identify a large number of local optima in pipe network design. Improvization is brought in by varying the pitch rate parameter, and harmony is maintained by accumulating improving solutions. Because in pipe networks optimization by its very nature removes any redundancy, a minimum power loss criterion is introduced to enhance feasibility. The efficacy of the algorithm is demonstrated by solving a test nonlinear program and a pipe network problem from the literature to global optimum. Several near-optimal solutions are reported.

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.

Novel derivative of harmony search algorithm for discrete design variables

Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valued or continuous-valued functions rather than discrete-valued functions while there are many situations where design variables contain not continuous values but discrete values by nature. In order to consider these realistic design situations, this study proposes a novel derivative for discrete design variables based on a harmony search algorithm. Detailed analysis shows how this new stochastic derivative works in the bench-mark function and fluid-transport network design. Hopefully this new derivative, as a fundamental technology, will be utilized in various science and engineering problems.

Music-Inspired Harmony Search Algorithm

This first chapter intends to review and analyze the powerful new Harmony Search (HS) algorithm in the context of metaheuristic algorithms. We will first outline the fundamental steps of HS, and show how it works. We then try to identify the characteristics of metaheuristics and analyze why HS is a good metaheuristic algorithm. We then review briefly other popular metaheuristics such as particle swarm optimization so as to find their similarities and differences with HS. Finally, we will discuss the ways to improve and develop new variants of HS, and make suggestions for further research including open questions.

Harmony search for generalized orienteering problem: best touring in China

In order to overcome the drawbacks of mathematical optimization techniques, soft computing algorithms have been vigorously introduced during the past decade. However, there are still some possibilities of devising new algorithms based on analogies with natural phenomena. A nature-inspired algorithm, mimicking the improvisation process of music players, has been recently developed and named Harmony Search (HS). The algorithm has been successfully applied to various engineering optimization problems. In this paper, the HS was applied to a TSP-like NP-hard Generalized Orienteering Problem (GOP) which is to find the utmost route under the total distance limit while satisfying multiple goals. Example area of the GOP is eastern part of China. The results of HS showed that the algorithm could find good solutions when compared to those of artificial neural network.

Parameter-setting-free harmony search algorithm

Abstract Various phenomenon-mimicking algorithms, such as genetic algorithm, simulated annealing, tabu search, ant colony optimization, and particle swarm optimization, have their own algorithm parameters. These parameters need to be skillfully assigned in order to obtain good results. It is burdensome, especially to novice users, to assign these parameters. The same is true for the harmony search algorithm which was inspired by music performance. Thus, this study proposes a novel technique to eliminate tedious and experience-requiring parameter assigning efforts. The new parameter-setting-free (PSF) technique which this study suggests contains one additional matrix which contains an operation type (random selection, memory consideration, or pitch adjustment) for every variable in harmony memory. Three examples illustrate that the PSF technique can find good solutions robustly.

Optimal scheduling of multiple dam system using harmony search algorithm

Musicians behavior-inspired harmony search (HS) algorithm was first applied to the optimal operation scheduling of a multiple dam system. The HS model tackled a popular benchmark system with four dams. Results showed that the HS model found five different global optimal solutions with identical maximum benefit from hydropower generation and irrigation, while enhanced GA model (real-value coding, tournament selection, uniform crossover, and modified uniform mutation) found only near-optimal solutions under the same number of function evaluations. Furthermore, the HS model arrived at the global optima without performing any sensitivity analysis of algorithm parameters whereas the GA model required tedious sensitivity analysis.

Recent Advances in Harmony Search Algorithm

Nowadays, music-inspired phenomenon-mimicking harmony search algorithm is fast growing with many applications. One of key success factors of the algorithm is the employment of a novel stochastic derivative which can be used even for discrete variables. Instead of traditional calculus-based gradient, the algorithm utilizes musicians experience as a derivative in searching for an optimal solution. This can be a new paradigm and main reason in the successes of various applications. The goal of this book is to introduce major advances of the harmony search algorithm in recent years. The book contains 14 chapters with the following subjects: State-of-the-art in the harmony search algorithm structure; robotics (robot terrain and manipulator trajectory); visual tracking; web text data mining; power flow planning; fuzzy control system; hybridization (with Taguchi method or SQP method); groundwater management; irrigation ; logistics; timetabling; and bioinformatics (RNA structure prediction). This book collects the above-mentioned theory and applications, which are dispersed in various technical publications, so that readers can have a good grasp of current status of the harmony search algorithm and foster new breakthroughs in their fields using the algorithm.