Standard Harmony Search Algorithm for Structural Design Optimization

Most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point. These algorithms, however, reveal a limited approach to complicated real-world optimization problems. If there is more than one local optimum in the problem, the result may depend on the selection of an initial point, and the obtained optimal solution may not necessarily be the global optimum. The computational drawbacks of numerical methods have forced researchers to rely on meta-heuristic algorithms based on simulations to solve optimization problems. This chapter describes a basic harmony search (HS) meta-heuristic algorithm-based approach for optimizing the size and configuration of structural systems with both discrete and continuous design variables. This basic HS algorithm is 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. Various truss examples, including large-scale trusses under multiple loading conditions, are introduced to demonstrate the effectiveness and robustness of the basic harmony search algorithm-based methods, as compared to existing structural optimization techniques. The results indicate that the HS technique is a powerful search and optimization method for solving structural engineering problems compared to conventional mathematical methods or genetic algorithm-based approaches.