Classical jazz performers and marching bands play different musical instruments that require harmonization to produce pleasant melodies. The synchronization of symphony orchestras has been attracting the attention of optimization research scientists since 2001. Approaches to this problem search for a perfect state of harmony of the pitches of instruments played concurrently by musicians. Solving alternative mathematical and engineering optimization problems requires setting the appropriate initial parameters of the design variables . The harmony search algorithm has been used to solve specific optimization problems, such as the scheduling of electric power generation systems . However, the reliable design of a variety of engineering projects, such as complex bridges, gas turbines, gas and liquid pressure vessels, and welded beams, requires solving difficult mathematical optimization problems. How should the objective function of a reliable engineering design be minimized or maximized, subject to the constraints on the probable values of an independent variable?
Sarvari and Zamanifar perceptively present a harmony search algorithm with embedded statistical techniques for generating the optimal solutions to various mathematical and engineering optimization problems without imposing many constraints on their initial parameters. This algorithm cleverly initializes the harmony memory and algorithmic parameters for each optimization problem. Then, it locally searches the harmony memory to diminish the effect of the initial parameters of diverse optimization problems, and to boost the convergence rate and precision of the harmony search algorithm. The authors’ algorithm creates similar harmonies by selecting the appropriate harmony memory, considering rate, pitch adjusting rate, harmony memory size, and bandwidth vector parameters for the algorithm. The bandwidth is automatically established with an oscillating function, which eventually turns out to be preset, to speed up the convergence pace and to enhance the accuracy of the algorithm.
The authors utilized this novel approach to solve a variety of well-known benchmark functional minimization and engineering optimization problems, exhibiting the effectiveness and strength of the meta-heuristic harmony search algorithm. Their algorithm reliably generated solutions to: unconstrained functional minimization problems, such as the concave banana function, the gear train inertia function, and the 2D six-hump camel back function; constrained functional minimization problems, such as the design of a welded beam at a minimal fabrication cost to grasp a definite load; and reliability problems, such as the design of a complex bridge system or an over-speed gas turbine safety system with many reliability requirements on the components in the subsystems. The authors’ approach consistently generated results for functional minimization problems and reliability optimization problems that are comparable to the solutions available in the literature. Consequently, the algorithm is a generic pliable harmony search algorithm for solving a variety of emerging functional minimization problems and engineering optimization problems.