یک الگوریتم فرا هیوریستیک جدید برای بهینه سازی مهندسی مستمر: جستجوی هارمونی تئوری و عمل

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. This paper describes a new harmony search (HS) meta-heuristic algorithm-based approach for engineering optimization problems with continuous design variables. This recently developed 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 engineering optimization problems, including mathematical function minimization and structural engineering optimization problems, are presented to demonstrate the effectiveness and robustness of the HS algorithm. The results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms.

Over the last four decades, a large number of algorithms have been developed to solve various engineering optimization problems. Most of these 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 numerical optimization algorithms provide a useful strategy to obtain the global optimum in simple and ideal models. Many real-world engineering optimization problems, however, are very complex in nature and quite difficult to solve using these algorithms. 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. Furthermore, the gradient search may become difficult and unstable when the objective function and constraints have multiple or sharp peaks. The computational drawbacks of existing numerical methods have forced researchers to rely on meta-heuristic algorithms based on simulations to solve engineering optimization problems. The common factor in meta-heuristic algorithms is that they combine rules and randomness to imitate natural phenomena. These phenomena include the biological evolutionary process (e.g., the evolutionary algorithm proposed by Fogel et al. [1], De Jong [2], and Koza [3] and the genetic algorithm (GA) proposed by Holland [4] and Goldberg [5]), animal behavior (e.g., tabu search proposed by Glover [6]), and the physical annealing process (e.g., simulated annealing proposed by Kirkpatrick et al. [7]). In the last decade, these meta-heuristic algorithms, especially GA-based methods have been studied by many researchers to solve various engineering optimization problems. The GA was originally proposed by Holland [4] and further developed by Goldberg [5] and by others. It is a global search algorithm that is based on concepts from natural genetics and the Darwinian survival-of-the-fittest code. Meta-heuristic algorithm-based engineering optimization methods, including GA-based methods, have occasionally overcome several deficiencies of conventional numerical methods. To solve difficult and complicated real-world optimization problems, however, new heuristic and more powerful algorithms based on analogies with natural or artificial phenomena must be explored. Recently, Geem et al. [8] developed a new harmony search (HS) meta-heuristic algorithm that was conceptualized using the musical process of searching for a perfect state of harmony. The harmony in music is analogous to the optimization solution vector, and the musician’s improvisations are analogous to local and global search schemes in optimization techniques. The HS algorithm does not require initial values for the decision variables. Furthermore, instead of a gradient search, the HS algorithm uses a stochastic random search that is based on the harmony memory considering rate and the pitch adjusting rate (defined in harmony search meta-heuristic algorithm section) so that derivative information is unnecessary. Compared to earlier meta-heuristic optimization algorithms, the HS algorithm imposes fewer mathematical requirements and can be easily adopted for various types of engineering optimization problems. In this study, we describe a brief overview of existing meta-heuristic algorithms and a new HS meta-heuristic algorithm-based approach for engineering optimization problems with continuous design variables. Various standard benchmark engineering optimization examples including function minimization problems and structural optimization problems from the literature are also presented to demonstrate the effectiveness and robustness of the HS meta-heuristic algorithm method.

The recently developed HS meta-heuristic optimization algorithm was conceptualized using the musical process of searching for a perfect state of harmony. Compared to gradient-based mathematical optimization algorithms, the HS algorithm imposes fewer mathematical requirements and does not require initial value settings of the decision variables. As the HS algorithm uses stochastic random searches, derivative information is also unnecessary. Furthermore, the HS algorithm generates a new vector, after considering all of the existing vectors based on the harmony memory considering rate (HMCR) and the pitch adjusting rate (PAR), whereas the GA only consider the two parent vectors. These features increase the flexibility of the HS algorithm and produce better solutions. This paper described the new HS meta-heuristic algorithm-based approach for engineering optimization problems with continuous design variables. Various engineering optimization problems, including (1) six unconstrained and (2) six constrained function minimization problems, and (3) five structural optimization problems (i.e., pressure vessel design, welded beam design, truss sizing optimization, truss configuration optimization, and hydrologic model parameter calibration) were presented to demonstrate the effectiveness and robustness of the new algorithm compared to other optimization methods, especially meta-heuristic algorithm-based optimization methods. These examples revealed that the new HS algorithm is a global search algorithm that can be easily applied to various engineering optimization problems. The results obtained using the HS algorithm may yield better solutions than those obtained using current algorithms, such as conventional mathematical optimization algorithms or GA-based approaches. Our study, therefore, suggests that the new HS algorithm is potentially a powerful search and optimization technique for solving complex engineering optimization problems.