The particle swarm optimization (PSO) method is an instance of a successful application of the philosophy of bounded rationality and decentralized decision making for solving global optimization problems. A number of advantages with respect to other evolutionary algorithms are attributed to PSO making it a prospective candidate for optimum structural design. The PSO-based algorithm is robust and well suited to handle nonlinear, nonconvex design spaces with discontinuities, exhibiting fast convergence characteristics. Furthermore, hybrid algorithms can exploit the advantages of the PSO and gradient methods. This article presents in detail the basic concepts and implementation of an enhanced PSO algorithm combined with a gradient-based quasi-Newton sequential quadratic programming (SQP) method for handling structural optimization problems. The proposed PSO is shown to explore the design space thoroughly and to detect the neighborhood of the global optimum. Then the mathematical optimizer, starting from the best estimate of the PSO and using gradient information, accelerates convergence toward the global optimum. A nonlinear weight update rule for PSO and a simple, yet effective, constraint handling technique for structural optimization are also proposed. The performance, the functionality, and the effect of different setting parameters are studied. The effectiveness of the approach is illustrated in some benchmark structural optimization problems. The numerical results confirm the ability of the proposed methodology to find better optimal solutions for structural optimization problems than other optimization algorithms.
Differential evolution (DE) is a population-based metaheuristic search algorithm that optimizes a problem by iteratively improving a candidate solution based on an evolutionary process. Such algorithms make few or no assumptions about the underlying optimization problem and can quickly explore very large design spaces. DE is arguably one of the most versatile and stable population-based search algorithms that exhibits robustness to multi-modal problems. In the field of structural engineering, most practical optimization problems are associated with one or several behavioral constraints. Constrained optimization problems are quite challenging to solve due to their complexity and high nonlinearity. In this work we examine the performance of several DE variants, namely the standard DE, the composite DE (CODE), the adaptive DE with optional external archive (JADE) and the self-adaptive DE (JDE and SADE), for handling constrained structural optimization problems associated with truss structures. The performance of each DE variant is evaluated by using five well-known benchmark structures in 2D and 3D. The evaluation is done on the basis of final optimum result and the rate of convergence. Valuable conclusions are obtained from the statistical analysis which can help a structural engineer in practice to choose the suitable algorithm for such kind of problems.
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