Over the last decade, metaheuristic algorithms have emerged as a powerful paradigm for global optimization of multimodal functions formulated by nonlinear problems arising from various engineering subjects. However, numerical analyses of many complex engineering design problems may be performed using finite element method (FEM) or computational fluid dynamics (CFD), by which function evaluations of population-based algorithms are repetitively computed to seek a global optimum. It is noted that these simulations become computationally prohibitive for design optimization of complex structures. To efficiently and effectively address this class of problems, an adaptively integrated swarm intelligence-metamodelling (ASIM) technique enabling multi-level search and model management for the optimal solution is proposed in this paper. The developed technique comprises two steps: in the first step, a global-level exploration for near optimal solution is performed by adaptive swarm-intelligence algorithm, and in the second step, a local-level exploitation for the fine optimal solution is studied on adaptive metamodels, which are constructed by the multipoint approximation method (MAM). To demonstrate the superiority of the proposed technique over other methods, such as conventional MAM, particle swarm optimization, hybrid cuckoo search, and water cycle algorithm in terms of computational expense associated with solving complex optimization problems, one benchmark mathematical example and two real-world complex design problems are examined. In particular, the key factors responsible for the balance between exploration and exploitation are discussed as well.
In this paper, a novel trust-region based surrogate-assisted optimization method, called CBOILA (Constrained Black-box Optimization by Intrinsically Linear Approximation), has been proposed to reduce the number of black-box function evaluations and enhance the efficient performance for solving complex optimization problems. This developed optimization approach utilizes an assembly of intrinsically linear approximations to seek the optimum with incorporation of three strategies: (1) extended-box selection strategy (EBS), ( 2) global intelligence selection strategy (GIS) and ( 3) balanced trust-region strategy. EBS aims at reducing the number of function evaluations in current iteration by selecting points close to the given trust region boundary. Whilst, GIS is designed to improve the exploration performance by adaptively choosing points outside the trust region. The balanced trust-region strategy works with four indicators, which will be triggered by the quality of the approximation, the movement direction of the search, the location of the sub-optimum, and the condition of the termination, respectively. By modifying the move limit of each dimension accordingly, CBOILA is capable of attaining a balanced search between exploitation and exploration for the optimal solutions. To demonstrate the potentials of the proposed optimization method, three widely used benchmark problems have been examined and the results have also been compared with solutions by other metamodel-based algorithms in published works. Results show that the proposed method can efficiently and robustly solve constrained black-box optimization problems within an acceptable computational time.
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