2021/07/16 by Charles F. Jekel, Jekel, Charles F., Raphael T. Haftka +1
Computer Science · Decision Sciences · #Advanced Multi-Objective Optimization Algorithms #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE) #Optimal Experimental Design Methods #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2107.08035
openalex publication_date 2021/07/16 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Some popular functions used to test global optimization algorithms have\nmultiple local optima, all with the same value, making them all global optima.\nIt is easy to make them more challenging by fortifying them via adding a\nlocalized bump at the location of one of the optima. In previous work the\nauthors illustrated this for the Branin-Hoo function and the popular\ndifferential evolution algorithm, showing that the fortified Branin-Hoo\nrequired an order of magnitude more function evaluations. This paper examines\nthe effect of fortifying the Branin-Hoo function on surrogate-based\noptimization, which usually proceeds by adaptive sampling. Two algorithms are\nconsidered. The EGO algorithm, which is based on a Gaussian process (GP) and an\nalgorithm based on radial basis functions (RBF). EGO is found to be more frugal\nin terms of the number of required function evaluations required to identify\nthe correct basin, but it is expensive to run on a desktop, limiting the number\nof times the runs could be repeated to establish sound statistics on the number\nof required function evaluations. The RBF algorithm was cheaper to run,\nproviding more sound statistics on performance. A four-dimensional version of\nthe Branin-Hoo function was introduced in order to assess the effect of\ndimensionality. It was found that the difference between the ordinary function\nand the fortified one was much more pronounced for the four-dimensional\nfunction compared to the two dimensional one.\n