Improving exploration strategies in large dimensions and rate of convergence of global random search algorithms

Jack Noonan and Anatoly Zhigljavsky ()
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Jack Noonan: Cardiff University
Anatoly Zhigljavsky: Cardiff University

Journal of Global Optimization, 2024, vol. 88, issue 1, No 1, 26 pages

Abstract: Abstract We consider global optimization problems, where the feasible region $${\mathcal {X}}$$ X is a compact subset of $$\mathbb {R}^d$$ R d with $$d \ge 10$$ d ≥ 10 . For these problems, we demonstrate that the actual convergence of global random search algorithms is much slower than that given by the classical estimates, based on the asymptotic properties of random points, and that the usually recommended space exploration schemes are inefficient in the non-asymptotic regime. Moreover, we show that uniform sampling on entire $${\mathcal {X}}$$ X is much less efficient than uniform sampling on a suitable subset of $${\mathcal {X}}$$ X , and that the effect of replacement of random points by low-discrepancy sequences can be felt in small dimensions only.

Keywords: Global Optimization; Stochastic optimization; Global random search; Space-filling; Large dimension; Central limit theorem (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01308-6

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