Adaptive random search for continuous simulation optimization

Abstract

Abstract:We present, analyze, and compare three random search methods for solving stochastic optimization problems with uncountable feasible regions. Our adaptive search with resampling (ASR) approach is a framework for designing provably convergent algorithms that are adaptive and may consequently involve local search. The deterministic and stochastic shrinking ball (DSB and SSB) approaches are also convergent, but they are based on pure random search with the only difference being the estimator of the optimal solution [the DSB method was originally proposed and analyzed by Baumert and Smith]. The three methods use different techniques to reduce the effects of noise in the estimated objective function values. Our ASR method achieves this goal through resampling of already sampled points, whereas the DSB and SSB approaches address it by averaging observations in balls that shrink with time. We present conditions under which the three methods are convergent, both in probability and almost surely, and provide a limited computational study aimed at comparing the methods. Although further investigation is needed, our numerical results suggest that the ASR approach is promising, especially for difficult problems where the probability of identifying good solutions using pure random search is small. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 57: 583-604, 2010 Keywords: continuous stochastic optimization; local search; pure random search; global convergence in probability and almost surely; adaptive search with resampling; deterministic and stochastic shrinking ball methods

Simulation Optimization: A Review and Exploration in the New Era of Cloud Computing and Big Data

“…These algorithms are designed primarily for discretevalued simulation optimization problems. But some of them can also work with continuous decision variables (Andradóttir and Prudius, 2010). The first class of algorithms can be roughly classified as random search algorithms (Andradóttir, 1996(Andradóttir, , 2006Alrefaei and Andradóttir, 1999;Prudius and Andradóttir, 2012).…”

“…The number of simulation replications is required approach infinity as the iteration goes to infinity. More adaptive random search algorithms such as R-BEESE (Andradóttir and Prudius, 2009) and random search with adaptive resampling (Andradóttir and Prudius, 2010), introduce a local search component to improve the finite-time performance of random search. By imposing relatively mild conditions on the distribution used to sample new solutions, the random search type of algorithms can achieve global convergence with probability 1.…”

A Review of Random Search Methods

“…They prove that their method is globally convergent in probability. Andradóttir and Prudius [16] present the Adaptive Search with Resampling (ASR) method and prove that it is globally convergent w.p.1. Their method includes both sampling and resampling steps (similar to the approach of Yakowitz and Lugosi [82]), but the search is adaptive, only promising sampled points are "accepted" for further consideration (and hence additional observations are not collected at points that are not promising), and the estimated optimal solution is the best point sampled so far.…”

“…Baumert and Smith [19] discuss at what rate the distance should decrease in order for the method to converge in probability. Their work was continued by Andradóttir and Prudius [16] who provide further analysis of the (deterministic) shrinking ball method of Baumert and Smith [19], develop and analyze the stochastic shrinking ball method, and provide numerical results.…”

Optimization via simulation using Gaussian Process-based Search

“…Many globally convergent random search algorithms have been proposed to solve optimization-via-simulation (OvS) problems, e.g., stochastic ruler of Yan and Mukai (1992), nested partition of Shi andÓlafsson (2000), model reference method of Hu et al (2007Hu et al ( , 2008, and the shrinking ball method of Andradóttir and Prudius (2010). In every iteration of these algorithms, a sampling distribution needs to be constructed based on all the information collected through the last iteration and it is used to guide the search effort in the current iteration.…”