Abstract
We consider the Nelder-Mead (NM) simplex algorithm for optimization of discrete-event stochastic simulation models. We propose new modifications of NM to reduce computational time and to improve quality of the estimated optimal solutions. Our means include utilizing past information of already seen solutions, expanding search space to their neighborhood and using adaptive sample sizes. We compare performance of these extensions on six test functions with 3 levels of random variations. We find that using past information leads to reduction of computational efforts by up to 20%. The adaptive modifications need more resources than the non-adaptive counterparts for up to 70% but give better-quality solutions. We recommend the adaptive algorithms with using memory with or without neighborhood structure.
Highlights
An Optimization via Simulation (OvS) is the problem of finding possible set of input variables or decision variables that give maximum or minimum objective function values
We find that using past information leads to reduction of computational efforts by up to 20%
A set-based strategy generates a set of candidate solutions from a subset of the feasible region, e.g., the Nested Partitions Method (Shi and Olafsson, 2009) and the Nelder-Mead Simplex (Nelder and Mead, 1965)
Summary
An Optimization via Simulation (OvS) is the problem of finding possible set of input variables or decision variables that give maximum or minimum objective function values. We are interested in the OvS problems that have stochastic objective functions and continuous decision variables (Alon et al, 2005; Henderson and Nelson, 2006; Olafsson and Kim, 2002; Swisher et al, 2004) for OvS surveys. Most of them are based on the random search method that takes objective function values from a set of sample points and uses that information to select the points. A point-based strategy involves sampling points in a neighborhood of the current solution, e.g., the Stochastic Ruler (Alrefaei and Andradottir, 2005) and the Simulated Annealing (Press et al, 2007). A population-based strategy creates a collection of candidate solutions using some properties of the previously visited solutions; for example, the Genetic Algorithm (Holland, 2000) and the Evolutionary Strategies (Beyer and Schwefel, 2002)
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