Abstract
Article history: Received March 4 2016 Received in Revised Format April 27 2016 Accepted May 14 2016 Available online May 16 2016 We introduce a new robust simulation optimization method in which the probability of occurrence of uncertain parameters is considered. It is assumed that the probability distributions are unknown but historical data are on hand and using φ-divergence functionality the uncertainty region for the uncertain probability vector is defined. We propose two approaches to formulate the robust counterpart problem for the objective function estimated by Kriging. The first method is a minimax problem and the second method is based on the chance constraint definition. To illustrate the methods and assess their performance, numerical experiments are conducted. Results show that the second method obtains better robust solutions with less simulation runs. © 2016 Growing Science Ltd. All rights reserved
Highlights
Simulation is a powerful and flexible tool to model problems in which either the closed-form of the objective function or the constraints is not in hand
We propose two approaches to formulate the robust counterpart problem for the objective function estimated by Kriging
Metamodel identifies and estimates the relationship between inputs and outputs of the simulation model in the form of an explicit deterministic function. Metamodels such as responsesurface methodology, Kriging, radial basis functions, splines or neural networks are viable alternatives to alleviate the magnitude of the computational cost
Summary
Simulation is a powerful and flexible tool to model problems in which either the closed-form of the objective function or the constraints is not in hand. One method is to optimize the objective function based on the worst-case probability distribution (for more details of this method, one can refer to Birge and Wets, (1986), Shapiro and Ahmed (2004) and Shapiro and Kleywegt (2002) Another method aims to construct an uncertainty region for the probability vectors estimated from historical data, in a way that bears a specific confidence level. Our method is different from other robust simulation optimization methods in: Using the probabilities of occurrence of uncertain parameters (random variables), that leads to tighter uncertainty sets and less conservative solutions, Employing a distribution-free structure in robust optimization, which does not need any assumptions about the probability distribution of the random variables, Proposing a method that can be applied to the constrained simulation optimization problems and consider robustness in both optimality and feasibility of a problem, Employing a new method for taking samples from the random and decision variables that leads to fewer simulation runs in metamodel construction, which is considered an advantage especially for expensive simulation models).
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