Simulation optimization using the cross-entropy method with optimal computing budget allocation

Abstract

We propose to improve the efficiency of simulation optimization by integrating the notion of optimal computing budget allocation into the Cross-Entropy (CE) method, which is a global optimization search approach that iteratively updates a parameterized distribution from which candidate solutions are generated. This article focuses on continuous optimization problems. In the stochastic simulation setting where replications are expensive but noise in the objective function estimate could mislead the search process, the allocation of simulation replications can make a significant difference in the performance of such global optimization search algorithms. A new allocation scheme is developed based on the notion of optimal computing budget allocation. The proposed approach improves the updating of the sampling distribution by carrying out this computing budget allocation in an efficient manner, by minimizing the expected mean-squared error of the CE weight function. Numerical experiments indicate that the computational efficiency of the CE method can be substantially improved if the ideas of computing budget allocation are applied.

Optimal Budget Allocation for Sample Average Approximation

“…The allocation may be between exploration of different designs and estimation of objective function values at specific designs as in global optimization [10,14], between estimation of different random variables nested by conditioning [21], or between estimation of different expected system performances in ranking and selection [9]. These studies typically define an optimal allocation as one that makes the estimator mean-squared error vanish at the fastest possible rate as the computing budget tends to infinity.…”

Performance improvement of distributed systems by autotuning of the configuration parameters

“…Some, such as Optimal computing budget allocation (OCBA) [10][11][12][13] and breadth & depth (B&D) [14] , can be used together to further reduce the test time. The vector ordinal optimization (VOO) [15] is also effective in dealing with multiple objective problems and other performance metrics.…”

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

“…As the algorithm iterates, the distribution model would eventually converge to a degenerate distribution with a point mass on a global optimal. Examples of this class of algorithms include cross entropy (Rubinstein, 1999;de Boer et al, 2004;Alon et al, 2004;He et al, 2010), estimation of distribution algorithms (EDAs) (Mühlenbein et al, 1996), model reference adaptive search (MRAS) and its stochastic extension SMRAS (Hu et al, 2008), and GASS (Zhou and Hu, 2014), an enhancement of MRAS using a gradient search procedure. The fourth class of algorithms can be roughly classified into metaheuristics that are "practically very useful" but lack a solid theoretical foundation to handle the noise in simulation estimates of objective values and consequently do not have convergence properties.…”

“…For example, another important extension of OCBA is to correctly select a subset of top solutions, either with a complete order or a partial order within this set Xiao et al, 2014b). This has important applications for some population-based optimization algorithms such as cross entropy (He et al, 2010), PSO and GA (Xiao and Lee, 2014) where a set of top solutions, instead of a single best solution, needs to be identified. …”