An Adaptive Hyperbox Algorithm for High-Dimensional Discrete Optimization via Simulation Problems

  • Authors:

  • Jie Xu;Barry L. Nelson;L. Jeff Hong

  • Affiliations:

  • Department of Systems Engineering and Operations Research, George Mason University, Fairfax, Virginia 22030;Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208;Department of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

  • Venue:
  • INFORMS Journal on Computing
  • Year:
  • 2013

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Abstract

We propose an adaptive hyperbox algorithm AHA, which is an instance of a locally convergent, random search algorithm for solving discrete optimization via simulation problems. Compared to the COMPASS algorithm, AHA is more efficient in high-dimensional problems. By analyzing models of the behavior of COMPASS and AHA, we show why COMPASS slows down significantly as dimension increases, whereas AHA is less affected. Both AHA and COMPASS can be used as the local search algorithm within the Industrial Strength COMPASS framework, which consists of a global search phase, a local search phase, and a final cleanup phase. We compare the performance of AHA to COMPASS within the framework of Industrial Strength COMPASS and as stand-alone algorithms. Numerical experiments demonstrate that AHA scales up well in high-dimensional problems and has similar performance to COMPASS in low-dimensional problems.