Efficient Simulation Budget Allocation for Ranking the TopmDesigns

Abstract

We consider the problem of ranking the topmdesigns out ofkalternatives. Using the optimal computing budget allocation framework, we formulate this problem as that of maximizing the probability of correctly ranking the topmdesigns subject to the constraint of a fixed limited simulation budget. We derive the convergence rate of the false ranking probability based on the large deviation theory. The asymptotically optimal allocation rule is obtained by maximizing this convergence rate function. To implement the simulation budget allocation rule, we suggest a heuristic sequential algorithm. Numerical experiments are conducted to compare the effectiveness of the proposed simulation budget allocation rule. The numerical results indicate that the proposed asymptotically optimal allocation rule performs the best comparing with other allocation rules.

Simulation optimization using genetic algorithms with optimal computing budget allocation

“…To illustrate the effectiveness of the proposed computing budget allocation rule, we conduct several numerical experiments in this section to compare the proposed allocation rule with the asymptotically optimal allocation rule, 23 and equal allocation. In the numerical experiments, the performance of each design is assumed to follow normal distribution.…”

“…Asymptotically optimal allocation (AOA-m): this allocation rule is proposed in the literature. 23 The allocation rule α i * , i = 1 , ⋯ , k is such that…”

“…In the literature, an asymptotically optimal allocation (AOA) rule was proposed to determine the ranking of the best m solutions. 23 However, obtaining the AOA rule requires solving a system of nonlinear equations. Besides, the AOA rule itself is implemented by a heuristic sequential allocation algorithm.…”