A Budget-Adaptive Allocation Rule for Optimal Computing Budget Allocation

TL;DR

The paper tackles fixed-budget ranking and selection by addressing the gap where budget size influences allocation decisions. It derives a budget-adaptive OCBA rule by bounding PCS with the APCS Bonferroni lower bound and linearizing around the OCBA solution, producing closed-form allocations that depend on the total budget $T$ and problem scale. Two sequential algorithms, FAA and DAA, implement the budget-adaptive rule and are shown to be consistent and to converge to the OCBA allocations as budgets grow, with clear improvements over classical OCBA under small budgets. Empirical results across synthetic and a facility-location problem demonstrate strong performance gains and budget-aware behavior, validating the approach's practical value for budget-constrained simulation optimization. The work offers a principled, budget-sensitive alternative to asymptotic OCBA, with meaningful implications for allocating simulations in large-scale DES design problems.

Abstract

Simulation-based ranking and selection (R&S) is a popular technique for optimizing discrete-event systems (DESs). It evaluates the mean performance of system designs by simulation outputs and aims to identify the best system design from a set of alternatives by intelligently allocating a limited simulation budget. In R&S, the optimal computing budget allocation (OCBA) is an efficient budget allocation rule that asymptotically maximizes the probability of correct selection (PCS). In this paper, we first show the asymptotic OCBA rule can be recovered by considering a large-scale problem with a specific large budget. Considering a sufficiently large budget can greatly simplify computations, but it also causes the asymptotic OCBA rule ignoring the impact of budget. To address this, we then derive a budget-adaptive rule under the setting where budget is not large enough to simplify computations. The proposed budget-adaptive rule determines the ratio of total budget allocated to designs based on the budget size, and its budget-adaptive property highlights the significant impact of budget on allocation strategy. Based on the proposed budget-adaptive rule, two heuristic algorithms are developed. In the numerical experiments, the superior efficiency of our proposed allocation rule is shown.

Figures (9)

• Figure 1: (Color online) Comparison of PCS and APCS
• Figure 2: (Color online) Illustration of $G_i$
• Figure 3: (Color online) Illustration of Example 1
• Figure 4: (Color online) Illustration of Example 2
• Figure 5: (Color online) Illustration of Example 3

Theorems & Definitions (15)

• Lemma 1
• Lemma 2
• Remark 1
• Proposition 1
• Proposition 2
• Remark 2
• Lemma 3
• Lemma 4
• Remark 3
• Theorem 1