SCOPE: Synthetic Conditional Objectives for Policy Evolution in Black-Box Combinatorial Optimization

2026-07-29

AI Summary

This work addresses the challenge of inefficient search guidance in budget-constrained black-box combinatorial optimization, where existing methods often struggle to effectively navigate the solution space. The authors propose SCOPE, a novel framework that reframes objective function design as a mechanism to guide strategy exploration. By learning synthetic conditional objectives conditioned on search history, SCOPE dynamically evolves a diverse set of search strategies. It integrates inner and outer optimization loops and employs black-box evaluations to select high-quality solutions. This approach simultaneously preserves strategy diversity and significantly enhances search efficiency. Empirical results demonstrate that SCOPE outperforms state-of-the-art methods across multiple benchmark problems and exhibits strong generalization capabilities across diverse combinatorial structures.

Abstract

Black-box combinatorial optimization requires systematically identifying high-quality solutions under a limited evaluation budget, yet the unknown objective function provides little guidance for deciding where the search should explore next. We introduce SCOPE, a general framework for Synthetic Conditional Objectives for Policy Evolution in Black-Box Combinatorial Optimization. Rather than directly optimizing the inaccessible objective, SCOPE learns a set of synthetic objectives conditioned on the accumulated search history, where each objective is designed to expose a distinct and potentially useful preference over candidate solutions. These objectives are then used to evolve search policies that generate diverse candidates, whose true quality is subsequently assessed through black-box evaluations. The outer loop adaptively updates and selects synthetic objectives according to how effectively their induced policies discover promising regions. In contrast, the inner loop returns a portfolio of top-performing policies to reduce the risk of relying on a single surrogate preference. This formulation reframes objective design as a mechanism for guiding policy exploration, enabling the search process to exploit observed evidence while maintaining structured diversity across discrete solution spaces. Extensive experiments across multiple benchmark problems demonstrate that SCOPE consistently improves black-box search performance under limited evaluation budgets and generalizes well across diverse combinatorial structures.

Problem

• black-box optimization
• combinatorial optimization
• limited evaluation budget
• objective function uncertainty
• search guidance

Innovation

• synthetic objectives
• policy evolution
• black-box optimization
• combinatorial optimization
• adaptive objective design