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

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.

On the Influence of the Feature Computation Budget on Per-Instance Algorithm Selection for Black-Box Optimization

Per-instance algorithm selection (PIAS) takes advantage of complementarity between a set of algorithms by deciding which algorithm to run on a given instance. This decision is based on features of the instances, which, in the context of black-box optimization (BBO), require a part of the optimization budget to be computed. This raises two questions: (a) from which fraction of the budget spent on feature computation does PIAS become worth it for BBO, and (b) which fraction of the budget optimizes the tradeoff between feature accuracy and PIAS performance. To this end, we perform a broad study where PIAS with varying sampling budgets for feature computation is compared to the single best algorithm on a broad range of algorithm selection scenarios. These scenarios consist of two portfolio sizes, three problem sets, 4 dimensionalities, and 10 target budgets. We find that PIAS is viable for the majority of tested scenarios, even when as much as a quarter of the total budget is spent on feature computation. The tradeoff for the fraction of the budget spent on feature computation to maximize the benefit of PIAS is highly dependent on the specific AS scenario. Further, on average 20 percent of PIAS loss to the virtual best solver is explained by the budget spent on feature computation, highlighting the importance of properly accounting for the feature budget.