Evolving Generalizable Parallel Algorithm Portfolios for Binary Optimization Problems via Domain-Agnostic Instance Generation

TL;DR

This work tackles the generalization challenge in automatic PAP construction for binary optimization by eliminating the need for domain-specific instance generators. It introduces DACE, which uses a domain-agnostic neural instance representation (NIR) to synthesize training instances and co-evolve a PAP with an instance population, leveraging BRKGA for configurations and a neural surrogate for instance generation. Across three real-world problem classes (CIMP, CAOP, CCP), DACE achieves superior generalization to unseen instances compared with domain-aware baselines like CEPS, often outperforming specialized PAPs. The results demonstrate that domain-agnostic instance generation paired with co-evolution yields robust PAPs with practical impact for parallel optimization in black-box, few-shot settings, while offering a pathway to richer data augmentation for learning-to-optimize frameworks.

Abstract

Generalization is the core objective when training optimizers from data. However, limited training instances often constrain the generalization capability of the trained optimizers. Co-evolutionary approaches address this challenge by simultaneously evolving a parallel algorithm portfolio (PAP) and an instance population to eventually obtain PAPs with good generalization. Yet, when applied to a specific problem class, these approaches have a major limitation. They require practitioners to provide instance generators specially tailored to the problem class, which is often non-trivial to design. This work proposes a general-purpose, off-the-shelf PAP construction approach, named domain-agnostic co-evolution of parameterized search (DACE), for binary optimization problems where decision variables take values of 0 or 1. The key novelty of DACE lies in its neural network-based domain-agnostic instance representation and generation mechanism that eliminates the need for domain-specific instance generators. The strong generality of DACE is validated across three real-world binary optimization problems: the complementary influence maximization problem (CIMP), the compiler arguments optimization problem (CAOP), and the contamination control problem (CCP). Given only a small set of training instances from these problem classes, DACE, without requiring domain knowledge, constructs PAPs with even better generalization performance than existing approaches on all three classes, despite their use of domain-specific instance generators.

Figures (7)

• Figure 1: A contrastive view of DACE and CEPS. While both follow the same co-evolutionary framework, CEPS requires domain-specific instance generators when applied to a problem class, whereas DACE employs neural network-based domain-agnostic instance representation and generation.
• Figure 2:
• Figure 3: An overview of DACE. It consists of an initialization phase followed by a co-evolution phase where the configuration population $P$ and the instance population $M$ evolve alternately.
• Figure 4: Visual comparison of the constructed PAPs using Boxplots of solution quality achieved on test instances in each problem class and dimension. The box contains the 25%-75% values. The line inside the box represents the median. The whiskers extend from the edges of the box to show the 2%-98% value. The "$\blacklozenge$" indicate outliers. A higher value is better. (a) CIMP. (b) CAOP. (c) CCP.
• Figure 5: Visualization of PAP's performance on the test set during DACE's initialization and co-evolution phases. The line plots show mean values with 95% confidence intervals shown as error bars. (a) CIMP. (b) CAOP. (c) CCP.