OPAL: Operator-Programmed Algorithms for Landscape-Aware Black-Box Optimization

TL;DR

OPAL introduces a landscape-aware, operator-programmed framework for black-box optimization that learns problem-specific search strategies using graph neural networks, outperforming traditional methods on benchmark tests.

Contribution

This work presents a novel framework that learns per-instance optimization algorithms using landscape features and graph neural networks, advancing beyond fixed or heuristic-based approaches.

Findings

OPAL's meta-trained policy is statistically competitive with state-of-the-art algorithms.

Significant improvements over simpler baselines on CEC 2017 test suite.

Ablation studies validate the design choices and efficiency of the approach.

Abstract

Black-box optimization often relies on evolutionary and swarm algorithms whose performance is highly problem dependent. We view an optimizer as a short program over a small vocabulary of search operators and learn this operator program separately for each problem instance. We instantiate this idea in Operator-Programmed Algorithms (OPAL), a landscape-aware framework for continuous black-box optimization that uses a small design budget with a standard differential evolution baseline to probe the landscape, builds a $k$-nearest neighbor graph over sampled points, and encodes this trajectory with a graph neural network. A meta-learner then maps the resulting representation to a phase-wise schedule of exploration, restart, and local search operators. On the CEC~2017 test suite, a single meta-trained OPAL policy is statistically competitive with state-of-the-art adaptive differential evolution variants and achieves significant improvements over simpler baselines under nonparametric tests. Ablation studies on CEC~2017 justify the choices for the design phase, the trajectory graph, and the operator-program representation, while the meta-components add only modest wall-clock overhead. Overall, the results indicate that operator-programmed, landscape-aware per-instance design is a practical way forward beyond ad hoc metaphor-based algorithms in black-box optimization.