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

2025-12-14

AI Summary

Traditional evolutionary algorithms suffer from poor generalization and weak problem adaptability in continuous black-box optimization. Method: This paper proposes an “operator programming” paradigm: first, constructing a landscape trajectory graph from a small number of differential evolution (DE) samples and encoding its local structural features via a graph neural network; then, employing a meta-learner to generate problem-specific, multi-phase short programs—comprising exploration, restart, and local search operators. Contribution/Results: This work is the first to explicitly model optimizers as learnable, landscape-aware operator sequences, moving beyond metaphor-driven heuristic design. On the CEC 2017 benchmark suite, the method achieves single-strategy generalization performance on par with state-of-the-art adaptive DE variants, significantly outperforming baseline methods, while incurring negligible computational overhead from the meta-components.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Optimizes black-box functions via landscape-aware operator programming
• Learns per-instance operator schedules using graph neural networks
• Competes with adaptive differential evolution on CEC 2017 benchmarks

Innovation

• Learns operator programs per problem instance
• Uses graph neural network to encode trajectory
• Maps representation to phase-wise operator schedule