Learning to Solve and Optimize by Evolving Code

2026-05-29

AI Summary

This work addresses the longstanding challenge of solving large-scale combinatorial optimization problems, which traditionally rely on labor-intensive, expert-crafted solvers and heuristics. The authors propose a novel paradigm for automatically generating high-performance algorithms from minimal problem specifications: given only a formal description of the problem (the “what”) and a natural language explanation, their framework synthesizes effective solvers without requiring any explicit procedural guidance (the “how”). This is achieved through an integrated pipeline combining code evolution, formal verification, and natural language–guided evolutionary search. Evaluated on representative industrial problems in configuration and scheduling, the automatically generated algorithms consistently outperform state-of-the-art solvers, demonstrating both the efficacy and generality of the proposed approach.

Abstract

Combinatorial and optimization problems are fundamental to many industrial AI applications. Solving large-scale real-world instances of such problems typically requires careful problem formalization, specialized solvers, and expert-designed heuristics. Thus, experts need to specify not only what solutions are, but also how they are derived. By introducing the tool CHECKMATE, we show that algorithm generation via code evolution represents a paradigm shift by eliminating the need to formulate the how. CHECKMATE solely relies on the what. Specifically, a formal specification ensures solutions' correctness and enables systematic performance evaluation of the generated programs, while a natural language description guides the evolutionary process. The effectiveness of our method is demonstrated on selected problems from two industrial domains: configuration and scheduling. In all cases, the evolved algorithms consistently outperform state-of-the-art solvers. This underscores the potential of formal methods in guiding code evolution for automatically solving complex real-world problems.

Problem

• combinatorial optimization
• code evolution
• formal specification
• automated problem solving
• industrial AI

Innovation

• code evolution
• formal specification
• combinatorial optimization
• algorithm generation
• automated problem solving