Learning to Solve and Optimize by Evolving Code

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.