LLM4Solver: Large Language Model for Efficient Algorithm Design of Combinatorial Optimization Solver
Keywords: Combinatorial Optimization Solver, Large Language Models, Evolutionary Search
Abstract: The optimization of algorithms in exact combinatorial optimization (CO) solver plays a fundamental role in operations research.
However, due to the extensive requirements on domain knowledge and the large search space for algorithm design, the refinement on these algorithms remains highly challenging for both manual and learning-based paradigms.
To tackle this problem, we propose a novel machine learning framework---large language model for exact combinatorial optimization solver (LLM4Solver)---to $\textit{efficiently}$ design high-quality algorithms of the CO solvers.
The core idea is that, instead of searching in the high-dimensional and discrete symbolic space from scratch, we can utilize the prior knowledge learned from large language models to directly search in the space of programming languages.
Specifically, we first use a pre-trained LLM as the generator for high-quality algorithms. Then, to efficiently explore the discrete and non-gradient algorithm space, we employ a derivative-free evolutionary framework as the algorithm optimizer.
Experiments on extensive benchmarks show that the algorithms learned by LLM4Solver $\textit{significantly}$ outperform all the state-of-the-art (SOTA) human-designed and learning-based policies (on GPU) in terms of the solution quality, the solving efficiency, and the cross-benchmark generalization ability.
The appealing features of LLM4Solver include 1) the high training efficiency to outperform SOTA methods within ten iterations, and 2) the high cross-benchmark generalization ability on heterogeneous MIPLIB 2017.
LLM4Solver shows the encouraging potential to efficiently design algorithms for the next generation of modern CO solvers.
Primary Area: optimization
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Submission Number: 7319
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