Efficient Combinatorial Optimization via Heat Diffusion
This addresses efficiency limitations in combinatorial optimization for applications requiring global optimal solutions, though it appears incremental by applying a thermodynamics-inspired method to this domain.
The paper tackles the challenge of combinatorial optimization by using heat diffusion to enable information propagation from distant regions to the solver, resulting in superior performance across a range of challenging problems.
Combinatorial optimization problems are widespread but inherently challenging due to their discrete nature. The primary limitation of existing methods is that they can only access a small fraction of the solution space at each iteration, resulting in limited efficiency for searching the global optimal. To overcome this challenge, diverging from conventional efforts of expanding the solver's search scope, we focus on enabling information to actively propagate to the solver through heat diffusion. By transforming the target function while preserving its optima, heat diffusion facilitates information flow from distant regions to the solver, providing more efficient navigation. Utilizing heat diffusion, we propose a framework for solving general combinatorial optimization problems. The proposed methodology demonstrates superior performance across a range of the most challenging and widely encountered combinatorial optimizations. Echoing recent advancements in harnessing thermodynamics for generative artificial intelligence, our study further reveals its significant potential in advancing combinatorial optimization.