Learn to Optimize Large-Scale Uncapacitated Facility Location Problems With an Adaptive Problem Reduction Strategy

Many large-scale combinatorial optimization problems (LSCOPs) are challenging to solve due to their high dimensionalities and complex search spaces. To deal with tens of thousands of decision variables, problem reduction approaches have proven effective in reducing the original problem instance to a more manageable size, thereby decreasing the dimensionality of problem instances before optimization. However, since the dimensionality of transformed problem instances remains fixed during the optimization process, the effectiveness of existing methods is highly dependent on the selected features. In this paper, instead of only transforming the original problem instance once prior to the optimization, we propose a novel learning-based adaptive problem reduction (LAPR) framework to facilitate solving LSCOPs. Based on a learning model, the LAPR framework initially transforms the original problem instance into a low-dimensional one, and then dynamically increases the problem dimensionality when necessary during the optimization. To evaluate the effectiveness and efficiency of our framework, we have applied it to solve uncapacitated facility location problems (UFLP) using three effective features to construct a machine learning model learning from small instances. Based on this model, the LAPR framework first identifies a subset of the most promising facilities to construct an initial reduced problem instance through a novel optimal-k estimation strategy. Then, it incrementally incorporates potentially promising facilities into candidate solutions during the evolutionary process to improve the optimization performance. Extensive experimental studies on a series of large-scale UFLP benchmarks demonstrate that our proposed LAPR framework significantly enhances the performance of existing solution methods and consistently outperforms state-of-the-art problem reduction frameworks.