Adaptive solution prediction for combinatorial optimization

Abstract

This paper aims to predict optimal solutions for combinatorial optimization problems (COPs) via machine learning (ML). To find high-quality solutions efficiently, existing work uses a ML prediction of the optimal solution to guide heuristic search, where the ML model is trained offline under the supervision of solved problem instances with known optimal solutions. To predict the optimal solution with sufficient accuracy, it is critical to provide a ML model with adequate features that can effectively characterize decision variables. However, acquiring such features is challenging due to the high complexity of COPs. This paper proposes a framework that can better characterize decision variables by harnessing feedback from a heuristic search over several iterative steps, enabling an offline-trained ML model to predict the optimal solution in an adaptive manner. We refer to this approach as adaptive solution prediction (ASP). Specifically, we employ a set of statistical measures as features, which can extract useful information from feasible solutions found by a heuristic search and inform the ML model as to which value a decision variable is likely to take in high-quality solutions. Our experiments on three NP-hard COPs show that ASP substantially improves the prediction quality of an offline-trained ML model and achieves competitive results compared to several heuristic methods in terms of solution quality. Furthermore, we demonstrate that ASP can be used as a heuristic-pricing method for column generation, to boost an exact branch-and-price algorithm for solving the graph coloring problem.