Learning to project in a criterion space search algorithm: an application to multi-objective binary linear programming

In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ one of the most effective and recently developed criterion space search algorithms, the so-called KSA, during our study. This algorithm computes all nondominated points of a problem with p objectives by searching on a projected criterion space, i.e., a (p-1) -dimensional criterion apace. We present an effective and fast learning approach to identify on which projected space the KSA should work. We also present several generic features/variables that can be used in machine learning techniques for identifying the best projected space. Finally, we present an effective bi-objective optimization-based heuristic for selecting the subset of the features to overcome the issue of overfitting in learning. Through an extensive computational study over 2000 instances of tri-objective knapsack and assignment problems, we demonstrate that an improvement of up to 18