Learning to Project in Multi-Objective Binary Linear Programming

TL;DR

This paper introduces a machine learning approach to enhance the efficiency of solving multi-objective binary linear programs by selecting optimal projected spaces for the KSA algorithm, leading to significant time savings.

Contribution

It proposes a novel learning-based method to identify the best projection space for the KSA algorithm in multi-objective binary linear programming, improving computational performance.

Findings

Up to 12% reduction in solution time for test instances.

Effective feature selection heuristic to prevent overfitting.

Validated on 2000 tri-objective problem instances.

Abstract

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 best 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 12% in time can be achieved by the proposed learning method compared to a random selection of the projected space.