Learning to Project in Multi-Objective Binary Linear Programming

Alvaro Sierra-Altamiranda; Hadi Charkhgard; Iman Dayarian; Ali Eshragh; Sorna Javadi

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arXiv · 1901.10868

Learning to Project in Multi-Objective Binary Linear Programming

Alvaro Sierra-Altamiranda·Hadi Charkhgard·Iman Dayarian·Ali Eshragh·Sorna Javadi

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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.

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Alvaro Sierra-Altamiranda, Hadi Charkhgard, Iman Dayarian, Ali Eshragh, Sorna Javadi. 2019-01-30. Learning to Project in Multi-Objective Binary Linear Programming. https://arxiv.org/abs/1901.10868

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