A matheuristic for tri-objective binary integer programming

TL;DR

This paper introduces a new linear programming-based matheuristic for tri-objective binary integer programming that improves the approximation of Pareto fronts compared to existing methods, leveraging vector linear programming and feasibility pump techniques.

Contribution

It presents a novel matheuristic combining vector linear programming, feasibility pump, and path relinking for tri-objective binary integer programming, outperforming existing algorithms.

Findings

Better approximation of Pareto front than benchmark method

Effective use of vector linear programming for bounds

Potential as a primal heuristic in branch-and-bound

Abstract

Many real-world optimisation problems involve multiple objectives. When considered concurrently, they give rise to a set of optimal trade-off solutions, also known as efficient solutions. These solutions have the property that neither objective can be improved without deteriorating another objective. Motivated by the success of matheuristics in the single-objective domain, we propose a linear programming-based matheuristic for tri-objective binary integer programming. To achieve a high-quality approximation of the optimal set of trade-off solutions, a lower bound set is first obtained using the vector linear programming solver Bensolve. Then, feasibility pump-based ideas in combination with path relinking are applied in novel ways so as to obtain a high quality upper bound set. Our matheuristic is compared to a recently-suggested algorithm that is, to the best of our knowledge, the only existing matheuristic method for tri-objective integer programming. In an extensive computational study, we show that our method generates a better approximation of the true Pareto front than the benchmark method on a large set of tri-objective benchmark instances. Since the developed approach starts from a potentially fractional lower bound set, it may also be used as a primal heuristic in the context of linear relaxation-based multi-objective branch-and-bound algorithms.