A LP relaxation based matheuristic for multi-objective integer programming

TL;DR

This paper introduces a simple LP-based matheuristic for tri-objective binary integer programming that efficiently approximates the Pareto front, outperforming existing methods in quality and speed.

Contribution

It presents a novel LP relaxation-based matheuristic combining vector LP solutions with heuristic refinement for tri-objective integer programming.

Findings

Produces better Pareto front approximations

Uses significantly less computational time

Outperforms existing matheuristic methods

Abstract

Motivated by their success in the single-objective domain, we propose a very simple linear programming-based matheuristic for tri-objective binary integer programming. To tackle the problem, we obtain lower bound sets by means of the vector linear programming solver Bensolve. Then, simple heuristic approaches, such as rounding and path relinking, are applied to this lower bound set to obtain high-quality approximations of the optimal set of trade-off solutions. The proposed algorithm is compared to a recently suggested algorithm which is, to the best of our knowledge, the only existing matheuristic method for tri-objective integer programming. Computational experiments show that our method produces a better approximation of the true Pareto front using significantly less time than the benchmark method on standard benchmark instances for the three-objective knapsack problem.