Pareto suboptimal solutions to large-scale multiobjective multidimensional knapsack problems with assessments of Pareto suboptimality gaps

TL;DR

This paper introduces a method to estimate the gap to Pareto optimality in large-scale multiobjective multidimensional knapsack problems, providing valuable information when solvers are limited by time or memory constraints.

Contribution

The authors propose a novel approach to assess Pareto suboptimality gaps using commercial MILP solvers for large-scale multiobjective knapsack problems.

Findings

Effective estimation of Pareto suboptimality gaps demonstrated

Method applied successfully to problems from Beasley OR Library

Provides insights into solution quality under solver limitations

Abstract

When solving large-scale multiobjective optimization problems, solvers can get stuck with the memory or time limit. In such cases, one is left with no information how far is the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information when solving multiobjective multidimensional knapsack problems by a commercial mixed-integer linear solver. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from singleobjective multidimensional knapsack problems from the Beasley OR Library.