Randomized heuristic repair for large-scale multidimensional knapsack problem

TL;DR

This paper introduces a randomized heuristic repair strategy for large-scale multidimensional knapsack problems, enhancing solution diversity and improving metaheuristic performance without sacrificing solution quality.

Contribution

It proposes a novel efficiency-based randomization method for heuristic repair, increasing solution variability in large-scale MKP metaheuristics.

Findings

Enhanced solution diversity in metaheuristics

Improved overall solution quality

Maintained efficiency with randomized repair

Abstract

The multidimensional knapsack problem (MKP) is an NP-hard combinatorial optimization problem whose solution is determining a subset of maximum total profit items that do not violate capacity constraints. Due to its hardness, large-scale MKP instances are usually a target for metaheuristics, a context in which effective feasibility maintenance strategies are crucial. In 1998, Chu and Beasley proposed an effective heuristic repair that is still relevant for recent metaheuristics. However, due to its deterministic nature, the diversity of solutions such heuristic provides is insufficient for long runs. As a result, the search for new solutions ceases after a while. This paper proposes an efficiency-based randomization strategy for the heuristic repair that increases the variability of the repaired solutions without deteriorating quality and improves the overall results.