Finding and Exploring Promising Search Space for the 0-1 Multidimensional Knapsack Problem

TL;DR

This paper introduces a hybrid evolutionary and exact algorithm for the 0-1 Multidimensional Knapsack Problem, effectively exploring promising search spaces to find superior solutions and bounds.

Contribution

It presents a novel hybrid approach combining evolutionary computation with exact methods to improve solution quality for the 0-1 MKP.

Findings

Outperforms state-of-the-art heuristics TPTEA and DQPSO

Finds better solutions for benchmark instances

Provides new lower bounds for large, hard instances

Abstract

The 0-1 Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem with many engineering applications. In this paper, we propose a novel algorithm combining evolutionary computation with the exact algorithm to solve the 0-1 MKP. It maintains a set of solutions and utilizes the information from the population to extract good partial assignments. To find high-quality solutions, an exact algorithm is applied to explore the promising search space specified by the good partial assignments. The new solutions are used to update the population. Thus, the good partial assignments evolve towards a better direction with the improvement of the population. Extensive experimentation with commonly used benchmark sets shows that our algorithm outperforms the state-of-the-art heuristic algorithms, TPTEA and DQPSO, as well as the commercial solver CPlex. It finds better solutions than the existing algorithms and provides new lower bounds for 10 large and hard instances.