A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem

TL;DR

This paper introduces a new multi-objective genetic algorithm with helper objectives that outperforms traditional algorithms in solving the 0-1 knapsack problem, achieving better solutions efficiently.

Contribution

It proposes a novel genetic algorithm leveraging helper objectives for improved performance on the 0-1 knapsack problem.

Findings

Outperforms greedy and mixed strategy genetic algorithms

Achieves better solutions within similar computational time

Demonstrates effectiveness of helper objectives in genetic algorithms

Abstract

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show that the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm.