Superior Exploration-Exploitation Balance with Quantum-Inspired Hadamard Walks

TL;DR

This paper introduces quantum-inspired Hadamard walks and a new evolutionary algorithm, HQEA, which leverage these walks to improve exploration and exploitation in solving combinatorial optimization problems.

Contribution

The paper proposes quantum-inspired Hadamard walks and integrates them into a novel evolutionary algorithm, HQEA, enhancing search efficiency and solution quality.

Findings

HQEA outperforms CGA, QEA, and NQEA in convergence speed.

HQEA achieves higher accuracy on the 0,1-knapsack problem.

Quantum-inspired Hadamard walks improve exploration-exploitation balance.

Abstract

This paper extends the analogies employed in the development of quantum-inspired evolutionary algorithms by proposing quantum-inspired Hadamard walks, called QHW. A novel quantum-inspired evolutionary algorithm, called HQEA, for solving combinatorial optimization problems, is also proposed. The novelty of HQEA lies in it's incorporation of QHW Remote Search and QHW Local Search - the quantum equivalents of classical mutation and local search, that this paper defines. The intuitive reasoning behind this approach, and the exploration-exploitation balance thus occurring is explained. From the results of the experiments carried out on the 0,1-knapsack problem, HQEA performs significantly better than a conventional genetic algorithm, CGA, and two quantum-inspired evolutionary algorithms - QEA and NQEA, in terms of convergence speed and accuracy.