Entanglement-Enhanced Quantum-Inspired Tabu Search Algorithm for Function Optimization

Abstract

Many metaheuristic algorithms have been proposed to solve combinatorial and numerical optimization problems. Most optimization problems have high dependence, meaning that variables are strongly dependent on one another. If a method were to attempt to optimize each variable independently, its performance would suffer significantly. When traditional optimization techniques are applied to high-dependence problems, they experience difficulty in finding the global optimum. To address this problem, this paper proposes a novel metaheuristic algorithm, the entanglement-enhanced quantum-inspired tabu search algorithm (Entanglement-QTS), which is based on the quantum-inspired tabu search (QTS) algorithm and the feature of quantum entanglement. Entanglement-QTS differs from other quantum-inspired evolutionary algorithms in that its $Q$ -bits have entangled states, which can express a high degree of correlation, rendering the variables more intertwined. Entangled Q-bits represent a state-of-the-art idea that can significantly improve the treatment of multimodal and high-dependence problems. Entanglement-QTS can discover optimal solutions, balance diversification and intensification, escape numerous local optimal solutions by using the quantum not gate, reinforce the intensification effect by local search and entanglement local search, and manage strong-dependence problems and accelerate the optimization process by using entangled states. This paper uses nine benchmark functions to test the search ability of the entanglement-QTS algorithm. The results demonstrate that Entanglement-QTS outperforms QTS and other metaheuristic algorithms in both its effectiveness at finding the global optimum and its computational efficiency.