Quantum-behaved particle swarm optimization based on solitons

Abstract

This paper introduces a novel variant of the quantum particle swarm optimization algorithm based on the quantum concept of particle-like solitons as the most common solutions of the quantum nonlinear Schrödinger equation. Soliton adaptation in external potentials is one of their most remarkable features which allows them to be stabilized even without a trapping potential, while the potential must be bounded for quantum particles to be localized. So we consider the motion scenario of the present algorithm based on the corresponding probability density function of quantum solitons. To evaluate the efficiency, we examine the proposed algorithm over a set of known benchmark functions, including a selection of test functions with different modalities and dimensions. Moreover, to achieve a more comprehensive conclusion about the performance, we compare it with the results obtained by particle swarm optimization (PSO), standard quantum-behaved particle swarm optimization QPSO, improved sine cosine Algorithm (ISCA), and JAYA optimization algorithm. The numerical experiments reveal that the proposed algorithm is an effective approach to solving optimization problems that provides promising results in terms of better global search capability, high accuracy, and faster convergence rate.