An enhanced consensus-guided homotopy-inspired QPSO method for multimodal optimization problems

Abstract

Quantum-behaved particle swarm optimization (QPSO) is a prominent swarm intelligence algorithm that has been widely used to solve diverse kinds of optimization problems. QPSO employs a quantum-inspired probabilistic position update mechanism driven by swarm cooperation. However, QPSO still suffers from premature convergence and insufficient optimization accuracy when tackling complex multimodal optimization problems. To deal with these disadvantages, an enhanced consensus-guided homotopy-inspired QPSO (CGQPSO) algorithm is presented. In the proposed CGQPSO, a consensus-guided framework is designed to improve the search efficiency. Additionally, in order to improve the optimization accuracy of the algorithm, a local refinement mechanism is incorporated after the consensus stage. Furthermore, to better balance the exploration ability of individuals and the global search capability of the algorithm, the local attractor is redefined based on the inspiration from the homotopy continuation method. For maintaining the diversity of the population, the bidirectional quantum sampling is applied to update individual locations. According to the results obtained by CGQPSO and nine other optimization algorithms on 29 benchmark functions under different dimensions, it is found that CGQPSO significantly outperforms the compared algorithms in approximately 80 % of the statistical comparisons across all evaluated dimensions, as further confirmed by the Friedman test. The proposed CGQPSO demonstrates its potential for solving complex multimodal optimization problems.