Complex-order particle swarm optimization - Machado, J. A. Tenreiro (2021)
In this paper, the generalization of the Particle Swarm Optimization (PSO) algorithm is proposed. The new algorithm involves the adoption of complex-order derivatives (CD). Since the CD produce complex-valued results, conjugate pairs of CD are considered for designing the Complex-Order PSO (CoPSO). First, an extensive sensitivity analysis is carried out for studying the influence of the control parameters on the performance of CoPSO. Then, a set of classical benchmark functions are tested to verify the performance of CoPSO. Both valued- and ranked-based methods are conducted to compare the performance of the algorithm on the whole test suite. The Friedman test is applied to determine the average ranking of the algorithms based on their performances. Additionally, the mean and the standard deviation of the best results are examined in each experiment. The results indicate that the CoPSO has outstanding performance in comparison with previous algorithms, including the standard PSO, the fractional order PSO and the linear and nonlinear decreasing inertia weight PSO. The experimental results indicate the feasibility and efficiency of the CoPSO.