Low-discrepancy sequence initialized particle swarm optimization algorithm with high-order nonlinear time-varying inertia weight

•Initial population particles are generated by the Halton sequence to fill the search space efficiently.•1/π2 order nonlinear function is selected to adjust the time-varying inertia weight.•Two acceleration coefficients are set to be constants.•Performance of the proposed method is tested by a set of well-known benchmark optimization problems.

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. The most important features of the PSO are easy implementation and few adjustable parameters. A novel PSO method called LHNPSO, with low-discrepancy sequence initialized particles and high-order (1/π2) nonlinear time-varying inertia weight and constant acceleration coefficients, is proposed in this paper. The initial population particles are generated by using the Halton sequence to fill the search space efficiently. Nonlinear functions with orders varied within big ranges are employed to adjust the inertial weight, cognitive and social parameters. Based on the sensitivity analysis of PSO performance to the changes of the orders of these nonlinear functions, 1/π2 order nonlinear function is selected to adjust the time-varying inertia weight and the two acceleration coefficients are set to be constants. A set of well-known benchmark optimization problems is then used to investigate the performance of the proposed LHNPSO algorithm and facilitate the comparison with other three types of PSO algorithms. The results show that the easily implemented LHNPSO can converge faster and give a much more accurate final solution for a variety of benchmark test functions.

Graphical abstract Performance of PSO, LPSO, LPSO-TVAC and the proposed LHNPSO for solving Ackley function.Figure optionsDownload full-size imageDownload as PowerPoint slide