| Particle Swarm Optimization(PSO) algorithm is a swarm intelligent algorithm which imitates the behavior of birds' foraging. Once been proposed, PSO algorithm has gained extensive attention both of domestic and overseas scholars in many research fields. After more than 20 years of development,PSO algorithm was more and more widely used in the fields of multimodal function optimization, combination optimization, neural network training and so on.Sun Jun proposed a Quantum Behaved Particle Swarm Optimization(QPSO)in 2004. This algorithm has a powerful global search ability but poor at local search in the optimization of high dimensional multimodal functions. So, combined the Nelder Mead Simplex algorithm and QPSO, we proposed an improved quantum behaved particle swarm optimization algorithm(NM-QPSO). This paper studies the fundamentals and basic procedure of NM-QPSO. An orthogonal experiment for parameter selection was designed to select a set of reasonable control parameters. A suite of 28 test functions from CEC'13 was used to do numerical experiments. NM-QPSO was compared with both of traditional PSO and QPSO by using the Wilcoxon signed ranks test. Simulation results show that the NM-QPSO algorithm has better performance than both of the traditional PSO and QPSO algorithms in a statistical sense, and it has obvious advantages in high-dimensional function optimization problems.Because of traditional PSO algorithm have a poor performance when it is used for optimization in discrete spaces, this paper further discussed the discrete PSO algorithm. We proposed a discrete Particle Swarm Optimization(DQPSO) algorithm which updates particles' position based on quantum rotation gate. It was applied to the location problem of multi-logistics centers. The validity of the algorithm was verified using simulation experiments. Experiment results show that the DQPSO algorithm has better performance than the Greedy Algorithm, Variable Neighborhood Search and Genetic Algorithms. |
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