Aiming at the nonlinear design optimization problems with multiple constraints in the field of engineering shape design, an Adaptive Gaussian Quantum-behaved Particle Swarm Optimization (AG-QPSO) algorithm was proposed. By adjusting the Gaussian distribution adaptively, AG-QPSO algorithm was able to have strong global search ability at the initial stage of search process, and with the search process continued, the algorithm was able to have stronger local search ability, so as to meet the demands of the algorithm at different stages of the search process. In order to verify the effectiveness of the algorithm, 50 rounds of independent experiments were carried out on the two engineering constraint optimization problems: pressure vessel design and tension string design. The experimental results show that AG-QPSO algorithm achieves the average result of 5 890.931 5 and the optimal result of 5 885.332 8 on the pressure vessel design problem, and achieves the average result of 0.010 96 and the optimal result of 0.010 96 on the tension string design problem, which are better than the results of the existing algorithms such as the standard Particle Swarm Optimization (PSO) algorithm, Quantum Particle Swarm Optimization (QPSO) algorithm and Gaussian Quantum-behaved Particle Swarm Optimization (G-QPSO) algorithm. At the same time, the small variance of the results obtained by AG-QPSO algorithm indicates that the algorithm is very robust.
According to the problem that better dimensions information of particles will loss in Quantum-behaved Particle Swarm Optimization (QPSO) algorithm when solving multi-dimensions problems, a strategy with crossover operator was introduced and the quality of solutions and the performance of algorithm would be improved. Firstly, the whole update and evaluation strategy on solutions in algorithm was analyzed and the better dimensions information of particles would loss because of the mutual interference between dimensions. Secondly, when the evolution was executed dimension by dimension, the algorithm complexity would increase exponentially. Finally, multi-crossover method was employed to increase the retaining probability of excellent dimension information. The comparison and analysis results of the proposed method, with linearly decreased coefficient control method and non-linearly decreased coefficient control method on 12 CEC2005 benchmark functions were given. The simulation results show the modified algorithm can greatly improve the QPSO performance compared with the basic QPSO in 10 functions and also get better performance in 7 functions compared with the other two QPSO variants. Therefore, the proposed method can improve the performance of QPSO effectively.
In order to reveal the evolution rules of supply chain network with the core of manufacturers, a kind of five-level local world network model was put forward. This model used the BA model and the multi-local world theory as the foundation, combined with the reality of network node generation and exit mechanism. First of all, the intrinsic characteristics and evolution mechanism of network were studied. Secondly, the topology structure and evolution rules of the network were analyzed, and the simulation model was established. Finally, the changes of network characteristic parameters were simulated and analyzed in different time step and different critical conditions, including nodes number, clustering coefficient and degree distribution, then the evolution law of the network was derived. The simulation results show that the supply chain network with the core of manufacturers has the characteristics of scale-free and high concentration. With the increase of time and the growth rate of the network nodes, the degree distribution of overall network approaches to the power-law distribution with the exponent three. The degree distribution of the network at all levels is different, sub-tier suppliers and retailers obey power-law distribution, suppliers and distributors obey exponential distribution, manufacturers generally obey the Poisson distribution.