Particle Swarm Motion Analysis And A Two Stage Particle Swarm Optimizer

Particle Swarm Optimization ( PSO ) is a stochastic searching method based on the cooperative behavior of a particle swarm. Due to its strong global optimization ability on multimodal problems, PSO has progressively attracted more attention from researchers in optimization field. Many international conferences have discussed PSO as a special topic. And IEEE Transactions on Evolutionary Computation has also published a special issue on PSO. Today the research on PSO has become a very active field.Howerver, there are still two problems about the research on PSO. The first one is that there is little theoretical analysis of the swarm's motion in the search space. But the analysis of the swarm's motion is very important because the swarm's motion is exactly the way in which PSO find the solutions. The existing analysis so far only deals with a single particle's motion rather than the swarm's motion. The second problem is that there is no PSO variant that can perform very well on both unimodal and complex multimodal problems, despite of so many existing PSO variants. PSO variants with strong global optimization ability usually converge too slowly on unimodal problems, whereas PSO variants with fast convergence speed on unimodal problems often performs very badly on complex multimodal problems.In order to solve the two problems above, research has been done as follows:1. A new method was employed to carry out the theoretical analysis of the the swarm's motion. The mathematical model of particle swarm's motion was established. The adjacency matrix, weighted degree diagonal matrix, and the Laplalacian matrix were brought into this model. By analyzing the properties of the eigenvalues of these matrixes, the swarm's motion behavior was studied.2. Under the particle swarm's motion model, in the case that the matrix of the particles' personal best positions updates most quickly, a sufficient condition and a necessary condition for the convergence of the swarm's motion were given. In another case that the matrix of the particles' personal best positions updates most slowly, a sufficient and necessary condition for the convergence of the swarm's motion was given. In general cases, the idea on how to analyze the swarm's motion was discussed and a necessary condition for the convergence of the swarm's motion was given. An example was analyzed using the conclusions above. And the results of the analysis were verified by a simulation experiment on this example.3. A new PSO variant called the Two-Stage Particle Swarm Optimizer ( TSPSO ) was proposed. TSPSO performs a gross searching algorithm at the fist stage, and switches to a fine-grained searching algorithm if it is stagnated in the first stage. A switching criterion was proposed. And a new fine-grained searching algorithm was devised for the second stage of TSPSO. As for the first stage, FIPS with U-square topology was adopted.4. The performance of TSPSO was compared with six other PSO variants including CLPS and CPSO-H on a test suite. The results of this experiment show that TSPSO's switching behavior makes it perform very well on both unimodal and complex multimodal problems. Especially on complex multimodal problems, TSPSO's performance is even better than the most state of the art PSO variants such as CLPS and CPSO-H.