2010 IEEE International Conference on Systems, Man, and Cybernetics (SMC2010) A Hybrid Particle Swarm Optimization Considering Accuracy and Diversity of Solutions Takeya Matsui1 Masato Noto1 Masanobu Numazawa2 1Kanagawa University, Japan 2Otaru University of Commerce, Japan 11, Oct., 2010

Outline Introduction Particle Swarm Optimization (PSO) Proposed Method Simulation Experiments Conclusion and Future Work 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Introduction Particle Swarm Optimization (PSO) An optimization method that emulates the behavior of creatures such as a flock of birds or a school of fish. Each of a number of candidate points (particles) has information about its own position and velocity. That information is shared within the swarm, and the search proceeds while information on the best solution is shared. A characteristic of PSO The PSO algorithms are extremely simple. PSO is applied to various different types of problem and its validity has been confirmed. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Particle Swarm Optimization (PSO) Gbest model The best solution discovered by the entire swarm is shared by the entire swarm. The most basic model for PSO. This model can converge quickly on a solution and may become trapped at a local solution. Lbest model Divides the swarm into a number of groups. Shares the best solution that is discovered by each group within that group. This model converges slowly on the solution but its global search capability is better. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

In this study We propose a hybrid PSO algorithm. In order to resolve the drawback of PSO in that it can easily get trapped at a local solution. The initial stages of the search maintain the diversity of the search by using the Lbest model. Then the method intensifies the search in the later stages by switching to the Gbest model. The method searches the optimal solution candidates vicinity carefully by limiting update of the shared information. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

PSO (Gbest model) algorithm Each Particle in the -dimension space Current position: Current velocity: Own best solutions: Evaluation value: ( is the Particle number, is the number of iterations) Shared by the entire swarm Best solutions discovered by the entire swarm: 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Travel of Particle in Gbest model Updating velocities Updating positions 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Lbest model Each Particle forms a group consisting of itself and neighboring Particles. Shares the best solution that is discovered by each group as within that group. Each group search regions that are mutually different. The global search capability is increased. Since the particles are formed into groups with overlapping portions, this means that there is some sharing of information within the entire swarm. The processing eventually converges on the best value within the values. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Degree of activity of swarm The degree of activity of the swarm has been proposed as an indicator for quantitively comprehending the search situation in PSO. The degree of activity of the swarm is defined as the root mean square of the velocities of the particles. Use of the degree of activity of the swarm makes it possible to know the activity state of the entire swarm. When the degree of activity is large --> Expanding When the degree of activity is small --> Converging : Number of Particles : Number of dimensions of the problem : -dimensional element of the velocity of the th particle in iterations 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Proposed method By using the degree of activity of the swarm to monitor the diversity of the search. The initial stages of the search maintain the diversity of the search by using the Lbest model. The final stages of the search intensifies the search by switching to the Gbest model. Furthermore, the method is adopting the lowest number of iterations of the shared information. Updating the shared information of the swarm, and then searching carefully in the vicinity of the optimal solution candidates without further updating the shared information until is reached. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Simulation experiments 2nminima function Subj. to Globally optimal solution: Rastrigin function Subj. to Globally optimal solution: 2nminima function ( ) Rastrigin function ( ) 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Simulation Parameters Dimension of the problem Number of Particles Weighting parameters Maximum number of iterations Threshold degree of activity for switching the search model Lowest number of iterations for sharing information Number of trials 100 : The maximum value of the degree of activity of the swarm during the iterations. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Simulation Results Gbest model Average Best Worst Lbest model 2nminima function Rastrigin function Gbest model Average -735.2585 8.9745 Best -783.3233 1.9899 Worst -641.9561 26.8639 Lbest model -749.9607 7.7748 0.9950 -698.5030 39.5371 Proposed method -767.7719 5.8604 3.7373E-9 12.9350 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Transitions in degree of activity 2nminima function Rastrigin function The proposed method maintains the degree of activity of the swarm right up to the end. This is thought to be because the diversity of the search is maintained for a long while with the proposed method. By using the Lbest model to search in different ranges for each group, until the degree of activity falls to a certain amount. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Transitions in best values 2nminima function Rastrigin function The proposed method took longer to converge on the solution than the Gbest model. Uses the Lbest model in the initial stages of the search. The adoption of delays the convergence on the solution. No great difference in convergence on the solution was seen in comparison with the Lbest model. The search is intensified by switching to the Gbest model in the final stages of the search. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

Conclusion and Future Work In this study, we proposed a hybrid method in order to resolve the drawback of PSO in that it can easily get trapped by a local solution. We have confirmed from the results of simulation experiments that the proposed method has superior search capabilities. Future work Optimization of and . Evaluations of various different benchmark problems. Verification of the validity of the method in real-life systems. 11, Oct., 2010 SMC2010 in Istanbul,TURKEY

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