Optimization Using Particle Swarm with Near Neighbor Interactions

1. Optimization Using Particle Swarm with Near Neighbor Interactions Kalyan Veeramachaneni Thanmaya Peram Chilukuri K Mohan Lisa Ann Osadciw

2. Overview Introduction Motivation Fitness- Distance Ratio FDR-PSO Algorithm Particle Dynamics Experimental Settings Results and Analysis Related Work Summary

3. Introduction : Particle Swarm Optimization Inspired from social impact theory Each particle influenced by its own previous experience, �pbest� Also influenced by local best in neighborhood, �lbest� Simulation results show that complete graph topology yields better results than other topologies

4. Motivation Problems with PSO execution Premature convergence Clustering of particles Goal : To overcome these problems, exploiting �social impact theory�

5. Fitness-Distance Ratio Evaluating influence of jth particle on the ith particle (along the dth dimension) where Pj is the previous best position visited by the jth particle Xi is the position of the particle under consideration

6. FDR-PSO Algorithm Each particle influenced by Its own previous best (pbest) Global best particle (gbest) Particle that maximizes FDR (nbest) Velocity Update Equation Position Update Equation

7. FDR-PSO Algorithm Algorithm FDR-PSO: For t= 1 to the max. bound on the number of generations, For i=1 to the population size, Find gbest; For d=1 to the problem dimensionality, Find nbest which maximizes the FDR; Apply the velocity update equation; Update Position; End- for-d; Compute fitness of the particle; If needed, update historical information regarding Pi and Pg; End-for-i; Terminate if Pg meets problem requirements; End-for-t; End algorithm.

8. Particle Dynamics � I Different nearest best neighbors for a particle along different dimensions Nearest best neighbor often poorer than global best Possible overlap between gbest or pbest and nbest for small populations Overlap of 40% found in a population size of 10

9. Particle Dynamics -II Greater exploration avoiding premature convergence Increased Population Diversity

10. Particle Dynamics -II

11. Particle Dynamics � II

12. Experimental Settings - I Experimental Settings

13. Experimental Settings - II FDR-PSO parameters Notation ?1, ?2, ?3 represent the weights given to pbest, gbest and nbest terms respectively Variations of FDR-PSO are obtained by varying the three weights PSO parameter selection Equal social and Cognitive learning rates

14. Results and Analysis -I

15. Results and Analysis -II

16. Summary of Results

17. Results and Analysis � III FDR-PSO variations consistently outperformed PSO FDR-PSO(112) was the best performer nbest term is more important for multimodal functions

18. Performance of FDR-PSO Variations FDR-PSO(112) and FDR-PSO(012) outperform PSO on 5 out of 6 benchmark problems FDR-PSO(102) outperform FDR-PSO(111) in 4 out of 6 benchmark problems FDR-PSO(002) outperforms FDR-PSO(111) and PSO in 3 out of 6 benchmark problems

19. Related Work ARPSO: Diversity measurement makes the algorithm alternate between attraction and repulsion phases PSO with mass extinction (HPSO) : Velocities are reinitialized after each extinction interval Hybrid PSO : Population is split into subpopulations and PSO algorithm is hybridized with features from genetic algorithms

20. FDR-PSO Vs Other Variations -I

21. FDR-PSO Vs Other Variations -II Many PSO variations introduce additional control parameters which are not easy to determine FDR-PSO achieves better minima without any additional parameters Other variations are extrinsic to particle dynamics, and hence can be applied to FDR-PSO as well

22. Summary Designed a new algorithm which partly follows �social impact theory� Modeled the �Fitness-Distance Ratio� metric Improved performance compared to PSO and its previous variations Significantly less affected than PSO by problems such as premature convergence, loss of diversity in population

23. Development and Research in Evolutionary Algorithms for Multisensor Smart Networks DreamsNet 277, Link Hall Syracuse University Syracuse, NY �13244