Insights to Particle Swarm Optimization Algorithm by Ojiako

Insights to Particle Swarm Optimization Algorithm by Ojiako Chika, Fasina Ebun, Sawyerr Babatunde Department of Computer Sciences, University of Lagos, Nigeria

Outline Introduction � Statement of the Problem � Particle Swarm Optimization (PSO) Algorithm Overview � Modifications to PSO � Conclusions � References � TOKI 2016 9/21/2021 2

INTRODUCTION: OPTIMIZATION What is Optimization? � TOKI 2016 9/21/2021 3

Optimization… Figure 1: Types of optima for unconstrained problems (Engelbrecht, 2007) TOKI 2016 9/21/2021 4

Background Exploration Exploitation � To improve PSO performance, a number of variants have been developed to solve the problem of premature convergence to local optima and slow convergence in complex multimodal problems. TOKI 2016 9/21/2021 5

OPTIMIZATION ALGORITHMS Optimization Deterministic � Stochastic/Probabilistic TOKI 2016 9/21/2021 6

Deterministic Method Merits Give exact solutions(predictable) Ø Do not use any stochastic technique Ø Demerits Not Robust- can only be applied to restricted class of problems. Ø Often too time consuming or sometimes unable to solve real world problems. Ø Examples: Newton Raphson, Bisection Method. TOKI 2016 9/21/2021 7

Stochastic Method Merits � Use the stochastic or probabilistic approach (random approach) � Applicable to wider set of problems Demerits � Converges to the global optima probabilistically � Some times get stuck at local optima. Ø Examples: Genetic Algorithm (GA) Ø Ant Colony Optimization (ACO) Ø Differential Evolution (DE) Ø Particle Swarm Optimization (PSO) TOKI 2016 9/21/2021 8

SWARM INTELLIGENCE Swarm Intelligence(SI): collective behaviour of decentralized, self organized systems. Interactions of the individuals in a group leads to emergent group behaviour. Proverb 6: 6 “Go to the ants, O sluggard consider her ways, and be wise. ” (RSV) “Ants aren’t smart, ant colonies are”. Gordon Deborah TOKI 2016 9/21/2021 9

PARTICLE SWARM OPTIMIZATION TOKI 2016 9/21/2021 10

PSO Basic Mathematical Equations � momentum cognitive social TOKI 2016 9/21/2021 11

Basic PSO Flowchart TOKI 2016 9/21/2021 12

PSO VERSIONS There are two basic PSO versions: ØGlobal best(gbest) and ØLocal best(lbest) PSO. They differ in the size of their neighborhoods. TOKI 2016 9/21/2021 13

Global Best PSO � 1 2 8 3 7 4 6 5 TOKI 2016 9/21/2021 14

Local Best PSO � TOKI 2016 9/21/2021 15

PSO VARIANTS Some basic modifications have been made to the basic PSO to improve the quality of the solution and the speed of convergence. � Modification based � Others on on parameter settings topology learning strategies hybridization TOKI 2016 9/21/2021 16

Modification based on parameter settings � TOKI 2016 9/21/2021 17

Modification based on topology � Kennedy and Mendes (2002): studied the effect of various population topologies(von Neumann topology as superior). � Liang and Suganthan (2005): dynamic multi swarm particle swarm optimizer (DMSPSO) a dynamically changing neighbourhood topology. � Liu et al. , 2016): provide a guide to topology selection for PSO. TOKI 2016 9/21/2021 18

Modification based on learning strategies � Liang et al (2006): Comprehensive learning PSO (CLPSO) particles use different personal best position. � Nasir et al (2012): dynamic neighbourhood learning based particle swarm optimizer (DNLPSO) strategy is same as CLPSO except that the leader is selected from a dynamic neighbourhood. � Lynn and Suganthan (2015): heterogeneous comprehensive learning particle swarm optimization (HCLPSO), with enhanced exploration and exploitation, the comprehensive learning strategy is used to generate the exemplars for both subpopulations. TOKI 2016 9/21/2021 19

Modification based on hybridization � Angeline (1998): Selection–based PSO. Combined GA with PSO. � Clerc (2001): Cheap PSO (reproduction). A particle is allowed to generate a new particle, kill itself, or modify its inertia and acceleration coefficients. � Xin et al (2009): combined the constriction factor PSO (CF-PSO) and the fully informed PSO to produce a novel hybrid particle swarm optimizer (NHPSO) to balance the convergence speed and search accuracy of PSO. TOKI 2016 9/21/2021 20

Conclusion Ø Ø This paper provided insights into optimization, the standard PSO algorithm and some variants of PSO were also presented. Despite the ever increasing research in this area, there still exist some unresolved issues: Ø Weak mathematical foundation of PSO behaviour. Ø Non- existence of a defined standard of the PSO algorithm. Ø Convergence issues. Ø Parallel implementation. Ø Absence of bio-inspired features of the algorithm and Ø PSO performance on high dimension problems. 9/21/2021 21

Thanks for your attention Merci de votre attention TOKI 2016 9/21/2021 22