A Study On Multi-Swarm Particle Swarm Optimization For Unimodal And Multi-Modal Function Opti- Mization

Particle Swarm Optimization (PSO) is an algorithm based on social behavior law of birds, fish and human. PSO has the disadvantages of prematurity since the particles fall into local extreme points, and poor accuracy since convergence speed at later evolution process is slow. Multi-swarm PSO is an important algorithm to improve the ability of glob-al search and reduce prematurity by increasing diversity of the particles. Dynamic Mul-ti-swarm PSO (DMS-PSO) is a class of algorithm to increase diversity by regrouping the swarms periodically in multi-swarm PSO algorithm, but experiment shows that such method increases the optimization time greatly because of frequent regroup operation, and the algorithm ignores the autonomy of particles in the evolutionary process, resulting in blind and forced searches, which brings down the optimization efficiency.Currently, most of the improved PSO algorithms are used for the unimodal optimiza-tion problems, but there are a lot of another type of problems called multi-modal optimiza-tion(MO) problems in scientific research and engineering practice. Currently niche PSO used to solve MO problems has a low accuracy both in niche recognition and same peaks’ recognition of extreme points, at the same time frequent distance calculations bring down the efficiency. Multi-swarm PSO can save the best individuals in each swarm because of independent evolution between swarms, which maks it good at solving MO problems.In order to solve above problems, we study on multi-swarm PSO for unimodal and multi-modal function optimization:Multi-swarm particle swarm optimization based on au-tonomic learning and elite swarm(ALEMSPSO) is proposed,which can maintain population diversity, improve particles’ learning autonomy, and reduce the time consumption; Mul-ti-swarm particle swarm optimization based on devision by different peaks for multi-modal function optimization (DPMSPSO) is also proposed,which can increase accuracy and effi-ciency of niche identification, improve accuracy of same peak identification of the extreme points in niche PSO,and it provides a new approach for solving multi-modal optimization problems.The main contributions of this paper are as follows:(1) Propose ALEMSPSO to enhance the search ability.We propose ALEMSPSO by introducing the concept of autonomic learning in educa-tional psychology and the population structure of elite swarm and base swarm. This algo-rithm has the following features:● New learning mechanism to update particles’volocity and position by autonomicly choosing learning objects. Particles in base swarms replace the regroup operations with autonomicly choosing learning objects in DMS-PSO to maintain high diversity as DMS-PSO without complex regroup operations; It can also improve learning mechanism of particles and the particles’autonomy in the process of evolution.● New mechanism of local search based on elite swarm. Elite swarms conduct local searches,while base swarms conduct global searches so as to enhance the local search capa-bility while maintaining nice global search capability.● New mechanism of swarms merger based on optimal particles in each base swarm. Elite swarms and base swarms merge into one elite swarm and one base swarm through measuring the diversity of optimal particles in each base swarm to improve convergence ability at later evolution process or while solving a function with single peak.Experiments on six typical high-dimensional and multi-modal test functions show that the new algorithm has a good performance in convergence speed, search accuracy and time, as well as its stability.(2) Propose DPMSPSO to improve search ability, and provide a new approach for solving MO problems.We propose DPMSPSO for multi-modal function optimization by introducing extreme point library(Llib) to store the found extreme points into new algorithm,and designing niche identification mechanism by different peaks and identification mechanism of the ex-treme points by improved insertion point method. This algorithm has the following fea-tures:● New niche identification mechanism by different peaks. Particles in base swarms are periodically devided into swarms dynamically according to different peaks,which takes full account of the characteristics of the function and peaks, and increases accuracy and ef-ficiency of niche identification.● Identification mechanism of the extreme points by improved insertion point meth-od.The best particles found by all the swarms conduct identification with improved inser-tion point method when entering Llib or getting out of Llib,which can improve the accuracy of same peak identification.● Improved mechanism of local search based on elite swarm and Llib. Elite swarms conduct local searches around the extreme particles in Llib to improve the convergence ac-curacy and speed.● Several new indices.We propose several new indices to evaluate algorithms for solving multi-modal optimization to improve the the correctness and fairness of perfor-mance evaluation.Comparison experiments on ten test functions show that the new algorithm has a higher accuracy of locating extreme points, and has a good performance in convergence accuracy and speed.