Coevolutionary Multiobjective Particle Swarm Optimization (CMPSO) [1]

Disclaimer:

• This repository acts as an implementation of the authors' [1] work in MATLAB.
• Ensure to download all MATLAB files as they are essential functions for the execution of CMPSO.m.

Introduction:

Inspired by Zhan et al., the CMPSO algorithm runs a regular particle swarm optimization scheme on multiple swarms (swarm size = number of objectives) and introduces an information sharing algorithm which outputs a set of non-dominated solutions in the Archive matrix in the code.

Further information about the methodology of the algorithm can be found in the reference paper.

Table of Variables

Variable	Definition
var	Number of optimization variables
varsize	Row vector form of solution
swarms	Number of objectives
NA	Max Archive size
xmax	Upper Limit of Search Space
xmin	Lower Limit of Search Space
vlim	Velocity Limit
iterations	Number of Iterations
particles	Number of Particles
wmin	Minimum Inertia
wmax	Maximum Inertia
co1	Personal Acceleration Coeff
co2	Social Acceleration Coeff
co3	Archive Acceleration Coeff
particle	Cell template of swarms
GlobalBestEF	Global Best Evaluation for Isolated Objectives
GlobalBestPos	Global Best Position for Isolated Objectives
BestEF	Best Evaluation at Each Iteration for Isolated Objectives
Archive	Pareto Set
ArchEF	Pareto Front
BP	Stores Best Positions across all swarms for the algorithm
BP_EF	Stores Best Positions' Evaluation across all swarms for the algorithm
wasemptyArch	Checks if the Archive is empty

Table of Functions

Function	Definition
sat	Limit a matrix of solutions to upperlimit and lowerlimit which must be row vectors
els	Elitist Learning Strategy [1]
nondom_sol	Extracts Non-dominated Solutions and their Positions
dbs	Density-Based Selection [1]

Evaluation Function:

Line 32 of CMPSO.m must be set to the evaluation function, create your MATLAB function that takes in positions and swarms and returns an evaluation of said positions.

• positions: matrix of input solutions (each row is a solution)

A for loop should be used to analyse the evaluation for each row of the positions input.

Example:

cone_ef.m showcases the evaluation function for this example.

Reference: https://www.math.unipd.it/~marcuzzi/DIDATTICA/LEZ&ESE_PIAI_Matematica/3_cones.pdf

Problem Statement:

• Input variables: radius and height of cone [r,h]
• Objectives: minimize Lateral Surface Area (S) and Total Area (T) [S,T]
• Constraint: Volume>200 cm^3

Results:

• Using 10 particles and 10 iterations:

Reference:

[1] Multiple Populations for Multiple Objectives: A Coevolutionary Technique for Solving Multiobjective Optimization Problems (Zhi-Hui Zhan, Jingjing Li, Jiannong Cao, Jun Zhang, Henry Shu-Hung Chung and Yu-Hui Shi) 2013