Particle Swarm Optimization

Non-linear parameter optimization with PSO. Includes many examples.

# Particle Swarm Optimization
This directory contains a simple implementation of particle swarm optimization (PSO.m), as well as scripts that use it to solve standard optimization test problems (TEST_PSO_*.m).

This implementation of PSO is designed for solving a bounded non-linear paramter optimization problem, with an initial guess. It is fully vectorized.

There are a variety of options that can be set by the user, but will be initialized to a default value if ommitted.

The output of the solver contains a full history of the optimization, which can be plotted using plotPsoHistory.m. Additionally, the user can define a plotting function to be called on each iteration.Both of these features are demonstrated in the TEST_PSO_*.m scripts.

The code supports both vectorized and non-vectorized objective function. If the objective function is vectorized, then the global best is updated synchronously, once per generation. If the objective function is not vectorized, then the optimization uses an asynchronous update, updating the global best after every particle update.

## Test Functions:

- TEST_PSO_1.m --> 2-D Sphere Function
- TEST_PSO_2.m --> Himmelblau's function
- TEST_PSO_3.m --> Goldstein-Price function
- TEST_PSO_4.m --> 2-D Styblinski-Tang function
- TEST_PSO_5.m --> N-D Styblinski-Tang function

## Help file for PSO.m

[xBest, fBest, info, dataLog] = PSO(objFun, x0, xLow, xUpp, options)

Particle Swarm Optimization

This function minimizes OBJFUN using a variant of particle swarm
optimization. The optimization uses an initial guess X0, and searches
over a search space bounded by XLOW and XUPP.

INPUTS:
objFun = objective function handle:
f = objFun(x)
x = [n, m] = search point in n-dimensional space (for m points)
f = [1, m] = objective function value, for each of m points
x0 = [n, 1] = initial search location
xLow = [n, 1] = lower bounds on search space
xUpp = [n, 1] = upper bounds on search space
options = option struct. All fields are optional, with defaults:
.alpha = 0.6 = search weight on current search direction
.beta = 0.9 = search weight on global best
.gamma = 0.9 = search weight on local best
.nPopulation = m = 3*n = population count
.maxIter = 100 = maximum number of generations
.tolFun = 1e-6 = exit when variance in objective is < tolFun
.tolX = 1e-10 = exit when norm of variance in state < tolX
.flagVectorize = false = is the objective function vectorized?
.flagMinimize = true = minimize objective
--> Set to false to maximize objective
.guessWeight = 0.5; trade-off for initialization; range (0.1,0.9)
--> 0.1 heavy weight on random initialization [xLow, xUpp]
--> 0.9 heavy weight on initial guess (x0)
.plotFun = function handle for plotting progress
plotFun( dataLog(iter), iter )
--> See OUTPUTS for details about dataLog
--> Leave empty to omit plotting (faster)
.display = 'iter';
--> 'iter' = print out info for each iteration
--> 'final' = print out some info on exit
--> 'off' = disable printing
.printMod = 1 (only used if display == 'iter')

OUTPUTS:
xBest = [n, 1] = best point ever found
fBest = [1, 1] = value of best point found

info = output struct with solver info
.input = copy of solver inputs:
.objFun
.x0
.xLow
.xUpp
.options
.exitFlag = how did optimization finish
0 = objective variance < tolFun
1 = reached max iteration count
2 = norm of state variance < tolX
.X_Global = [n,iter] = best point in each generation
.F_Global = [1,iter] = value of the best point ever
.I_Global = [1,iter] = index of the best point ever
.X_Best_Var = [n,iter] = variance in best point along each dim
.X_Var = [n,iter] = variance in current search along each dim
.X_Best_Mean = [n,iter] = mean in best point along each dim
.X_Mean = [n,iter] = mean in current search along each dim
.F_Best_Var = [1,iter] = variance in the best val at each gen
.F_Var = [1,iter] = variance in the current val at each gen
.F_Best_Mean = [1,iter] = mean of the population best value
.F_Mean = [1,iter] = mean of the current population value

dataLog(iter) = struct array with data from each iteration