Particle-Swarm-Optimization(PSO)

This code for multi-purpose of Particle Swarm Optimization(PSO) Algortihm. PSO algorithm is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality.

Examples of Applied PSO Algorithm

To use this code for optimizes a problems,You required to passing two arguments. The statement argument mush following the rules below

Step 1 : Cost function or objective function is the mathematical function that minimize the output when the global minumum are given. The Cost function or objective function must be in lambdafunction. Noted if your Cost function or objective function is complex, you can encapsulated in def function, and call it from lambda function. Example below,

def surface_function(position):
    x = position[0]
    y = position[1]
    z = 3*np.exp(-1*(y + 1)**2 - x**2) * (x-1)**2 - ((np.exp(-(x+1)**2 - 8**2))/3) + np.exp(-x**2 - y**2) *(10*x**3 - 2*x +     10*y**5)

    return z

cost_function = lambda position : surface_function(position)

Step 2 : Problems Argument is to defines your specify the argument, Problems Argument must be in dict type, all keys name must same to this examples below,

#your initial models
var_min = -10       #lower bound of unknown variable/model
var_max = 10        #upper bound of unknown variable/model
num_pop = 50        #number of population
num_var = 2         #number of unknown variable
seed = 12345        #by default is None. Seed is key generator of random number

#problems arguments
problem = {
    'cost_function' : cost_function,
    'var_min' : var_min,
    'var_max' : var_max,
    'num_var' : num_var,
    'num_pop' : num_pop,
    'seed'    : 12345
}

Step 3 : Params Arguments is parameters of the PSO iterative, like Problems Argument, type of Params Arguments must be in dict type, all keys name must same to this examples below,

#youre params
num_iter = 1000     #minimum of iteratian
w_damp = 1          #damping constant

kappa = 1           
phi_1 = 2.05
phi_2 = 2.05
phi = phi_1 + phi_2
chi = kappa/np.abs(2 - phi - np.sqrt(phi**2 - 4*phi))
params = {
    'num_iter' : num_iter,
    'w'        : chi,
    'w_damp'   : w_damp,
    'c1'       : chi*phi_1,
    'c2'       : chi*phi_2
}

Step 4 : Call PSO, PSO() is a class in directory \src, below how to call it,

pso = PSO()
pso.optimize(problem, params)
global_best, cost_hist = pso.run(verbose=False, show_iter=False)

print(global_best)
plt.show()

1. Optimize global minum of Surface Equation

Given a surface equation that have local and global minumun, the surface equation is

2. Invertion Modelling of Vertical Electrical Sounding(VES)

Vertical Electrical Sounding(VES) is geophysical methods that inject the current to the subsurface to identification of subsurface. The output of conducting VES methods are apperant resistivities. Apperant resistivities is ambiguity to interpreted due to coresponding of geometry factor, so we need to inverted apperant resistivities to true resistivites. PSO algortihm can applied to invertion modelling of VES. See my previous repository about VES https://github.com/asidosaputra/PyVES