Swarm Intelligence Optimization.

globpso

Features

This package collects the powerful variants of particle swarm optimization (PSO) and differential evolution (DE) algorithms for R users.

Currently it supports five types of PSO:

• Particle Swarm Optimization (PSO, Eberhart and Kennedy, 1995)
• Quantum-behaved particle Swarm Optimization (QPSO, Sun et al., 2004a,b)
• Locally convergent rotationally invariant particle swarm optimization (LcRiPSO, Bonyadi and Michalewicz, 2014)
• Competitive Swarm Optimizer (CSO, Cheng and Jin, 2015)
• Double exponential particle swarm optimization (DExPSO, Stehlik et al., 2024+)

and six types of DE (Storn, R. and Price, K., 1997):

• DE/rand/1: Mutation operation on the current position with one random direction.
• DE/rand/2: Mutation operation on the current position with two random directions.
• DE/best/1: Mutation operation on the best position with one random direction.
• DE/best/2: Mutation operation on the best position with two random directions.
• DE/rand_to-best/1: Mutation operation on the current position with direction to the best and one random direction.
• DE/rand-to-best/2: Mutation operation on the current position with direction to the best and two random directions.

Installation

Install the stable version of globpso on CRAN via

install.packages("globpso")

(Not recommended) Or, install the latest under-development version from github with

install.packages("devtools")
devtools::install_github("PingYangChen/globpso")

Examples of PSO

For setting the PSO type, please find the instruction through the command.

?getPSOInfo

library(globpso)

# Optimize the 3-dimensional quadratic objective function with location shift
objf <- function(x, loc) {
 val <- 0
 for (i in 1:length(x)) val <- val + (x[i] - loc)^2
 return(val)
}

# The search domain is [-5, 5]^3
upp_bound <- rep(5, 3)
low_bound <- rep(-5, 3)

# Define the location shift to be 1
loc_shift <- 1

# Run PSO for this optimization problem
# Also input the enviorment variable, the location shift 'loc_shift'
res <- globpso(objFunc = objf, lower = low_bound, upper = upp_bound, 
               loc = loc_shift)
res$par
res$val

# Set initial values to run PSO
initSwarm <- c(2, 2, 2)
# initSwarm <- rbind(c(2, 2, 2), c(1, 0.1, 1)) # for more than 2 initial points
res_i <- globpso(objFunc = objf, lower = low_bound, upper = upp_bound, 
                 init = initSwarm, loc = loc_shift)

# One can also write C++ objective function to further accelerate the computation
library(Rcpp)
library(RcppArmadillo)
objf_c <- cppFunction('double objf_c(SEXP x, SEXP loc) {
   double val = 0;
   double loc_c = (double)Rcpp::as<double>(loc);
   arma::rowvec x_c = (arma::rowvec)Rcpp::as<arma::rowvec>(x);
   for (arma::uword i = 0; i < x_c.n_elem; i++) {
     val += (x_c(i) - loc_c)*(x_c(i) - loc_c);
   }
   return val;
 }', depends = "RcppArmadillo")
res_c <- globpso(objFunc = objf_c, lower = low_bound, upper = upp_bound, 
                 loc = loc_shift)
res_c$par
res_c$val

# Use getPSOInfo() to change the PSO options
alg_setting <- getPSOInfo(nSwarm = 64, maxIter = 200, psoType = "quantum")
res_c_large <- globpso(objFunc = objf_c, lower = low_bound, upper = upp_bound, PSO_INFO = alg_setting, loc = loc_shift)
res_c_large$history

Examples of DE

For setting the DE type, please find the instruction through the command.

?getDEInfo

library(globpso)

# Optimize the 3-dimensional quadratic objective function with location shift
objf <- function(x, loc) {
  val <- 0
  for (i in 1:length(x)) val <- val + (x[i] - loc)^2
  return(val)
}

# The search domain is [-5, 5]^3
upp_bound <- rep(5, 3)
low_bound <- rep(-5, 3)

# Define the location shift to be 1
loc_shift <- 1

# Use getDEInfo() to setup the DE options
de_setting <- getDEInfo(nPop = 64, maxIter = 200, deType = "best-2", sf = 0.5, cr = 0.1)

# Run DE for this optimization problem
# Also input the enviorment variable, the location shift 'loc_shift'
res <- diffevo(objFunc = objf, lower = low_bound, upper = upp_bound, 
               DE_INFO = de_setting, verbose = FALSE, loc = loc_shift)
res$par
res$val

# Simialr to PSO, 
# One can also write C++ objective function to further accelerate the computation

Reference

• Bonyadi, M. R. and Michalewicz, Z. (2014). A locally convergent rotationally invariant particle swarm optimization algorithm. Swarm Intelligence, 8(3):159-198.
• Cheng, R. and Jin, Y. (2015). A competitive swarm optimizer for large scale optimization. IEEE transactions on cybernetics, 45(2):191-204.
• Eberhart, R. and Kennedy, J. (1995). A new optimizer using particle swarm theory. In The 6th International Symposium on Micro Machine and Human Science, pages 39-43. IEEE.
• Stehlík, M., Chen, P. Y., Wong, W. K., and Kiseľák, J. (2024). A double exponential particle swarm optimization with non-uniform variates as stochastic tuning and guaranteed convergence to a global optimum with sample applications to finding optimal exact designs in biostatistics. Applied Soft Computing, 163, 111913.
• Storn, R., & Price, K. (1997). Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, 11, 341-359.
• Sun, J., Feng, B., and Xu, W. (2004a). Particle swarm optimization with particles having quantum behavior. In Evolutionary Computation, 2004. CEC2004. Congress on, volume 1, pages 325-331. IEEE.
• Sun, J., Xu, W., and Feng, B. (2004b). A global search strategy of quantum-behaved particle swarm optimization. In Cybernetics and Intelligent Systems, 2004 IEEE Conference on, volume 1, pages 111-116. IEEE.

If you encounter a bug, please file a reproducible example on github.