**globpso**: Particle Swarm Optimization Algorithms and Differential Evolution for Minimization Problems

Description

A fast and flexible general-purpose implementation of Particle Swarm Optimization (PSO) and Differential Evolution (DE) for solving global minimization problems is provided. It is designed to handle complex optimization tasks with nonlinear, non-differentiable, and multi-modal objective functions defined by users. There are five types of PSO variants: Particle Swarm Optimization (PSO, Eberhart & Kennedy, 1995) <doi:10.1109/MHS.1995.494215>, Quantum-behaved particle Swarm Optimization (QPSO, Sun et al., 2004) <doi:10.1109/CEC.2004.1330875>, Locally convergent rotationally invariant particle swarm optimization (LcRiPSO, Bonyadi & Michalewicz, 2014) <doi:10.1007/s11721-014-0095-1>, Competitive Swarm Optimizer (CSO, Cheng & Jin, 2015) <doi:10.1109/TCYB.2014.2322602> and Double exponential particle swarm optimization (DExPSO, Stehlik et al., 2024) <doi:10.1016/j.asoc.2024.111913>. For the DE algorithm, six types in Storn, R. & Price, K. (1997) <doi:10.1023/A:1008202821328> are included: DE/rand/1, DE/rand/2, DE/best/1, DE/best/2, DE/rand_to-best/1 and DE/rand_to-best/2.

Author(s)

Ping-Yang Chen <pychen.ping@gmail.com>

References

1. Bonyadi, M. R., & Michalewicz, Z. (2014). A locally convergent rotationally invariant particle swarm optimization algorithm. Swarm intelligence, 8(3), 159-198.

2. Cheng, R., & Jin, Y. (2014). A competitive swarm optimizer for large scale optimization. IEEE transactions on cybernetics, 45(2), 191-204.

3. Shi, Y., & Eberhart, R. (1998, May). A modified particle swarm optimizer. In Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73). IEEE.

4. 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.

5. 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.

6. 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.

Differential Evolution Algorithms for Minimization Problems

Description

The general-purpose implementation of differential evolution algorithms for minimizing an user-defined objective function.

Usage

diffevo(
  objFunc,
  lower,
  upper,
  init = NULL,
  fixed = NULL,
  DE_INFO = NULL,
  seed = NULL,
  verbose = TRUE,
  ...
)

Arguments

Value

An List.

par

the global best particle.

val

the objective function value of the global best particle.

history

a vector of objective function values of the global best particle in DE search history.

cputime

the computational time in seconds.

References

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.

Examples

# three-dimensional function
objf <- function(x, loc) {
  val <- 0
  for (i in 1:length(x)) {
    val <- val + (x[i] - loc)^2
  }
  return(val)
}

upp_bound <- rep(5, 3)
low_bound <- rep(-5, 3)
loc_shift <- 1

alg_setting <- getDEInfo(nPop = 32, maxIter = 100, deType = "rand-1", 
                         sf = 0.5, cr = 0.1)
res <- diffevo(objFunc = objf, lower = low_bound, upper = upp_bound, 
               DE_INFO = alg_setting, loc = loc_shift)
res$par
res$val

# C++ function example

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")

alg_setting <- getDEInfo(nPop = 32, maxIter = 100, deType = "rand-1", 
                         sf = 0.5, cr = 0.1)
res_c <- diffevo(objFunc = objf_c, lower = low_bound, upper = upp_bound, 
                       DE_INFO = alg_setting, loc = 1)
res_c$par
res_c$val

Generation function of DE parameter settings

Description

Create a list with DE parameters for Minimization.

Usage

getDEInfo(
  nPop = 32,
  maxIter = 100,
  deType = "rand-1",
  freeRun = 1,
  tol = 1e-06,
  sf = 0.5,
  cr = 0.1
)

Arguments

Value

A list of DE parameter settings.

Examples

DE_INFO <- getDEInfo(nPop = 32, maxIter = 100)

Generation function of PSO parameter settings

Description

Create a list with PSO parameters for Minimization.

Usage

getPSOInfo(
  nSwarm = 32,
  maxIter = 100,
  psoType = "basic",
  freeRun = 1,
  tol = 1e-06,
  c1 = 2.05,
  c2 = 2.05,
  w0 = 1.2,
  w1 = 0.2,
  w_var = 0.8,
  vk = 4,
  Q_cen_type = 1,
  Q_a0 = 1.7,
  Q_a1 = 0.7,
  Q_a_var = 0.8,
  LcRi_L = 0.01,
  CSO_phi = 0.1,
  TE_b = 2
)

Arguments

Value

A list of PSO parameter settings.

Examples

PSO_INFO <- getPSOInfo(nSwarm = 32, maxIter = 100)

Particle Swarm Optimization Algorithms for Minimization Problems

Description

The general-purpose implementation of particle swarm Optimization algorithms for minimizing an user-defined objective function.

Usage

globpso(
  objFunc,
  lower,
  upper,
  init = NULL,
  fixed = NULL,
  PSO_INFO = NULL,
  seed = NULL,
  verbose = TRUE,
  ...
)

Arguments

Value

An List.

par

the global best particle.

val

the objective function value of the global best particle.

history

a vector of objective function values of the global best particle in PSO search history.

cputime

the computational time in seconds.

References

1. Bonyadi, M. R., & Michalewicz, Z. (2014). A locally convergent rotationally invariant particle swarm optimization algorithm. Swarm intelligence, 8(3), 159-198.

2. Cheng, R., & Jin, Y. (2014). A competitive swarm optimizer for large scale optimization. IEEE transactions on cybernetics, 45(2), 191-204.

3. Shi, Y., & Eberhart, R. (1998, May). A modified particle swarm optimizer. In Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73). IEEE.

4. 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.

5. 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.

Examples

# three-dimensional function
objf <- function(x, loc) {
  val <- 0
  for (i in 1:length(x)) {
    val <- val + (x[i] - loc)^2
  }
  return(val)
}

upp_bound <- rep(5, 3)
low_bound <- rep(-5, 3)
loc_shift <- 1

alg_setting <- getPSOInfo(nSwarm = 32, maxIter = 100, psoType = "basic")
res <- globpso(objFunc = objf, lower = low_bound, upper = upp_bound, 
               PSO_INFO = alg_setting, loc = loc_shift)
res$par
res$val

# C++ function example

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")
  
alg_setting <- getPSOInfo(nSwarm = 32, maxIter = 100, psoType = "quantum")
res_c <- globpso(objFunc = objf_c, lower = low_bound, upper = upp_bound, 
                 PSO_INFO = alg_setting, loc = 1)
res_c$par
res_c$val