BSASoptim: Implementation of the Beetle Swarm Antennae Search (BSAS)...
In jywang2016/rBAS: Implementation of the BAS algorithm and its mutation

Description Usage Arguments Value References Examples

You could find more information about BSAS in https://arxiv.org/abs/1807.10470.

BSASoptim(fn, init = NULL, lower = c(-6, 0), upper = c(-1, 2),
  k = 5, constr = NULL, d0 = 0.001, d1 = 3, eta_d = 0.95,
  l0 = 0, l1 = 0, eta_l = 0.95, step = 0.8, eta_step = 0.95,
  n = 200, seed = NULL, trace = T, steptol = 0.01, p_min = 0.2,
  p_step = 0.2, n_flag = 2, pen = 1e+05)

`fn`	objective function; function need to be optimized
`init`	default = NULL, it will generate randomly; Of course, you can specify it.
`lower`	lower of parameters to be estimated; Default = c(-6,0) because of the test on Michalewicz function of which thelower is c(-6,0); By the way, you should set one of init or lower parameter at least to make the code know the dimensionality of your problem.
`upper`	upper of parameters; Default = c(-1,2).
`k`	a positive integer.k is the number of beetles for exploring in every iteration.
`constr`	constraint function. For example, you can formulate x<=10 as constr = function(x) return(x - 10).
`d0`	a constant to gurantee that sensing length of antennae d doesn't equal to zero. More specifically, d^t = η_d d^{t-1} + d_0* where attenuation coefficient η_d belongs to [0,1]
`d1`	initial value of antenae length. You can specify it according to your problem scale
`eta_d`	attenuation coefficient of sensing length of antennae
`l0`	position jitter factor constant.Default = 0.
`l1`	initial position jitter factor.Default = 0. x = x - step dir * sign(fn(left) - fn(right)) + l random(npars)
`eta_l`	attenuation coefficient of jitter factor. l^t = η_l l^{t-1} + l_0*
`step`	initial step-size of beetle
`eta_step`	attenuation coefficient of step-size. step^t = η_step step^{t-1}*
`n`	iterations times
`seed`	random seed; default = NULL ; The results of BAS depend on random init value and random directions. Therefore, if you set a random seed, for example,`seed = 1`, the results will remain the same no matter how many times you repeat your experiments.
`trace`	default = T; trace the process of BAS iteration.
`steptol`	default = 0.01; Iteration will stop if step-size in current moment is less than steptol.
`p_min`	a constant belongs to [0,1]. If random generated value is lager than p_min and there are better positions in k beetles than current position, the next position of beetle will be the best position in k beetles. x_{best} = argmin(fn(x_i^t)) where i belongs [1,2,...,k] If random generated value is smaller than(<=) p_min and there are better positions in k beetles than current position, the next position of the beetle could be the random position within better positions.
`p_step`	a constant belongs to [0,1].If no better position in k beetles than current position, there is still a samll probability that step-size doesn't update. If you set a little k, you could set p_step slightly large.
`n_flag`	an positive integer; default = 2; If step-size doesn't update for successive n_flag times because p_step is larger than random generated value, the step-size will be forced updating. If you set a large p_step, set a small n_flag is suggested.
`pen`	penalty conefficient usually predefined as a large enough value, default 1e5

A list including best beetle position (parameters) and corresponding objective function value.

X. Y. Jiang, and S. Li, BAS: beetle antennae search algorithm for optimization problems, arXiv:1710.10724v1.

#======== examples start =======================
# >>>>>> example without constraint: Michalewicz function <<<<<<
library(rBAS)
mich <- function(x){
   y1 <- -sin(x[1])*(sin((x[1]^2)/pi))^20
   y2 <- -sin(x[2])*(sin((2*x[2]^2)/pi))^20
   return(y1+y2)
}
result <- BSASoptim(fn = mich,
                    lower = c(-6,0), upper = c(-1,2),
                    seed = 1, n = 100,k=5,step = 0.6,
                    trace = FALSE)
result$par
result$value

# >>>> example with constraint: Mixed integer nonlinear programming <<<<
pressure_Vessel <- list(
  obj = function(x){
    x1 <- floor(x[1])*0.0625
    x2 <- floor(x[2])*0.0625
    x3 <- x[3]
    x4 <- x[4]
    result <- 0.6224*x1*x3*x4 + 1.7781*x2*x3^2 +3.1611*x1^2*x4 + 19.84*x1^2*x3
  },
  con = function(x){
    x1 <- floor(x[1])*0.0625
    x2 <- floor(x[2])*0.0625
    x3 <- x[3]
    x4 <- x[4]
    c(
      0.0193*x3 - x1,
      0.00954*x3 - x2,
      750.0*1728.0 - pi*x3^2*x4 - 4/3*pi*x3^3
    )
  }
)
result <- BSASoptim(fn = pressure_Vessel$obj,
                    k = 10,
                    lower =c( 1, 1, 10, 10),
                    upper = c(100, 100, 200, 200),
                    constr = pressure_Vessel$con,
                    n = 200,
                    step = 100,
                    d1 = 4,
                    pen = 1e6,
                    steptol = 1e-6,
                    n_flag = 2,
                    seed = 2,trace = FALSE)

result$par
result$value

# >>>> example with constraint: Himmelblau function <<<<
himmelblau <- list(
  obj = function(x){
    x1 <- x[1]
    x3 <- x[3]
    x5 <- x[5]
    result <- 5.3578547*x3^2 + 0.8356891*x1*x5 + 37.29329*x[1] - 40792.141
  },
  con = function(x){
    x1 <- x[1]
    x2 <- x[2]
    x3 <- x[3]
    x4 <- x[4]
    x5 <- x[5]
    g1 <- 85.334407 + 0.0056858*x2*x5 + 0.00026*x1*x4 - 0.0022053*x3*x5
    g2 <- 80.51249 + 0.0071317*x2*x5 + 0.0029955*x1*x2 + 0.0021813*x3^2
    g3 <- 9.300961 + 0.0047026*x3*x5 + 0.0012547*x1*x3 + 0.0019085*x3*x4
    c(
      -g1,
      g1-92,
      90-g2,
      g2 - 110,
      20 - g3,
      g3 - 25
    )
  }
)
result <- BSASoptim(fn = himmelblau$obj,
                    k = 5,
                    lower =c(78,33,27,27,27),
                    upper = c(102,45,45,45,45),
                    constr = himmelblau$con,
                    n = 200,
                    step = 100,
                    d1 = 10,
                    pen = 1e6,
                    steptol = 1e-6,
                    n_flag = 2,
                    seed = 11,trace = FALSE)
result$par # 78.01565 33.00000 27.07409 45.00000 44.95878
result$value # -31024.17
#======== examples end =======================