isres: Improved Stochastic Ranking Evolution Strategy

In nloptr: R Interface to NLopt

Improved Stochastic Ranking Evolution Strategy

Description

The Improved Stochastic Ranking Evolution Strategy (ISRES) is an algorithm for nonlinearly constrained global optimization, or at least semi-global, although it has heuristics to escape local optima.

Usage

isres(
  x0,
  fn,
  lower,
  upper,
  hin = NULL,
  heq = NULL,
  maxeval = 10000,
  pop.size = 20 * (length(x0) + 1),
  xtol_rel = 1e-06,
  nl.info = FALSE,
  deprecatedBehavior = TRUE,
  ...
)

Arguments

x0	initial point for searching the optimum.
fn	objective function that is to be minimized.
lower, upper	lower and upper bound constraints.
hin	function defining the inequality constraints, that is hin <= 0 for all components.
heq	function defining the equality constraints, that is heq = 0 for all components.
maxeval	maximum number of function evaluations.
pop.size	population size.
xtol_rel	stopping criterion for relative change reached.
nl.info	logical; shall the original NLopt info be shown.
deprecatedBehavior	logical; if TRUE (default for now), the old behavior of the Jacobian function is used, where the equality is \ge 0 instead of \le 0. This will be reversed in a future release and eventually removed.
...	additional arguments passed to the function.

Details

The evolution strategy is based on a combination of a mutation rule—with a log-normal step-size update and exponential smoothing—and differential variation—a Nelder-Mead-like update rule). The fitness ranking is simply via the objective function for problems without nonlinear constraints, but when nonlinear constraints are included the stochastic ranking proposed by Runarsson and Yao is employed.

This method supports arbitrary nonlinear inequality and equality constraints in addition to the bounds constraints.

Value

List with components:

par	the optimal solution found so far.
value	the function value corresponding to par.
iter	number of (outer) iterations, see maxeval.
convergence	integer code indicating successful completion (> 0) or a possible error number (< 0).
message	character string produced by NLopt and giving additional information.

Note

The initial population size for CRS defaults to 20x(n+1) in n dimensions, but this can be changed. The initial population must be at least n+1.

Author(s)

Hans W. Borchers

References

Thomas Philip Runarsson and Xin Yao, “Search biases in constrained evolutionary optimization,” IEEE Trans. on Systems, Man, and Cybernetics Part C: Applications and Reviews, vol. 35 (no. 2), pp. 233-243 (2005).

Examples

## Rosenbrock Banana objective function

rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2}

x0 <- c(-1.2, 1)
lb <- c(-3, -3)
ub <- c(3,  3)

## The function as written above has a minimum of 0 at (1, 1)

isres(x0 = x0, fn = rbf, lower = lb, upper = ub)

## Now subject to the inequality that x[1] + x[2] <= 1.5

hin <- function(x) {x[1] + x[2] - 1.5}

S <- isres(x0 = x0, fn = rbf, hin = hin, lower = lb, upper = ub,
           maxeval = 2e5L, deprecatedBehavior = FALSE)

S

sum(S$par)

nloptr documentation built on July 4, 2024, 1:08 a.m.