R: Improved Stochastic Ranking Evolution Strategy

isres {nloptr} | R Documentation

## Improved Stochastic Ranking Evolution Strategy

### Description

The Improved Stochastic Ranking Evolution Strategy (ISRES) 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, ...)

### 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 been shown.
`...` | 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 bound 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
    fn <- function(x)
        return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 )

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

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

[Package nloptr version 1.2.2.2 Index]