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.
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.
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).