isres  R Documentation 
The Improved Stochastic Ranking Evolution Strategy (ISRES) is an algorithm for nonlinearly constrained global optimization, or at least semiglobal, although it has heuristics to escape local optima.
isres(
x0,
fn,
lower,
upper,
hin = NULL,
heq = NULL,
maxeval = 10000,
pop.size = 20 * (length(x0) + 1),
xtol_rel = 1e06,
nl.info = FALSE,
deprecatedBehavior = TRUE,
...
)
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

heq 
function defining the equality constraints, that is 
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 
... 
additional arguments passed to the function. 
The evolution strategy is based on a combination of a mutation rule—with a lognormal stepsize update and exponential smoothing—and differential variation—a NelderMeadlike 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.
List with components:
par 
the optimal solution found so far. 
value 
the function value corresponding to 
iter 
number of (outer) iterations, see 
convergence 
integer code indicating successful completion (> 0) or a possible error number (< 0). 
message 
character string produced by NLopt and giving additional information. 
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
.
Hans W. Borchers
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. 233243 (2005).
## 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)
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