1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
|
JDEoptim <- function(lower, upper, fn, constr = NULL, meq = 0, eps = 1e-5,
NP = 10*length(lower), Fl = 0.1, Fu = 1,
tau_F = 0.1, tau_CR = 0.1, tau_pF = 0.1,
jitter_factor = 0.001,
tol = 1e-15, maxiter = 2000*length(lower), fnscale = 1,
compare_to = c("median", "max"),
add_to_init_pop = NULL,
trace = FALSE, triter = 1,
details = FALSE, ...)
# Copyright 2013, 2014, 2016, 2023, 2025, Eduardo L. T. Conceicao
# Available under the GPL (>= 2)
{
handle.bounds <- function(x, u) {
# Check feasibility of bounds and enforce parameters limits
# by a deterministic variant of bounce-back resetting
# (also known as midpoint target/base)
# Price, KV, Storn, RM, and Lampinen, JA (2005)
# Differential Evolution: A Practical Approach to Global Optimization.
# Springer, p 206
bad <- x > upper
x[bad] <- 0.5*(upper[bad] + u[bad])
bad <- x < lower
x[bad] <- 0.5*(lower[bad] + u[bad])
x
}
performReproduction <- function() { # Mutate/recombine
ignore <- runif(d) > CRtrial
if (all(ignore)) # ensure that trial gets at least
ignore[sample(d, 1)] <- FALSE # one mutant parameter
# Source for trial is the base vector plus weighted differential
trial <- if (runif(1) <= pFtrial)
X.base + Ftrial*(X.r1 - X.r2)
else X.base + 0.5*(Ftrial + 1)*(X.r1 + X.r2 - 2*X.base)
# or trial parameter comes from target vector X.i itself.
trial[ignore] <- X.i[ignore]
trial
}
which.best <- if (!is.null(constr))
function(x) {
ind <- TAVpop <= mu
if (all(ind))
which.min(x)
else if (any(ind))
which(ind)[which.min(x[ind])]
else which.min(TAVpop)
}
else which.min
# Check input parameters
compare_to <- match.arg(compare_to)
stopifnot(length(upper) == length(lower),
length(lower) > 0, is.numeric(lower), is.finite(lower),
length(upper) > 0, is.numeric(upper), is.finite(upper),
lower <= upper,
is.function(fn))
if (!is.null(constr))
stopifnot(is.function(constr),
length(meq) == 1, meq == as.integer(meq), meq >= 0,
is.numeric(eps), is.finite(eps), eps > 0,
length(eps) == 1 || length(eps) == meq)
stopifnot(length(NP) == 1, NP == as.integer(NP), NP >= 0,
length(Fl) == 1, is.numeric(Fl),
length(Fu) == 1, is.numeric(Fu),
Fl <= Fu)
stopifnot(length(tau_F) == 1, is.numeric(tau_F), 0 <= tau_F, tau_F <= 1,
length(tau_CR) == 1, is.numeric(tau_CR), 0 <= tau_CR, tau_CR <= 1,
length(tau_pF) == 1, is.numeric(tau_pF), 0 <= tau_pF, tau_pF <= 1)
if (!is.null(jitter_factor))
stopifnot(length(jitter_factor) == 1,
is.numeric(jitter_factor),
is.finite(jitter_factor))
stopifnot(length(tol) == 1, is.numeric(tol), is.finite(tol),
length(maxiter) == 1, maxiter == as.integer(maxiter),
maxiter >= 0,
length(fnscale) == 1, is.numeric(fnscale),
is.finite(fnscale), fnscale > 0)
if (!is.null(add_to_init_pop))
stopifnot(NROW(add_to_init_pop) == length(lower),
is.numeric(add_to_init_pop),
is.finite(add_to_init_pop),
add_to_init_pop >= lower,
add_to_init_pop <= upper)
stopifnot(length(trace) == 1, is.logical(trace), !is.na(trace),
length(triter) == 1, triter == as.integer(triter), triter >= 1,
length(details) == 1, is.logical(details), !is.na(details))
child <- if (is.null(constr)) { # Evaluate/select
expression({
ftrial <- fn1(trial)
if (ftrial <= fpop[i]) {
pop[, i] <- trial
fpop[i] <- ftrial
F[, i] <- Ftrial
CR[i] <- CRtrial
pF[i] <- pFtrial
}
})
} else if (meq > 0) { # equality constraints are present
# alongside the inequalities
# Zhang, Haibo, and Rangaiah, G. P. (2012).
# An efficient constraint handling method with integrated differential
# evolution for numerical and engineering optimization.
# Computers and Chemical Engineering 37, 74-88.
expression({
htrial <- constr1(trial)
TAVtrial <- sum( pmax(htrial, 0) )
if (TAVtrial > mu) {
if (TAVtrial <= TAVpop[i]) { # trial and target are both
pop[, i] <- trial # infeasible, the one with smaller
hpop[, i] <- htrial # constraint violation is chosen
F[, i] <- Ftrial # or trial vector when both are
CR[i] <- CRtrial # solutions of equal quality
pF[i] <- pFtrial
TAVpop[i] <- TAVtrial
}
} else if (TAVpop[i] > mu) { # trial is feasible and target is not
pop[, i] <- trial
fpop[i] <- fn1(trial)
hpop[, i] <- htrial
F[, i] <- Ftrial
CR[i] <- CRtrial
pF[i] <- pFtrial
TAVpop[i] <- TAVtrial
} else { # between two feasible solutions, the
ftrial <- fn1(trial) # one with better objective function
if (ftrial <= fpop[i]) { # value is chosen
pop[, i] <- trial # or trial vector when both are
fpop[i] <- ftrial # solutions of equal quality
hpop[, i] <- htrial
F[, i] <- Ftrial
CR[i] <- CRtrial
pF[i] <- pFtrial
TAVpop[i] <- TAVtrial
FF <- sum(TAVpop <= mu)/NP
mu <- mu*(1 - FF/NP)
}
}
})
} else { # only inequality constraints are present
expression({
htrial <- constr1(trial)
TAVtrial <- sum( pmax(htrial, 0) )
if (TAVtrial > mu) {
if (TAVtrial <= TAVpop[i]) { # trial and target both infeasible
pop[, i] <- trial
hpop[, i] <- htrial
F[, i] <- Ftrial
CR[i] <- CRtrial
pF[i] <- pFtrial
TAVpop[i] <- TAVtrial
}
} else if (TAVpop[i] > mu) { # trial is feasible and target is not
pop[, i] <- trial
fpop[i] <- fn1(trial)
hpop[, i] <- htrial
F[, i] <- Ftrial
CR[i] <- CRtrial
pF[i] <- pFtrial
TAVpop[i] <- TAVtrial
FF <- sum(TAVpop <= mu)/NP
mu <- mu*(1 - FF/NP)
} else { # two feasible solutions
ftrial <- fn1(trial)
if (ftrial <= fpop[i]) {
pop[, i] <- trial
fpop[i] <- ftrial
hpop[, i] <- htrial
F[, i] <- Ftrial
CR[i] <- CRtrial
pF[i] <- pFtrial
TAVpop[i] <- TAVtrial
FF <- sum(TAVpop <= mu)/NP
mu <- mu*(1 - FF/NP)
}
}
})
}
fn1 <- function(par) fn(par, ...)
if (!is.null(constr))
constr1 <-
if (meq > 0) {
eqI <- 1:meq
function(par) {
h <- constr(par, ...)
h[eqI] <- abs(h[eqI]) - eps
h
}
} else function(par) constr(par, ...)
use.jitter <- !is.null(jitter_factor)
# Zielinski, Karin, and Laur, Rainer (2008).
# Stopping criteria for differential evolution in
# constrained single-objective optimization.
# In: U. K. Chakraborty (Ed.), Advances in Differential Evolution,
# SCI 143, Springer-Verlag, pp 111-138
conv <- expression(
( do.call(compare_to, list(fpop)) - fpop[x.best.ind] )/fnscale
)
# Initialization
d <- length(lower)
pop <- matrix(runif(NP*d, lower, upper), nrow = d)
if (!is.null(add_to_init_pop)) {
pop <- unname(cbind(pop, add_to_init_pop))
NP <- ncol(pop)
}
stopifnot(NP >= 4)
# Combine jitter with dither
# Storn, Rainer (2008).
# Differential evolution research - trends and open questions.
# In: U. K. Chakraborty (Ed.), Advances in Differential Evolution,
# SCI 143, Springer-Verlag, pp 11-12
F <- if (use.jitter)
(1 + jitter_factor*runif(d, -0.5, 0.5)) %o% runif(NP, Fl, Fu)
else matrix(runif(NP, Fl, Fu), nrow = 1)
CR <- runif(NP)
pF <- runif(NP)
fpop <- apply(pop, 2, fn1)
stopifnot(is.vector(fpop), !anyNA(fpop), !is.nan(fpop), !is.logical(fpop))
if (!is.null(constr)) {
hpop <- apply(pop, 2, constr1)
stopifnot(is.matrix(hpop) || is.vector(hpop),
!anyNA(hpop), !is.nan(hpop), !is.logical(hpop))
if (is.vector(hpop)) dim(hpop) <- c(1, length(hpop))
TAVpop <- apply( hpop, 2, function(x) sum(pmax(x, 0)) )
mu <- median(TAVpop)
}
popIndex <- 1:NP
x.best.ind <- which.best(fpop)
converge <- eval(conv)
rule <- if (!is.null(constr))
expression(converge >= tol || any(hpop[, x.best.ind] > 0))
else expression(converge >= tol)
convergence <- 0
iteration <- 0
while (eval(rule)) { # Generation loop
if (iteration >= maxiter) {
warning("maximum number of iterations reached without convergence")
convergence <- 1
break
}
iteration <- iteration + 1
for (i in popIndex) { # Start loop through population
# Equalize the mean lifetime of all vectors
# Price, KV, Storn, RM, and Lampinen, JA (2005)
# Differential Evolution: A Practical Approach to
# Global Optimization. Springer, p 284
i <- ((iteration + i) %% NP) + 1
# Self-adjusting parameter control scheme
Ftrial <- if (runif(1) <= tau_F) {
# Combine jitter with dither
if (use.jitter)
runif(1, Fl, Fu) * (1 + jitter_factor*runif(d, -0.5, 0.5))
else runif(1, Fl, Fu)
} else F[, i]
CRtrial <- if (runif(1) <= tau_CR) runif(1) else CR[i]
pFtrial <- if (runif(1) <= tau_pF) runif(1) else pF[i]
# DE/rand/1/either-or/bin
X.i <- pop[, i]
# Randomly pick 3 vectors all diferent from target vector
r <- sample(popIndex[-i], 3)
X.base <- pop[, r[1L]]
X.r1 <- pop[, r[2L]]
X.r2 <- pop[, r[3L]]
trial <- handle.bounds(performReproduction(), X.base)
eval(child)
x.best.ind <- which.best(fpop)
}
converge <- eval(conv)
if (trace && (iteration %% triter == 0))
cat(iteration, ":", "<", converge, ">", "(", fpop[x.best.ind], ")",
pop[, x.best.ind],
if (!is.null(constr))
paste("{", which(hpop[, x.best.ind] > 0), "}"),
fill = TRUE)
}
res <- list(par = pop[, x.best.ind],
value = fpop[x.best.ind],
iter = iteration,
convergence = convergence)
if (details) {
res$poppar <- pop
res$popcost <- fpop
}
res
}
## Not exported, and only used because CRAN checks must be faster
doExtras <- function() {
interactive() || nzchar(Sys.getenv("R_DEoptimR_check_extra")) ||
identical("true", unname(Sys.getenv("R_PKG_CHECKING_doExtras")))
}
|
