func main() {
// GA parameters
opt := new(goga.Optimiser)
opt.Default()
opt.Nsol = 50
opt.Ncpu = 1
opt.Tf = 1000
opt.Nsamples = 10
opt.EpsH = 1e-3
opt.Verbose = false
opt.GenType = "latin"
opt.NormFlt = false
// options for report
opt.HistNsta = 6
opt.HistLen = 13
opt.RptFmtF = "%.5f"
opt.RptFmtFdev = "%.2e"
opt.RptFmtX = "%.3f"
opt.RptName = "9"
opt.RptFref = []float64{0.0539498478}
opt.RptXref = []float64{-1.717143, 1.595709, 1.827247, -0.7636413, -0.7636450}
opt.FltMin = []float64{-2.3, -2.3, -3.2, -3.2, -3.2}
opt.FltMax = []float64{+2.3, +2.3, +3.2, +3.2, +3.2}
ng, nh := 0, 3
fcn := func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = math.Exp(x[0] * x[1] * x[2] * x[3] * x[4])
h[0] = x[0]*x[0] + x[1]*x[1] + x[2]*x[2] + x[3]*x[3] + x[4]*x[4] - 10.0
h[1] = x[1]*x[2] - 5.0*x[3]*x[4]
h[2] = math.Pow(x[0], 3.0) + math.Pow(x[1], 3.0) + 1.0
}
// check
if false {
f := make([]float64, 1)
h := make([]float64, 3)
fcn(f, nil, h, opt.RptXref, nil, 0)
io.Pforan("f(xref) = %g (%g)\n", f[0], opt.RptFref[0])
io.Pforan("h0(xref) = %g\n", h[0])
io.Pforan("h1(xref) = %g\n", h[1])
io.Pforan("h2(xref) = %g\n", h[2])
return
}
// initialise optimiser
nf := 1
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// solve
//opt.RunMany("/tmp/goga", "functions")
opt.RunMany("", "")
goga.StatF(opt, 0, true)
opts := []*goga.Optimiser{opt}
textSize := `\scriptsize \setlength{\tabcolsep}{0.5em}`
miniPageSz, histTextSize := "4.1cm", `\fontsize{5pt}{6pt}`
nRowPerTab := 9
title := "Constrained single objective problem 9"
goga.TexReport("/tmp/goga", "tmp_one-obj-prob9", title, "one-ob-prob9", 1, nRowPerTab, true, false, textSize, miniPageSz, histTextSize, opts)
goga.TexReport("/tmp/goga", "one-obj-prob9", title, "one-obj-prob9", 1, nRowPerTab, false, false, textSize, miniPageSz, histTextSize, opts)
}
func solve_problem(fnkey string, problem int) (opt *goga.Optimiser) {
// GA parameters
opt = new(goga.Optimiser)
opt.Default()
// options for report
opt.RptFmtF = "%.4f"
opt.RptFmtX = "%.3f"
opt.RptFmtFdev = "%.1e"
opt.RptWordF = "\\beta"
opt.HistFmt = "%.2f"
opt.HistNdig = 3
opt.HistDelFmin = 0.005
opt.HistDelFmax = 0.005
// FORM data
var lsft LSF_T
var vars rnd.Variables
// simple problem or FEM sim
if fnkey == "simple" {
opt.Read("ga-simple.json")
opt.ProbNum = problem
lsft, vars = get_simple_data(opt)
fnkey += io.Sf("-%d", opt.ProbNum)
io.Pf("\n----------------------------------- simple problem %d --------------------------------\n", opt.ProbNum)
} else {
opt.Read("ga-" + fnkey + ".json")
lsft, vars = get_femsim_data(opt, fnkey)
io.Pf("\n----------------------------------- femsim %s --------------------------------\n", fnkey)
}
// set limits
nx := len(vars)
opt.FltMin = make([]float64, nx)
opt.FltMax = make([]float64, nx)
for i, dat := range vars {
opt.FltMin[i] = dat.Min
opt.FltMax[i] = dat.Max
}
// log input
var buf bytes.Buffer
io.Ff(&buf, "%s", opt.LogParams())
io.WriteFileVD("/tmp/gosl", fnkey+".log", &buf)
// initialise distributions
err := vars.Init()
if err != nil {
chk.Panic("cannot initialise distributions:\n%v", err)
}
// plot distributions
if opt.PlotSet1 {
io.Pf(". . . . . . . . plot distributions . . . . . . . .\n")
np := 201
for i, dat := range vars {
plt.SetForEps(0.75, 250)
dat.PlotPdf(np, "'b-',lw=2,zorder=1000")
//plt.AxisXrange(dat.Min, dat.Max)
plt.SetXnticks(15)
plt.SaveD("/tmp/sims", io.Sf("distr-%s-%d.eps", fnkey, i))
}
return
}
// objective function
nf := 1
var ng, nh int
var fcn goga.MinProb_t
var obj goga.ObjFunc_t
switch opt.Strategy {
// argmin_x{ β(y(x)) | lsf(x) ≤ 0 }
// f ← sqrt(y dot y)
// g ← -lsf(x) ≥ 0
// h ← out-of-range in case Transform fails
case 0:
ng, nh = 1, 1
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
// original and normalised variables
h[0] = 0
y, invalid := vars.Transform(x)
if invalid {
h[0] = 1
return
}
// objective value
f[0] = math.Sqrt(la.VecDot(y, y)) // β
// inequality constraint
lsf, failed := lsft(x, cpu)
g[0] = -lsf
h[0] = failed
}
// argmin_x{ β(y(x)) | lsf(x) = 0 }
// f ← sqrt(y dot y)
// h0 ← lsf(x)
// h1 ← out-of-range in case Transform fails
case 1:
ng, nh = 0, 2
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
// original and normalised variables
h[0], h[1] = 0, 0
y, invalid := vars.Transform(x)
if invalid {
h[0], h[1] = 1, 1
return
}
// objective value
f[0] = math.Sqrt(la.VecDot(y, y)) // β
// equality constraint
lsf, failed := lsft(x, cpu)
h[0] = lsf
h[1] = failed
// induce minmisation of h0
//f[0] += math.Abs(lsf)
}
case 2:
opt.Nova = 1
opt.Noor = 2
obj = func(sol *goga.Solution, cpu int) {
// clear out-of-range values
sol.Oor[0] = 0 // invalid transformation or FEM failed
sol.Oor[1] = 0 // g(x) ≤ 0 was violated
// original and normalised variables
x := sol.Flt
y, invalid := vars.Transform(x)
if invalid {
sol.Oor[0] = goga.INF
sol.Oor[1] = goga.INF
return
}
// objective value
sol.Ova[0] = math.Sqrt(la.VecDot(y, y)) // β
// inequality constraint
lsf, failed := lsft(x, cpu)
sol.Oor[0] = failed
sol.Oor[1] = fun.Ramp(lsf)
}
default:
chk.Panic("strategy %d is not available", opt.Strategy)
}
// initialise optimiser
opt.Init(goga.GenTrialSolutions, obj, fcn, nf, ng, nh)
// solve
io.Pf(". . . . . . . . running . . . . . . . .\n")
opt.RunMany("", "")
goga.StatF(opt, 0, true)
io.Pfblue2("Tsys = %v\n", opt.SysTimeAve)
// check
goga.CheckFront0(opt, true)
// results
sols := goga.GetFeasible(opt.Solutions)
if len(sols) > 0 {
goga.SortByOva(sols, 0)
best := sols[0]
io.Pforan("x = %.6f\n", best.Flt)
io.Pforan("xref = %.6f\n", opt.RptXref)
io.Pforan("β = %v (%v)\n", best.Ova[0], opt.RptFref[0])
}
return
}
func main() {
// GA parameters
opt := new(goga.Optimiser)
opt.Default()
opt.Tf = 500
opt.Nsamples = 1000
opt.Verbose = false
opt.GenType = "latin"
// enlarge box; add more constraint equations
strategy2 := true
// options for report
opt.HistNsta = 6
opt.HistLen = 13
opt.RptFmtF = "%.5f"
opt.RptFmtFdev = "%.2e"
opt.RptFmtX = "%.3f"
opt.Ncpu = 4
opt.RptName = "2"
opt.RptFref = []float64{-15.0}
opt.RptXref = []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1}
opt.FltMin = make([]float64, 13)
opt.FltMax = make([]float64, 13)
xmin, xmax := 0.0, 1.0
if strategy2 {
xmin, xmax = -0.5, 1.5
}
for i := 0; i < 9; i++ {
opt.FltMin[i], opt.FltMax[i] = xmin, xmax
}
opt.FltMin[12], opt.FltMax[12] = xmin, xmax
xmin, xmax = 0, 100
if strategy2 {
xmin, xmax = -1, 101
}
for i := 9; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = xmin, xmax
}
ng := 9
if strategy2 {
ng += 9 + 9 + 3 + 3 + 2
}
fcn := func(f, g, h, x []float64, ξ []int, cpu int) {
s1, s2, s3 := 0.0, 0.0, 0.0
for i := 0; i < 4; i++ {
s1 += x[i]
s2 += x[i] * x[i]
}
for i := 4; i < 13; i++ {
s3 += x[i]
}
f[0] = 5.0*(s1-s2) - s3
g[0] = 10.0 - 2.0*x[0] - 2.0*x[1] - x[9] - x[10]
g[1] = 10.0 - 2.0*x[0] - 2.0*x[2] - x[9] - x[11]
g[2] = 10.0 - 2.0*x[1] - 2.0*x[2] - x[10] - x[11]
g[3] = 8.0*x[0] - x[9]
g[4] = 8.0*x[1] - x[10]
g[5] = 8.0*x[2] - x[11]
g[6] = 2.0*x[3] + x[4] - x[9]
g[7] = 2.0*x[5] + x[6] - x[10]
g[8] = 2.0*x[7] + x[8] - x[11]
if strategy2 {
for i := 0; i < 9; i++ {
g[9+i] = x[i]
g[18+i] = 1.0 - x[i]
}
for i := 0; i < 3; i++ {
g[27+i] = x[9+i]
g[30+i] = 100.0 - x[9+i]
}
g[33] = x[12]
g[34] = 1.0 - x[12]
}
}
// number of trial solutions
opt.Nsol = len(opt.FltMin) * 10
// initialise optimiser
nf, nh := 1, 0
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// solve
opt.RunMany("", "")
goga.StatF(opt, 0, true)
opts := []*goga.Optimiser{opt}
textSize := `\scriptsize \setlength{\tabcolsep}{0.5em}`
miniPageSz, histTextSize := "4.1cm", `\fontsize{5pt}{6pt}`
nRowPerTab := 9
title := "Constrained single objective problem 2"
goga.TexReport("/tmp/goga", "tmp_one-obj-prob2", title, "one-ob-prob2", 1, nRowPerTab, true, false, textSize, miniPageSz, histTextSize, opts)
goga.TexReport("/tmp/goga", "one-obj-prob2", title, "one-obj-prob2", 1, nRowPerTab, false, false, textSize, miniPageSz, histTextSize, opts)
}