func main() {
// GA parameters
opt := new(goga.Optimiser)
opt.Default()
opt.Nsol = 6
opt.Ncpu = 1
opt.Tf = 10
opt.EpsH = 1e-3
opt.Verbose = true
opt.GenType = "latin"
//opt.GenType = "halton"
//opt.GenType = "rnd"
opt.NormFlt = false
opt.UseMesh = true
opt.Nbry = 3
// define problem
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])
}
// initialise optimiser
nf := 1
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// output function
T := make([]float64, opt.Tf+1) // [nT]
X := utl.Deep3alloc(opt.Nflt, opt.Nsol, opt.Tf+1) // [nx][nsol][nT]
F := utl.Deep3alloc(opt.Nova, opt.Nsol, opt.Tf+1) // [nf][nsol][nT]
U := utl.Deep3alloc(opt.Noor, opt.Nsol, opt.Tf+1) // [nu][nsol][nT]
opt.Output = func(time int, sols []*goga.Solution) {
T[time] = float64(time)
for j, s := range sols {
for i := 0; i < opt.Nflt; i++ {
X[i][j][time] = s.Flt[i]
}
for i := 0; i < opt.Nova; i++ {
F[i][j][time] = s.Ova[i]
}
for i := 0; i < opt.Noor; i++ {
U[i][j][time] = s.Oor[i]
}
}
}
// initial population
fnk := "one-obj-prob9-dbg"
//S0 := opt.GetSolutionsCopy()
goga.WriteAllValues("/tmp/goga", fnk, opt)
// solve
opt.Solve()
// print
if false {
io.Pf("%13s%13s%13s%13s%10s\n", "f0", "u0", "u1", "u2", "feasible")
for _, s := range opt.Solutions {
io.Pf("%13.5e%13.5e%13.5e%13.5e%10v\n", s.Ova[0], s.Oor[0], s.Oor[1], s.Oor[2], s.Feasible())
}
}
// plot: time series
//a, b := 100, len(T)
a, b := 0, 1 //len(T)
if false {
plt.SetForEps(2.0, 400)
nrow := opt.Nflt + opt.Nova + opt.Noor
for j := 0; j < opt.Nsol; j++ {
for i := 0; i < opt.Nflt; i++ {
plt.Subplot(nrow, 1, 1+i)
plt.Plot(T[a:b], X[i][j][a:b], "")
plt.Gll("$t$", io.Sf("$x_%d$", i), "")
}
}
for j := 0; j < opt.Nsol; j++ {
for i := 0; i < opt.Nova; i++ {
plt.Subplot(nrow, 1, 1+opt.Nflt+i)
plt.Plot(T[a:b], F[i][j][a:b], "")
plt.Gll("$t$", io.Sf("$f_%d$", i), "")
}
}
for j := 0; j < opt.Nsol; j++ {
for i := 0; i < opt.Noor; i++ {
plt.Subplot(nrow, 1, 1+opt.Nflt+opt.Nova+i)
plt.Plot(T[a:b], U[i][j][a:b], "")
plt.Gll("$t$", io.Sf("$u_%d$", i), "")
}
}
plt.SaveD("/tmp/goga", fnk+"-time.eps")
}
// plot: x-relationships
if true {
plt.SetForEps(1, 700)
ncol := opt.Nflt - 1
for i := 0; i < opt.Nflt-1; i++ {
for j := i + 1; j < opt.Nflt; j++ {
plt.Subplot(ncol, ncol, i*ncol+j)
if opt.UseMesh {
opt.Meshes[i][j].CalcDerived(0)
opt.Meshes[i][j].Draw2d(false, false, nil, 0)
}
for k := 0; k < opt.Nsol; k++ {
plt.Plot(X[i][k][a:b], X[j][k][a:b], "ls='none', marker='.'")
}
plt.Gll(io.Sf("$x_%d$", i), io.Sf("$x_%d$", j), "")
}
}
plt.SaveD("/tmp/goga", fnk+"-x.eps")
}
}
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)
}
// Output:
// lsf -- limit state function
// βref -- reference β (if available)
// vars -- random variables data
func get_simple_data(opt *goga.Optimiser) (lsf LSF_T, vars rnd.Variables) {
var desc string
var βref float64
var xref []float64
switch opt.ProbNum {
case 1:
desc = "SMB1/BS5"
lsf = func(x []float64, cpu int) (float64, float64) {
return 0.1*math.Pow(x[0]-x[1], 2) - (x[0]+x[1])/SQ2 + 2.5, 0.0
}
βref = 2.5 // from SMB
xref = []float64{1.7677, 1.7677}
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
}
case 2:
desc = "SMB2/BS6"
lsf = func(x []float64, cpu int) (float64, float64) {
return -0.5*math.Pow(x[0]-x[1], 2) - (x[0]+x[1])/SQ2 + 3, 0.0
}
βref = 1.658 // from BS6
xref = []float64{-0.7583, 1.4752}
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
}
case 3:
desc = "SMB3/GR6"
lsf = func(x []float64, cpu int) (float64, float64) {
return 2 - x[1] - 0.1*math.Pow(x[0], 2) + 0.06*math.Pow(x[0], 3), 0.0
}
βref = 2 // from SMB
xref = []float64{0, 2}
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
}
case 4:
desc = "SMB4/GR8"
lsf = func(x []float64, cpu int) (float64, float64) {
return 3 - x[1] + 256*math.Pow(x[0], 4), 0.0
}
βref = 3 // from SMB
xref = []float64{0, 3}
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
}
case 5:
desc = "SMB5/GW1" // modified GW1
shift := 0.0 // 0.1
lsf = func(x []float64, cpu int) (float64, float64) {
return 1 + math.Pow(x[0]+x[1]+shift, 2)/4 - 4*math.Pow(x[0]-x[1]+shift, 2), 0.0
}
βref = 0.3536 // from SMB
xref = []float64{-βref * SQ2 / 2.0, βref * SQ2 / 2.0}
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
&rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20},
}
case 6:
desc = "SMB7/SSGK1a" // SSGK case 1
lsf = func(x []float64, cpu int) (float64, float64) {
return math.Pow(x[0], 3) + math.Pow(x[1], 3) - 18, 0.0
}
βref = 2.2401 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 5, Min: -50, Max: 50},
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 5, Min: -50, Max: 50},
}
case 7:
desc = "SMB8/SSGK1b" // SSGK case 2
lsf = func(x []float64, cpu int) (float64, float64) {
return math.Pow(x[0], 3) + math.Pow(x[1], 3) - 18, 0.0
}
βref = 2.2260 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 5, Min: -50, Max: 50},
&rnd.VarData{D: rnd.D_Normal, M: 9.9, S: 5, Min: -50, Max: 50},
}
case 8:
desc = "SMB9/GR7"
lsf = func(x []float64, cpu int) (float64, float64) {
return 2.5 - 0.2357*(x[0]-x[1]) + 0.0046*math.Pow(x[0]+x[1]-20, 4), 0.0
}
βref = 2.5 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 3, Min: -50, Max: 50},
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 3, Min: -50, Max: 50},
}
case 9:
desc = "SMB10/SSGK2"
lsf = func(x []float64, cpu int) (float64, float64) {
return math.Pow(x[0], 3) + math.Pow(x[1], 3) - 67.5, 0.0
}
βref = 1.9003 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 5, Min: -50, Max: 50},
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 5, Min: -50, Max: 50},
}
case 10:
desc = "SMB11/GR2"
lsf = func(x []float64, cpu int) (float64, float64) {
return x[0]*x[1] - 146.14, 0.0
}
βref = 5.4280 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 78064.4, S: 11709.7, Min: 1000, Max: 150000},
&rnd.VarData{D: rnd.D_Normal, M: 0.0104, S: 0.00156, Min: -0.05, Max: 0.05},
}
case 11:
desc = "SMB12/GW2"
lsf = func(x []float64, cpu int) (float64, float64) {
return 2.2257 - 0.025*SQ2*math.Pow(x[0]+x[1]-20, 3)/27 + 0.2357*(x[0]-x[1]), 0.0
}
βref = 2.2257 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 3, Min: -50, Max: 50},
&rnd.VarData{D: rnd.D_Normal, M: 10, S: 3, Min: -50, Max: 50},
}
case 12:
desc = "SMB14/HM7.6"
lsf = func(x []float64, cpu int) (float64, float64) {
return x[0]*x[1] - 1140, 0.0
}
βref = 5.2127 // from SMB // from here: 5.210977819456551
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Lognormal, M: 38, S: 3.8, Min: 20, Max: 60},
&rnd.VarData{D: rnd.D_Lognormal, M: 54, S: 2.7, Min: 40, Max: 70},
}
// more than 2 variables -----------------------------------------------------------------
case 13:
desc = "SMB6/GR3"
lsf = func(x []float64, cpu int) (float64, float64) {
sum := 0.0
for i := 0; i < 9; i++ {
sum += x[i] * x[i]
}
return 2.0 - 0.015*sum - x[9], 0.0
}
βref = 2.0 // from SMB
vars = make([]*rnd.VarData, 10)
for i := 0; i < 10; i++ {
vars[i] = &rnd.VarData{D: rnd.D_Normal, M: 0, S: 1, Min: -20, Max: 20}
}
opt.Nsol = 120
opt.Ncpu = 4
case 14:
desc = "KLH1/CX1"
lsf = func(x []float64, cpu int) (float64, float64) {
return x[0] + 2.0*x[1] + 2.0*x[2] + x[3] - 5.0*x[4] - 5.0*x[5], 0.0
}
βref = 2.348 // from CX1
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 50, S: 15, Min: 5, Max: 150},
&rnd.VarData{D: rnd.D_Lognormal, M: 40, S: 12, Min: 5, Max: 120},
}
opt.Nsol = 60
opt.Ncpu = 2
case 15:
desc = "SMB16/KLH2"
lsf = func(x []float64, cpu int) (float64, float64) {
s := x[0] + 2.0*x[1] + 2.0*x[2] + x[3] - 5.0*x[4] - 5.0*x[5]
for i := 0; i < 6; i++ {
s += 0.001 * math.Sin(1000*x[i])
}
return s, 0.0
}
βref = 2.3482 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 120, S: 12, Min: 50, Max: 200},
&rnd.VarData{D: rnd.D_Lognormal, M: 50, S: 15, Min: 5, Max: 150},
&rnd.VarData{D: rnd.D_Lognormal, M: 40, S: 12, Min: 5, Max: 120},
}
opt.Nsol = 60
opt.Ncpu = 2
case 16:
desc = "SMB17/MS5"
lsf = func(x []float64, cpu int) (float64, float64) {
return -240758.1777 + 10467.364*x[0] + 11410.63*x[1] +
3505.3015*x[2] - 246.81*x[0]*x[0] - 285.3275*x[1]*x[1] - 195.46*x[2]*x[2], 0.0
}
βref = 0.8292 // from SMB
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Lognormal, M: 21.2, S: 0.1, Min: 20, Max: 22},
&rnd.VarData{D: rnd.D_Lognormal, M: 20.0, S: 0.2, Min: 19, Max: 21},
&rnd.VarData{D: rnd.D_Lognormal, M: 9.2, S: 0.1, Min: 8, Max: 10},
}
opt.Nsol = 30
case 17:
desc = "SMB18/SSGK4a" // SSGK case 1
lsf = func(x []float64, cpu int) (float64, float64) {
return x[0]*x[1] - 78.12*x[2], 0.0
}
βref = 3.3221 // from SMB or 3.31819 from SSGK
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Normal, M: 2e7, S: 5e6, Min: 1e6, Max: 4e7},
&rnd.VarData{D: rnd.D_Normal, M: 1e-4, S: 2e-5, Min: 1e-5, Max: 2e-4},
&rnd.VarData{D: rnd.D_Gumbel, M: 4, S: 1.0, Min: 1, Max: 15},
}
opt.Nsol = 30
case 18:
desc = "SMB19/SSGK4b" // SSGK case 2
lsf = func(x []float64, cpu int) (float64, float64) {
return x[0]*x[1] - 78.12*x[2], 0.0
}
βref = 4.45272 // from SSGK
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Lognormal, M: 2e7, S: 5e6, Min: 1e6, Max: 5e7},
&rnd.VarData{D: rnd.D_Lognormal, M: 1e-4, S: 2e-5, Min: 1e-5, Max: 3e-4},
&rnd.VarData{D: rnd.D_Gumbel, M: 4, S: 1.0, Min: 1, Max: 15},
}
opt.Nsol = 30
case 19:
desc = "SMB20/SSGK5"
lsf = func(x []float64, cpu int) (float64, float64) {
return 1.1 - 0.00115*x[0]*x[1] + 0.00157*x[1]*x[1] + 0.00117*x[0]*x[0] +
+0.0135*x[1]*x[2] - 0.0705*x[1] - 0.00534*x[0] - 0.0149*x[0]*x[2] +
-0.0611*x[1]*x[3] + 0.0717*x[0]*x[3] - 0.226*x[2] + 0.0333*x[2]*x[2] +
-0.558*x[2]*x[3] + 0.998*x[3] - 1.339*x[3]*x[3], 0.0
}
βref = 2.42031 // from SSGK
vars = rnd.Variables{
&rnd.VarData{D: rnd.D_Frechet, L: 8.782275, A: 4.095645, Min: 8, Max: 12},
&rnd.VarData{D: rnd.D_Normal, M: 25, S: 5, Min: 5, Max: 50},
&rnd.VarData{D: rnd.D_Normal, M: 0.8, S: 0.2, Min: 0.1, Max: 2.0},
&rnd.VarData{D: rnd.D_Lognormal, M: 0.0625, S: 0.0625, Min: 0.001, Max: 0.4},
}
opt.Nsol = 40
default:
chk.Panic("simple problem number %d is invalid", opt.ProbNum)
}
opt.RptName = desc
opt.RptName = io.Sf("%d", opt.ProbNum)
opt.RptFref = []float64{βref}
opt.RptXref = xref
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)
}
