func solve_problem(problem int) (opt *goga.Optimiser) {
io.Pf("\n\n------------------------------------- problem = %d ---------------------------------------\n", problem)
// GA parameters
opt = new(goga.Optimiser)
opt.Default()
opt.Nsol = 200
opt.Ncpu = 5
opt.Tf = 500
opt.Nsamples = 2
opt.DEC = 0.01
// options for report
opt.HistNsta = 6
opt.HistLen = 13
opt.RptFmtE = "%.4e"
opt.RptFmtL = "%.4e"
opt.RptFmtEdev = "%.3e"
opt.RptFmtLdev = "%.3e"
opt.RptFmin = make([]float64, 3)
opt.RptFmax = make([]float64, 3)
for i := 0; i < 3; i++ {
opt.RptFmax[i] = 1
}
// problem variables
var αcone float64 // cone half-opening angle
var nf, ng, nh int // number of functions
var fcn goga.MinProb_t // functions
var plot_solution func() // plot solution in 3D
// problems
switch problem {
// DTLZ1
case 1:
opt.RptName = "DTLZ1"
opt.FltMin = make([]float64, 7)
opt.FltMax = make([]float64, 7)
for i := 0; i < 7; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
nf, ng, nh = 3, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
c := 5.0
for i := 2; i < 7; i++ {
c += math.Pow((x[i]-0.5), 2.0) - math.Cos(20.0*PI*(x[i]-0.5))
}
c *= 100.0
f[0] = 0.5 * x[0] * x[1] * (1.0 + c)
f[1] = 0.5 * x[0] * (1.0 - x[1]) * (1.0 + c)
f[2] = 0.5 * (1.0 - x[0]) * (1.0 + c)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return f[0] + f[1] + f[2] - 0.5
}
plot_solution = func() { plot_plane(false) }
opt.RptFmax = []float64{0.5, 0.5, 0.5}
// DTLZ2
case 2:
opt.RptName = "DTLZ2"
opt.FltMin = make([]float64, 12)
opt.FltMax = make([]float64, 12)
for i := 0; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
nf, ng, nh = 3, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
var c float64
for i := 2; i < 12; i++ {
c += math.Pow((x[i] - 0.5), 2.0)
}
f[0] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Cos(x[1]*PI/2.0)
f[1] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Sin(x[1]*PI/2.0)
f[2] = (1.0 + c) * math.Sin(x[0]*PI/2.0)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return f[0]*f[0] + f[1]*f[1] + f[2]*f[2] - 1.0
}
plot_solution = func() { plot_sphere(false) }
// DTLZ3
case 3:
opt.RptName = "DTLZ3"
opt.FltMin = make([]float64, 12)
opt.FltMax = make([]float64, 12)
for i := 0; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
nf, ng, nh = 3, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
c := 10.0
for i := 2; i < 12; i++ {
c += math.Pow((x[i]-0.5), 2.0) - math.Cos(20.0*PI*(x[i]-0.5))
}
c *= 100.0
f[0] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Cos(x[1]*PI/2.0)
f[1] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Sin(x[1]*PI/2.0)
f[2] = (1.0 + c) * math.Sin(x[0]*PI/2.0)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return f[0]*f[0] + f[1]*f[1] + f[2]*f[2] - 1.0
}
plot_solution = func() { plot_sphere(false) }
// DTLZ4
case 4:
opt.RptName = "DTLZ4"
opt.FltMin = make([]float64, 12)
opt.FltMax = make([]float64, 12)
for i := 0; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
nf, ng, nh = 3, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
var c float64
for i := 2; i < 12; i++ {
c += math.Pow((x[i] - 0.5), 2.0)
}
a := 100.0
f[0] = (1.0 + c) * math.Cos(math.Pow(x[0], a)*PI/2.0) * math.Cos(math.Pow(x[1], a)*PI/2.0)
f[1] = (1.0 + c) * math.Cos(math.Pow(x[0], a)*PI/2.0) * math.Sin(math.Pow(x[1], a)*PI/2.0)
f[2] = (1.0 + c) * math.Sin(math.Pow(x[0], a)*PI/2.0)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return f[0]*f[0] + f[1]*f[1] + f[2]*f[2] - 1.0
}
plot_solution = func() { plot_sphere(false) }
// DTLZ2x (convex)
case 5:
opt.RptName = "DTLZ2x"
opt.FltMin = make([]float64, 12)
opt.FltMax = make([]float64, 12)
for i := 0; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
nf, ng, nh = 3, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
var c float64
for i := 2; i < 12; i++ {
c += math.Pow((x[i] - 0.5), 2.0)
}
f[0] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Cos(x[1]*PI/2.0)
f[1] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Sin(x[1]*PI/2.0)
f[2] = (1.0 + c) * math.Sin(x[0]*PI/2.0)
f[0] = math.Pow(f[0], 4.0)
f[1] = math.Pow(f[1], 4.0)
f[2] = math.Pow(f[2], 2.0)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return math.Pow(math.Abs(f[0]), 0.5) + math.Pow(math.Abs(f[1]), 0.5) + f[2] - 1.0
}
plot_solution = func() { plot_convex(1.0, false) }
// DTLZ2c (constraint)
case 6:
opt.RptName = "DTLZ2c"
opt.FltMin = make([]float64, 12)
opt.FltMax = make([]float64, 12)
for i := 0; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
nf, ng, nh = 3, 1, 0
//αcone = math.Atan(1.0 / SQ2) // <<< touches lower plane
//αcone = PI/2.0 - αcone // <<< touches upper plane
αcone = 15.0 * PI / 180.0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
var c float64
for i := 2; i < 12; i++ {
c += math.Pow((x[i] - 0.5), 2.0)
}
f[0] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Cos(x[1]*PI/2.0)
f[1] = (1.0 + c) * math.Cos(x[0]*PI/2.0) * math.Sin(x[1]*PI/2.0)
f[2] = (1.0 + c) * math.Sin(x[0]*PI/2.0)
g[0] = math.Tan(αcone) - cone_angle(f)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return f[0]*f[0] + f[1]*f[1] + f[2]*f[2] - 1.0
}
plot_solution = func() {
plot_sphere(false)
plot_cone(αcone, true)
}
// Superquadric 1
case 7:
opt.RptName = "SUQ1"
opt.FltMin = make([]float64, 12)
opt.FltMax = make([]float64, 12)
for i := 0; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
a, b, c := 0.5, 0.5, 0.5
A, B, C := 2.0/a, 2.0/b, 2.0/c
nf, ng, nh = 3, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
var c float64
for i := 2; i < 12; i++ {
c += math.Pow((x[i] - 0.5), 2.0)
}
f[0] = (1.0 + c) * cosX(x[0]*PI/2.0, A) * cosX(x[1]*PI/2.0, A)
f[1] = (1.0 + c) * cosX(x[0]*PI/2.0, B) * sinX(x[1]*PI/2.0, B)
f[2] = (1.0 + c) * sinX(x[0]*PI/2.0, C)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return math.Pow(math.Abs(f[0]), a) + math.Pow(math.Abs(f[1]), b) + math.Pow(math.Abs(f[2]), c) - 1.0
}
plot_solution = func() { plot_superquadric(a, b, c, false) }
// Superquadric 2
case 8:
opt.RptName = "SUQ2"
opt.FltMin = make([]float64, 12)
opt.FltMax = make([]float64, 12)
for i := 0; i < 12; i++ {
opt.FltMin[i], opt.FltMax[i] = 0, 1
}
a, b, c := 2.0, 1.0, 0.5
A, B, C := 2.0/a, 2.0/b, 2.0/c
nf, ng, nh = 3, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
var c float64
for i := 2; i < 12; i++ {
c += math.Pow((x[i] - 0.5), 2.0)
}
f[0] = (1.0 + c) * cosX(x[0]*PI/2.0, A) * cosX(x[1]*PI/2.0, A)
f[1] = (1.0 + c) * cosX(x[0]*PI/2.0, B) * sinX(x[1]*PI/2.0, B)
f[2] = (1.0 + c) * sinX(x[0]*PI/2.0, C)
}
opt.Multi_fcnErr = func(f []float64) float64 {
return math.Pow(math.Abs(f[0]), a) + math.Pow(math.Abs(f[1]), b) + math.Pow(math.Abs(f[2]), c) - 1.0
}
plot_solution = func() { plot_superquadric(a, b, c, false) }
default:
chk.Panic("problem %d is not available", problem)
}
// initialise optimiser
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// solve
opt.RunMany("", "")
goga.StatMulti(opt, true)
// check
goga.CheckFront0(opt, true)
// print results
if false {
goga.SortByOva(opt.Solutions, 0)
m, l := opt.Nsol/2, opt.Nsol-1
A, B, C := opt.Solutions[0], opt.Solutions[m], opt.Solutions[l]
io.Pforan("A = %v\n", A.Flt)
io.Pforan("B = %v\n", B.Flt)
io.Pforan("C = %v\n", C.Flt)
}
// plot results
if false {
py_plot3(0, 1, nf-1, opt, plot_solution, true, true)
}
// vtk
if false {
ptRad := 0.015
if opt.RptName == "DTLZ1" {
ptRad = 0.01
}
vtk_plot3(opt, αcone, ptRad, true, true)
}
// star plot
if false {
plt.SetForEps(1, 300)
goga.PlotStar(opt)
plt.SaveD("/tmp/goga", io.Sf("starplot_%s.eps", opt.RptName))
}
// write all results
if false {
goga.WriteAllValues("/tmp/goga", "res_three-obj", opt)
}
return
}
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")
}
}