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 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 = 300
opt.Ncpu = 6
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"
// problem variables
var nf, ng, nh int // number of functions
var fcn goga.MinProb_t // functions
// problems
switch problem {
case 1:
nf = 5
opt.RptName = io.Sf("DTLZ2m%d", nf)
ng, fcn = DTLZ2mGenerator(opt, nf)
case 2:
nf = 7
opt.RptName = io.Sf("DTLZ2m%d", nf)
ng, fcn = DTLZ2mGenerator(opt, nf)
case 3:
nf = 10
opt.RptName = io.Sf("DTLZ2m%d", nf)
ng, fcn = DTLZ2mGenerator(opt, nf)
case 4:
nf = 13
opt.RptName = io.Sf("DTLZ2m%d", nf)
ng, fcn = DTLZ2mGenerator(opt, nf)
case 5:
nf = 15
opt.RptName = io.Sf("DTLZ2m%d", nf)
ng, fcn = DTLZ2mGenerator(opt, nf)
case 6:
nf = 20
opt.RptName = io.Sf("DTLZ2m%d", nf)
ng, fcn = DTLZ2mGenerator(opt, nf)
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)
// star plot
if true {
plt.SetForEps(1, 300)
goga.PlotStar(opt)
plt.SaveD("/tmp/goga", io.Sf("starplot_%s.eps", opt.RptName))
}
return
}