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 runone(ncpu int) (nsol, tf int, elaspsedTime time.Duration) {
// input filename
fn, fnkey := io.ArgToFilename(0, "ground10", ".sim", true)
// GA parameters
var opt goga.Optimiser
opt.Read("ga-" + fnkey + ".json")
opt.GenType = "rnd"
nsol, tf = opt.Nsol, opt.Tf
postproc := true
if ncpu > 0 {
opt.Ncpu = ncpu
postproc = false
}
// FEM
data := make([]*FemData, opt.Ncpu)
for i := 0; i < opt.Ncpu; i++ {
data[i] = NewData(fn, fnkey, i)
}
io.Pforan("MaxWeight = %v\n", data[0].MaxWeight)
// set integers
if data[0].Opt.BinInt {
opt.CxInt = goga.CxInt
opt.MtInt = goga.MtIntBin
opt.BinInt = data[0].Ncells
}
// set floats
opt.FltMin = make([]float64, data[0].Nareas)
opt.FltMax = make([]float64, data[0].Nareas)
for i := 0; i < data[0].Nareas; i++ {
opt.FltMin[i] = data[0].Opt.Amin
opt.FltMax[i] = data[0].Opt.Amax
}
// initialise optimiser
opt.Nova = 2 // weight and deflection
opt.Noor = 4 // mobility, feasibility, maxdeflection, stress
opt.Init(goga.GenTrialSolutions, func(sol *goga.Solution, cpu int) {
mob, fail, weight, umax, _, errU, errS := data[cpu].RunFEM(sol.Int, sol.Flt, 0, false)
sol.Ova[0] = weight
sol.Ova[1] = umax
sol.Oor[0] = mob
sol.Oor[1] = fail
sol.Oor[2] = errU
sol.Oor[3] = errS
}, nil, 0, 0, 0)
// initial solutions
var sols0 []*goga.Solution
if false {
sols0 = opt.GetSolutionsCopy()
}
// benchmark
initialTime := time.Now()
defer func() {
elaspsedTime = time.Now().Sub(initialTime)
}()
// solve
opt.Verbose = true
opt.Solve()
goga.SortByOva(opt.Solutions, 0)
// post processing
if !postproc {
return
}
// check
nfailed, front0 := goga.CheckFront0(&opt, true)
// save results
var log, res bytes.Buffer
io.Ff(&log, opt.LogParams())
io.Ff(&res, PrintSolutions(data[0], opt.Solutions))
io.Ff(&res, io.Sf("\n\nnfailed = %d\n", nfailed))
io.WriteFileVD("/tmp/goga", fnkey+".log", &log)
io.WriteFileVD("/tmp/goga", fnkey+".res", &res)
// plot Pareto-optimal front
feasibleOnly := true
plt.SetForEps(0.8, 350)
if strings.HasPrefix(fnkey, "ground10") {
_, ref, _ := io.ReadTable("p460_fig300.dat")
plt.Plot(ref["w"], ref["u"], "'b-', label='reference'")
}
fmtAll := &plt.Fmt{L: "final solutions", M: ".", C: "orange", Ls: "none", Ms: 3}
fmtFront := &plt.Fmt{L: "final Pareto front", C: "r", M: "o", Ms: 3, Ls: "none"}
goga.PlotOvaOvaPareto(&opt, sols0, 0, 1, feasibleOnly, fmtAll, fmtFront)
plt.Gll("weight ($f_0$)", "deflection ($f_1)$", "") //, "leg_out=1, leg_ncol=4, leg_hlen=1.5")
if strings.HasPrefix(fnkey, "ground10") {
plt.AxisRange(1800, 14000, 1, 6)
}
// plot selected results
ia, ib, ic, id, ie := 0, 0, 0, 0, 0
nfront0 := len(front0)
io.Pforan("nfront0 = %v\n", nfront0)
if nfront0 > 4 {
ib = nfront0 / 10
ic = nfront0 / 5
id = nfront0 / 2
ie = nfront0 - 1
}
A := front0[ia]
B := front0[ib]
C := front0[ic]
D := front0[id]
E := front0[ie]
wid, hei := 0.20, 0.10
draw_truss(data[0], "A", A, 0.17, 0.75, wid, hei)
draw_truss(data[0], "B", B, 0.20, 0.55, wid, hei)
draw_truss(data[0], "C", C, 0.28, 0.33, wid, hei)
draw_truss(data[0], "D", D, 0.47, 0.22, wid, hei)
draw_truss(data[0], "E", E, 0.70, 0.18, wid, hei)
// save figure
plt.SaveD("/tmp/goga", fnkey+".eps")
// tex file
title := "Shape and topology optimisation. Results."
label := "topoFront"
document := true
compact := true
tex_results("/tmp/goga", "tmp_"+fnkey, title, label, data[0], A, B, C, D, E, document, compact)
document = false
tex_results("/tmp/goga", fnkey, title, label, data[0], A, B, C, D, E, document, compact)
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 = 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)
// parameters
opt = new(goga.Optimiser)
opt.Default()
opt.Ncpu = 1
opt.Tf = 500
opt.Verbose = false
opt.Nsamples = 2
opt.GenType = "latin"
opt.DEC = 0.1
// options for report
opt.HistNsta = 6
opt.HistLen = 13
opt.RptFmtE = "%.4e"
opt.RptFmtL = "%.4e"
opt.RptFmtEdev = "%.3e"
opt.RptFmtLdev = "%.3e"
// problem variables
var fmin, fmax []float64
var nf, ng, nh int
var fcn goga.MinProb_t
// problems
switch problem {
// problem # 1 -- ZDT1, Deb 2001, p356
case 1:
opt.Ncpu = 6
opt.RptName = "ZDT1"
n := 30
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
c0 := 1.0 + 9.0*sum/float64(n-1)
c1 := 1.0 - math.Sqrt(f[0]/c0)
f[1] = c0 * c1
}
fmin = []float64{0, 0}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Sqrt(f0)
}
// arc length = sqrt(5)/2 + log(sqrt(5)+2)/4 ≈ 1.4789428575445975
opt.F1F0_arcLenRef = math.Sqrt(5.0)/2.0 + math.Log(math.Sqrt(5.0)+2.0)/4.0
// problem # 2 -- ZDT2, Deb 2001, p356
case 2:
opt.Ncpu = 6
opt.RptName = "ZDT2"
n := 30
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
c0 := 1.0 + 9.0*sum/float64(n-1)
c1 := 1.0 - math.Pow(f[0]/c0, 2.0)
f[1] = c0 * c1
}
fmin = []float64{0, 0}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Pow(f0, 2.0)
}
// arc length = sqrt(5)/2 + log(sqrt(5)+2)/4 ≈ 1.4789428575445975
opt.F1F0_arcLenRef = math.Sqrt(5.0)/2.0 + math.Log(math.Sqrt(5.0)+2.0)/4.0
// problem # 3 -- ZDT3, Deb 2001, p356
case 3:
opt.Ncpu = 6
opt.RptName = "ZDT3"
n := 30
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
c0 := 1.0 + 9.0*sum/float64(n-1)
c1 := 1.0 - math.Sqrt(f[0]/c0) - math.Sin(10.0*math.Pi*f[0])*f[0]/c0
f[1] = c0 * c1
}
fmin = []float64{0, -1}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Sqrt(f0) - math.Sin(10.0*math.Pi*f0)*f0
}
opt.F1F0_f0ranges = [][]float64{
{0.000000100000000, 0.083001534925223},
{0.182228728029413, 0.257762363387862},
{0.409313674808657, 0.453882104088830},
{0.618396794416602, 0.652511703804663},
{0.823331798326633, 0.851832865436414},
}
opt.F1F0_arcLenRef = 1.811
// problem # 4 -- ZDT4, Deb 2001, p358
case 4:
opt.Ncpu = 2
opt.RptName = "ZDT4"
n := 10
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
opt.FltMin[0] = 0
opt.FltMax[0] = 1
for i := 1; i < n; i++ {
opt.FltMin[i] = -5
opt.FltMax[i] = 5
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
w := 4.0 * math.Pi
for i := 1; i < n; i++ {
sum += x[i]*x[i] - 10.0*math.Cos(w*x[i])
}
c0 := 1.0 + 10.0*float64(n-1) + sum
c1 := 1.0 - math.Sqrt(f[0]/c0)
f[1] = c0 * c1
}
fmin = []float64{0, 0}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Sqrt(f0)
}
// arc length = sqrt(5)/2 + log(sqrt(5)+2)/4 ≈ 1.4789428575445975
opt.F1F0_arcLenRef = math.Sqrt(5.0)/2.0 + math.Log(math.Sqrt(5.0)+2.0)/4.0
// problem # 5 -- FON (Fonseca and Fleming 1995), Deb 2001, p339
case 5:
opt.DEC = 0.8
opt.Ncpu = 2
opt.RptName = "FON"
n := 10
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = -4
opt.FltMax[i] = 4
}
nf, ng, nh = 2, 0, 0
coef := 1.0 / math.Sqrt(float64(n))
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
sum0, sum1 := 0.0, 0.0
for i := 0; i < n; i++ {
sum0 += math.Pow(x[i]-coef, 2.0)
sum1 += math.Pow(x[i]+coef, 2.0)
}
f[0] = 1.0 - math.Exp(-sum0)
f[1] = 1.0 - math.Exp(-sum1)
}
fmin = []float64{0, 0}
fmax = []float64{0.98, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Exp(-math.Pow(2.0-math.Sqrt(-math.Log(1.0-f0)), 2.0))
}
opt.F1F0_arcLenRef = 1.45831385
// problem # 6 -- ZDT6, Deb 2001, p360
case 6:
opt.Ncpu = 2
opt.RptName = "ZDT6"
n := 10
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
w := 6.0 * math.Pi
f[0] = 1.0 - math.Exp(-4.0*x[0])*math.Pow(math.Sin(w*x[0]), 6.0)
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
w = float64(n - 1)
c0 := 1.0 + 9.0*math.Pow(sum/w, 0.25)
c1 := 1.0 - math.Pow(f[0]/c0, 2.0)
f[1] = c0 * c1
}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Pow(f0, 2.0)
}
xs := math.Atan(9.0*math.Pi) / (6.0 * math.Pi)
f0min := 1.0 - math.Exp(-4.0*xs)*math.Pow(math.Sin(6.0*math.Pi*xs), 6.0)
f1max := opt.F1F0_func(f0min)
io.Pforan("xs=%v f0min=%v f1max=%v\n", xs, f0min, f1max)
// xs=0.08145779687998356 f0min=0.2807753188153699 f1max=0.9211652203441274
fmin = []float64{f0min, 0}
fmax = []float64{1, 1}
opt.F1F0_arcLenRef = 1.184
default:
chk.Panic("problem %d is not available", problem)
}
// number of trial solutions and number of groups
opt.Nsol = len(opt.FltMin) * 10
// initialise optimiser
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// initial solutions
var sols0 []*goga.Solution
if false {
sols0 = opt.GetSolutionsCopy()
}
// solve
opt.RunMany("", "")
goga.StatF1F0(opt, true)
// check
goga.CheckFront0(opt, true)
// plot
if true {
feasibleOnly := true
plt.SetForEps(0.8, 300)
fmtAll := &plt.Fmt{L: "final solutions", M: ".", C: "orange", Ls: "none", Ms: 3}
fmtFront := &plt.Fmt{L: "final Pareto front", C: "r", M: "o", Ms: 3, Ls: "none"}
goga.PlotOvaOvaPareto(opt, sols0, 0, 1, feasibleOnly, fmtAll, fmtFront)
np := 201
F0 := utl.LinSpace(fmin[0], fmax[0], np)
F1 := make([]float64, np)
for i := 0; i < np; i++ {
F1[i] = opt.F1F0_func(F0[i])
}
plt.Plot(F0, F1, io.Sf("'b-', label='%s'", opt.RptName))
for _, f0vals := range opt.F1F0_f0ranges {
f0A, f0B := f0vals[0], f0vals[1]
f1A, f1B := opt.F1F0_func(f0A), opt.F1F0_func(f0B)
plt.PlotOne(f0A, f1A, "'g_', mew=1.5, ms=10, clip_on=0")
plt.PlotOne(f0B, f1B, "'g|', mew=1.5, ms=10, clip_on=0")
}
plt.AxisRange(fmin[0], fmax[0], fmin[1], fmax[1])
plt.Gll("$f_0$", "$f_1$", "")
plt.SaveD("/tmp/goga", io.Sf("%s.eps", opt.RptName))
}
return
}
func solve_problem(problem int) (opt *goga.Optimiser) {
io.Pf("\n\n------------------------------------- problem = %d ---------------------------------------\n", problem)
// parameters
opt = new(goga.Optimiser)
opt.Default()
opt.Ncpu = 3
opt.Tf = 500
opt.Verbose = false
opt.Nsamples = 1000
opt.GenType = "latin"
opt.DEC = 0.1
// options for report
opt.HistNsta = 6
opt.HistLen = 13
opt.RptFmtE = "%.4e"
opt.RptFmtL = "%.4e"
opt.RptFmtEdev = "%.3e"
opt.RptFmtLdev = "%.3e"
// problem variables
nx := 10
opt.RptName = io.Sf("CTP%d", problem)
opt.Nsol = 120
opt.FltMin = make([]float64, nx)
opt.FltMax = make([]float64, nx)
for i := 0; i < nx; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh := 2, 1, 0
// extra problem variables
var f1max float64
var fcn goga.MinProb_t
var extraplot func()
// problems
switch problem {
// problem # 0 -- TNK
case 0:
ng = 2
f1max = 1.21
opt.RptName = "TNK"
opt.FltMin = []float64{0, 0}
opt.FltMax = []float64{PI, PI}
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
f[1] = x[1]
g[0] = x[0]*x[0] + x[1]*x[1] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(x[0], x[1]))
g[1] = 0.5 - math.Pow(x[0]-0.5, 2.0) - math.Pow(x[1]-0.5, 2.0)
}
extraplot = func() {
np := 301
X, Y := utl.MeshGrid2D(0, 1.3, 0, 1.3, np, np)
Z1, Z2, Z3 := utl.DblsAlloc(np, np), utl.DblsAlloc(np, np), utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
g1 := 0.5 - math.Pow(X[i][j]-0.5, 2.0) - math.Pow(Y[i][j]-0.5, 2.0)
if g1 >= 0 {
Z1[i][j] = X[i][j]*X[i][j] + Y[i][j]*Y[i][j] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(Y[i][j], X[i][j]))
} else {
Z1[i][j] = -1
}
Z2[i][j] = X[i][j]*X[i][j] + Y[i][j]*Y[i][j] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(Y[i][j], X[i][j]))
Z3[i][j] = g1
}
}
plt.Contour(X, Y, Z1, "levels=[0,2],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
plt.Text(0.3, 0.95, "0.000", "size=5,rotation=10")
plt.ContourSimple(X, Y, Z2, false, 7, "linestyles=['-'], linewidths=[0.7], colors=['k'], levels=[0]")
plt.ContourSimple(X, Y, Z3, false, 7, "linestyles=['-'], linewidths=[1.0], colors=['k'], levels=[0]")
}
opt.Multi_fcnErr = func(f []float64) float64 {
return f[0]*f[0] + f[1]*f[1] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(f[0], f[1]))
}
// problem # 1 -- CTP1, Deb 2001, p367, fig 225
case 1:
ng = 2
f1max = 1.0
a0, b0 := 0.858, 0.541
a1, b1 := 0.728, 0.295
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
c0 := 1.0
for i := 1; i < len(x); i++ {
c0 += x[i]
}
f[0] = x[0]
f[1] = c0 * math.Exp(-x[0]/c0)
if true {
g[0] = f[1] - a0*math.Exp(-b0*f[0])
g[1] = f[1] - a1*math.Exp(-b1*f[0])
}
}
f0a := math.Log(a0) / (b0 - 1.0)
f1a := math.Exp(-f0a)
f0b := math.Log(a0/a1) / (b0 - b1)
f1b := a0 * math.Exp(-b0*f0b)
opt.Multi_fcnErr = func(f []float64) float64 {
if f[0] < f0a {
return f[1] - math.Exp(-f[0])
}
if f[0] < f0b {
return f[1] - a0*math.Exp(-b0*f[0])
}
return f[1] - a1*math.Exp(-b1*f[0])
}
extraplot = func() {
np := 201
X, Y := utl.MeshGrid2D(0, 1, 0, 1, np, np)
Z := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
Z[i][j] = opt.Multi_fcnErr([]float64{X[i][j], Y[i][j]})
}
}
plt.Contour(X, Y, Z, "levels=[0,0.6],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
F0 := utl.LinSpace(0, 1, 21)
F1r := make([]float64, len(F0))
F1s := make([]float64, len(F0))
F1t := make([]float64, len(F0))
for i, f0 := range F0 {
F1r[i] = math.Exp(-f0)
F1s[i] = a0 * math.Exp(-b0*f0)
F1t[i] = a1 * math.Exp(-b1*f0)
}
plt.Plot(F0, F1r, "'k--',color='blue'")
plt.Plot(F0, F1s, "'k--',color='green'")
plt.Plot(F0, F1t, "'k--',color='gray'")
plt.PlotOne(f0a, f1a, "'k|', ms=20")
plt.PlotOne(f0b, f1b, "'k|', ms=20")
}
// problem # 2 -- CTP2, Deb 2001, p368/369, fig 226
case 2:
f1max = 1.2
θ, a, b := -0.2*PI, 0.2, 10.0
c, d, e := 1.0, 6.0, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 3 -- CTP3, Deb 2001, p368/370, fig 227
case 3:
f1max = 1.2
θ, a, b := -0.2*PI, 0.1, 10.0
c, d, e := 1.0, 0.5, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 4 -- CTP4, Deb 2001, p368/370, fig 228
case 4:
f1max = 2.0
θ, a, b := -0.2*PI, 0.75, 10.0
c, d, e := 1.0, 0.5, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 5 -- CTP5, Deb 2001, p368/371, fig 229
case 5:
f1max = 1.2
θ, a, b := -0.2*PI, 0.1, 10.0
c, d, e := 2.0, 0.5, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 6 -- CTP6, Deb 2001, p368/372, fig 230
case 6:
f1max = 5.0
θ, a, b := 0.1*PI, 40.0, 0.5
c, d, e := 1.0, 2.0, -2.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = func() {
np := 201
X, Y := utl.MeshGrid2D(0, 1, 0, 20, np, np)
Z := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
Z[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
}
}
plt.Contour(X, Y, Z, "levels=[-30,-15,0,15,30],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
}
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 7 -- CTP7, Deb 2001, p368/373, fig 231
case 7:
f1max = 1.2
θ, a, b := -0.05*PI, 40.0, 5.0
c, d, e := 1.0, 6.0, 0.0
fcn = CTPgenerator(θ, a, b, c, d, e)
opt.Multi_fcnErr = func(f []float64) float64 { return f[1] - (1.0 - f[0]) }
extraplot = func() {
np := 201
X, Y := utl.MeshGrid2D(0, 1, 0, f1max, np, np)
Z1 := utl.DblsAlloc(np, np)
Z2 := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
Z1[i][j] = opt.Multi_fcnErr([]float64{X[i][j], Y[i][j]})
Z2[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
}
}
plt.Contour(X, Y, Z2, "levels=[0,3],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['b'], levels=[0]")
}
// problem # 8 -- CTP8, Deb 2001, p368/373, fig 232
case 8:
ng = 2
f1max = 5.0
θ1, a, b := 0.1*PI, 40.0, 0.5
c, d, e := 1.0, 2.0, -2.0
θ2, A, B := -0.05*PI, 40.0, 2.0
C, D, E := 1.0, 6.0, 0.0
sin1, cos1 := math.Sin(θ1), math.Cos(θ1)
sin2, cos2 := math.Sin(θ2), math.Cos(θ2)
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
c0 := 1.0
for i := 1; i < len(x); i++ {
c0 += x[i]
}
f[0] = x[0]
f[1] = c0 * (1.0 - f[0]/c0)
if true {
c1 := cos1*(f[1]-e) - sin1*f[0]
c2 := sin1*(f[1]-e) + cos1*f[0]
c3 := math.Sin(b * PI * math.Pow(c2, c))
g[0] = c1 - a*math.Pow(math.Abs(c3), d)
d1 := cos2*(f[1]-E) - sin2*f[0]
d2 := sin2*(f[1]-E) + cos2*f[0]
d3 := math.Sin(B * PI * math.Pow(d2, C))
g[1] = d1 - A*math.Pow(math.Abs(d3), D)
}
}
extraplot = func() {
np := 401
X, Y := utl.MeshGrid2D(0, 1, 0, 20, np, np)
Z1 := utl.DblsAlloc(np, np)
Z2 := utl.DblsAlloc(np, np)
Z3 := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
c1 := cos1*(Y[i][j]-e) - sin1*X[i][j]
c2 := sin1*(Y[i][j]-e) + cos1*X[i][j]
c3 := math.Sin(b * PI * math.Pow(c2, c))
d1 := cos2*(Y[i][j]-E) - sin2*X[i][j]
d2 := sin2*(Y[i][j]-E) + cos2*X[i][j]
d3 := math.Sin(B * PI * math.Pow(d2, C))
Z1[i][j] = c1 - a*math.Pow(math.Abs(c3), d)
Z2[i][j] = d1 - A*math.Pow(math.Abs(d3), D)
if Z1[i][j] >= 0 && Z2[i][j] >= 0 {
Z3[i][j] = 1
} else {
Z3[i][j] = -1
}
}
}
plt.Contour(X, Y, Z3, "colors=['white','gray'],clabels=0,cbar=0,lwd=0.5,fsz=5")
plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['gray'], levels=[0]")
plt.ContourSimple(X, Y, Z2, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['gray'], levels=[0]")
}
opt.Multi_fcnErr = CTPerror1(θ1, a, b, c, d, e)
default:
chk.Panic("problem %d is not available", problem)
}
// initialise optimiser
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// initial solutions
var sols0 []*goga.Solution
if false {
sols0 = opt.GetSolutionsCopy()
}
// solve
opt.RunMany("", "")
goga.StatMulti(opt, true)
io.PfYel("Tsys = %v\n", opt.SysTime)
// check
goga.CheckFront0(opt, true)
// plot
if true {
feasibleOnly := false
plt.SetForEps(0.8, 300)
fmtAll := &plt.Fmt{L: "final solutions", M: ".", C: "orange", Ls: "none", Ms: 3}
fmtFront := &plt.Fmt{L: "final Pareto front", C: "r", M: "o", Ms: 3, Ls: "none"}
goga.PlotOvaOvaPareto(opt, sols0, 0, 1, feasibleOnly, fmtAll, fmtFront)
extraplot()
//plt.AxisYrange(0, f1max)
if problem > 0 && problem < 6 {
plt.Text(0.05, 0.05, "unfeasible", "color='gray', ha='left',va='bottom'")
plt.Text(0.95, f1max-0.05, "feasible", "color='white', ha='right',va='top'")
}
if opt.RptName == "CTP6" {
plt.Text(0.02, 0.15, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
plt.Text(0.02, 6.50, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
plt.Text(0.02, 13.0, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
plt.Text(0.50, 2.40, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
plt.Text(0.50, 8.80, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
plt.Text(0.50, 15.30, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
}
if opt.RptName == "TNK" {
plt.Text(0.05, 0.05, "unfeasible", "color='gray', ha='left',va='bottom'")
plt.Text(0.80, 0.85, "feasible", "color='white', ha='left',va='top'")
plt.Equal()
plt.AxisRange(0, 1.22, 0, 1.22)
}
plt.SaveD("/tmp/goga", io.Sf("%s.eps", opt.RptName))
}
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
}
func solve_problem(problem string) (opt *goga.Optimiser) {
// GA parameters
opt = new(goga.Optimiser)
opt.Default()
opt.RptName = problem
opt.EpsH = 0.0001
opt.Nsamples = 1
opt.Tf = 5000
// problem data
opt.FltMin = cec09.Xmin[problem]
opt.FltMax = cec09.Xmax[problem]
nx := cec09.Nx[problem]
nf := cec09.Nf[problem]
ng := cec09.Nf[problem]
nh := cec09.Nf[problem]
chk.IntAssert(nx, len(opt.FltMin))
chk.IntAssert(nx, len(opt.FltMax))
// function
var fcn goga.MinProb_t
switch problem {
case "UF1":
fcn = cec09.UF1
case "UF2":
fcn = cec09.UF2
case "UF3":
fcn = cec09.UF3
default:
chk.Panic("problem %d is not available", problem)
}
nx = 3
// load reference values
opt.Multi_fStar = cec09.PFdata(problem)
// number of trial solutions
opt.Nsol = 600
opt.Ncpu = 16
if nf == 3 {
opt.Nsol = 150
opt.Ncpu = 3
}
if nf > 3 {
opt.Nsol = 800
opt.Ncpu = 8
}
// initialise optimiser
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// solve
opt.RunMany("", "")
goga.StatMulti(opt, true)
// check
goga.CheckFront0(opt, true)
// plot
if nf == 2 {
plot2(opt, true)
}
plot3x(opt, false, 0, 1, 2, 0.02)
return
}