func DTLZ2mGenerator(opt *goga.Optimiser, nf int) (ng int, fcn goga.MinProb_t) {
nx := nf + 10
ng = nx * 2
opt.FltMin = make([]float64, nx)
opt.FltMax = make([]float64, nx)
for i := 0; i < nx; i++ {
opt.FltMin[i], opt.FltMax[i] = -0.01, 1.01
}
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
var failed bool
for i := 0; i < nx; i++ {
g[0+i*2] = x[i]
g[1+i*2] = 1.0 - x[i]
if g[0+i*2] < 0 {
failed = true
}
if g[1+i*2] < 0 {
failed = true
}
}
if failed {
return
}
var c float64
for i := nf - 1; i < nx; i++ {
c += math.Pow((x[i] - 0.5), 2.0)
}
for i := 0; i < nf; i++ {
f[i] = (1.0 + c)
for j := 0; j < nf-1-i; j++ {
f[i] *= math.Cos(x[j] * PI / 2.0)
}
if i > 0 {
j := nf - 1 - i
f[i] *= math.Sin(x[j] * PI / 2.0)
}
}
}
opt.Multi_fcnErr = func(f []float64) float64 {
var sum float64
for i := 0; i < nf; i++ {
sum += f[i] * f[i]
}
return sum - 1.0
}
opt.RptFmin = make([]float64, nf)
opt.RptFmax = make([]float64, nf)
for i := 0; i < nf; i++ {
opt.RptFmax[i] = 1
}
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 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)
}
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)
}