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") } }