Exemple #1
0
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
}
Exemple #2
0
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
}
Exemple #3
0
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
}
Exemple #4
0
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
}