ОТЧЕТ ПО МО. Методы оптимизации
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Приложение В (обязательное) namespace MO22 { public class Program { public static double D(double a, double b) { return b - a; } private static double DeFfirst(double X1, double X2) { return 402 * X1 + 200 * X2 - 1204; } private static double DeFsecond(double X1, double X2) { return 200 * X1 + 102 * X2 - 614; } private static double Function(double X1, double X2) { return (X1 - 2) * (X1 - 2) + (X2 - 7) * (X2 - 7) + 50 * (X2 + 2 * X1 - 6) * (X2 + 2 * X1 - 6) + 7.6; } private static void FastDown() { double X11 = 0; double X12 = 0; double epsilon = 0.001; double border_a = -2000; double border_b = 2000; double Alfa = 0.618; double Beta = 0.382; int count = 0; do { double t = Gold(border_a, border_b, Alfa, Beta, X11, X12); double tempX1 = X11; double tempX2 = X12; X11 = X11 - t * DeFfirst(tempX1, tempX2); X12 = X12 - t * DeFsecond(tempX1, tempX2); count++; Console.WriteLine(Math.Round(X11, 3) + " " + Math.Round(X12, 3) + " " + Math.Round(Function(X11, X12), 3) + " " + Math.Round(t, 3) + " " + count); } while (Math.Abs(DeFfirst(X11, X12)) > epsilon && Math.Abs(DeFsecond(X11, X12)) > epsilon); } private static void GelfCeit() { double t1, t2, X01 = 0, X02 = 0, GlobalCount = 0, Count1 = 0, Count2 = 0, G1, G2, Alf = 0.618, Bet = 1 - Alf; do { do { if (Math.Abs(DeFfirst(X01, X02)) > 0.01) { G1 = DeFfirst(X01, X02); } else G1 = 0; if (Math.Abs(DeFsecond(X01, X02)) > 0.01) { G2 = DeFsecond(X01, X02); } else G2 = 0; t1 = Gold(-2000, 2000, Alf, Bet, X01, X02); X01 -= t1 * G1; X02 -= t1 * G2; Count1++; } while (Count1 < 10); Count1 = 0; do { if (Math.Abs(DeFfirst(X01, X02)) > 0.01) { G1 = DeFfirst(X01, X02); } else G1 = 0; if (Math.Abs(DeFsecond(X01, X02)) > 0.01) { G2 = DeFsecond(X01, X02); } else G2 = 0; t2 = Gold(-2000, 2000, Alf, Bet, X01, X02); X01 -= t2 * G1; X02 -= t2 * G2; Count2++; } while (Count2 < 10); Count2 = 0; GlobalCount++; Console.WriteLine(Math.Round(X01, 6) + " " + Math.Round(X02, 6) + " " + Math.Round(Function(X01, X02), 6) + " " + Math.Round(G1, 6) + " " + Math.Round(G2, 6) + " " + GlobalCount); } while (GlobalCount < 50); } public static double Gold(double a, double b, double Alf, double Bet, double X11, double X12) { var count = 0; double XB; double XA; do { XB = a + Bet * D(a, b); XA = a + Alf * D(a, b); if (T(X11, X12, XB) >= T(X11, X12, XA)) { a = XB; } else { b = XA; } count++; } while (D(a, b) >= 0.01); if (T(X11, X12, XA) <= T(X11, X12, XB)) { return XA; } else { return XB; } } private static void Main(string[] args) { Console.WriteLine("\nДля ВТОРОЙ функции\n"); Console.WriteLine("\nМетод Нелдера-Мида\n"); NelderMid(); Console.WriteLine("\nМетод быстрого спуска\n"); FastDown(); Console.WriteLine("\nМетод Гельфанда-Цейтлина\n"); GelfCeit(); } private static void NelderMid() { var n = 2; var count = 1; double Xh = 0, Xh1, Xh2, Xl = 0, Xl1, Xl2, t = 10, X11, X12, X21, X22, X31, X32, X61, X62, X71, X72, A, X51, X52, X41, X42, Max, Min; var d2 = t * (Math.Pow(n + 1, 0.5) - 1) / (Math.Pow(2, 0.5) * n); var d1 = t * (Math.Pow(n + 1, 0.5) + n - 1) / (Math.Pow(2, 0.5) * n); X11 = 0; X12 = 0; X21 = d1; X22 = d2; X31 = d2; X32 = d1; Max = double.MinValue; Min = double.MaxValue; if (Function(X11, X12) > Function(X21, X22) && Function(X11, X12) > Function(X31, X32)) { Xh = Function(X11, X12); Xh1 = X11; Xh2 = X12; } else if (Function(X21, X22) > Function(X11, X12) && Function(X21, X22) > Function(X31, X32)) { Xh = Function(X21, X22); Xh1 = X21; Xh2 = X22; } else { Xh = Function(X31, X32); Xh1 = X31; Xh2 = X32; } if (Function(X11, X12) < Function(X21, X22) && Function(X11, X12) < Function(X31, X32)) { Xl = Function(X11, X12); Xl1 = X11; Xl2 = X12; } else if (Function(X21, X22) < Function(X11, X12) && Function(X21, X22) < Function(X31, X32)) { Xl = Function(X21, X22); Xl1 = X21; Xl2 = X22; } else { Xl = Function(X31, X32); Xl1 = X31; Xl2 = X32; } do { Console.Write("(" + Math.Round(X11, 2) + ";" + Math.Round(X12, 2) + ") " + Math.Round(Function(X11, X12), 2) + " "); Console.Write("(" + Math.Round(X21, 2) + ";" + Math.Round(X22, 2) + ") " + Math.Round(Function(X21, X22), 2) + " "); Console.Write("(" + Math.Round(X31, 2) + ";" + Math.Round(X32, 2) + ") " + Math.Round(Function(X31, X32), 2) + " "); Console.WriteLine(count); //смещенный центр тяжести if (Xh == Function(X11, X12)) { X41 = (X21 + X31) / n; X42 = (X22 + X32) / n; } else if (Xh == Function(X21, X22)) { X41 = (X11 + X31) / n; X42 = (X12 + X32) / n; } else { X41 = (X11 + X21) / n; X42 = (X12 + X22) / n; } //точка отражения X51 = 2 * X41 - Xh1; X52 = 2 * X42 - Xh2; if (Function(X51, X52) < Xl) { //точка растяжения X61 = 2 * X51 - X41; X62 = 2 * X52 - X42; if (Function(X61, X62) < Xl) { Xh1 = X61; Xh2 = X62; Xh = Function(Xh1, Xh2); } else { Xh1 = X51; Xh2 = X52; Xh = Function(Xh1, Xh2); } } else { if (Function(X51, X52) > Function(X11, X12) && Function(X51, X52) > Function(X21, X22) && Function(X51, X52) > Function(X31, X32)) { if (Function(X51, X52) > Xh) { //редукция X11 = 0.5 * Xl1 + 0.5 * X11; X12 = 0.5 * Xl2 + 0.5 * X12; X21 = 0.5 * Xl1 + 0.5 * X21; X22 = 0.5 * Xl2 + 0.5 * X22; X31 = 0.5 * Xl1 + 0.5 * X31; X32 = 0.5 * Xl2 + 0.5 * X32; if (Function(X11, X12) > Function(X21, X22) && Function(X11, X12) > Function(X31, X32) && Function(X11, X12) > Max) { Xh = Function(X11, X12); Xh1 = X11; Xh2 = X12; } else if (Function(X21, X22) > Function(X11, X12) && Function(X21, X22) > Function(X31, X32) && Function(X21, X22) > Max) { Xh = Function(X21, X22); Xh1 = X21; Xh2 = X22; } else { Xh = Function(X31, X32); Xh1 = X31; Xh2 = X32; } if (Function(X11, X12) < Function(X21, X22) && Function(X11, X12) < Function(X31, X32) && Function(X11, X12) < Min) { Xl = Function(X11, X12); Xl1 = X11; Xl2 = X12; } else if (Function(X21, X22) < Function(X11, X12) && Function(X21, X22) < Function(X31, X32) && Function(X21, X22) < Min) { Xl = Function(X21, X22); Xl1 = X21; Xl2 = X22; } else { Xl = Function(X31, X32); Xl1 = X31; Xl2 = X32; } } else { //Сжатие X71 = 0.5 * X51 - X41; X72 = 0.5 * X52 - X42; if (Function(X71, X72) > Xh) { //редукция X11 = 0.5 * Xl1 + 0.5 * X11; X12 = 0.5 * Xl2 + 0.5 * X12; X21 = 0.5 * Xl1 + 0.5 * X21; X22 = 0.5 * Xl2 + 0.5 * X22; X31 = 0.5 * Xl1 + 0.5 * X31; X32 = 0.5 * Xl2 + 0.5 * X32; if (Function(X11, X12) > Function(X21, X22) && Function(X11, X12) > Function(X31, X32) && Function(X11, X12) > Max) { Xh = Function(X11, X12); Xh1 = X11; Xh2 = X12; } else if (Function(X21, X22) > Function(X11, X12) && Function(X21, X22) > Function(X31, X32) && Function(X21, X22) > Max) { Xh = Function(X21, X22); Xh1 = X21; Xh2 = X22; } else { Xh = Function(X31, X32); Xh1 = X31; Xh2 = X32; } if (Function(X11, X12) < Function(X21, X22) && Function(X11, X12) < Function(X31, X32) && Function(X11, X12) < Min) { Xl = Function(X11, X12); Xl1 = X11; Xl2 = X12; } else if (Function(X21, X22) < Function(X11, X12) && Function(X21, X22) < Function(X31, X32) && Function(X21, X22) < Min) { Xl = Function(X21, X22); Xl1 = X21; Xl2 = X22; } else { Xl = Function(X31, X32); Xl1 = X31; Xl2 = X32; } } else { Xh1 = X71; Xh2 = X72; Xh = Function(Xh1, Xh2); } } } else { Xh1 = X51; Xh2 = X52; Xh = Function(Xh1, Xh2); } } count++; A = (Math.Pow(Function(X11, X12) - Function(X41, X42), 2) + Math.Pow(Function(X21, X22) - Function(X41, X42), 2) + Math.Pow(Function(X31, X32) - Function(X41, X42), 2)) / (n + 1); } while (A >= 0.01); Console.WriteLine(); } public static double T(double X11, double X12, double t) { return (X11 - t * DeFfirst(X11, X12) - 2) * (X11 - t * DeFfirst(X11, X12) - 2) + (X12 - t * DeFsecond(X11, X12) - 7) * (X12 - t * DeFsecond(X11, X12) - 7) + 50 * (X12 - t * DeFsecond(X11, X12) + 2 * (X11 - t * DeFfirst(X11, X12)) - 6) * (X12 - t * DeFsecond(X11, X12) + 2 * (X11 - t * DeFfirst(X11, X12)) - 6) + 7.6; } } } |