1 | #*------------------------------------------------------------------- |
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2 | * EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC. |
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3 | * |
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4 | * This LIBRARY is free software; you can distribute it and/or modify |
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5 | * it under the therms of the ALSOC FREE LICENSE as available at |
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6 | * http://www.enq.ufrgs.br/alsoc. |
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7 | * |
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8 | * EMSO Copyright (C) 2004 - 2007 ALSOC, original code |
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9 | * from http://www.rps.eng.br Copyright (C) 2002-2004. |
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10 | * All rights reserved. |
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11 | * |
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12 | * EMSO is distributed under the therms of the ALSOC LICENSE as |
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13 | * available at http://www.enq.ufrgs.br/alsoc. |
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14 | * |
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15 | *-------------------------------------------------------------------- |
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16 | * More test problems |
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17 | *-------------------------------------------------------------------- |
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18 | * Author: Argimiro R Secchi |
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19 | * $Id$ |
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20 | *--------------------------------------------------------------------*# |
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21 | Optimization test27 # solution: x1=0.7411, x2=0.7411, obj=-17.96 |
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22 | PARAMETERS |
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23 | pi as Real; |
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24 | |
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25 | VARIABLES |
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26 | x1 as Real(Default=0,Lower=-1,Upper=1); |
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27 | x2 as Real(Default=0,Lower=-1,Upper=1); |
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28 | |
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29 | SET |
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30 | pi = 4*atan(1)/'rad'; |
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31 | |
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32 | MINIMIZE |
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33 | -(abs(20*x1)+abs(20*x2)+2*(x1+x2)) * sin(20*'rad'*x1/pi)^2 * |
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34 | sin(20*'rad'*x2/pi)^2 + 40*(x1^2+x2^2)/3; |
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35 | |
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36 | OPTIONS |
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37 | NLPSolver(MaxIterations=2000, |
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38 | AbsoluteAccuracy=1e-6, |
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39 | RelativeAccuracy=1e-4, |
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40 | #File = "ipopt_emso", hessian_approximation = "exact" |
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41 | #File = "complex" |
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42 | #File = "optpp_emso" |
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43 | #File = "arshj" |
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44 | #File = "PSO" |
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45 | File = "direct", MinimumRectangle=1e-4,MaxEvals=5000 |
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46 | ); |
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47 | Dynamic = false; |
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48 | end |
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49 | |
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50 | # Alpina function |
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51 | Optimization test28 # solution: x1=7.917, x2=7.917, obj=-7.8856 |
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52 | VARIABLES |
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53 | x1 as Real(Default=3,Lower=0,Upper=10); |
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54 | x2 as Real(Default=1,Lower=0,Upper=10); |
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55 | |
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56 | MINIMIZE |
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57 | -sqrt(x1*x2)*sin(x1*'rad')*sin(x2*'rad'); |
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58 | |
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59 | OPTIONS |
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60 | NLPSolver(MaxIterations=2000, |
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61 | AbsoluteAccuracy=1e-6, |
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62 | RelativeAccuracy=1e-4, |
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63 | #File = "ipopt_emso", hessian_approximation = "exact" |
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64 | #File = "complex" |
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65 | #File = "optpp_emso" |
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66 | #File = "arshj" |
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67 | #File = "PSO" |
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68 | File = "direct", MinimumRectangle=1e-4,MaxEvals=5000 |
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69 | ); |
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70 | Dynamic = false; |
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71 | end |
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72 | |
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73 | # Griewank function |
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74 | Optimization test29 # solution: x1=0, x2=0, obj=0 |
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75 | VARIABLES |
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76 | # x1 as Real(Default=0,Lower=-100,Upper=100); |
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77 | # x2 as Real(Default=9,Lower=-100,Upper=100); |
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78 | x1 as Real(Default=0,Lower=-100,Upper=90); |
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79 | x2 as Real(Default=9,Lower=-100,Upper=90); |
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80 | |
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81 | MINIMIZE |
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82 | 1+(x1^2+x2^2)/4000-cos(x1*'rad')*cos(x2*'rad'/sqrt(2)); |
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83 | |
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84 | OPTIONS |
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85 | NLPSolver(MaxIterations=4000, |
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86 | AbsoluteAccuracy=1e-6, |
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87 | RelativeAccuracy=1e-4, |
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88 | #File = "ipopt_emso", hessian_approximation = "exact" |
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89 | #File = "complex" |
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90 | #File = "optpp_emso" |
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91 | #File = "arshj" |
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92 | #File = "PSO" |
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93 | #File = "direct", MinimumRectangle=1e-4,MaxEvals=5000 |
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94 | File = "direct", MinimumRectangle=1e-10,Epsilon=1e-2,MaxEvals=10000 |
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95 | ); |
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96 | Dynamic = false; |
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97 | end |
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98 | |
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99 | Optimization test31 # solution: x=8.817, obj=-8.13 |
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100 | VARIABLES |
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101 | x as Real(Default=-10,Lower=-10,Upper=10); |
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102 | |
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103 | MINIMIZE |
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104 | (x+10)*(x+6)*(x+5)*(x+1)*(x-7)*(x-10)*1e-4; |
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105 | |
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106 | OPTIONS |
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107 | NLPSolver(MaxIterations=2000, |
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108 | AbsoluteAccuracy=1e-6, |
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109 | RelativeAccuracy=1e-4, |
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110 | #File = "ipopt_emso", hessian_approximation = "exact" |
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111 | #File = "complex" |
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112 | #File = "optpp_emso" |
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113 | #File = "arshj" |
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114 | #File = "PSO" |
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115 | File = "direct", MinimumRectangle=1e-4,MaxEvals=5000 |
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116 | ); |
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117 | Dynamic = false; |
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118 | end |
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119 | |
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120 | # Levy 5 function |
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121 | Optimization test32 # solution: x1=-1.3068, x2=-1.4248, obj=-176.1376 |
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122 | PARAMETERS |
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123 | i(5) as Integer; |
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124 | |
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125 | VARIABLES |
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126 | x1 as Real(Default=0,Lower=-10,Upper=10); |
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127 | x2 as Real(Default=0,Lower=-10,Upper=10); |
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128 | |
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129 | SET |
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130 | i = [1:5]; |
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131 | |
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132 | MINIMIZE |
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133 | sum(i*cos(((i-1)*x1+i)*'rad'))*sum(i*cos(((i+1)*x2+i)*'rad'))+(x1+1.42513)^2+(x2+0.80032)^2; |
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134 | |
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135 | OPTIONS |
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136 | NLPSolver(MaxIterations=2000, |
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137 | AbsoluteAccuracy=1e-6, |
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138 | RelativeAccuracy=1e-4, |
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139 | #File = "ipopt_emso", hessian_approximation = "exact" |
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140 | #File = "complex" |
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141 | #File = "optpp_emso" |
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142 | #File = "arshj" |
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143 | #File = "PSO" |
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144 | File = "direct", MinimumRectangle=1e-5,Epsilon=1e-1,MaxEvals=10000 |
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145 | ); |
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146 | Dynamic = false; |
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147 | end |
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148 | |
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149 | # H1 function |
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150 | Optimization test33 # solution: x1=8.6998, x2=6.7665, obj=-2 |
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151 | VARIABLES |
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152 | x1 as Real(Default=0,Lower=-100,Upper=100); |
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153 | x2 as Real(Default=0,Lower=-100,Upper=100); |
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154 | |
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155 | MINIMIZE |
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156 | -(sin((x1-x2/8)*'rad')^2+sin((x2+x1/8)*'rad')^2)/(1+sqrt((x1-8.6998)^2+(x2-6.7665)^2)); |
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157 | |
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158 | OPTIONS |
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159 | NLPSolver(MaxIterations=2000, |
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160 | AbsoluteAccuracy=1e-6, |
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161 | RelativeAccuracy=1e-4, |
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162 | #File = "ipopt_emso", hessian_approximation = "exact" |
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163 | #File = "complex" |
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164 | #File = "optpp_emso" |
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165 | #File = "arshj" |
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166 | #File = "PSO" |
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167 | File = "direct", MinimumRectangle=1e-4,Epsilon=1e-1,MaxEvals=10000 |
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168 | ); |
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169 | Dynamic = false; |
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170 | end |
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171 | |
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172 | # Ackley function |
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173 | Optimization test34 # solution: x=0, obj=0 |
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174 | PARAMETERS |
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175 | n as Integer(Default=3); |
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176 | pi as Real; |
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177 | |
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178 | VARIABLES |
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179 | x(n) as Real(Default=10,Lower=-32.68,Upper=32.68/2); |
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180 | # x(n) as Real(Default=10,Lower=-32.68,Upper=32.68); |
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181 | |
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182 | SET |
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183 | pi = 4*atan(1)/'rad'; |
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184 | |
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185 | MINIMIZE |
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186 | -20*exp(-0.2*sqrt(sum(x^2)/n))-exp(sum(cos(2*pi*x*'rad'))/n)+20+exp(1); |
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187 | |
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188 | OPTIONS |
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189 | NLPSolver(MaxIterations=2000, |
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190 | AbsoluteAccuracy=1e-6, |
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191 | RelativeAccuracy=1e-4, |
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192 | #File = "ipopt_emso", hessian_approximation = "exact" |
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193 | #File = "complex" |
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194 | #File = "optpp_emso" |
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195 | #File = "arshj" |
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196 | #File = "PSO" |
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197 | File = "direct", MinimumRectangle=1e-8,Epsilon=1e-1,MaxEvals=20000 |
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198 | ); |
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199 | Dynamic = false; |
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200 | end |
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201 | |
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202 | # Schwefel function |
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203 | Optimization test35 # solution: x=420.9687, obj=-n (approx.) |
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204 | PARAMETERS |
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205 | n as Integer(Default=4); |
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206 | |
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207 | VARIABLES |
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208 | x(n) as Real(Default=0,Lower=-500,Upper=500); |
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209 | |
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210 | MINIMIZE |
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211 | 418*n-sum(x*sin(sqrt(abs(x))*'rad')); |
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212 | |
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213 | OPTIONS |
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214 | NLPSolver(MaxIterations=2000, |
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215 | AbsoluteAccuracy=1e-6, |
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216 | RelativeAccuracy=1e-4, |
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217 | #File = "ipopt_emso", hessian_approximation = "exact" |
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218 | #File = "complex" |
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219 | #File = "optpp_emso" |
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220 | #File = "arshj" |
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221 | #File = "PSO" |
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222 | File = "direct", MinimumRectangle=1e-8,Epsilon=1e-3,MaxEvals=30000 |
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223 | ); |
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224 | Dynamic = false; |
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225 | end |
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