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 | * Some MINLP test problems |
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17 | *-------------------------------------------------------------------- |
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18 | * Author: Edson Cordeiro do Valle, Rafael de Pelegrini Soares |
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19 | * $Id$ |
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20 | *--------------------------------------------------------------------*# |
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21 | |
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22 | Optimization minlp1 |
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23 | VARIABLES |
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24 | x0 as Integer(Default=0, Lower=0, Upper=1); |
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25 | x1 as Real(Default=0, Lower=0, Upper=1.0e10); |
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26 | x2 as Real(Default=0, Lower=0, Upper=1.0e10); |
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27 | x3 as Integer(Default=0, Lower=0, Upper=5); |
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28 | |
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29 | |
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30 | MINIMIZE |
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31 | -1*(x0 + x1 + x2); |
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32 | |
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33 | EQUATIONS |
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34 | |
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35 | (x1 - 0.5)^2 + (x2 - 0.5)^2 <= 0.25; |
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36 | x0 - x1 <= 0; |
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37 | x0 + x2 + x3 <= 2; |
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38 | |
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39 | OPTIONS |
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40 | Dynamic = false; |
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41 | NLPSolveNLA = true; |
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42 | |
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43 | NLPSolver(File = "minlp_emso", derivative_test = "second-order", |
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44 | print_level = 5); |
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45 | |
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46 | end |
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47 | |
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48 | Optimization minlp2 |
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49 | VARIABLES |
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50 | x as Real(Default=0, Lower=0.2, Upper=1); |
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51 | y1 as Integer(Default=1, Lower=0, Upper=1); |
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52 | y2 as Integer(Default=1, Lower=0, Upper=1); |
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53 | y3 as Integer(Default=0, Lower=0, Upper=1); |
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54 | |
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55 | |
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56 | MINIMIZE |
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57 | y1 + y2 + y3 + 5*x^2; |
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58 | |
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59 | EQUATIONS |
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60 | 3*x -y1 -y2 <= 0; |
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61 | -x + 0.1*y2 + 0.25* y3 <= 0; |
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62 | y1 + y2 + y3 >= 2; |
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63 | y1 + y2 + 2*(y3 - 1) >=0; |
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64 | |
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65 | OPTIONS |
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66 | Dynamic = false; |
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67 | NLPSolveNLA = true; |
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68 | |
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69 | NLPSolver(File = "minlp_emso", derivative_test = "second-order", |
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70 | print_level = 5); |
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71 | |
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72 | end |
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73 | |
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74 | Optimization minlp3 |
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75 | VARIABLES |
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76 | x1 as Real(Default=0, Lower=0, Upper=1e10); |
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77 | x2 as Real(Default=0, Lower=0, Upper=1e10); |
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78 | x3 as Real(Default=1, Lower=0, Upper=1e10); |
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79 | y1 as Integer(Default=0, Lower=0, Upper=1); |
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80 | y2 as Integer(Default=1, Lower=0, Upper=1); |
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81 | y3 as Integer(Default=0, Lower=0, Upper=1); |
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82 | |
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83 | |
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84 | MINIMIZE |
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85 | -2.9*x3 -8.9*ln(1+x1) - 10.44*ln(1+x2) + 1.8*x1 + |
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86 | 1.8*x2 + 3.5*y1 + y2 + 1.5*y3; |
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87 | |
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88 | EQUATIONS |
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89 | |
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90 | -y1 + 0.9*ln(1+x1) + 1.08*ln(1+x2) +0.9*x3 <=0; |
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91 | -10*y2 + ln(1+ x1) <=0; |
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92 | -10*y3 + 1.2*ln(1+x2) <=0; |
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93 | y2 + y3 -1 <=0; |
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94 | |
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95 | OPTIONS |
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96 | Dynamic = false; |
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97 | NLPSolveNLA = true; |
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98 | |
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99 | NLPSolver(File = "minlp_emso", derivative_test = "second-order", |
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100 | bonmin_algorithm = "B-BB", print_level = 5); |
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101 | |
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102 | end |
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103 | FlowSheet minlp_flow |
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104 | VARIABLES |
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105 | |
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106 | p1a as Real(Default=10, Lower=0, Upper=50); |
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107 | p1b as Real(Default=10, Lower=0, Upper=50); |
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108 | p2a as Real(Default=10, Lower=0, Upper=50); |
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109 | p2b as Real(Default=10, Lower=0, Upper=50); |
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110 | f1 as Real(Default=10, Lower=0, Upper=25); |
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111 | f2 as Real(Default=10, Lower=0, Upper=25); |
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112 | f3a as Real(Default=10, Lower=0, Upper=50); |
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113 | f3b as Real(Default=10, Lower=0, Upper=50); |
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114 | f4a as Real(Default=10, Lower=0, Upper=50); |
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115 | f4b as Real(Default=10, Lower=0, Upper=50); |
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116 | f5a as Real(Default=10, Lower=0, Upper=50); |
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117 | f5b as Real(Default=10, Lower=0, Upper=50); |
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118 | f6a as Real(Default=10, Lower=0, Upper=50); |
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119 | f6b as Real(Default=10, Lower=0, Upper=50); |
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120 | f7a as Real(Default=10, Lower=0, Upper=50); |
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121 | f7b as Real(Default=10, Lower=0, Upper=50); |
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122 | f8a as Real(Default=10, Lower=0, Upper=50); |
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123 | f8b as Real(Default=10, Lower=0, Upper=50); |
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124 | f9a as Real(Default=10, Lower=0, Upper=50); |
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125 | f9b as Real(Default=10, Lower=0, Upper=50); |
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126 | f10a as Real(Default=10, Lower=0, Upper=50); |
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127 | f10b as Real(Default=10, Lower=0, Upper=50); |
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128 | f11a as Real(Default=10, Lower=0, Upper=50); |
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129 | f11b as Real(Default=10, Lower=0, Upper=50); |
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130 | e4 as Real(Default=10, Lower=0, Upper=1); |
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131 | e5 as Real(Default=10, Lower=0, Upper=1); |
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132 | e6 as Real(Default=10, Lower=0, Upper=1); |
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133 | |
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134 | # yd as Integer(Default=1, Lower=0, Upper=1); |
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135 | # yf as Integer(Default=0, Lower=0, Upper=1); |
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136 | |
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137 | EQUATIONS |
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138 | |
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139 | f3a = 0.55*f1 + 0.50*f2; #mixer11: |
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140 | f3b = 0.45*f1 + 0.50*f2; #mixer12: |
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141 | f4a = e4*f3a; #splitter1 |
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142 | f4b = e4*f3b; #splitter2 |
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143 | f5a = e5*f3a; #splitter3 |
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144 | f5b = e5*f3b; #splitter4 |
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145 | f6a = e6*f3a; #splitter5 |
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146 | f6b = e6*f3b; #splitter6 |
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147 | f7a = f3a - f4a - f5a - f6a; #splitter7 |
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148 | f7b = f3b - f4b - f5b - f6b; #splitter8 |
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149 | f8a = 0.85*f4a; #flash1 |
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150 | f8b = 0.20*f4b; #flash2 |
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151 | f9a = 0.15*f4a; #flash3 |
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152 | f9b = 0.80*f4b; #flash4 |
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153 | f10a = 0.975*f5a; #distil1 |
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154 | f10b = 0.050*f5b; #distil2 |
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155 | f11a = 0.025*f5a; # distil3 |
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156 | f11b = 0.950*f5b; # distil4 |
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157 | p1a = f8a + f10a + f6a; # mixer21 |
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158 | p1b = f8b + f10b + f6b; # mixer22 |
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159 | p2a = f9a + f11a + f7a; # mixer31 |
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160 | p2b = f9b + f11b + f7b; # mixer32 |
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161 | |
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162 | SPECIFY |
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163 | f3a = 1; |
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164 | f4a = 1; |
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165 | f5a = 1; |
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166 | f6a = 1; |
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167 | f8b = 1; |
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168 | |
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169 | OPTIONS |
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170 | Dynamic = false; |
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171 | NLASolver( |
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172 | File = "homotopy", |
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173 | RelativeAccuracy = 1e-5 |
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174 | ); |
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175 | |
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176 | end |
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177 | |
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178 | Optimization opt_minlp_flow as minlp_flow |
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179 | VARIABLES |
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180 | yd as Integer(Default=1, Lower=0, Upper=1); |
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181 | yf as Integer(Default=0, Lower=0, Upper=1); |
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182 | |
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183 | MINIMIZE |
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184 | -35*p1a - 30*p2b + 10*f1 + 8*f2 + f4a + f4b + 4*f5a |
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185 | + 4*f5b + 2*yf + 50*yd; |
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186 | |
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187 | EQUATIONS |
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188 | |
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189 | f4a + f4b >= 2.5*yf; #logical1 |
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190 | f4a + f4b <= 25*yf;#logical2 |
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191 | f5a + f5b >= 2.5*yd;#logical3 |
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192 | f5a + f5b <= 25*yd;#logical4 |
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193 | p1a >= 4*p1b;#spec1 |
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194 | p2b >= 3*p2a;#spec2 |
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195 | p1a + p1b <= 15;#spec3 |
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196 | p2a + p2b <= 18;#spec4 |
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197 | |
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198 | FREE |
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199 | f3a; |
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200 | f4a; |
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201 | f5a; |
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202 | f6a; |
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203 | f8b; |
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204 | |
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205 | OPTIONS |
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206 | Dynamic = false; |
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207 | NLPSolveNLA = false; |
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208 | NLPSolver(#File = "complex", |
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209 | #File = "optpp_emso", |
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210 | File = "minlp_emso", |
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211 | bonmin_algorithm = "B-BB", |
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212 | bonmin_bb_log_level = 2, |
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213 | #Hessian_approximation = "exact", |
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214 | MaxIterations = 10000, |
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215 | RelativeAccuracy = 1e-6); |
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216 | |
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217 | end |
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