# MINLP written by GAMS Convert at 02/17/22 17:22:16 # # Equation counts # Total E G L N X C B # 20 2 2 16 0 0 0 0 # # Variable counts # x b i s1s s2s sc si # Total cont binary integer sos1 sos2 scont sint # 17 9 8 0 0 0 0 0 # FX 0 # # Nonzero counts # Total const NL # 65 49 16 # # Reformulation has removed 1 variable and 1 equation from pyomo.environ import * model = m = ConcreteModel() m.x1 = Var(within=Reals, bounds=(0,None), initialize=0) m.x2 = Var(within=Reals, bounds=(0,None), initialize=0) m.x3 = Var(within=Reals, bounds=(0,None), initialize=0) m.x4 = Var(within=Reals, bounds=(0,None), initialize=0) m.x5 = Var(within=Reals, bounds=(0,None), initialize=0) m.x6 = Var(within=Reals, bounds=(0,None), initialize=0) m.x7 = Var(within=Reals, bounds=(0,None), initialize=0) m.x8 = Var(within=Reals, bounds=(0,None), initialize=0) m.x9 = Var(within=Reals, bounds=(0,None), initialize=0) m.b10 = Var(within=Binary, bounds=(0,1), initialize=0) m.b11 = Var(within=Binary, bounds=(0,1), initialize=0) m.b12 = Var(within=Binary, bounds=(0,1), initialize=0) m.b13 = Var(within=Binary, bounds=(0,1), initialize=0) m.b14 = Var(within=Binary, bounds=(0,1), initialize=0) m.b15 = Var(within=Binary, bounds=(0,1), initialize=0) m.b16 = Var(within=Binary, bounds=(0,1), initialize=0) m.b17 = Var(within=Binary, bounds=(0,1), initialize=0) m.obj = Objective(sense=minimize, expr= m.x9) m.e1 = Constraint(expr= -sqrt(0.0476190476190476 * (-0.00313636363636371 * m.x1 - 0.150909090909091 * m.x2 - 0.267772727272727 * m.x3 - 0.308636363636363 * m.x4 - 0.423318181818182 * m.x5 - 0.0687727272727274 * m.x6 - 0.290227272727273 * m.x7 + 0.548045454545455 * m.x8)**2 + 0.0476190476190476 * (0.0058636363636364 * m.x1 - 0.0729090909090906 * m.x2 - 0.384772727272727 * m.x3 - 0.407636363636363 * m.x4 - 0.459318181818182 * m.x5 - 0.0897727272727273 * m.x6 - 0.373227272727273 * m.x7 + 0.593045454545455 * m.x8)**2 + 0.0476190476190476 * (-0.0171363636363637 * m.x1 - 0.0369090909090906 * m.x2 + 0.251227272727273 * m.x3 + 0.261363636363637 * m.x4 + 0.196681818181818 * m.x5 + 0.0312272727272727 * m.x6 + 0.212772727272727 * m.x7 - 0.368954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0261363636363636 * m.x1 + 0.0820909090909094 * m.x2 + 0.116227272727273 * m.x3 + 0.142363636363637 * m.x4 + 0.158681818181818 * m.x5 + 0.0642272727272726 * m.x6 - 0.116227272727273 * m.x7 - 0.168954545454545 * m.x8)**2 + 0.0476190476190476 * ( -0.0231363636363637 * m.x1 - 0.0909090909090906 * m.x2 - 0.193772727272727 * m.x3 - 0.149636363636363 * m.x4 - 0.0283181818181817 * m.x5 - 0.0617727272727273 * m.x6 + 0.0397727272727273 * m.x7 + 0.0710454545454546 * m.x8)**2 + 0.0476190476190476 * (-0.00113636363636371 * m.x1 - 0.110909090909091 * m.x2 - 0.0557727272727273 * m.x3 - 0.0306363636363634 * m.x4 + 0.0246818181818182 * m.x5 - 0.0797727272727273 * m.x6 + 0.184772727272727 * m.x7 + 0.166045454545455 * m.x8)**2 + 0.0476190476190476 * (0.0308636363636363 * m.x1 - 0.114909090909091 * m.x2 + 0.0642272727272726 * m.x3 + 0.132363636363637 * m.x4 + 0.185681818181818 * m.x5 - 0.0687727272727274 * m.x6 - 0.0932272727272727 * m.x7 + 1.08304545454545 * m.x8)**2 + 0.0476190476190476 * (0.0488636363636363 * m.x1 - 0.145909090909091 * m.x2 + 0.203227272727273 * m.x3 + 0.213363636363637 * m.x4 + 0.245681818181818 * m.x5 - 0.0607727272727274 * m.x6 + 0.0847727272727272 * m.x7 + 0.167045454545455 * m.x8)**2 + 0.0476190476190476 * (0.0778636363636362 * m.x1 - 0.0899090909090907 * m.x2 - 0.170772727272727 * m.x3 - 0.160636363636363 * m.x4 - 0.131318181818182 * m.x5 - 0.0187727272727274 * m.x6 - 0.164227272727273 * m.x7 - 0.440954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0388636363636363 * m.x1 + 0.372090909090909 * m.x2 + 0.0952272727272727 * m.x3 + 0.0633636363636367 * m.x4 + 0.0916818181818184 * m.x5 + 0.219227272727273 * m.x6 - 0.160227272727273 * m.x7 - 0.0449545454545452 * m.x8)**2 + 0.0476190476190476 * (0.0138636363636364 * m.x1 - 0.107909090909091 * m.x2 + 0.104227272727273 * m.x3 + 0.111363636363637 * m.x4 + 0.0956818181818184 * m.x5 - 0.0117727272727273 * m.x6 + 0.0957727272727273 * m.x7 - 0.256954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0248636363636363 * m.x1 + 0.0660909090909094 * m.x2 - 0.0587727272727274 * m.x3 - 0.0936363636363633 * m.x4 - 0.218318181818182 * m.x5 + 0.0582272727272726 * m.x6 - 0.0672272727272727 * m.x7 - 0.303954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0018636363636364 * m.x1 + 0.273090909090909 * m.x2 + 0.196227272727273 * m.x3 + 0.202363636363637 * m.x4 + 0.211681818181818 * m.x5 + 0.121227272727273 * m.x6 + 0.420772727272727 * m.x7 - 0.122954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0151363636363637 * m.x1 + 0.216090909090909 * m.x2 + 0.0662272727272726 * m.x3 + 0.0373636363636367 * m.x4 - 0.0353181818181816 * m.x5 + 0.0642272727272726 * m.x6 + 0.552772727272727 * m.x7 + 0.0870454545454546 * m.x8)**2 + 0.0476190476190476 * (-0.0171363636363637 * m.x1 - 0.167909090909091 * m.x2 - 0.0677727272727273 * m.x3 - 0.100636363636363 * m.x4 - 0.162318181818182 * m.x5 - 0.0687727272727274 * m.x6 + 0.104772727272727 * m.x7 + 0.115045454545455 * m.x8)**2 + 0.0476190476190476 * (-0.00713636363636372 * m.x1 - 0.00690909090909053 * m.x2 + 0.0452272727272727 * m.x3 + 0.0553636363636367 * m.x4 + 0.0436818181818184 * m.x5 - 0.0157727272727273 * m.x6 + 0.141772727272727 * m.x7 - 0.267954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0088636363636363 * m.x1 + 0.119090909090909 * m.x2 + 0.196227272727273 * m.x3 + 0.168363636363637 * m.x4 + 0.0826818181818183 * m.x5 + 0.0502272727272726 * m.x6 - 0.0362272727272728 * m.x7 - 0.151954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0018636363636364 * m.x1 - 0.0389090909090906 * m.x2 - 0.151772727272727 * m.x3 - 0.185636363636363 * m.x4 - 0.291318181818182 * m.x5 - 0.00877272727272738 * m.x6 - 0.375227272727273 * m.x7 - 0.206954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0211363636363637 * m.x1 + 0.100090909090909 * m.x2 + 0.184227272727273 * m.x3 + 0.218363636363637 * m.x4 + 0.472681818181818 * m.x5 + 0.0692272727272727 * m.x6 - 0.0202272727272728 * m.x7 - 0.170954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0421363636363636 * m.x1 - 0.0139090909090906 * m.x2 - 0.0437727272727273 * m.x3 - 0.0336363636363632 * m.x4 + 0.0526818181818183 * m.x5 - 0.0157727272727273 * m.x6 - 0.263227272727273 * m.x7 - 0.202954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0471363636363638 * m.x1 + 0.124090909090909 * m.x2 - 0.0197727272727273 * m.x3 - 0.0106363636363633 * m.x4 + 0.0406818181818183 * m.x5 + 0.0182272727272728 * m.x6 + 0.184772727272727 * m.x7 + 0.0170454545454546 * m.x8)**2 + 0.0476190476190476 * ( -0.0331363636363637 * m.x1 - 0.203909090909091 * m.x2 - 0.107772727272727 * m.x3 - 0.124636363636363 * m.x4 - 0.153318181818182 * m.x5 - 0.126772727272727 * m.x6 - 0.0632272727272727 * m.x7 - 0.138954545454545 * m.x8)**2) + 1.07813636363636 * m.x1 + 1.09290909090909 * m.x2 + 1.11977272727273 * m.x3 + 1.12363636363636 * m.x4 + 1.12131818181818 * m.x5 + 1.09177272727273 * m.x6 + 1.14122727272727 * m.x7 + 1.12895454545455 * m.x8 >= 0.05) m.e2 = Constraint(expr= -sqrt(0.0476190476190476 * (-0.00313636363636371 * m.x1 - 0.150909090909091 * m.x2 - 0.267772727272727 * m.x3 - 0.308636363636363 * m.x4 - 0.423318181818182 * m.x5 - 0.0687727272727274 * m.x6 - 0.290227272727273 * m.x7 + 0.548045454545455 * m.x8)**2 + 0.0476190476190476 * (0.0058636363636364 * m.x1 - 0.0729090909090906 * m.x2 - 0.384772727272727 * m.x3 - 0.407636363636363 * m.x4 - 0.459318181818182 * m.x5 - 0.0897727272727273 * m.x6 - 0.373227272727273 * m.x7 + 0.593045454545455 * m.x8)**2 + 0.0476190476190476 * (-0.0171363636363637 * m.x1 - 0.0369090909090906 * m.x2 + 0.251227272727273 * m.x3 + 0.261363636363637 * m.x4 + 0.196681818181818 * m.x5 + 0.0312272727272727 * m.x6 + 0.212772727272727 * m.x7 - 0.368954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0261363636363636 * m.x1 + 0.0820909090909094 * m.x2 + 0.116227272727273 * m.x3 + 0.142363636363637 * m.x4 + 0.158681818181818 * m.x5 + 0.0642272727272726 * m.x6 - 0.116227272727273 * m.x7 - 0.168954545454545 * m.x8)**2 + 0.0476190476190476 * ( -0.0231363636363637 * m.x1 - 0.0909090909090906 * m.x2 - 0.193772727272727 * m.x3 - 0.149636363636363 * m.x4 - 0.0283181818181817 * m.x5 - 0.0617727272727273 * m.x6 + 0.0397727272727273 * m.x7 + 0.0710454545454546 * m.x8)**2 + 0.0476190476190476 * (-0.00113636363636371 * m.x1 - 0.110909090909091 * m.x2 - 0.0557727272727273 * m.x3 - 0.0306363636363634 * m.x4 + 0.0246818181818182 * m.x5 - 0.0797727272727273 * m.x6 + 0.184772727272727 * m.x7 + 0.166045454545455 * m.x8)**2 + 0.0476190476190476 * (0.0308636363636363 * m.x1 - 0.114909090909091 * m.x2 + 0.0642272727272726 * m.x3 + 0.132363636363637 * m.x4 + 0.185681818181818 * m.x5 - 0.0687727272727274 * m.x6 - 0.0932272727272727 * m.x7 + 1.08304545454545 * m.x8)**2 + 0.0476190476190476 * (0.0488636363636363 * m.x1 - 0.145909090909091 * m.x2 + 0.203227272727273 * m.x3 + 0.213363636363637 * m.x4 + 0.245681818181818 * m.x5 - 0.0607727272727274 * m.x6 + 0.0847727272727272 * m.x7 + 0.167045454545455 * m.x8)**2 + 0.0476190476190476 * (0.0778636363636362 * m.x1 - 0.0899090909090907 * m.x2 - 0.170772727272727 * m.x3 - 0.160636363636363 * m.x4 - 0.131318181818182 * m.x5 - 0.0187727272727274 * m.x6 - 0.164227272727273 * m.x7 - 0.440954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0388636363636363 * m.x1 + 0.372090909090909 * m.x2 + 0.0952272727272727 * m.x3 + 0.0633636363636367 * m.x4 + 0.0916818181818184 * m.x5 + 0.219227272727273 * m.x6 - 0.160227272727273 * m.x7 - 0.0449545454545452 * m.x8)**2 + 0.0476190476190476 * (0.0138636363636364 * m.x1 - 0.107909090909091 * m.x2 + 0.104227272727273 * m.x3 + 0.111363636363637 * m.x4 + 0.0956818181818184 * m.x5 - 0.0117727272727273 * m.x6 + 0.0957727272727273 * m.x7 - 0.256954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0248636363636363 * m.x1 + 0.0660909090909094 * m.x2 - 0.0587727272727274 * m.x3 - 0.0936363636363633 * m.x4 - 0.218318181818182 * m.x5 + 0.0582272727272726 * m.x6 - 0.0672272727272727 * m.x7 - 0.303954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0018636363636364 * m.x1 + 0.273090909090909 * m.x2 + 0.196227272727273 * m.x3 + 0.202363636363637 * m.x4 + 0.211681818181818 * m.x5 + 0.121227272727273 * m.x6 + 0.420772727272727 * m.x7 - 0.122954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0151363636363637 * m.x1 + 0.216090909090909 * m.x2 + 0.0662272727272726 * m.x3 + 0.0373636363636367 * m.x4 - 0.0353181818181816 * m.x5 + 0.0642272727272726 * m.x6 + 0.552772727272727 * m.x7 + 0.0870454545454546 * m.x8)**2 + 0.0476190476190476 * (-0.0171363636363637 * m.x1 - 0.167909090909091 * m.x2 - 0.0677727272727273 * m.x3 - 0.100636363636363 * m.x4 - 0.162318181818182 * m.x5 - 0.0687727272727274 * m.x6 + 0.104772727272727 * m.x7 + 0.115045454545455 * m.x8)**2 + 0.0476190476190476 * (-0.00713636363636372 * m.x1 - 0.00690909090909053 * m.x2 + 0.0452272727272727 * m.x3 + 0.0553636363636367 * m.x4 + 0.0436818181818184 * m.x5 - 0.0157727272727273 * m.x6 + 0.141772727272727 * m.x7 - 0.267954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0088636363636363 * m.x1 + 0.119090909090909 * m.x2 + 0.196227272727273 * m.x3 + 0.168363636363637 * m.x4 + 0.0826818181818183 * m.x5 + 0.0502272727272726 * m.x6 - 0.0362272727272728 * m.x7 - 0.151954545454545 * m.x8)**2 + 0.0476190476190476 * (0.0018636363636364 * m.x1 - 0.0389090909090906 * m.x2 - 0.151772727272727 * m.x3 - 0.185636363636363 * m.x4 - 0.291318181818182 * m.x5 - 0.00877272727272738 * m.x6 - 0.375227272727273 * m.x7 - 0.206954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0211363636363637 * m.x1 + 0.100090909090909 * m.x2 + 0.184227272727273 * m.x3 + 0.218363636363637 * m.x4 + 0.472681818181818 * m.x5 + 0.0692272727272727 * m.x6 - 0.0202272727272728 * m.x7 - 0.170954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0421363636363636 * m.x1 - 0.0139090909090906 * m.x2 - 0.0437727272727273 * m.x3 - 0.0336363636363632 * m.x4 + 0.0526818181818183 * m.x5 - 0.0157727272727273 * m.x6 - 0.263227272727273 * m.x7 - 0.202954545454545 * m.x8)**2 + 0.0476190476190476 * (-0.0471363636363638 * m.x1 + 0.124090909090909 * m.x2 - 0.0197727272727273 * m.x3 - 0.0106363636363633 * m.x4 + 0.0406818181818183 * m.x5 + 0.0182272727272728 * m.x6 + 0.184772727272727 * m.x7 + 0.0170454545454546 * m.x8)**2 + 0.0476190476190476 * ( -0.0331363636363637 * m.x1 - 0.203909090909091 * m.x2 - 0.107772727272727 * m.x3 - 0.124636363636363 * m.x4 - 0.153318181818182 * m.x5 - 0.126772727272727 * m.x6 - 0.0632272727272727 * m.x7 - 0.138954545454545 * m.x8)**2) + m.x9 >= 0) m.e3 = Constraint(expr= m.x1 + m.x2 + m.x3 + m.x4 + m.x5 + m.x6 + m.x7 + m.x8 == 1) m.e4 = Constraint(expr= m.x1 - m.b10 <= 0) m.e5 = Constraint(expr= m.x2 - m.b11 <= 0) m.e6 = Constraint(expr= m.x3 - m.b12 <= 0) m.e7 = Constraint(expr= m.x4 - m.b13 <= 0) m.e8 = Constraint(expr= m.x5 - m.b14 <= 0) m.e9 = Constraint(expr= m.x6 - m.b15 <= 0) m.e10 = Constraint(expr= m.x7 - m.b16 <= 0) m.e11 = Constraint(expr= m.x8 - m.b17 <= 0) m.e12 = Constraint(expr= -m.x1 + 0.05 * m.b10 <= 0) m.e13 = Constraint(expr= -m.x2 + 0.05 * m.b11 <= 0) m.e14 = Constraint(expr= -m.x3 + 0.05 * m.b12 <= 0) m.e15 = Constraint(expr= -m.x4 + 0.05 * m.b13 <= 0) m.e16 = Constraint(expr= -m.x5 + 0.05 * m.b14 <= 0) m.e17 = Constraint(expr= -m.x6 + 0.05 * m.b15 <= 0) m.e18 = Constraint(expr= -m.x7 + 0.05 * m.b16 <= 0) m.e19 = Constraint(expr= -m.x8 + 0.05 * m.b17 <= 0) m.e20 = Constraint(expr= m.b10 + m.b11 + m.b12 + m.b13 + m.b14 + m.b15 + m.b16 + m.b17 == 5)