# NLP written by GAMS Convert at 02/17/22 17:20:13 # # Equation counts # Total E G L N X C B # 128 109 3 16 0 0 0 0 # # Variable counts # x b i s1s s2s sc si # Total cont binary integer sos1 sos2 scont sint # 124 124 0 0 0 0 0 0 # FX 0 # # Nonzero counts # Total const NL # 382 249 133 # # Reformulation has removed 1 variable and 1 equation from pyomo.environ import * model = m = ConcreteModel() m.x1 = Var(within=Reals, bounds=(None,None), initialize=0) m.x2 = Var(within=Reals, bounds=(None,None), initialize=0) m.x3 = Var(within=Reals, bounds=(None,None), initialize=0) m.x4 = Var(within=Reals, bounds=(None,None), initialize=0) m.x5 = Var(within=Reals, bounds=(None,None), initialize=0) m.x6 = Var(within=Reals, bounds=(None,None), initialize=0) m.x7 = Var(within=Reals, bounds=(None,None), initialize=0) m.x8 = Var(within=Reals, bounds=(None,None), initialize=0) m.x9 = Var(within=Reals, bounds=(None,None), initialize=0) m.x10 = Var(within=Reals, bounds=(None,None), initialize=0) m.x11 = Var(within=Reals, bounds=(None,None), initialize=0) m.x12 = Var(within=Reals, bounds=(None,None), initialize=0) m.x13 = Var(within=Reals, bounds=(None,None), initialize=0) m.x14 = Var(within=Reals, bounds=(None,None), initialize=0) m.x15 = Var(within=Reals, bounds=(None,None), initialize=0) m.x16 = Var(within=Reals, bounds=(None,None), initialize=0) m.x17 = Var(within=Reals, bounds=(None,None), initialize=0) m.x18 = Var(within=Reals, bounds=(None,None), initialize=0) m.x19 = Var(within=Reals, bounds=(None,None), initialize=0) m.x20 = Var(within=Reals, bounds=(None,None), initialize=0) m.x21 = Var(within=Reals, bounds=(None,None), initialize=0) m.x22 = Var(within=Reals, bounds=(-1.69454444444444,1.69454444444444) , initialize=0) m.x23 = Var(within=Reals, bounds=(-1.69454444444444,1.69454444444444) , initialize=0) m.x24 = Var(within=Reals, bounds=(-1.69454444444444,1.69454444444444) , initialize=0) m.x25 = Var(within=Reals, bounds=(-1.69444444444444,1.69444444444444) , initialize=0) m.x26 = Var(within=Reals, bounds=(-1.69454444444444,1.69454444444444) , initialize=0) m.x27 = Var(within=Reals, bounds=(-1.69454444444444,1.69454444444444) , initialize=0) m.x28 = Var(within=Reals, bounds=(-1.69444444444444,1.69444444444444) , initialize=0) m.x29 = Var(within=Reals, bounds=(-1.69444444444444,1.69444444444444) , initialize=0) m.x30 = Var(within=Reals, bounds=(-1.69454444444444,1.69454444444444) , initialize=0) m.x31 = Var(within=Reals, bounds=(-3.48536077097506,3.48536077097506) , initialize=0) m.x32 = Var(within=Reals, bounds=(-3.48536077097506,3.48536077097506) , initialize=0) m.x33 = Var(within=Reals, bounds=(-3.48536077097506,3.48536077097506) , initialize=0) m.x34 = Var(within=Reals, bounds=(-3.48526077097506,3.48526077097506) , initialize=0) m.x35 = Var(within=Reals, bounds=(-3.48536077097506,3.48536077097506) , initialize=0) m.x36 = Var(within=Reals, bounds=(-3.48536077097506,3.48536077097506) , initialize=0) m.x37 = Var(within=Reals, bounds=(-3.48526077097506,3.48526077097506) , initialize=0) m.x38 = Var(within=Reals, bounds=(-3.48526077097506,3.48526077097506) , initialize=0) m.x39 = Var(within=Reals, bounds=(-3.48536077097506,3.48536077097506) , initialize=0) m.x40 = Var(within=Reals, bounds=(-1,1), initialize=1) m.x41 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x42 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x43 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x44 = Var(within=Reals, bounds=(-1,1), initialize=1) m.x45 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x46 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x47 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x48 = Var(within=Reals, bounds=(-1,1), initialize=1) m.x49 = Var(within=Reals, bounds=(-1,1), initialize=1) m.x50 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x51 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x52 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x53 = Var(within=Reals, bounds=(-1,1), initialize=1) m.x54 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x55 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x56 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x57 = Var(within=Reals, bounds=(-1,1), initialize=1) m.x58 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x59 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x60 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x61 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x62 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x63 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x64 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x65 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x66 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x67 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x68 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x69 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x70 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x71 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x72 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x73 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x74 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x75 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x76 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x77 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x78 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x79 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x80 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x81 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x82 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x83 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x84 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x85 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x86 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x87 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x88 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x89 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x90 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x91 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x92 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x93 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x94 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x95 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x96 = Var(within=Reals, bounds=(-1,1), initialize=0) m.x97 = Var(within=Reals, bounds=(16.9646003293849,None) , initialize=16.9646003293849) m.x98 = Var(within=Reals, bounds=(0.333333333333333,0.666666666666667) , initialize=0.333333333333333) m.x99 = Var(within=Reals, bounds=(0.333333333333333,0.666666666666667) , initialize=0.333333333333333) m.x100 = Var(within=Reals, bounds=(0.333333333333333,0.666666666666667) , initialize=0.333333333333333) m.x101 = Var(within=Reals, bounds=(0.666666666666667,1.42857142857143) , initialize=0.666666666666667) m.x102 = Var(within=Reals, bounds=(0.666666666666667,1.42857142857143) , initialize=0.666666666666667) m.x103 = Var(within=Reals, bounds=(0.666666666666667,1.42857142857143) , initialize=0.666666666666667) m.x104 = Var(within=Reals, bounds=(4.5,7), initialize=4.5) m.x105 = Var(within=Reals, bounds=(2.5,4), initialize=2.5) m.x106 = Var(within=Reals, bounds=(2,4), initialize=2) m.x107 = Var(within=Reals, bounds=(1,6), initialize=1) m.x108 = Var(within=Reals, bounds=(1,3), initialize=1) m.x109 = Var(within=Reals, bounds=(1,3), initialize=1) m.x110 = Var(within=Reals, bounds=(0.7,6.3), initialize=0.7) m.x111 = Var(within=Reals, bounds=(0.7,3.3), initialize=0.7) m.x112 = Var(within=Reals, bounds=(0.7,3.3), initialize=0.7) m.x113 = Var(within=Reals, bounds=(0,10), initialize=0) m.x114 = Var(within=Reals, bounds=(0,4), initialize=0) m.x115 = Var(within=Reals, bounds=(0,4), initialize=0) m.x116 = Var(within=Reals, bounds=(0,10), initialize=0) m.x117 = Var(within=Reals, bounds=(0,4), initialize=0) m.x118 = Var(within=Reals, bounds=(0,4), initialize=0) m.x119 = Var(within=Reals, bounds=(0,10), initialize=0) m.x120 = Var(within=Reals, bounds=(0,4), initialize=0) m.x121 = Var(within=Reals, bounds=(0,4), initialize=0) m.x122 = Var(within=Reals, bounds=(0,10), initialize=0) m.x123 = Var(within=Reals, bounds=(0,4), initialize=0) m.x124 = Var(within=Reals, bounds=(0,4), initialize=0) m.obj = Objective(sense=minimize, expr= m.x97) m.e1 = Constraint(expr= -m.x104 * m.x105 * m.x106 + m.x97 == 0) m.e2 = Constraint(expr= m.x40 * m.x44 * m.x48 - m.x40 * m.x45 * m.x47 - m.x41 * m.x43 * m.x48 + m.x41 * m.x46 * m.x45 + m.x43 * m.x42 * m.x47 - m.x42 * m.x44 * m.x46 == 1) m.e3 = Constraint(expr= m.x49 * m.x53 * m.x57 - m.x49 * m.x54 * m.x56 - m.x50 * m.x52 * m.x57 + m.x50 * m.x55 * m.x54 + m.x52 * m.x51 * m.x56 - m.x51 * m.x53 * m.x55 == 1) m.e4 = Constraint(expr= m.x61 + m.x62 + m.x63 == 1) m.e5 = Constraint(expr= m.x64 + m.x65 + m.x66 == 0) m.e6 = Constraint(expr= m.x67 + m.x68 + m.x69 == 0) m.e7 = Constraint(expr= m.x70 + m.x71 + m.x72 == 1) m.e8 = Constraint(expr= m.x73 + m.x74 + m.x75 == 0) m.e9 = Constraint(expr= m.x76 + m.x77 + m.x78 == 1) m.e10 = Constraint(expr= m.x79 + m.x80 + m.x81 == 1) m.e11 = Constraint(expr= m.x82 + m.x83 + m.x84 == 0) m.e12 = Constraint(expr= m.x85 + m.x86 + m.x87 == 0) m.e13 = Constraint(expr= m.x88 + m.x89 + m.x90 == 1) m.e14 = Constraint(expr= m.x91 + m.x92 + m.x93 == 0) m.e15 = Constraint(expr= m.x94 + m.x95 + m.x96 == 1) m.e16 = Constraint(expr= m.x22 - 0.25 * m.x61 - 0.444444444444444 * m.x62 - m.x63 == 0) m.e17 = Constraint(expr= m.x23 - 0.25 * m.x64 - 0.444444444444444 * m.x65 - m.x66 == 0) m.e18 = Constraint(expr= m.x24 - 0.25 * m.x67 - 0.444444444444444 * m.x68 - m.x69 == 0) m.e19 = Constraint(expr= m.x26 - 0.25 * m.x70 - 0.444444444444444 * m.x71 - m.x72 == 0) m.e20 = Constraint(expr= m.x27 - 0.25 * m.x73 - 0.444444444444444 * m.x74 - m.x75 == 0) m.e21 = Constraint(expr= m.x30 - 0.25 * m.x76 - 0.444444444444444 * m.x77 - m.x78 == 0) m.e22 = Constraint(expr= m.x31 - 0.444444444444444 * m.x79 - m.x80 - 2.04081632653061 * m.x81 == 0) m.e23 = Constraint(expr= m.x32 - 0.444444444444444 * m.x82 - m.x83 - 2.04081632653061 * m.x84 == 0) m.e24 = Constraint(expr= m.x33 - 0.444444444444444 * m.x85 - m.x86 - 2.04081632653061 * m.x87 == 0) m.e25 = Constraint(expr= m.x35 - 0.444444444444444 * m.x88 - m.x89 - 2.04081632653061 * m.x90 == 0) m.e26 = Constraint(expr= m.x36 - 0.444444444444444 * m.x91 - m.x92 - 2.04081632653061 * m.x93 == 0) m.e27 = Constraint(expr= m.x39 - 0.444444444444444 * m.x94 - m.x95 - 2.04081632653061 * m.x96 == 0) m.e28 = Constraint(expr= -m.x23 + m.x25 == 0) m.e29 = Constraint(expr= -m.x24 + m.x28 == 0) m.e30 = Constraint(expr= -m.x27 + m.x29 == 0) m.e31 = Constraint(expr= -m.x32 + m.x34 == 0) m.e32 = Constraint(expr= -m.x33 + m.x37 == 0) m.e33 = Constraint(expr= -m.x36 + m.x38 == 0) m.e34 = Constraint(expr= -m.x104 + m.x107 <= -1) m.e35 = Constraint(expr= -m.x105 + m.x108 <= -1) m.e36 = Constraint(expr= -m.x106 + m.x109 <= -1) m.e37 = Constraint(expr= -m.x104 + m.x110 <= -0.7) m.e38 = Constraint(expr= -m.x105 + m.x111 <= -0.7) m.e39 = Constraint(expr= -m.x106 + m.x112 <= -0.7) m.e40 = Constraint(expr= m.x98**2 - m.x26 * m.x30 + m.x27 * m.x29 == 0) m.e41 = Constraint(expr= m.x101**2 - m.x35 * m.x39 + m.x36 * m.x38 == 0) m.e42 = Constraint(expr= m.x99**2 - m.x22 * m.x30 + m.x24 * m.x28 == 0) m.e43 = Constraint(expr= m.x102**2 - m.x31 * m.x39 + m.x33 * m.x37 == 0) m.e44 = Constraint(expr= m.x100**2 - m.x22 * m.x26 + m.x23 * m.x25 == 0) m.e45 = Constraint(expr= m.x103**2 - m.x31 * m.x35 + m.x32 * m.x34 == 0) m.e46 = Constraint(expr= 3 * m.x98 - m.x107 + m.x113 == 0) m.e47 = Constraint(expr= 3 * m.x99 - m.x108 + m.x114 == 0) m.e48 = Constraint(expr= 3 * m.x100 - m.x109 + m.x115 == 0) m.e49 = Constraint(expr= 1.05 * m.x101 - m.x110 + m.x116 == 0) m.e50 = Constraint(expr= 1.05 * m.x102 - m.x111 + m.x117 == 0) m.e51 = Constraint(expr= 1.05 * m.x103 - m.x112 + m.x118 == 0) m.e52 = Constraint(expr= -3 * m.x98 - m.x107 + m.x119 == 0) m.e53 = Constraint(expr= -3 * m.x99 - m.x108 + m.x120 == 0) m.e54 = Constraint(expr= -3 * m.x100 - m.x109 + m.x121 == 0) m.e55 = Constraint(expr= -1.05 * m.x101 - m.x110 + m.x122 == 0) m.e56 = Constraint(expr= -1.05 * m.x102 - m.x111 + m.x123 == 0) m.e57 = Constraint(expr= -1.05 * m.x103 - m.x112 + m.x124 == 0) m.e58 = Constraint(expr= -m.x104 + m.x119 <= 0) m.e59 = Constraint(expr= -m.x105 + m.x120 <= 0) m.e60 = Constraint(expr= -m.x106 + m.x121 <= 0) m.e61 = Constraint(expr= -m.x104 + m.x122 <= 0) m.e62 = Constraint(expr= -m.x105 + m.x123 <= 0) m.e63 = Constraint(expr= -m.x106 + m.x124 <= 0) m.e64 = Constraint(expr= m.x104 - m.x105 >= 0) m.e65 = Constraint(expr= m.x105 - m.x106 >= 0) m.e66 = Constraint(expr= -0.5 * m.x104 + m.x107 <= 0) m.e67 = Constraint(expr= -0.5 * m.x105 + m.x108 <= 0) m.e68 = Constraint(expr= -0.5 * m.x106 + m.x109 <= 0) m.e69 = Constraint(expr= m.x58**2 + m.x59**2 + m.x60**2 == 1) m.e70 = Constraint(expr= -m.x40 * m.x40 + m.x61 == 0) m.e71 = Constraint(expr= -m.x41 * m.x41 + m.x62 == 0) m.e72 = Constraint(expr= -m.x42 * m.x42 + m.x63 == 0) m.e73 = Constraint(expr= -m.x40 * m.x43 + m.x64 == 0) m.e74 = Constraint(expr= -m.x41 * m.x44 + m.x65 == 0) m.e75 = Constraint(expr= -m.x42 * m.x45 + m.x66 == 0) m.e76 = Constraint(expr= -m.x40 * m.x46 + m.x67 == 0) m.e77 = Constraint(expr= -m.x41 * m.x47 + m.x68 == 0) m.e78 = Constraint(expr= -m.x42 * m.x48 + m.x69 == 0) m.e79 = Constraint(expr= -m.x43 * m.x43 + m.x70 == 0) m.e80 = Constraint(expr= -m.x44 * m.x44 + m.x71 == 0) m.e81 = Constraint(expr= -m.x45 * m.x45 + m.x72 == 0) m.e82 = Constraint(expr= -m.x43 * m.x46 + m.x73 == 0) m.e83 = Constraint(expr= -m.x44 * m.x47 + m.x74 == 0) m.e84 = Constraint(expr= -m.x45 * m.x48 + m.x75 == 0) m.e85 = Constraint(expr= -m.x46 * m.x46 + m.x76 == 0) m.e86 = Constraint(expr= -m.x47 * m.x47 + m.x77 == 0) m.e87 = Constraint(expr= -m.x48 * m.x48 + m.x78 == 0) m.e88 = Constraint(expr= -m.x49 * m.x49 + m.x79 == 0) m.e89 = Constraint(expr= -m.x50 * m.x50 + m.x80 == 0) m.e90 = Constraint(expr= -m.x51 * m.x51 + m.x81 == 0) m.e91 = Constraint(expr= -m.x49 * m.x52 + m.x82 == 0) m.e92 = Constraint(expr= -m.x50 * m.x53 + m.x83 == 0) m.e93 = Constraint(expr= -m.x51 * m.x54 + m.x84 == 0) m.e94 = Constraint(expr= -m.x49 * m.x55 + m.x85 == 0) m.e95 = Constraint(expr= -m.x50 * m.x56 + m.x86 == 0) m.e96 = Constraint(expr= -m.x51 * m.x57 + m.x87 == 0) m.e97 = Constraint(expr= -m.x52 * m.x52 + m.x88 == 0) m.e98 = Constraint(expr= -m.x53 * m.x53 + m.x89 == 0) m.e99 = Constraint(expr= -m.x54 * m.x54 + m.x90 == 0) m.e100 = Constraint(expr= -m.x52 * m.x55 + m.x91 == 0) m.e101 = Constraint(expr= -m.x53 * m.x56 + m.x92 == 0) m.e102 = Constraint(expr= -m.x54 * m.x57 + m.x93 == 0) m.e103 = Constraint(expr= -m.x55 * m.x55 + m.x94 == 0) m.e104 = Constraint(expr= -m.x56 * m.x56 + m.x95 == 0) m.e105 = Constraint(expr= -m.x57 * m.x57 + m.x96 == 0) m.e106 = Constraint(expr= m.x106**3 - m.x97 <= 0) m.e107 = Constraint(expr= m.x19 - m.x107 + m.x110 == 0) m.e108 = Constraint(expr= m.x20 - m.x108 + m.x111 == 0) m.e109 = Constraint(expr= m.x21 - m.x109 + m.x112 == 0) m.e110 = Constraint(expr= m.x58 * m.x19 + m.x59 * m.x20 + m.x60 * m.x21 + (- sqrt((m.x1 * m.x58)**2 + (m.x4 * m.x59)**2 + (m.x7 * m.x60)**2 + (m.x2 * m.x58)**2 + (m.x5 * m.x59)**2 + (m.x8 * m.x60)**2 + (m.x3 * m.x58)**2 + ( m.x6 * m.x59)**2 + (m.x9 * m.x60)**2)) - sqrt((m.x10 * m.x58)**2 + (m.x13 * m.x59)**2 + (m.x16 * m.x60)**2 + (m.x11 * m.x58)**2 + (m.x14 * m.x59)**2 + (m.x17 * m.x60)**2 + (m.x12 * m.x58)**2 + (m.x15 * m.x59)**2 + (m.x18 * m.x60)**2) >= 0) m.e111 = Constraint(expr= m.x1 - 2 * m.x40 == 0) m.e112 = Constraint(expr= m.x2 - 1.5 * m.x41 == 0) m.e113 = Constraint(expr= m.x3 - m.x42 == 0) m.e114 = Constraint(expr= m.x4 - 2 * m.x43 == 0) m.e115 = Constraint(expr= m.x5 - 1.5 * m.x44 == 0) m.e116 = Constraint(expr= m.x6 - m.x45 == 0) m.e117 = Constraint(expr= m.x7 - 2 * m.x46 == 0) m.e118 = Constraint(expr= m.x8 - 1.5 * m.x47 == 0) m.e119 = Constraint(expr= m.x9 - m.x48 == 0) m.e120 = Constraint(expr= m.x10 - 1.5 * m.x49 == 0) m.e121 = Constraint(expr= m.x11 - m.x50 == 0) m.e122 = Constraint(expr= m.x12 - 0.7 * m.x51 == 0) m.e123 = Constraint(expr= m.x13 - 1.5 * m.x52 == 0) m.e124 = Constraint(expr= m.x14 - m.x53 == 0) m.e125 = Constraint(expr= m.x15 - 0.7 * m.x54 == 0) m.e126 = Constraint(expr= m.x16 - 1.5 * m.x55 == 0) m.e127 = Constraint(expr= m.x17 - m.x56 == 0) m.e128 = Constraint(expr= m.x18 - 0.7 * m.x57 == 0)