# MINLP written by GAMS Convert at 02/17/22 17:23:33 # # Equation counts # Total E G L N X C B # 103 55 15 33 0 0 0 0 # # Variable counts # x b i s1s s2s sc si # Total cont binary integer sos1 sos2 scont sint # 69 60 9 0 0 0 0 0 # FX 0 # # Nonzero counts # Total const NL # 343 91 252 # # 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=(None,None), initialize=0) m.x23 = Var(within=Reals, bounds=(None,None), initialize=0) m.x24 = Var(within=Reals, bounds=(None,None), initialize=0) m.x25 = Var(within=Reals, bounds=(None,None), initialize=0) m.x26 = Var(within=Reals, bounds=(None,None), initialize=0) m.x27 = Var(within=Reals, bounds=(None,None), initialize=0) m.x28 = Var(within=Reals, bounds=(None,None), initialize=0) m.x29 = Var(within=Reals, bounds=(None,None), initialize=0) m.x30 = Var(within=Reals, bounds=(None,None), initialize=0) m.x31 = Var(within=Reals, bounds=(None,None), initialize=0) m.x32 = Var(within=Reals, bounds=(None,None), initialize=0) m.x33 = Var(within=Reals, bounds=(None,None), initialize=0) m.x34 = Var(within=Reals, bounds=(None,None), initialize=0) m.x35 = Var(within=Reals, bounds=(None,None), initialize=0) m.x36 = Var(within=Reals, bounds=(None,None), initialize=0) m.x37 = Var(within=Reals, bounds=(None,None), initialize=0) m.x38 = Var(within=Reals, bounds=(None,None), initialize=0) m.x39 = Var(within=Reals, bounds=(None,None), initialize=0) m.x40 = Var(within=Reals, bounds=(None,None), initialize=0) m.x41 = Var(within=Reals, bounds=(None,None), initialize=0) m.x42 = Var(within=Reals, bounds=(None,None), initialize=0) m.x43 = Var(within=Reals, bounds=(None,None), initialize=0) m.x44 = Var(within=Reals, bounds=(None,None), initialize=0) m.x45 = Var(within=Reals, bounds=(None,None), initialize=0) m.x46 = Var(within=Reals, bounds=(None,None), initialize=0) m.x47 = Var(within=Reals, bounds=(None,None), initialize=0) m.x48 = Var(within=Reals, bounds=(None,None), initialize=0) m.x49 = Var(within=Reals, bounds=(None,None), initialize=0) m.x50 = Var(within=Reals, bounds=(None,None), initialize=0) m.x51 = Var(within=Reals, bounds=(None,None), initialize=0) m.x52 = Var(within=Reals, bounds=(None,None), initialize=0) m.x53 = Var(within=Reals, bounds=(None,None), initialize=0) m.x54 = Var(within=Reals, bounds=(None,None), initialize=0) m.b55 = Var(within=Binary, bounds=(0,1), initialize=0) m.b56 = Var(within=Binary, bounds=(0,1), initialize=0) m.b57 = Var(within=Binary, bounds=(0,1), initialize=0) m.b58 = Var(within=Binary, bounds=(0,1), initialize=0) m.b59 = Var(within=Binary, bounds=(0,1), initialize=0) m.b60 = Var(within=Binary, bounds=(0,1), initialize=0) m.b61 = Var(within=Binary, bounds=(0,1), initialize=0) m.b62 = Var(within=Binary, bounds=(0,1), initialize=0) m.b63 = Var(within=Binary, bounds=(0,1), initialize=0) m.x64 = Var(within=Reals, bounds=(None,None), initialize=0) m.x65 = Var(within=Reals, bounds=(None,None), initialize=0) m.x66 = Var(within=Reals, bounds=(None,None), initialize=0) m.x67 = Var(within=Reals, bounds=(None,None), initialize=0) m.x68 = Var(within=Reals, bounds=(None,None), initialize=0) m.x69 = Var(within=Reals, bounds=(None,None), initialize=0) m.obj = Objective(sense=minimize, expr= 1100 * m.x64**2 + 500 * m.x64 + 850 * m.x65**2 + 120 * m.x65 + 1225 * m.x66**2 + 100 * m.x66 + 1085) m.e1 = Constraint(expr= -17.0648464163823 * (m.x39 * m.x51 - m.x42 * m.x48) * m.b55 + m.x1 == 0) m.e2 = Constraint(expr= -17.0648464163823 * (m.x42 * m.x48 - m.x39 * m.x51) * m.b55 + m.x2 == 0) m.e3 = Constraint(expr= -m.b56 * (1.61712247324614 * (m.x43**2 + m.x52**2) - 1.61712247324614 * (m.x43 * m.x44 + m.x52 * m.x53) + 13.6979785969084 * ( m.x43 * m.x53 - m.x44 * m.x52)) + m.x3 == 0) m.e4 = Constraint(expr= -m.b56 * (1.61712247324614 * (m.x44**2 + m.x53**2) - 1.61712247324614 * (m.x44 * m.x43 + m.x53 * m.x52) + 13.6979785969084 * ( m.x44 * m.x52 - m.x43 * m.x53)) + m.x4 == 0) m.e5 = Constraint(expr= -m.b57 * (1.28200913842411 * (m.x41**2 + m.x50**2) - 1.28200913842411 * (m.x41 * m.x42 + m.x50 * m.x51) + 5.58824496236153 * ( m.x41 * m.x51 - m.x42 * m.x50)) + m.x5 == 0) m.e6 = Constraint(expr= -m.b57 * (1.28200913842411 * (m.x42**2 + m.x51**2) - 1.28200913842411 * (m.x42 * m.x41 + m.x51 * m.x50) + 5.58824496236153 * ( m.x42 * m.x50 - m.x41 * m.x51)) + m.x6 == 0) m.e7 = Constraint(expr= -m.b58 * (1.1550874808901 * (m.x42**2 + m.x51**2) - 1.1550874808901 * (m.x42 * m.x43 + m.x51 * m.x52) + 9.78427042636317 * ( m.x42 * m.x52 - m.x43 * m.x51)) + m.x7 == 0) m.e8 = Constraint(expr= -m.b58 * (1.1550874808901 * (m.x43**2 + m.x52**2) - 1.1550874808901 * (m.x43 * m.x42 + m.x52 * m.x51) + 9.78427042636317 * ( m.x43 * m.x51 - m.x42 * m.x52)) + m.x8 == 0) m.e9 = Constraint(expr= -16 * (m.x44 * m.x47 - m.x38 * m.x53) * m.b59 + m.x9 == 0) m.e10 = Constraint(expr= -16 * (m.x38 * m.x53 - m.x44 * m.x47) * m.b59 + m.x10 == 0) m.e11 = Constraint(expr= -m.b60 * (1.94219124871473 * (m.x40**2 + m.x49**2) - 1.94219124871473 * (m.x40 * m.x41 + m.x49 * m.x50) + 10.5106820518679 * ( m.x40 * m.x50 - m.x41 * m.x49)) + m.x11 == 0) m.e12 = Constraint(expr= -m.b60 * (1.94219124871473 * (m.x41**2 + m.x50**2) - 1.94219124871473 * (m.x41 * m.x40 + m.x50 * m.x49) + 10.5106820518679 * ( m.x41 * m.x49 - m.x40 * m.x50)) + m.x12 == 0) m.e13 = Constraint(expr= -17.3611111111111 * (m.x37 * m.x49 - m.x40 * m.x46) * m.b61 + m.x13 == 0) m.e14 = Constraint(expr= -17.3611111111111 * (m.x40 * m.x46 - m.x37 * m.x49) * m.b61 + m.x14 == 0) m.e15 = Constraint(expr= -m.b62 * (1.36518771331058 * (m.x45**2 + m.x54**2) - 1.36518771331058 * (m.x45 * m.x40 + m.x54 * m.x49) + 11.6040955631399 * ( m.x45 * m.x49 - m.x40 * m.x54)) + m.x15 == 0) m.e16 = Constraint(expr= -m.b62 * (1.36518771331058 * (m.x40**2 + m.x49**2) - 1.36518771331058 * (m.x40 * m.x45 + m.x49 * m.x54) + 11.6040955631399 * ( m.x40 * m.x54 - m.x45 * m.x49)) + m.x16 == 0) m.e17 = Constraint(expr= -m.b63 * (1.18760437929115 * (m.x44**2 + m.x53**2) - 1.18760437929115 * (m.x44 * m.x45 + m.x53 * m.x54) + 5.97513453330859 * ( m.x44 * m.x54 - m.x45 * m.x53)) + m.x17 == 0) m.e18 = Constraint(expr= -m.b63 * (1.18760437929115 * (m.x45**2 + m.x54**2) - 1.18760437929115 * (m.x45 * m.x44 + m.x54 * m.x53) + 5.97513453330859 * ( m.x45 * m.x53 - m.x44 * m.x54)) + m.x18 == 0) m.e19 = Constraint(expr= -m.b55 * (17.0648464163823 * (m.x39**2 + m.x48**2) - 17.0648464163823 * (m.x39 * m.x42 + m.x48 * m.x51)) + m.x19 == 0) m.e20 = Constraint(expr= -m.b55 * (17.0648464163823 * (m.x42**2 + m.x51**2) - 17.0648464163823 * (m.x42 * m.x39 + m.x51 * m.x48)) + m.x20 == 0) m.e21 = Constraint(expr= -m.b56 * (13.6234785969084 * (m.x43**2 + m.x52**2) - 13.6979785969084 * (m.x43 * m.x44 + m.x52 * m.x53) - 1.61712247324614 * ( m.x43 * m.x53 - m.x44 * m.x52)) + m.x21 == 0) m.e22 = Constraint(expr= -m.b56 * (13.6234785969084 * (m.x44**2 + m.x53**2) - 13.6979785969084 * (m.x44 * m.x43 + m.x53 * m.x52) - 1.61712247324614 * ( m.x44 * m.x52 - m.x43 * m.x53)) + m.x22 == 0) m.e23 = Constraint(expr= -m.b57 * (5.40924496236153 * (m.x41**2 + m.x50**2) - 5.58824496236153 * (m.x41 * m.x42 + m.x50 * m.x51) - 1.28200913842411 * ( m.x41 * m.x51 - m.x42 * m.x50)) + m.x23 == 0) m.e24 = Constraint(expr= -m.b57 * (5.40924496236153 * (m.x42**2 + m.x51**2) - 5.58824496236153 * (m.x42 * m.x41 + m.x51 * m.x50) - 1.28200913842411 * ( m.x42 * m.x50 - m.x41 * m.x51)) + m.x24 == 0) m.e25 = Constraint(expr= -m.b58 * (9.67977042636317 * (m.x42**2 + m.x51**2) - 9.78427042636317 * (m.x42 * m.x43 + m.x51 * m.x52) - 1.1550874808901 * ( m.x42 * m.x52 - m.x43 * m.x51)) + m.x25 == 0) m.e26 = Constraint(expr= -m.b58 * (9.67977042636317 * (m.x43**2 + m.x52**2) - 9.78427042636317 * (m.x43 * m.x42 + m.x52 * m.x51) - 1.1550874808901 * ( m.x43 * m.x51 - m.x42 * m.x52)) + m.x26 == 0) m.e27 = Constraint(expr= -m.b59 * (16 * (m.x44**2 + m.x53**2) - 16 * (m.x44 * m.x38 + m.x53 * m.x47)) + m.x27 == 0) m.e28 = Constraint(expr= -m.b59 * (16 * (m.x38**2 + m.x47**2) - 16 * (m.x38 * m.x44 + m.x47 * m.x53)) + m.x28 == 0) m.e29 = Constraint(expr= -m.b60 * (10.4316820518679 * (m.x40**2 + m.x49**2) - 10.5106820518679 * (m.x40 * m.x41 + m.x49 * m.x50) - 1.94219124871473 * ( m.x40 * m.x50 - m.x41 * m.x49)) + m.x29 == 0) m.e30 = Constraint(expr= -m.b60 * (10.4316820518679 * (m.x41**2 + m.x50**2) - 10.5106820518679 * (m.x41 * m.x40 + m.x50 * m.x49) - 1.94219124871473 * ( m.x41 * m.x49 - m.x40 * m.x50)) + m.x30 == 0) m.e31 = Constraint(expr= -m.b61 * (17.3611111111111 * (m.x37**2 + m.x46**2) - 17.3611111111111 * (m.x37 * m.x40 + m.x46 * m.x49)) + m.x31 == 0) m.e32 = Constraint(expr= -m.b61 * (17.3611111111111 * (m.x40**2 + m.x49**2) - 17.3611111111111 * (m.x40 * m.x37 + m.x49 * m.x46)) + m.x32 == 0) m.e33 = Constraint(expr= -m.b62 * (11.5160955631399 * (m.x45**2 + m.x54**2) - 11.6040955631399 * (m.x45 * m.x40 + m.x54 * m.x49) - 1.36518771331058 * ( m.x45 * m.x49 - m.x40 * m.x54)) + m.x33 == 0) m.e34 = Constraint(expr= -m.b62 * (11.5160955631399 * (m.x40**2 + m.x49**2) - 11.6040955631399 * (m.x40 * m.x45 + m.x49 * m.x54) - 1.36518771331058 * ( m.x40 * m.x54 - m.x45 * m.x49)) + m.x34 == 0) m.e35 = Constraint(expr= -m.b63 * (5.82213453330859 * (m.x44**2 + m.x53**2) - 5.97513453330859 * (m.x44 * m.x45 + m.x53 * m.x54) - 1.18760437929115 * ( m.x44 * m.x54 - m.x45 * m.x53)) + m.x35 == 0) m.e36 = Constraint(expr= -m.b63 * (5.82213453330859 * (m.x45**2 + m.x54**2) - 5.97513453330859 * (m.x45 * m.x44 + m.x54 * m.x53) - 1.18760437929115 * ( m.x45 * m.x53 - m.x44 * m.x54)) + m.x36 == 0) m.e37 = Constraint(expr= m.x1**2 + m.x19**2 <= 9) m.e38 = Constraint(expr= m.x2**2 + m.x20**2 <= 9) m.e39 = Constraint(expr= m.x3**2 + m.x21**2 <= 6.25) m.e40 = Constraint(expr= m.x4**2 + m.x22**2 <= 6.25) m.e41 = Constraint(expr= m.x5**2 + m.x23**2 <= 2.25) m.e42 = Constraint(expr= m.x6**2 + m.x24**2 <= 2.25) m.e43 = Constraint(expr= m.x7**2 + m.x25**2 <= 2.25) m.e44 = Constraint(expr= m.x8**2 + m.x26**2 <= 2.25) m.e45 = Constraint(expr= m.x9**2 + m.x27**2 <= 6.25) m.e46 = Constraint(expr= m.x10**2 + m.x28**2 <= 6.25) m.e47 = Constraint(expr= m.x11**2 + m.x29**2 <= 6.25) m.e48 = Constraint(expr= m.x12**2 + m.x30**2 <= 6.25) m.e49 = Constraint(expr= m.x13**2 + m.x31**2 <= 6.25) m.e50 = Constraint(expr= m.x14**2 + m.x32**2 <= 6.25) m.e51 = Constraint(expr= m.x15**2 + m.x33**2 <= 6.25) m.e52 = Constraint(expr= m.x16**2 + m.x34**2 <= 6.25) m.e53 = Constraint(expr= m.x17**2 + m.x35**2 <= 6.25) m.e54 = Constraint(expr= m.x18**2 + m.x36**2 <= 6.25) m.e55 = Constraint(expr= m.x37**2 + m.x46**2 <= 1.21) m.e56 = Constraint(expr= m.x38**2 + m.x47**2 <= 1.21) m.e57 = Constraint(expr= m.x39**2 + m.x48**2 <= 1.21) m.e58 = Constraint(expr= m.x40**2 + m.x49**2 <= 1.21) m.e59 = Constraint(expr= m.x41**2 + m.x50**2 <= 1.21) m.e60 = Constraint(expr= m.x42**2 + m.x51**2 <= 1.21) m.e61 = Constraint(expr= m.x43**2 + m.x52**2 <= 1.21) m.e62 = Constraint(expr= m.x44**2 + m.x53**2 <= 1.21) m.e63 = Constraint(expr= m.x45**2 + m.x54**2 <= 1.21) m.e64 = Constraint(expr= m.x37**2 + m.x46**2 >= 0.81) m.e65 = Constraint(expr= m.x38**2 + m.x47**2 >= 0.81) m.e66 = Constraint(expr= m.x39**2 + m.x48**2 >= 0.81) m.e67 = Constraint(expr= m.x40**2 + m.x49**2 >= 0.81) m.e68 = Constraint(expr= m.x41**2 + m.x50**2 >= 0.81) m.e69 = Constraint(expr= m.x42**2 + m.x51**2 >= 0.81) m.e70 = Constraint(expr= m.x43**2 + m.x52**2 >= 0.81) m.e71 = Constraint(expr= m.x44**2 + m.x53**2 >= 0.81) m.e72 = Constraint(expr= m.x45**2 + m.x54**2 >= 0.81) m.e73 = Constraint(expr= m.x64 <= 2.5) m.e74 = Constraint(expr= m.x65 <= 3) m.e75 = Constraint(expr= m.x66 <= 2.7) m.e76 = Constraint(expr= m.x64 >= 0.1) m.e77 = Constraint(expr= m.x65 >= 0.1) m.e78 = Constraint(expr= m.x66 >= 0.1) m.e79 = Constraint(expr= m.x67 <= 3) m.e80 = Constraint(expr= m.x68 <= 3) m.e81 = Constraint(expr= m.x69 <= 3) m.e82 = Constraint(expr= m.x67 >= -3) m.e83 = Constraint(expr= m.x68 >= -3) m.e84 = Constraint(expr= m.x69 >= -3) m.e85 = Constraint(expr= m.x46 == 0) m.e86 = Constraint(expr= m.x13 - m.x64 == 0) m.e87 = Constraint(expr= m.x10 - m.x65 == 0) m.e88 = Constraint(expr= m.x1 - m.x66 == 0) m.e89 = Constraint(expr= m.x31 - m.x67 == 0) m.e90 = Constraint(expr= m.x28 - m.x68 == 0) m.e91 = Constraint(expr= m.x19 - m.x69 == 0) m.e92 = Constraint(expr= m.x11 + m.x14 + m.x16 == 0) m.e93 = Constraint(expr= m.x5 + m.x12 == -0.9) m.e94 = Constraint(expr= m.x2 + m.x6 + m.x7 == 0) m.e95 = Constraint(expr= m.x3 + m.x8 == -1) m.e96 = Constraint(expr= m.x4 + m.x9 + m.x17 == 0) m.e97 = Constraint(expr= m.x15 + m.x18 == -1.25) m.e98 = Constraint(expr= m.x29 + m.x32 + m.x34 == 0) m.e99 = Constraint(expr= m.x23 + m.x30 == -0.3) m.e100 = Constraint(expr= m.x20 + m.x24 + m.x25 == 0) m.e101 = Constraint(expr= m.x21 + m.x26 == -0.35) m.e102 = Constraint(expr= m.x22 + m.x27 + m.x35 == 0) m.e103 = Constraint(expr= m.x33 + m.x36 == -0.5)