$ontext
 Filename: primary.bar
 Author:  Nick Sahinidis, August 2002
          based on an earlier implementation of M. Yu and M. Tawarmalani

 Purpose:
 Solve the molecular design problem described in 
 Sahinidis, N. V., M. Tawarmalani and M. Yu,
 "Design of Alternative Refrigerants via Global Optimization,"
 AIChE J., submitted, 2002.

$offtext

$eolcom //

options optcr=0, optca=1e-6, reslim= 3600000;
option sysout=on;

INTEGER VARIABLES
n01, n02, n03, n04, n05, n06, n07, n08, n09, n10, 
n11, n12, n13, n14, n15, n16, n17, n18, n19, n20, 
n21, n22, n23, n24, n25, n26, n27, n28, n29, n30,
n31, n32, n33, n34, n35, n36, n37, n38, n39, n40, 
n41, n42, n43, n44,
intB, intS, intSR, intD, intDR, intT, nr, nrd;

BINARY VARIABLES
binx,    biny,    binz,
binR,
//binSDx,  binSDy,  binSDz,
//binSTx,  binSTy,  binSTz,
//binSSRx, binSSRy, binSSRz,
//binSDRx, binSDRy, binSDRz,
//binDSRx, binDSRy, binDSRz,
binA,    binM,    binH,  cl1;

POSITIVE VARIABLES
Tb, Tc, Pc, Cpl0, Tbr, Tavgr, Tcndr, Tevpr, omega, Cpla, dHvb, dHve, h, G,
Pvpcr, Pvpc, Pvper, Pvpe;

VARIABLES alpha, beta, k, obj;

*lower bounds

n01.lo = 0;
n02.lo = 0;
n03.lo = 0;
n04.lo = 0;
n05.lo = 0;
n06.lo = 0;
n07.lo = 0;
n08.lo = 0;
n09.lo = 0;
n10.lo = 0;

n11.lo = 0;
n12.lo = 0;
n13.lo = 0;
n14.lo = 0;
n15.lo = 0;
n16.lo = 0;
n17.lo = 0;
n18.lo = 0;
n19.lo = 0;
n20.lo = 0;

n21.lo = 0;
n22.lo = 0;
n23.lo = 0;
n24.lo = 0;
n25.lo = 0;
n26.lo = 0;
n27.lo = 0;
n28.lo = 0;
n29.lo = 0;
n30.lo = 0;

n31.lo = 0;
n32.lo = 0;
n33.lo = 0;
n34.lo = 0;
n35.lo = 0;
n36.lo = 0;
n37.lo = 0;
n38.lo = 0;
n39.lo = 0;
n40.lo = 0;

n41.lo = 0;
n42.lo = 0;
n43.lo = 0;
n44.lo = 0;

intB.lo = 0;
intS.lo = 0;
intSR.lo = 0;
intD.lo = 0;
intDR.lo = 0;
intT.lo = 0;

nr.lo = 0;
nrd.lo = 0;

Cpla.lo = 1;
dHve.lo = 18.4;
Pvpc.lo = 1.4;
Pvpe.lo = 1.4;
Tb.lo = 50;
Tc.lo = 100;
Pc.lo = 2;
Cpl0.lo = 1;
Tbr.lo = 0.001;
Tavgr.lo = 0.001;
Tcndr.lo = 0.001;
Tevpr.lo = 0.001;
alpha.lo = -5.4;
beta.lo = -16000;
omega.lo = -1;
dHvb.lo = 10;
h.lo = 0;
G.lo = 0.48;
k.lo = -1;
Pvpcr.lo = 0.001;
Pvper.lo = 0.001;

*upper bounds

n01.up = 15;
n02.up = 15;
n03.up = 15;
n04.up = 15;
n05.up = 15;
n06.up = 15;
n07.up = 15;
n08.up = 15;
n09.up = 15;
n10.up = 15;

n11.up = 15;
n12.up = 15;
n13.up = 15;
n14.up = 15;
n15.up = 15;
n16.up = 15;
n17.up = 15;
n18.up = 15;
n19.up = 15;
n20.up = 15;

n21.up = 15;
n22.up = 15;
n23.up = 15;
n24.up = 15;
n25.up = 15;
n26.up = 15;
n27.up = 15;
n28.up = 15;
n29.up = 15;
n30.up = 15;

n31.up = 15;
n32.up = 15;
n33.up = 15;
n34.up = 15;
n35.up = 15;
n36.up = 15;
n37.up = 15;
n38.up = 15;
n39.up = 15;
n40.up = 15;

n41.up = 15;
n42.up = 15;
n43.up = 15;
n44.up = 15;

intB.up = 172;
intS.up = 330;
intSR.up = 232;
intD.up = 60;
intDR.up = 30;
intT.up = 15;

nr.up = 225;
nrd.up = 60;

Cpla.up = 32.2;
dHve.up = 100;
Pvpc.up = 14;
Pvpe.up = 14;
Tb.up = 1000;
Tc.up = 2000;
Pc.up = 200;
Cpl0.up = 135;
Tbr.up = 1;
Tavgr.up = 1;
Tcndr.up = 1;
Tevpr.up = 1;
alpha.up = 6100;
beta.up = 0;
omega.up = 1.3;
dHvb.up = 110;
h.up = 5300;
G.up = 2500;
k.up = 10;
Pvpcr.up = 1;
Pvper.up = 1;

EQUATIONS 
e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15, e16, e17, 
e18, e19, e20, e21, 

st1, 
st2a1, 
//st2a2, 
st2a2_1, st2a2_2, st2a2_3, st2a2_4, st2a2_5,
st2a2_6, st2a2_7, st2a2_8, st2a2_9, st2a2_10,
st2a2_11, st2a2_12, st2a2_13, st2a2_14, st2a2_15,
st2a2_16, st2a2_17, st2a2_18, st2a2_19, st2a2_20,
st2a2_21, st2a2_22, st2a2_23, st2a2_24, st2a2_25,
st2a2_26, st2a2_27, st2a2_28, st2a2_29,

st2b1, 
//st2b2,
st2b2_1, st2b2_2, st2b2_3, st2b2_4, st2b2_5,
st2b2_6, st2b2_7, st2b2_8, st2b2_9, st2b2_10,

st2c1, 
//st2c2,
st2c2_1, st2c2_2, st2c2_3, st2c2_4, st2c2_5,

st2d1, st2d2,
st4a, 
//st4b,
st4b_1, st4b_2, st4b_3, st4b_4, st4b_5,
st4b_6, st4b_7, st4b_8, st4b_9, st4b_10,
st4b_11, st4b_12, st4b_13, st4b_14, st4b_15,

st5, 
st6, 
st7, 
//st8 not used here

st9a1,
//st9a2,
st9a2_1, st9a2_2, st9a2_3, st9a2_4, st9a2_5,

st9b,
st10a1,
//st10a2,
st10a2_1, st10a2_2, st10a2_3, st10a2_4, st10a2_5,
st10a2_6, st10a2_7, st10a2_8, st10a2_9, st10a2_10,
st10a2_11, st10a2_12, st10a2_13, st10a2_14, st10a2_15,

st10b1, st10b2, 
st11S, st11SR, st11D, st11DR, st11T,

odmacch02, odmacch03, odmacch04, odmacch06, odmacch07, odmacch08, odmacch10,
odmacch26, odmacch28, odmacch32, 
odmacch35, odmacch37, odmacch38,
odmacch43,

myH1, 
//myH2,
myH2_1, myH2_2, myH2_3, myH2_4, myH2_5,
myH2_6, myH2_7, myH2_8, myH2_9, myH2_10,
myH2_11, myH2_12, myH2_13, myH2_14, myH2_15,

myS, myD, myT, mya, myb,

er, erd, er1, er2, er3,

gn1, gn2, gn3, objdef ;

e1 .. 
Tb-(n01*23.58+n02*22.88+n03*21.74+n04*18.25+n05*18.18+n06*24.96+n07*24.14
+n08*26.15+n09*9.2+n10*27.38+n11*27.15+n12*21.78+n13*21.78+n14*21.32+n15*21.32
+n16*21.32+n17*26.73+n18*31.01+n19*31.01+n20*31.01-n21*0.03+n22*38.13
+n23*66.86+n24*93.84+n25*92.88+n26*22.42+n27*31.22+n28*76.75+n29*94.97
+n30*72.24+n31*169.09+n32*81.1-n33*10.5+n34*73.23+n35*50.17+n36*52.82
+n37*11.74+n38*74.6+n39*57.55+n40*125.66+n41*152.54+n42*63.56+n43*68.78
+n44*52.1) =E= 198.2;

e2 .. 
Tc-Tb/(0.584+0.965*(n01*0.0141+n02*0.0189+n03*0.0164+n04*0.0067+n05*0.0113
+n06*0.0129+n07*0.0117+n08*0.0026+n09*0.0027+n10*0.002+n11*0.01+n12*0.0122
+n13*0.0122+n14*0.0042+n15*0.0042+n16*0.0042+n17*0.0082+n18*0.0143+n19*0.0143
+n20*0.0143+n21*0.0111+n22*0.0105+n23*0.0133+n24*0.0068+n25*0.0741+n26*0.0168
+n27*0.0098+n28*0.038+n29*0.0284+n30*0.0379+n31*0.0791+n32*0.0481+n33*0.0143
+n34*0.0243+n35*0.0295+n36*0.013+n37*0.0169+n38*0.0255+n39*0.0085+n40*0.0496
+n41*0.0437+n42*0.0031+n43*0.0119+n44*0.0019)
-(n01*0.0141+n02*0.0189+n03*0.0164+n04*0.0067+n05*0.0113+n06*0.0129+n07*0.0117
+n08*0.0026+n09*0.0027+n10*0.002+n11*0.01+n12*0.0122+n13*0.0122+n14*0.0042
+n15*0.0042+n16*0.0042+n17*0.0082+n18*0.0143+n19*0.0143+n20*0.0143+n21*0.0111
+n22*0.0105+n23*0.0133+n24*0.0068+n25*0.0741+n26*0.0168+n27*0.0098+n28*0.038
+n29*0.0284+n30*0.0379+n31*0.0791+n32*0.0481+n33*0.0143+n34*0.0243+n35*0.0295
+n36*0.013+n37*0.0169+n38*0.0255+n39*0.0085+n40*0.0496+n41*0.0437+n42*0.0031
+n43*0.0119+n44*0.0019)**2) =E= 0;

e3 .. 
Pc-1/(0.113+0.0032*(n01*4+n02*3+n03*2+n04*1+n05*3+n06*2+n07*1+n08*1+n09*2
+n10*1+n11*3+n12*2+n13*2+n14*1+n15*1+n16*1+n17*2+n18*1+n19*1+n20*1+n21*1
+n22*1+n23*1+n24*1+n25*2+n26*1+n27*1+n28*2+n29*2+n30*3+n31*4+n32*3+n33*1+n34*3
+n35*2+n36*2+n37*1+n38*1+n39*1+n40*2+n41*3+n42*2+n43*1+n44*1)
-(-n01*0.0012+n02*0+n03*0.002+n04*0.0043-n05*0.0028-n06*0.0006+n07*0.0011
+n08*0.0028-n09*0.0008+n10*0.0016+n11*0.0025+n12*0.0004+n13*0.0004+n14*0.0061
+n15*0.0061+n16*0.0061+n17*0.0011+n18*0.0008+n19*0.0008+n20*0.0008-n21*0.0057
-n22*0.0049+n23*0.0057-n24*0.0034+n25*0.0112+n26*0.0015+n27*0.0048+n28*0.0031
+n29*0.0028+n30*0.003+n31*0.0077+n32*0.0005+n33*0.0101+n34*0.0109+n35*0.0077
+n36*0.0114+n37*0.0074-n38*0.0099+n39*0.0076-n40*0.0101+n41*0.0064+n42*0.0084
+n43*0.0049+n44*0.0051))**2 =E= 0;

e4 .. 
Cpl0-(n01*1.95e1-n02*9.09e-1-n03*2.3e1-n04*6.62e1+n05*2.36e1-n06*8-n07*2.81e1
+n08*2.74e1+n09*2.45e1+n10*7.87-n11*6.03-n12*2.05e1-n13*2.05e1-n14*9.09e1
-n15*9.09e1-n16*9.09e1-n17*2.14-n18*8.25-n19*8.25-n20*8.25+n21*2.65e1
+n22*3.33e1+n23*2.86e1+n24*3.21e1+n25*2.57e1+n26*2.55e1+n27*1.22e1+n28*6.45
+n29*3.04e1+n30*3.09e1+n31*2.41e1+n32*2.45e1+n33*6.82+n34*2.69e1-n35*1.21
+n36*1.18e1-n37*3.11e1+n38*0+n39*8.83+n40*3.65e1+n41*2.59e1+n42*3.53e1
+n43*1.96e1+n44*1.67e1)
-(-n01*8.08e-3+n02*9.5e-2+n03*2.04e-1+n04*4.27e-1-n05*3.81e-2+n06*1.05e-1
+n07*2.08e-1-n08*5.57e-2-n09*2.71e-2+n10*2.01e-2+n11*8.54e-2+n12*1.62e-1
+n13*1.62e-1+n14*5.57e-1+n15*5.57e-1+n16*5.57e-1+n17*5.74e-2+n18*1.01e-1
+n19*1.01e-1+n20*1.01e-1-n21*9.13e-2-n22*9.63e-2-n23*6.49e-2-n24*6.41e-2
-n25*6.91e-2-n26*6.32e-2-n27*1.26e-2+n28*6.7e-2-n29*8.29e-2-n30*3.36e-2
+n31*4.27e-2+n32*4.02e-2+n33*1.96e-2-n34*4.12e-2+n35*7.62e-2-n36*2.3e-2
+n37*2.27e-1+n38*0-n39*3.84e-3-n40*7.33e-2-n41*3.74e-3-n42*7.58e-2-n43*5.61e-3
+n44*4.81e-3+0.21)*294.25
-(n01*1.53e-4-n02*5.44e-5-n03*2.65e-4-n04*6.41e-4+n05*1.72e-4-n06*9.63e-5
-n07*3.06e-4+n08*1.01e-4+n09*1.11e-4-n10*8.33e-6-n11*8e-6-n12*1.6e-4
-n13*1.6e-4-n14*9e-4-n15*9e-4-n16*9e-4-n17*1.64e-6-n18*1.42e-4-n19*1.42e-4
-n20*1.42e-4+n21*1.91e-4+n22*1.87e-4+n23*1.36e-4+n24*1.26e-4+n25*1.77e-4
+n26*1.11e-4+n27*6.03e-5-n28*3.57e-5+n29*2.36e-4+n30*1.6e-4+n31*8.04e-5
+n32*4.02e-5+n33*1.27e-5+n34*1.64e-4-n35*4.86e-5+n36*1.07e-4-n37*3.2e-4+n38*0
+n39*4.35e-5+n40*1.84e-4+n41*1.29e-4+n42*1.85e-4+n43*4.02e-5+n44*2.77e-5
-3.91e-4)*294.25**2
-(-n01*9.67e-8+n02*1.19e-8+n03*1.2e-7+n04*3.01e-7-n05*1.03e-7+n06*3.56e-8
+n07*1.46e-7-n08*5.02e-8-n09*6.78e-8+n10*1.39e-9-n11*1.8e-8+n12*6.24e-8
+n13*6.24e-8+n14*4.69e-7+n15*4.69e-7+n16*4.69e-7-n17*1.59e-8+n18*6.78e-8
+n19*6.78e-8+n20*6.78e-8-n21*1.03e-7-n22*9.96e-8-n23*7.45e-8-n24*6.87e-8
-n25*9.88e-8-n26*5.48e-8-n27*3.86e-8+n28*2.86e-9-n29*1.31e-7-n30*9.88e-8
-n31*6.87e-8-n32*4.52e-8-n33*1.78e-8-n34*9.76e-8+n35*1.05e-8-n36*6.28e-8
+n37*1.46e-7+n38*0-n39*2.6e-8-n40*1.03e-7-n41*8.88e-8-n42*1.03e-7-n43*2.76e-8
-n44*2.11e-8+2.06e-7)*294.25**3 =E= -37.93;

e5 .. 
Tbr-Tb/Tc =E= 0;

e6 .. 
Tavgr-294.25/Tc =E= 0;

e7 .. 
Tcndr-316.45/Tc =E= 0;

e8 .. 
Tevpr-272.05/Tc =E= 0;

e9 .. 
alpha+log(Pc/1.013)-6.09648/Tbr-1.28862*log(Tbr)+0.169347*Tbr**6 =E= -5.97214;

e10 .. 
beta+15.6875/Tbr+13.4721*log(Tbr)-0.43577*Tbr**6 =E= 15.2518;

e11 .. 
omega*beta-alpha =E= 0;

// e12 .. 
// Cpla-(Cpl0+8.314*(1.45+0.45/(1-Tavgr)+0.25*omega*(17.11+25.2*(1-Tavgr)**(1/3)
// /Tavgr+1.742/(1-Tavgr))))/4.1868 =E= 0;

e12 .. 
4.1868 * Cpla
- ( Cpl0 + 3.7413/(1-Tavgr) + 35.563135 * omega 
    + 52.3782 * omega * (1-Tavgr)**(1/3) / Tavgr
    +  3.620747 * omega / (1-Tavgr)
  ) =E= 12.0553 ;

e13 .. 
dHvb-(n01*2.373+n02*2.226+n03*1.691+n04*0.636+n05*1.724+n06*2.205+n07*2.138
+n08*2.661+n09*1.155+n10*3.302+n11*2.398+n12*1.942+n13*1.942+n14*0.664
+n15*0.664+n16*0.664+n17*2.544+n18*3.059+n19*3.059+n20*3.059-n21*0.67
+n22*4.532+n23*6.582+n24*9.52+n25*16.826+n26*2.41+n27*4.682+n28*8.972
+n29*6.645+n30*9.093+n31*19.537+n32*9.633+n33*5.909+n34*10.788+n35*6.436
+n36*6.93+n37*1.896+n38*3.335+n39*6.528+n40*12.851+n41*16.738+n42*6.884
+n43*6.817+n44*5.984) =E= 15.3;

e14 .. 
dHve-dHvb*((1-Tevpr)/(1-Tbr))**0.38 =E= 0;

e15 .. 
h-Tbr*log(Pc/1.013)/(1-Tbr) =E= 0;

e16 .. 
G-0.4605*h =E= 0.4835;

e17 .. 
k-(h-(1+Tbr)*G)/G/(3+Tbr)/(1-Tbr)**2 =E= 0;

e18 .. 
Pvpcr-exp(-G*(1-Tcndr**2+k*(3+Tcndr)*(1-Tcndr)**3)/Tcndr) =E= 0;

e19 .. 
Pvpc-Pvpcr*Pc =E= 0;

e20 .. 
Pvper-exp(-G*(1-Tevpr**2+k*(3+Tevpr)*(1-Tevpr)**3)/Tevpr) =E= 0;

e21 .. 
Pvpe-Pvper*Pc =E= 0;

st1 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44 
=G= 2;

st2a1 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n21+n22+n23+n24+
n25+n26+n28+n30+n31+n32+n33+
n34+n35+n37+n38+n40+n41+
n42+n43
-binx =G= 0;

//st2a2 .. 
//n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
//n21+n22+n23+n24+
//n25+n26+n28+n30+n31+n32+n33+
//n34+n35+n37+n38+n40+n41+
//n42+n43
//-29*15*binx =L= 0;

st2a2_1 ..  n01 - 15*binx =L= 0;
st2a2_2 ..  n02 - 15*binx =L= 0;
st2a2_3 ..  n03 - 15*binx =L= 0;
st2a2_4 ..  n04 - 15*binx =L= 0;
st2a2_5 ..  n05 - 15*binx =L= 0;
st2a2_6 ..  n06 - 15*binx =L= 0;
st2a2_7 ..  n07 - 15*binx =L= 0;
st2a2_8 ..  n08 - 15*binx =L= 0;
st2a2_9 ..  n09 - 15*binx =L= 0;
st2a2_10 ..  n10 - 15*binx =L= 0;
st2a2_11 ..  n21 - 15*binx =L= 0;
st2a2_12 ..  n22 - 15*binx =L= 0;
st2a2_13 ..  n23 - 15*binx =L= 0;
st2a2_14 ..  n24 - 15*binx =L= 0;
st2a2_15 ..  n25 - 15*binx =L= 0;
st2a2_16 ..  n26 - 15*binx =L= 0;
st2a2_17 ..  n28 - 15*binx =L= 0;
st2a2_18 ..  n30 - 15*binx =L= 0;
st2a2_19 ..  n31 - 15*binx =L= 0;
st2a2_20 ..  n32 - 15*binx =L= 0;
st2a2_21 ..  n33 - 15*binx =L= 0;
st2a2_22 ..  n34 - 15*binx =L= 0;
st2a2_23 ..  n35 - 15*binx =L= 0;
st2a2_24 ..  n37 - 15*binx =L= 0;
st2a2_25 ..  n38 - 15*binx =L= 0;
st2a2_26 ..  n40 - 15*binx =L= 0;
st2a2_27 ..  n41 - 15*binx =L= 0;
st2a2_28 ..  n42 - 15*binx =L= 0;
st2a2_29 ..  n43 - 15*binx =L= 0;

st2b1 .. 
n11+n12+n14+n17+n18+
n27+n29+
n36+n39+
n44
-biny =G= 0; 

//st2b2 .. 
//n11+n12+n14+n17+n18+
//n27+n29+
//n36+n39+
//n44
//-10*15*biny =L= 0;

st2b2_1 ..  n11 - 15*biny =L= 0;
st2b2_2 ..  n12 - 15*biny =L= 0;
st2b2_3 ..  n14 - 15*biny =L= 0;
st2b2_4 ..  n17 - 15*biny =L= 0;
st2b2_5 ..  n18 - 15*biny =L= 0;
st2b2_6 ..  n27 - 15*biny =L= 0;
st2b2_7 ..  n29 - 15*biny =L= 0;
st2b2_8 ..  n36 - 15*biny =L= 0;
st2b2_9 ..  n29 - 15*biny =L= 0;
st2b2_10 ..  n44 -15*biny =L= 0;

st2c1 ..  n13+n15+n16+n19+n20 - binz =G= 0;

//st2c2 ..  n13+n15+n16+n19+n20 -5*15*binz =L= 0;

st2c2_1 ..  n13 -15*binz =L= 0;
st2c2_2 ..  n15 -15*binz =L= 0;
st2c2_3 ..  n16 -15*binz =L= 0;
st2c2_4 ..  n19 -15*binz =L= 0;
st2c2_5 ..  n20 -15*binz =L= 0;

st2d1 ..  binz - (binx+biny) =G= -1;

st2d2 ..  binz - (binx+biny) =L= 0;

st4a .. 
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n27+n29+
n36+n39+
n44
-3*binR =G= 0;

//st4b .. 
//n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
//n27+n29+
//n36+n39+
//n44
//-15*15*binR =L= 0;

st4b_1 ..  n11 - 15 * binR =L= 0;
st4b_2 ..  n12 - 15 * binR =L= 0;
st4b_3 ..  n13 - 15 * binR =L= 0;
st4b_4 ..  n14 - 15 * binR =L= 0;
st4b_5 ..  n15 - 15 * binR =L= 0;
st4b_6 ..  n16 - 15 * binR =L= 0;
st4b_7 ..  n17 - 15 * binR =L= 0;
st4b_8 ..  n18 - 15 * binR =L= 0;
st4b_9 ..  n19 - 15 * binR =L= 0;
st4b_10 ..  n20 - 15 * binR =L= 0;
st4b_11 ..  n27 - 15 * binR =L= 0;
st4b_12 ..  n29 - 15 * binR =L= 0;
st4b_13 ..  n36 - 15 * binR =L= 0;
st4b_14 ..  n39 - 15 * binR =L= 0;
st4b_15 ..  n44 - 15 * binR =L= 0;

st5 .. 
n01+n03+n05+n07+n09+
n12+n13+n18+n19+n20+
n21+n22+n23+n24+
n25+n30+n31+n33+
n34+n37+n40+n41+
n42
-2*intB =E= 0;

st6 .. 
(n01*1+n02*2+n03*3+n04*4+n05*1+n06*2+n07*3+n08*2+n09*1+n10*2
+n11*2+n12*3+n13*3+n14*4+n15*4+n16*4+n17*2+n18*3+n19*3+n20*3
+n21*1+n22*1+n23*1+n24*1+n25*1+n26*2+n27*2+n28*2+n29*2+n30*1
+n31*1+n32*2+n33*1+n34*1+n35*2+n36*2+n37*3+n38*2+n39*2+n40*1
+n41*1+n42*1+n43*2+n44*2)-2*(
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44) 
=G= -2;

st7 .. 
(n01*1+n02*2+n03*3+n04*4+n05*1+n06*2+n07*3+n08*2+n09*1+n10*2
+n11*2+n12*3+n13*3+n14*4+n15*4+n16*4+n17*2+n18*3+n19*3+n20*3
+n21*1+n22*1+n23*1+n24*1+n25*1+n26*2+n27*2+n28*2+n29*2+n30*1
+n31*1+n32*2+n33*1+n34*1+n35*2+n36*2+n37*3+n38*2+n39*2+n40*1
+n41*1+n42*1+n43*2+n44*2)-(
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44)**2+(
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44) 
=L= 0;

st9a1 ..  n13+n15+n16+n19+n20 - binM =G= 0;

//st9a2 ..  n13+n15+n16+n19+n20 -5*15*binM =L= 0;
st9a2_1 ..  n13 - 15 * binM =L= 0;
st9a2_2 ..  n15 - 15 * binM =L= 0;
st9a2_3 ..  n16 - 15 * binM =L= 0;
st9a2_4 ..  n19 - 15 * binM =L= 0;
st9a2_5 ..  n20 - 15 * binM =L= 0;

st9b ..  n01+n05+n09+n21+n22+n23+n24+n25+n30+n31+n33+n34+n40+n41+n42
 -(n13*(3-2)+n15*(4-2)+n16*(4-2)+n19*(3-2)+n20*(3-2))-(n03+n07+n37)-2*n04
 -15*15*(1-binM) =L= 0;

st10a1 .. 
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n27+n29+
n36+n39+
n44
-binA =G= 0;

//st10a2 .. 
//n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
//n27+n29+
//n36+n39+
//n44
//-15*15*binA
//=L= 0;

st10a2_1 ..  n11 - 15 * binA =L= 0;
st10a2_2 ..  n12 - 15 * binA =L= 0;
st10a2_3 ..  n13 - 15 * binA =L= 0;
st10a2_4 ..  n14 - 15 * binA =L= 0;
st10a2_5 ..  n15 - 15 * binA =L= 0;
st10a2_6 ..  n16 - 15 * binA =L= 0;
st10a2_7 ..  n17 - 15 * binA =L= 0;
st10a2_8 ..  n18 - 15 * binA =L= 0;
st10a2_9 ..  n19 - 15 * binA =L= 0;
st10a2_10 ..  n20 - 15 * binA =L= 0;
st10a2_11 ..  n27 - 15 * binA =L= 0;
st10a2_12 ..  n29 - 15 * binA =L= 0;
st10a2_13 ..  n36 - 15 * binA =L= 0;
st10a2_14 ..  n39 - 15 * binA =L= 0;
st10a2_15 ..  n44 - 15 * binA =L= 0;

st10b1 .. 
n01+n05+n09+n21+n22+n23+n24+n25+n30+n31+n33+n34+n40+n41+n42
-2-(n03+n07+n37)-2*n04
+(5*15+2)*binA =G= 0;

st10b2 .. 
n01+n05+n09+n21+n22+n23+n24+n25+n30+n31+n33+n34+n40+n41+n42
-2-(n03+n07+n37)-2*n04
-(15*15-2)*binA =L= 0;

//S
st11S .. 
n01+n02*2+n03*3+n04*4+n06+n07*2+n10+
n13+n15+n16*2+n19+
n21+n22+n23+n24+
n25+n26*2+n28*2+n30+n31+n32*2+ 
n34+n35*2+n37*3+n38+n40+n41+
n42+n43*2
-2*intS =E= 0;

st11SR .. 
n11*2+n12*3+n13*2+n14*4+n15*3+n16*2+n17+n18*2+n19+n20*2+ 
n27*2+n29*2+
n36*2+n39+ 
n44*2
-2*intSR =E= 0;

st11D .. 
n05+n06+n07+n08*2+ 
n20+
n33+
n38 
-2*intD =E= 0;

st11DR .. 
n17+n18+n19+ 
n39 
-2*intDR =E= 0;

st11T .. 
n09+n10 
-2*intT =E= 0;

odmacch02 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n02*(2-1)
=G= 2;

odmacch03 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n03*(3-1)
=G= 2;

odmacch04 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n04*(4-1)
=G= 2;

odmacch06 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n06*(2-1)
=G= 2;

odmacch07 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n07*(3-1)
=G= 2;

odmacch08 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n08*(2-1)
=G= 2;

odmacch10 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n10*(2-1)
=G= 2;

odmacch26 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n26*(2-1)
=G= 2;

odmacch28 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n28*(2-1)
=G= 2;

odmacch32 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n32*(2-1)
=G= 2;

odmacch35 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n35*(2-1)
=G= 2;

odmacch37 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n37*(3-1)
=G= 2;

odmacch38 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n38*(2-1)
=G= 2;

odmacch43 .. 
n01+n02+n03+n04+n05+n06+n07+n08+n09+n10+
n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+
n21+n22+n23+n24+n25+n26+n27+n28+n29+n30+
n31+n32+n33+n34+n35+n36+n37+n38+n39+n40+
n41+n42+n43+n44
-n43*(2-1)
=G= 2;

myH1 ..  
n02+n03+n04+n06+n07+n08+n10+
n16+
n26+n28+n32+
n35+n37+n38+
n43
-binH =G= 0;

//myH2 .. 
//n02+n03+n04+n06+n07+n08+n10+
//n16+
//n26+n28+n32+
//n35+n37+n38+
//n43
//-15*15*binH =L= 0;

myH2_1 ..  n02 - 15 * binH =L= 0;
myH2_2 ..  n03 - 15 * binH =L= 0;
myH2_3 ..  n04 - 15 * binH =L= 0;
myH2_4 ..  n06 - 15 * binH =L= 0;
myH2_5 ..  n07 - 15 * binH =L= 0;
myH2_6 ..  n08 - 15 * binH =L= 0;
myH2_7 ..  n10 - 15 * binH =L= 0;
myH2_8 ..  n16 - 15 * binH =L= 0;
myH2_9 ..  n26 - 15 * binH =L= 0;
myH2_10 ..  n28 - 15 * binH =L= 0;
myH2_11 ..  n32 - 15 * binH =L= 0;
myH2_12 ..  n35 - 15 * binH =L= 0;
myH2_13 ..  n37 - 15 * binH =L= 0;
myH2_14 ..  n38 - 15 * binH =L= 0;
myH2_15 ..  n43 - 15 * binH =L= 0;

myS .. 
(n01+
 n13+n15+n19+
 n21+n22+n23+n24+
 n25+n30+n31+
 n34+n40+n41+
 n42)
-(n02*2+n03*3+n04*4+n06+n07*2+n10+
 n16*2+
 n26*2+n28*2+n32*2+
 n35*2+n37*3+n38+
 n43*2) 
-15*15*(1-binH+binR) =L= 0;

myD .. 
(n05+
 n20+
 n33)
-(n06+n07+n08*2+
 n38) 
-3*15*(1-binH+binR) =L= 0;

myT .. 
n09
-n10 
-15*(1-binH+binR) =L= 0;

mya .. 
(n02*2+n03*3+n04*4+n06*2+n07*3+n08*2+n10*2+
 n16*2+
 n26*2+n28*2+n32*2+
 n35*2+n37*3+n38*2+
 n43*2)
-(n01+n05+n09+
 n13+n15+n19+n20+
 n21+n22+n23+n24+
 n25+n30+n31+n33+
 n34+n40+n41+
 n42)
-(n02+n03+n04+n06+n07+n08+n10+
 n16+
 n26+n28+n32+
 n35+n37+n38+
 n43)*2 
-15*35*binR =L= -2;

myb .. 
(n02*2+n03*3+n04*4+n06*2+n07*3+n08*2+n10*2+
 n16*2+
 n26*2+n28*2+n32*2+
 n35*2+n37*3+n38*2+
 n43*2)
-(n01+n05+n09+
 n13+n15+n19+n20+
 n21+n22+n23+n24+
 n25+n30+n31+n33+
 n34+n40+n41+
 n42)
-(n02+n03+n04+n06+n07+n08+n10+
 n16+
 n26+n28+n32+
 n35+n37+n38+
 n43)*2
+15*35*binR =G= -2;

er ..  n11+n12+n13+n14+n15+n16+n17+n18+n19+n20+n27+n29+n36+n39+n44 - nr =E= 0;
erd ..  n17+n18+n19+n39 - nrd =E= 0;
er1 ..  2*intSR + nr - nr**2 + 1 - cl1 =L= 0;
er2 ..  2*intDR + nrd - nrd**2 =L= 0;
er3 ..    cl1*n01 + 2*cl1*n02 + 3*cl1*n03 + 4*cl1*n04 +
       cl1*n06 + 2*cl1*n07 +   cl1*n10 +   cl1*n21 +
       cl1*n22 +   cl1*n23 +   cl1*n24 +   cl1*n25 +
     2*cl1*n26 + 2*cl1*n28 +   cl1*n30 +   cl1*n31 +
     2*cl1*n32 +   cl1*n34 + 2*cl1*n35 + 3*cl1*n37 +
       cl1*n38 +   cl1*n40 +   cl1*n41 +   cl1*n42 +
     2*cl1*n43 -
       cl1*n13 -   cl1*n15 - 2*cl1*n16 - cl1*n19 =G= 0;

gn1 .. 
  n07*n08 + n06*n08 + n20*n08
+ n07*n38 + n06*n38 + n20*n38
- n07*n33 - n06*n33 - n20*n33
=G= 0 ;

gn2 .. 
  n28*n01 + n28*n02 + n28*n03 + n28*n04 + n28*n06 + n28*n07 + n28*n10 
+ n28*n13 + n28*n15 + n28*n16 + n28*n19 + n28*n21 + n28*n22 + n28*n23
+ n28*n24 + n28*n26 + n28*n30 + n28*n31 + n28*n32 + n28*n34
+ n28*n35 + n28*n37 + n28*n38 + n28*n40 + n28*n41 + n28*n42 + n28*n43
- n28*n25 =G= 0;

gn3 .. 
  n02*n28*n26 + n03*n28*n26 + n04*n28*n26 + n07*n28*n26 + n16*n28*n26
+ n32*n28*n26 + n35*n28*n26 + n37*n28*n26 + n43*n28*n26
- n28*n26*n26/2 - n28*n26*n28/2 
+ 0.5*n28*n26*((n26-n28)*(n26-n28))**0.5 =G= 0;

objdef ..  obj =E= -dHve/Cpla;

model primary /all/;

solve primary minimizing obj using minlp;