* Bilinear heat exchanger problem
* Visweswaran and Floudas (1996)

* Refer to Figure 5.10 in test problem collection.
* f denotes a flowrate
* T denotes a temperature 

VARIABLES
	 dT11  temperature difference at hot end of exchanger H1-C
	 dT12  temperature difference at cold end of exchanger H1-C
	 dT21  temperature difference at hot end of exchanger H2-C
	 dT22  temperature difference at cold end of exchanger H2-C
	 f11   
	 f12  
	 f13  
	 f14  
	 f21  
	 f22  
	 f23  
	 f24  
	 T1i  
	 T1o  
	 T2i  
	 T2o  
     objval    Automatically generated objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 g1  
	 g2  
	 g3  
	 g4  
	 g5  
	 g6  
	 g7  
	 g8  
	 g9 
	 g10  
	 g11  
	 g12  
	 g13  
	 f Objective function;

f  .. objval =e=1300*(1000/(1/30*dT11*dT12+1/6*(dT11+dT12)))**0.6+1300*(600/(1/30*dT21*dT22+1/6*(dT21+dT22)))**0.6;
g1  .. f11+f21 =e= 10;
g2  .. f11+f23-f12 =e= 0;
g3  .. f21+f13-f22 =e= 0;
g4  .. f14+f13-f12 =e= 0;
g5  .. f24+f23-f22 =e= 0;
g6  .. 150*f11+T2o*f23-T1i*f12 =e= 0;
g7  .. 150*f21+T2i*f13-T1o*f22 =e= 0;
g8  .. f12*T2i-f12*T1i =e= 1000;
g9  .. f22*T2o-f22*T1o =e= 600;
g10  .. dT11+T2i =e= 500;
g11  .. dT12+T1i =e= 250;
g12  .. dT21+T2o =e= 350;
g13  .. dT22+T1o =e= 200;

* Bounds
dT11.LO = 10; dT11.UP = 350;
dT12.LO = 10; dT12.UP = 350;
dT21.LO = 10; dT21.UP = 200;
dT22.LO = 10; dT22.UP = 200;
f11.LO = 0; f11.UP = 10;
f12.LO = 0; f12.UP = 10;
f13.LO = 0; f13.UP = 10;
f14.LO = 0; f14.UP = 10;
f21.LO = 0; f21.UP = 10;
f22.LO = 0; f22.UP = 10;
f23.LO = 0; f23.UP = 10;
f24.LO = 0; f24.UP = 10;
T1i.LO = 150; T1i.UP = 310;
T1o.LO = 150; T1o.UP = 310;
T2i.LO = 150; T2i.UP = 310;
T2o.LO = 150; T2o.UP = 310;

* Starting point (global solution)
* dT11.L = 190; dT12.L = 40;
* dT21.L = 140; dT22.L = 50;
* f11.L = 0; f12.L = 10; f13.L = 0; f14.L = 0;
* f21.L = 10; f22.L = 10; f23.L = 10; f24.L = 0;
* T1i.L = 210; T1o.L = 150; T2i.L = 310; T2o.L = 210;

MODEL test /ALL/;
SOLVE test USING NLP MINIMIZING objval;