* MINLP literature problem * Yuan et al., 1988. * NOTE: The problem has been reformulated so that no binary * variables appear in nonlinear terms as this cannot be * handled by GAMS solvers. VARIABLES x1 x2 x3 xy1 xy2 xy3 xy4 y1 y2 y3 y4 objval objective function variable; FREE VARIABLES objval; BINARY VARIABLE y1; BINARY VARIABLE y2; BINARY VARIABLE y3; BINARY VARIABLE y4; EQUATIONS g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g11 g12 g13 f Objective function; f .. objval =e=POWER(xy1-1,2)+POWER(xy2-2,2)+POWER(xy3-1,2)-(LOG(xy4+1))+POWER(x1-1,2)+POWER(x2-2,2)+POWER(x3-3,2); g1 .. y1+y2+y3+x1+x2+x3 =l= 5; g2 .. POWER(xy3,2)+POWER(x1,2)+POWER(x2,2)+POWER(x3,2) =l= 5.5; g3 .. y1+x1 =l= 1.2; g4 .. y2+x2 =l= 1.8; g5 .. y3+x3 =l= 2.5; g6 .. y4+x1 =l= 1.2; g7 .. POWER(xy2,2)+POWER(x2,2) =l= 1.64; g8 .. POWER(xy3,2)+POWER(x3,2) =l= 4.25; g9 .. POWER(xy2,2)+POWER(x3,2) =l= 4.64; g10 .. xy1-y1 =e= 0; g11 .. xy2-y2 =e= 0; g12 .. xy3-y3 =e= 0; g13 .. xy4-y4 =e= 0; * Bounds x1.LO = 0; x1.UP = 10; x2.LO = 0; x2.UP = 10; x3.LO = 0; x3.UP = 10; xy1.LO = 0; xy1.UP = 1; xy2.LO = 0; xy2.UP = 1; xy3.LO = 0; xy3.UP = 1; xy4.LO = 0; xy4.UP = 1; MODEL test /ALL/; SOLVE test USING MINLP MINIMIZING objval;