// This is a gear train design problem taken from the GAMS test library
//
// A compound gear train is to be designed to achieve a specific
// gear ratio between the driver and driven shafts. The objective
// of the gear train design is to find the number of teeth of the
// four gears and to obtain a required gear ratio of 1/6.931.
//
// The problem originated from:
// Deb, K, and Goyal, M, Optimizing Engineering Designs Using a
// Combined Genetic Search. In Back, T, Ed, Proceedings of the
// Seventh International Conference on Genetic Algorithms. 1997,
// pp. 521-528.
INTEGER_VARIABLES i1,i2,i3,i4; // number of teeth in each of the gears
LOWER_BOUNDS{
i1: 12;
i2: 12;
i3: 12;
i4: 12;
}
UPPER_BOUNDS{
i1: 60;
i2: 60;
i3: 60;
i4: 60;
}
EQUATIONS e2,e3; // symmetry constraints
e2: - i3 + i4 >= 0;
e3: i1 - i2 >= 0;
// the objective aimms to make the reciprocal of the
// gear ratio as close to 6.931 as possible.
// an ideal design will have an objective equal to 1.
OBJ: minimize (6.931 - i1*i2/(i3*i4))^2 + 1;
STARTING_POINT{
i1: 24;
i2: 24;
i3: 24;
i4: 24;
}