"""
Minimization of the weight of a speed reducer
The weight of the speed reducer is to be minimized subject to constraints
on bending stress of the gear teeth, surface stress, transverse deflections
of the shafts and stresses in the shaft.
Datseris, P., Weight minimization of a speed reducer by heuristic
and decomposition technique. Mechanism and Machine Theory, vol.17, 1982,
pp. 255-262.
Aguirre, A.H., Munoz Zavala, A.E., Villa Diharce, E., Botello Rionada, S.,
COPSO: Constrained optimization via PSO algorithm. Comunicacion Tecnica
No I-07-04/22-02-2007. Center for Research in Mathematics (CIMAT), Mexico.
"""
import gamspy.math as gams_math
from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Variable
def main():
m = Container(delayed_execution=True)
# VARIABLES #
x1 = Variable(m, name="x1")
x2 = Variable(m, name="x2")
x3 = Variable(m, name="x3")
x4 = Variable(m, name="x4")
x5 = Variable(m, name="x5")
x6 = Variable(m, name="x6")
x7 = Variable(m, name="x7")
obj = Variable(m, name="obj")
# EQUATION #
g1 = Equation(m, name="g1", type="regular")
g2 = Equation(m, name="g2", type="regular")
g3 = Equation(m, name="g3", type="regular")
g4 = Equation(m, name="g4", type="regular")
g5 = Equation(m, name="g5", type="regular")
g6 = Equation(m, name="g6", type="regular")
g7 = Equation(m, name="g7", type="regular")
g8 = Equation(m, name="g8", type="regular")
g9 = Equation(m, name="g9", type="regular")
g10 = Equation(m, name="g10", type="regular")
g11 = Equation(m, name="g11", type="regular")
g = Equation(m, name="g", type="regular")
# Objective function to be minimized:
g[...] = obj == (
0.7854
* x1
* gams_math.power(x2, 2)
* (3.3333 * gams_math.power(x3, 2) + 14.9334 * x3 - 43.0934)
- 1.508 * x1 * (gams_math.power(x6, 2) + gams_math.power(x7, 2))
+ 7.4777 * (gams_math.power(x6, 3) + gams_math.power(x7, 3))
+ 0.7854 * (x4 * gams_math.power(x6, 2) + x5 * gams_math.power(x7, 2))
)
# Constraints:
g1[...] = 27 / (x1 * gams_math.power(x2, 2) * x3) - 1 <= 0
g2[...] = (
397.5 / (x1 * gams_math.power(x2, 2) * gams_math.power(x3, 2)) - 1 <= 0
)
g3[...] = (1.93 * gams_math.power(x4, 3)) / (
x2 * x3 * gams_math.power(x6, 4)
) - 1 <= 0
g4[...] = (1.93 * gams_math.power(x5, 3)) / (
x2 * x3 * gams_math.power(x7, 4)
) - 1 <= 0
g5[...] = (
gams_math.sqrt(gams_math.power((745 * x4) / (x2 * x3), 2) + 16900000)
) / (110 * gams_math.power(x6, 3)) - 1 <= 0
g6[...] = (
gams_math.sqrt(gams_math.power((745 * x5) / (x2 * x3), 2) + 15750000)
) / (85 * gams_math.power(x7, 3)) - 1 <= 0
g7[...] = (x2 * x3) / 40 - 1 <= 0
g8[...] = (5 * x2) / x1 - 1 <= 0
g9[...] = x1 / (12 * x2) - 1 <= 0
g10[...] = (1.5 * x6 + 1.9) / x4 - 1 <= 0
g11[...] = (1.1 * x7 + 1.9) / x5 - 1 <= 0
# Bounds on variables
x1.lo[...] = 2.6
x1.up[...] = 3.6
x2.lo[...] = 0.7
x2.up[...] = 0.8
x3.lo[...] = 17
x3.up[...] = 28
x4.lo[...] = 7.3
x4.up[...] = 8.3
x5.lo[...] = 7.8
x5.up[...] = 8.3
x6.lo[...] = 2.9
x6.up[...] = 3.9
x7.lo[...] = 5.0
x7.up[...] = 5.5
speed = Model(
m,
name="speed",
equations=m.getEquations(),
problem="nlp",
sense="MIN",
objective=obj,
)
speed.solve()
print("Objective Function Value: ", round(obj.toValue(), 4))
# End speed
if __name__ == "__main__":
main()
