from desdeo_problem.problem.Variable import Variable
from desdeo_problem.problem.Objective import ScalarObjective
from desdeo_problem.problem.Problem import MOProblem, ProblemBase
import numpy as np
[docs]def vehicle_crashworthiness(var_iv: np.array = np.array([2, 2, 2, 2, 2])) -> MOProblem:
"""The crash safety design problem with 3 objectives.
Liao, X., Li, Q., Yang, X., Zhang, W. & Li, W. (2007).
Multiobjective optimization for crash safety design of vehicles
using stepwise regression model. Structural and multidisciplinary
optimization, 35(6), 561-569. https://doi.org/10.1007/s00158-007-0163-x
Arguments:
var_iv (np.array): Optional, initial variable values. Must be between
1 and 3. Defaults are [2, 2, 2, 2, 2].
Returns:
MOProblem: a problem object.
"""
if np.any(3 < var_iv) or np.any(var_iv < 1):
raise ValueError("Initial variable values need to be between lower and upper bounds")
# Mass
def f_1(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
1640.2823
+ 2.3573285 * x[:, 0]
+ 2.3220035 * x[:, 1]
+ 4.5688768 * x[:, 2]
+ 7.7213633 * x[:, 3]
+ 4.4559504 * x[:, 4]
)
# Ain
def f_2(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
6.5856
+ 1.15 * x[:, 0]
- 1.0427 * x[:, 1]
+ 0.9738 * x[:, 2]
+ 0.8364 * x[:, 3]
- 0.3695 * x[:, 0] * x[:, 3]
+ 0.0861 * x[:, 0] * x[:, 4]
+ 0.3628 * x[:, 1] * x[:, 3]
- 0.1106 * x[:, 0] ** 2
- 0.3437 * x[:, 2] ** 2
+ 0.1764 * x[:, 3] ** 2
)
# Intrusion
def f_3(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
-0.0551
+ 0.0181 * x[:, 0]
+ 0.1024 * x[:, 1]
+ 0.0421 * x[:, 2]
- 0.0073 * x[:, 0] * x[:, 1]
+ 0.024 * x[:, 1] * x[:, 2]
- 0.0118 * x[:, 1] * x[:, 3]
- 0.0204 * x[:, 2] * x[:, 3]
- 0.008 * x[:, 2] * x[:, 4]
- 0.0241 * x[:, 1] ** 2
+ 0.0109 * x[:, 3] ** 2
)
objective_1 = ScalarObjective(name="the mass of the vehicle", evaluator=f_1, maximize=[False])
objective_2 = ScalarObjective(name="acceleration-induced biomechanical damage of occupants", evaluator=f_2, maximize=[False])
objective_3 = ScalarObjective(name="the toe board intrusion in the 'offset-frontal crash'", evaluator=f_3, maximize=[False])
objectives = [objective_1, objective_2, objective_3]
x_1 = Variable("x_1", var_iv[0], 1.0, 3.0)
x_2 = Variable("x_2", var_iv[1], 1.0, 3.0)
x_3 = Variable("x_3", var_iv[2], 1.0, 3.0)
x_4 = Variable("x_4", var_iv[3], 1.0, 3.0)
x_5 = Variable("x_5", var_iv[4], 1.0, 3.0)
variables = [x_1, x_2, x_3, x_4, x_5]
problem = MOProblem(variables=variables, objectives=objectives)
return problem
