import numpy as np
import pkgutil
import io
from ddmtolab.Methods.mtop import MTOP
class CEC21MTMOFunctions:
"""
Helper class containing all g-function implementations for CEC21 MTMO benchmark.
This class provides implementations of various benchmark functions used in the
CEC 2021 Multi-Task Multi-Objective Optimization competition, including:
- Basic functions: Rosenbrock (F4), Rastrigin (F8, F9)
- Complex functions: Modified Schwefel (F11), ExGriewRosen (F15)
- Hybrid functions: F17, F18, F19, F20, F22
"""
@staticmethod
def eval_f1_linear(x):
"""Linear f1 function for MMZDT problems."""
# MATLAB: A = sum(x, 2); F1Function = A ./ size(x, 2);
return np.sum(x, axis=1) / x.shape[1]
@staticmethod
def eval_F4(x, shift, rotation):
"""Rosenbrock Function F4."""
x = x.copy()
x = x - shift
x = x * (2.048 / 100)
x = (rotation @ x.T).T
# Rosenbrock - 使用副本
x_copy = x.copy()
x_copy[:, 0] = x_copy[:, 0] + 1
t = np.zeros(x.shape[0])
for i in range(x.shape[1] - 1):
x_copy[:, i + 1] = x_copy[:, i + 1] + 1
t += 100 * (x_copy[:, i] ** 2 - x_copy[:, i + 1]) ** 2 + (1 - x_copy[:, i]) ** 2
return t
@staticmethod
def eval_F8(x, shift, rotation):
"""
Rastrigin Function F8 (non-rotated).
A highly multimodal function with many local optima.
Parameters
----------
x : np.ndarray
Input array of shape (n_samples, n_dims).
shift : np.ndarray
Shift vector.
rotation : np.ndarray
Rotation matrix (not used in this variant).
Returns
-------
np.ndarray
Function values of shape (n_samples,).
"""
x = x - shift
x = x * (5.12 / 100)
# Rastrigin
a = 10 * x.shape[1]
result = np.sum(x ** 2 - 10 * np.cos(2 * np.pi * x), axis=1) + a
return result
@staticmethod
def eval_F9(x, shift, rotation):
"""
Rastrigin Function F9 (rotated).
Rotated version of the Rastrigin function.
Parameters
----------
x : np.ndarray
Input array of shape (n_samples, n_dims).
shift : np.ndarray
Shift vector.
rotation : np.ndarray
Rotation matrix.
Returns
-------
np.ndarray
Function values of shape (n_samples,).
"""
x = x - shift
x = x * (5.12 / 100)
x = (rotation @ x.T).T
# Rastrigin
a = 10 * x.shape[1]
result = np.sum(x ** 2 - 10 * np.cos(2 * np.pi * x), axis=1) + a
return result
@staticmethod
def eval_F11(x, shift, rotation):
"""
Modified Schwefel Function F11.
A deceptive function with a second-best minimum far from the global optimum.
Parameters
----------
x : np.ndarray
Input array of shape (n_samples, n_dims).
shift : np.ndarray
Shift vector.
rotation : np.ndarray
Rotation matrix.
Returns
-------
np.ndarray
Function values of shape (n_samples,).
"""
x = x - shift
x = x * (1000.0 / 100)
x = (rotation @ x.T).T
# Modified Schwefel
n = x.shape[1]
result = CEC21MTMOFunctions._modified_schwefel(x, n)
return result
@staticmethod
def eval_F15(x, shift, rotation):
"""Expanded Griewank plus Rosenbrock Function F15."""
x = x.copy()
x = x - shift
x = x * (5.0 / 100)
x = (rotation @ x.T).T
# ExGriewRosen - 使用副本
x_copy = x.copy()
x_copy[:, 0] = x_copy[:, 0] + 1
result = np.zeros(x.shape[0])
for i in range(x.shape[1] - 1):
x_copy[:, i + 1] = x_copy[:, i + 1] + 1
t = 100 * ((x_copy[:, i] ** 2 - x_copy[:, i + 1]) ** 2) + (x_copy[:, i] - 1) ** 2
result += (t ** 2) / 4000 - np.cos(t) + 1
# Wrap around: last to first
index = x.shape[1] - 1
t = 100 * ((x_copy[:, index] ** 2 - x_copy[:, 0]) ** 2) + (x_copy[:, index] - 1) ** 2
result += (t ** 2) / 4000 - np.cos(t) + 1
return result
@staticmethod
def eval_F17(x, shift, rotation):
"""
Hybrid Composition Function F17.
"""
# 确保shift的广播正确
x = x - shift.reshape(1, -1) # 明确reshape
x = (rotation @ x.T).T
D = x.shape[1]
n1 = int(np.ceil(0.3 * D))
n2 = int(np.ceil(0.3 * D))
n3 = D - n1 - n2
x1 = x[:, :n1] * (1000.0 / 100)
x2 = x[:, n1:n1 + n2] * (5.12 / 100)
x3 = x[:, n1 + n2:]
# Modified Schwefel
result = CEC21MTMOFunctions._modified_schwefel(x1, n1)
# Rastrigin
a = 10 * n2
result += np.sum(x2 ** 2 - 10 * np.cos(2 * np.pi * x2), axis=1) + a
# Elliptic
a = 1e6
for i in range(n3):
result += (a ** (i / max(n3 - 1, 1))) * (x3[:, i] ** 2)
return result
@staticmethod
def eval_F18(x, shift, rotation):
"""
Hybrid Composition Function F18.
Combines Cigar (30%) + HGBat (30%) + Rastrigin (40%).
Parameters
----------
x : np.ndarray
Input array of shape (n_samples, n_dims).
shift : np.ndarray
Shift vector.
rotation : np.ndarray
Rotation matrix.
Returns
-------
np.ndarray
Function values of shape (n_samples,).
"""
x = x - shift
x = (rotation @ x.T).T
D = x.shape[1]
n1 = int(np.ceil(0.3 * D))
n2 = int(np.ceil(0.3 * D))
n3 = D - n1 - n2
x1 = x[:, :n1]
x2 = x[:, n1:n1 + n2] * (5.0 / 100)
x3 = x[:, n1 + n2:] * (5.12 / 100)
# Cigar
a = np.sum(x1[:, 1:] ** 2, axis=1)
result = x1[:, 0] ** 2 + a * 1e6
# HGBat
x2 = x2 - 1
sum1 = np.sum(x2 ** 2, axis=1)
sum2 = np.sum(x2, axis=1)
result += (np.abs(sum1 ** 2 - sum2 ** 2)) ** 0.5 + (0.5 * sum1 + sum2) / n2 + 0.5
# Rastrigin
a = 10 * n3
result += np.sum(x3 ** 2 - 10 * np.cos(2 * np.pi * x3), axis=1) + a
return result
@staticmethod
def eval_F19(x, shift, rotation):
"""
Hybrid Composition Function F19.
Combines Griewank (20%) + Weierstrass (20%) + Rosenbrock (30%) + Schaffer F6 (30%).
"""
x = x.copy()
x = x - shift
x = (rotation @ x.T).T
D = x.shape[1]
n1 = int(np.ceil(0.2 * D))
n2 = int(np.ceil(0.2 * D))
n3 = int(np.ceil(0.3 * D))
n4 = D - n1 - n2 - n3
x1 = x[:, :n1] * (600.0 / 100)
x2 = x[:, n1:n1 + n2] * (0.5 / 100)
x3 = x[:, n1 + n2:n1 + n2 + n3] * (2.048 / 100)
x4 = x[:, n1 + n2 + n3:]
# Griewank
t = np.arange(1, n1 + 1)
sum1 = np.sum(x1 ** 2, axis=1)
prod1 = np.prod(np.cos(x1 / np.sqrt(t)), axis=1)
result = 1 + sum1 / 4000 - prod1
# Weierstrass
a = 0.5
b = 3
kmax = 20
part1 = np.zeros(x.shape[0])
for i in range(n2):
for k in range(kmax + 1):
part1 += a ** k * np.cos(2 * np.pi * (b ** k) * (x2[:, i] + 0.5))
part2 = 0
for k in range(kmax + 1):
part2 += a ** k * np.cos(2 * np.pi * (b ** k) * 0.5)
result += part1 - n2 * part2
# Rosenbrock - 修正：使用副本
t = np.zeros(x.shape[0])
x3_copy = x3.copy()
x3_copy[:, 0] = x3_copy[:, 0] + 1
for i in range(n3 - 1):
x3_copy[:, i + 1] = x3_copy[:, i + 1] + 1
t += 100 * (x3_copy[:, i] ** 2 - x3_copy[:, i + 1]) ** 2 + (1 - x3_copy[:, i]) ** 2
result += t
# Schaffer F6
t = np.zeros(x.shape[0])
for i in range(n4):
next_idx = (i + 1) % n4
pSum = x4[:, i] ** 2 + x4[:, next_idx] ** 2
t += 0.5 + ((np.sin(pSum ** 0.5)) ** 2 - 0.5) / ((1 + 0.001 * pSum) ** 2)
result += t
return result
@staticmethod
def eval_F20(x, shift, rotation):
"""Hybrid Composition Function F20."""
x = x.copy()
x = x - shift
x = (rotation @ x.T).T
D = x.shape[1]
n1 = int(np.ceil(0.2 * D))
n2 = int(np.ceil(0.2 * D))
n3 = int(np.ceil(0.3 * D))
n4 = D - n1 - n2 - n3
x1 = x[:, :n1] * (5.0 / 100)
x2 = x[:, n1:n1 + n2]
x3 = x[:, n1 + n2:n1 + n2 + n3] * (5.0 / 100)
x4 = x[:, n1 + n2 + n3:] * (5.12 / 100)
# HGBat - 使用副本
x1_copy = x1.copy()
x1_copy = x1_copy - 1
sum1 = np.sum(x1_copy ** 2, axis=1)
sum2 = np.sum(x1_copy, axis=1)
result = (np.abs(sum1 ** 2 - sum2 ** 2)) ** 0.5 + (0.5 * sum1 + sum2) / n1 + 0.5
# Discus
result += 1e6 * (x2[:, 0] ** 2) + np.sum(x2[:, 1:] ** 2, axis=1)
# ExGriewRosen - 使用副本
x3_copy = x3.copy()
x3_copy[:, 0] = x3_copy[:, 0] + 1
for i in range(n3 - 1):
x3_copy[:, i + 1] = x3_copy[:, i + 1] + 1
t = 100 * (x3_copy[:, i] ** 2 - x3_copy[:, i + 1]) ** 2 + (x3_copy[:, i] - 1) ** 2
result += (t ** 2) / 4000 - np.cos(t) + 1
t = 100 * (x3_copy[:, n3 - 1] ** 2 - x3_copy[:, 0]) ** 2 + (x3_copy[:, n3 - 1] - 1) ** 2
result += (t ** 2) / 4000 - np.cos(t) + 1
# Rastrigin
a = 10 * n4
result += np.sum(x4 ** 2 - 10 * np.cos(2 * np.pi * x4), axis=1) + a
return result
@staticmethod
def eval_F22(x, shift, rotation):
"""
Hybrid Composition Function F22.
Combines Katsuura (10%) + HappyCat (20%) + ExGriewRosen (20%) +
Modified Schwefel (20%) + Ackley (30%).
"""
x = x.copy()
x = x - shift
x = (rotation @ x.T).T
D = x.shape[1]
n1 = int(np.ceil(0.1 * D))
n2 = int(np.ceil(0.2 * D))
n3 = int(np.ceil(0.2 * D))
n4 = int(np.ceil(0.2 * D))
n5 = D - n1 - n2 - n3 - n4
x1 = x[:, :n1].copy() * (5.0 / 100)
x2 = x[:, n1:n1 + n2].copy() * (5.0 / 100)
x3 = x[:, n1 + n2:n1 + n2 + n3].copy() * (5.0 / 100)
x4 = x[:, n1 + n2 + n3:n1 + n2 + n3 + n4].copy() * (1000.0 / 100)
x5 = x[:, n1 + n2 + n3 + n4:].copy()
# Katsuura - 修正
index = 32
prod1 = np.zeros(x.shape[0]) # ✓ 在外层循环外初始化
result = np.ones(x.shape[0])
for i in range(n1):
for j in range(1, index + 1):
prod1 += np.abs(2 ** j * x1[:, i] - np.round(2 ** j * x1[:, i])) / (2 ** j)
result *= (1 + i * prod1) ** (10 / (n1 ** 1.2)) # ✓ 使用 i 而不是 (i+1)
result = (10 / (n1 ** 1.2)) * (result - 1)
# HappyCat
x2 = x2 - 1
sum1 = np.sum(x2 ** 2, axis=1)
sum2 = np.sum(x2, axis=1)
result += np.abs(sum1 - n2) ** 0.25 + (0.5 * sum1 + sum2) / n2 + 0.5
# ExGriewRosen
x3[:, 0] = x3[:, 0] + 1
for i in range(n3 - 1):
x3[:, i + 1] = x3[:, i + 1] + 1
t = 100 * ((x3[:, i] ** 2 - x3[:, i + 1]) ** 2) + (x3[:, i] - 1) ** 2
result += (t ** 2) / 4000 - np.cos(t) + 1
t = 100 * ((x3[:, n3 - 1] ** 2 - x3[:, 0]) ** 2) + (x3[:, n3 - 1] - 1) ** 2
result += (t ** 2) / 4000 - np.cos(t) + 1
# Modified Schwefel
result += CEC21MTMOFunctions._modified_schwefel(x4, n4)
# Ackley
sum1 = np.sum(x5 ** 2, axis=1) / n5
sum2 = np.sum(np.cos(2 * np.pi * x5), axis=1) / n5
result += (-20) * np.exp(-0.2 * np.sqrt(sum1)) - np.exp(sum2) + 20 + np.e
return result
@staticmethod
def _modified_schwefel(x, n):
"""
Modified Schwefel function helper.
Parameters
----------
x : np.ndarray
Input array of shape (n_samples, n_dims).
n : int
Number of dimensions.
Returns
-------
np.ndarray
Function values of shape (n_samples,).
"""
prod1 = np.zeros(x.shape[0])
for i in range(x.shape[1]):
z = x[:, i] + 4.209687462275036e+002
gz = np.zeros_like(z)
mask1 = np.abs(z) <= 500
mask2 = z > 500
mask3 = ~(mask1 | mask2)
# Case 1: |z| <= 500
gz[mask1] = z[mask1] * np.sin(np.abs(z[mask1]) ** 0.5)
# Case 2: z > 500
temp = 500 - np.mod(z[mask2], 500)
gz[mask2] = temp * np.sin(np.abs(temp) ** 0.5) - ((z[mask2] - 500) ** 2) / (10000 * n)
# Case 3: z < -500
temp = np.mod(np.abs(z[mask3]), 500) - 500
gz[mask3] = temp * np.sin(np.abs(500 - np.mod(np.abs(z[mask3]), 500)) ** 0.5) - ((z[mask3] + 500) ** 2) / (
10000 * n)
prod1 += gz
return 418.9829 * n - prod1
[docs]
class CEC21MTMO:
"""
Implementation of the CEC 2021 Competition on Evolutionary Multi-Task Multi-Objective
Optimization (MTMO) benchmark problems.
These problems consist of two multi-objective optimization tasks (MO-tasks)
with shared variables, designed to test knowledge transfer in the presence of
multiple conflicting objectives. All tasks are minimization problems.
Notes
-----
Fixed parameters by benchmark definition:
- K=2 (number of tasks)
- D=50, M=2 for all problems
Attributes
----------
data_dir : str
The directory path for problem data files.
funcs : CEC21MTMOFunctions
Instance of the functions helper class.
"""
problem_information = {
'n_cases': 10,
'n_tasks': '2',
'n_dims': '50',
'n_objs': '2',
'n_cons': '0',
'type': 'synthetic',
}
def __init__(self):
self.data_dir = 'data_cec21mtmo'
self.funcs = CEC21MTMOFunctions()
[docs]
def P1(self) -> MTOP:
"""
Generates Problem 1: **T1 (MMDTLZ, F17) vs T2 (MMZDT, F17)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F17 (Modified Schwefel + Rastrigin + Elliptic).
- T2: MMZDT-type with linear f1, hybrid function F17, and concave h.
- Relationship: Different task types but same g-function complexity.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_1/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_1/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_1/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_1/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F17 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F17)
g = self.funcs.eval_F17(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F17 g-function, and concave h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F17)
g = self.funcs.eval_F17(x[:, 1:], shift2, rotation2)
g = g + 1
# Concave h-function
f2 = g * (1 - (f1 / g) ** 2)
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P2(self) -> MTOP:
"""
Generates Problem 2: **T1 (MMDTLZ, F19) vs T2 (MMDTLZ, F19)**.
"""
dim = 50
# 加载rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_2/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_2/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_2/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_2/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x): # 这是任务0，应该用 rotation1, shift1
"""Task 0: MMDTLZ with F19 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F19)
g = self.funcs.eval_F19(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x): # 这是任务1，应该用 rotation2, shift2
"""Task 1: MMDTLZ with F19 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F19)
g = self.funcs.eval_F19(x[:, 1:], shift2, rotation2)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P3(self) -> MTOP:
"""
Generates Problem 3: **T1 (MMDTLZ, F22) vs T2 (MMZDT, F22)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F22 (Katsuura + HappyCat + ExGriewRosen + Modified Schwefel + Ackley).
- T2: MMZDT-type with linear f1, hybrid function F22, and convex h.
- Relationship: Different task types but same g-function complexity.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_3/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_3/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_3/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_3/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F22 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F22)
g = self.funcs.eval_F22(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F22 g-function, and convex h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F22)
g = self.funcs.eval_F22(x[:, 1:], shift2, rotation2)
g = g + 1
# Convex h-function
f2 = g * (1 - np.sqrt(f1 / g))
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P4(self) -> MTOP:
"""
Generates Problem 4: **T1 (MMZDT, F15) vs T2 (MMZDT, F15)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMZDT-type with linear f1, hybrid function F15 (ExGriewRosen), and convex h.
- T2: MMZDT-type with linear f1, hybrid function F15 (ExGriewRosen), and convex h.
- Relationship: Same task type and g-function, both convex.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_4/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_4/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_4/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_4/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMZDT with linear f1, F15 g-function, and convex h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F15)
g = self.funcs.eval_F15(x[:, 1:], shift1, rotation1)
g = g + 1
# Convex h-function
f2 = g * (1 - np.sqrt(f1 / g))
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F15 g-function, and convex h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F15)
g = self.funcs.eval_F15(x[:, 1:], shift2, rotation2)
g = g + 1
# Convex h-function
f2 = g * (1 - np.sqrt(f1 / g))
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P5(self) -> MTOP:
"""
Generates Problem 5: **T1 (MMDTLZ, F4) vs T2 (MMZDT, F4)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F4 (Rosenbrock).
- T2: MMZDT-type with linear f1, hybrid function F4 (Rosenbrock), and concave h.
- Relationship: Different task types but same g-function (Rosenbrock).
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_5/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_5/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_5/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_5/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F4 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F4 - Rosenbrock)
g = self.funcs.eval_F4(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F4 g-function, and concave h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F4 - Rosenbrock)
g = self.funcs.eval_F4(x[:, 1:], shift2, rotation2)
g = g + 1
# Concave h-function
f2 = g * (1 - (f1 / g) ** 2)
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P6(self) -> MTOP:
"""
Generates Problem 6: **T1 (MMDTLZ, F9) vs T2 (MMDTLZ, F9)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F9 (Rastrigin, rotated).
- T2: MMDTLZ-type with hybrid function F9 (Rastrigin, rotated).
- Relationship: Same task type and g-function.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_6/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_6/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_6/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_6/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F9 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F9 - Rastrigin rotated)
g = self.funcs.eval_F9(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMDTLZ with F9 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F9 - Rastrigin rotated)
g = self.funcs.eval_F9(x[:, 1:], shift2, rotation2)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P7(self) -> MTOP:
"""
Generates Problem 7: **T1 (MMDTLZ, F8) vs T2 (MMZDT, F8)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F8 (Rastrigin, non-rotated).
- T2: MMZDT-type with linear f1, hybrid function F8 (Rastrigin, non-rotated), and convex h.
- Relationship: Different task types but same g-function.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_7/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_7/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_7/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_7/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F8 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F8 - Rastrigin non-rotated)
g = self.funcs.eval_F8(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F8 g-function, and convex h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F8 - Rastrigin non-rotated)
g = self.funcs.eval_F8(x[:, 1:], shift2, rotation2)
g = g + 1
# Convex h-function
f2 = g * (1 - np.sqrt(f1 / g))
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P8(self) -> MTOP:
"""
Generates Problem 8: **T1 (MMDTLZ, F18) vs T2 (MMZDT, F20)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F18 (Cigar + HGBat + Rastrigin).
- T2: MMZDT-type with linear f1, hybrid function F20 (HGBat + Discus + ExGriewRosen + Rastrigin), and concave h.
- Relationship: Different task types and different g-functions.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_8/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_8/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_8/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_8/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F18 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F18)
g = self.funcs.eval_F18(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F20 g-function, and concave h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F20)
g = self.funcs.eval_F20(x[:, 1:], shift2, rotation2)
g = g + 1
# Concave h-function
f2 = g * (1 - (f1 / g) ** 2)
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P9(self) -> MTOP:
"""
Generates Problem 9: **T1 (MMDTLZ, F11) vs T2 (MMZDT, F18)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F11 (Modified Schwefel).
- T2: MMZDT-type with linear f1, hybrid function F18 (Cigar + HGBat + Rastrigin), and concave h.
- Relationship: Different task types and different g-functions.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_9/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_9/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_9/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_9/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F11 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F11 - Modified Schwefel)
g = self.funcs.eval_F11(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F18 g-function, and concave h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F18)
g = self.funcs.eval_F18(x[:, 1:], shift2, rotation2)
g = g + 1
# Concave h-function
f2 = g * (1 - (f1 / g) ** 2)
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
[docs]
def P10(self) -> MTOP:
"""
Generates Problem 10: **T1 (MMDTLZ, F15) vs T2 (MMZDT, F17)**.
Both tasks are 2-objective, 50-dimensional.
- T1: MMDTLZ-type with hybrid function F15 (ExGriewRosen).
- T2: MMZDT-type with linear f1, hybrid function F17 (Modified Schwefel + Rastrigin + Elliptic), and concave h.
- Relationship: Different task types and different g-functions.
Returns
-------
MTOP
A Multi-Task Multi-Objective Optimization Problem instance.
"""
dim = 50
# Load rotation matrices and shift vectors
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_10/matrix_1')
rotation1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_10/bias_1')
shift1 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_10/matrix_2')
rotation2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
data_bytes = pkgutil.get_data('ddmtolab.Problems.MTMO', f'{self.data_dir}/benchmark_10/bias_2')
shift2 = np.loadtxt(io.BytesIO(data_bytes), dtype=float)
def T1(x):
"""Task 1: MMDTLZ with F15 g-function"""
x = np.atleast_2d(x)
# Evaluate g-function (F15 - ExGriewRosen)
g = self.funcs.eval_F15(x[:, 1:], shift1, rotation1)
# MMDTLZ objectives
f1 = (1 + g) * np.cos(x[:, 0] * 0.5 * np.pi)
f2 = (1 + g) * np.sin(x[:, 0] * 0.5 * np.pi)
return np.vstack([f1, f2]).T
def T2(x):
"""Task 2: MMZDT with linear f1, F17 g-function, and concave h"""
x = np.atleast_2d(x)
# Evaluate f1 (linear)
f1 = self.funcs.eval_f1_linear(x[:, 0:1])
# Evaluate g-function (F17)
g = self.funcs.eval_F17(x[:, 1:], shift2, rotation2)
g = g + 1
# Concave h-function
f2 = g * (1 - (f1 / g) ** 2)
return np.vstack([f1, f2]).T
# Bounds
lb = np.concatenate([[0.0], -100.0 * np.ones(49)])
ub = np.concatenate([[1.0], 100.0 * np.ones(49)])
problem = MTOP()
problem.add_task(T1, dim=dim, lower_bound=lb, upper_bound=ub)
problem.add_task(T2, dim=dim, lower_bound=lb, upper_bound=ub)
return problem
# --- True Pareto Front (PF) Functions ---
def _circle_PF(N, M=2) -> np.ndarray:
"""
Quarter circle arc PF: unit circle in first quadrant.
Used for MMDTLZ tasks.
"""
theta = np.linspace(0, np.pi / 2, N)
f1 = np.cos(theta)
f2 = np.sin(theta)
return np.column_stack([f1, f2])
def _convex_PF(N, M=2) -> np.ndarray:
"""
Convex PF: f_2 = 1 - sqrt(f_1).
Used for MMZDT tasks with convex h-function.
"""
f1 = np.linspace(0, 1, N)
f2 = 1 - np.sqrt(f1)
return np.column_stack([f1, f2])
def _concave_PF(N, M=2) -> np.ndarray:
"""
Concave PF: f_2 = 1 - f_1^2.
Used for MMZDT tasks with concave h-function.
"""
f1 = np.linspace(0, 1, N)
f2 = 1 - f1 ** 2
return np.column_stack([f1, f2])
# Problem-specific PF assignments
P1_T1_PF = _circle_PF # MMDTLZ, F17
P1_T2_PF = _circle_PF # MMZDT, F17, concave (special case: circle)
P2_T1_PF = _circle_PF # MMDTLZ, F19
P2_T2_PF = _circle_PF # MMDTLZ, F19
P3_T1_PF = _circle_PF # MMDTLZ, F22
P3_T2_PF = _convex_PF # MMZDT, F22, convex
P4_T1_PF = _convex_PF # MMZDT, F15, convex
P4_T2_PF = _convex_PF # MMZDT, F15, convex
P5_T1_PF = _circle_PF # MMDTLZ, F4
P5_T2_PF = _concave_PF # MMZDT, F4, concave
P6_T1_PF = _circle_PF # MMDTLZ, F9
P6_T2_PF = _circle_PF # MMDTLZ, F9
P7_T1_PF = _circle_PF # MMDTLZ, F8
P7_T2_PF = _convex_PF # MMZDT, F8, convex
P8_T1_PF = _circle_PF # MMDTLZ, F18
P8_T2_PF = _concave_PF # MMZDT, F20, concave
P9_T1_PF = _circle_PF # MMDTLZ, F11
P9_T2_PF = _concave_PF # MMZDT, F18, concave
P10_T1_PF = _circle_PF # MMDTLZ, F15
P10_T2_PF = _concave_PF # MMZDT, F17, concave
SETTINGS = {
'metric': 'IGD',
'n_pf': 1000,
'pf_path': './MOReference',
'P1': {'T1': P1_T1_PF, 'T2': P1_T2_PF},
'P2': {'T1': P2_T1_PF, 'T2': P2_T2_PF},
'P3': {'T1': P3_T1_PF, 'T2': P3_T2_PF},
'P4': {'T1': P4_T1_PF, 'T2': P4_T2_PF},
'P5': {'T1': P5_T1_PF, 'T2': P5_T2_PF},
'P6': {'T1': P6_T1_PF, 'T2': P6_T2_PF},
'P7': {'T1': P7_T1_PF, 'T2': P7_T2_PF},
'P8': {'T1': P8_T1_PF, 'T2': P8_T2_PF},
'P9': {'T1': P9_T1_PF, 'T2': P9_T2_PF},
'P10': {'T1': P10_T1_PF, 'T2': P10_T2_PF},
}