"""
Strength Pareto Evolutionary Algorithm 2 (SPEA2)
This module implements SPEA2 for multi-objective optimization problems.
References
----------
[1] Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization. In Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems. Proceedings of the EUROGEN'2001.
Notes
-----
Author: Jiangtao Shen
Email: j.shen5@exeter.ac.uk
Date: 2025.12.13
Version: 1.1
"""
from tqdm import tqdm
import time
import numpy as np
from ddmtolab.Methods.Algo_Methods.algo_utils import *
[docs]
class SPEA2:
"""
Strength Pareto Evolutionary Algorithm 2 for multi-objective optimization.
Attributes
----------
algorithm_information : dict
Dictionary containing algorithm capabilities and requirements
"""
algorithm_information = {
'n_tasks': '[1, K]',
'dims': 'unequal',
'objs': 'unequal',
'n_objs': '[2, M]',
'cons': 'unequal',
'n_cons': '[0, C]',
'expensive': 'False',
'knowledge_transfer': 'False',
'n': 'unequal',
'max_nfes': 'unequal'
}
@classmethod
def get_algorithm_information(cls, print_info=True):
return get_algorithm_information(cls, print_info)
[docs]
def __init__(self, problem, n=None, max_nfes=None, muc=20.0, mum=20.0, epsilon=0, save_data=True,
save_path='./Data', name='SPEA2', disable_tqdm=True):
"""
Initialize SPEA2 algorithm.
Parameters
----------
problem : MTOP
Multi-task optimization problem instance
n : int or List[int], optional
Population size per task (default: 100)
max_nfes : int or List[int], optional
Maximum number of function evaluations per task (default: 10000)
muc : float, optional
Distribution index for simulated binary crossover (SBX) (default: 20.0)
mum : float, optional
Distribution index for polynomial mutation (PM) (default: 20.0)
epsilon : float, optional
Constraint epsilon value for epsilon-constraint method (default: 0)
save_data : bool, optional
Whether to save optimization data (default: True)
save_path : str, optional
Path to save results (default: './Data')
name : str, optional
Name for the experiment (default: 'SPEA2')
disable_tqdm : bool, optional
Whether to disable progress bar (default: True)
"""
self.problem = problem
self.n = n if n is not None else 100
self.max_nfes = max_nfes if max_nfes is not None else 10000
self.muc = muc
self.mum = mum
self.epsilon = epsilon
self.save_data = save_data
self.save_path = save_path
self.name = name
self.disable_tqdm = disable_tqdm
[docs]
def optimize(self):
"""
Execute the SPEA2 algorithm.
Returns
-------
Results
Optimization results containing decision variables, objectives, constraints, and runtime
"""
start_time = time.time()
problem = self.problem
nt = problem.n_tasks
n_per_task = par_list(self.n, nt)
max_nfes_per_task = par_list(self.max_nfes, nt)
# Initialize population and evaluate for each task
decs = initialization(problem, n_per_task)
objs, cons = evaluation(problem, decs)
nfes_per_task = n_per_task.copy()
all_decs, all_objs, all_cons = init_history(decs, objs, cons)
# Calculate initial fitness for each task
fitness = []
for i in range(nt):
fitness.append(self._cal_fitness(objs[i], cons[i]))
pbar = tqdm(total=sum(max_nfes_per_task), initial=sum(n_per_task), desc=f"{self.name}",
disable=self.disable_tqdm)
while sum(nfes_per_task) < sum(max_nfes_per_task):
# Skip tasks that have exhausted their evaluation budget
active_tasks = [i for i in range(nt) if nfes_per_task[i] < max_nfes_per_task[i]]
if not active_tasks:
break
for i in active_tasks:
# Parent selection via binary tournament based on fitness
matingpool = tournament_selection(2, n_per_task[i], fitness[i])
# Generate offspring through crossover and mutation
off_decs = ga_generation(decs[i][matingpool, :], muc=self.muc, mum=self.mum)
off_objs, off_cons = evaluation_single(problem, off_decs, i)
# Merge parent and offspring populations
objs[i], decs[i], cons[i] = vstack_groups((objs[i], off_objs), (decs[i], off_decs),
(cons[i], off_cons))
# Environmental selection to obtain the next population
selected_indices, fitness[i] = self._spea2_selection(objs[i], cons[i], n_per_task[i])
objs[i], decs[i], cons[i] = select_by_index(selected_indices, objs[i], decs[i], cons[i])
nfes_per_task[i] += n_per_task[i]
pbar.update(n_per_task[i])
append_history(all_decs[i], decs[i], all_objs[i], objs[i], all_cons[i], cons[i])
pbar.close()
runtime = time.time() - start_time
# Save results
results = build_save_results(all_decs=all_decs, all_objs=all_objs, runtime=runtime, max_nfes=nfes_per_task,
all_cons=all_cons, bounds=problem.bounds, save_path=self.save_path,
filename=self.name, save_data=self.save_data)
return results
def _cal_fitness(self, objs, cons):
"""
Calculate SPEA2 fitness with (epsilon-relaxed) constrained dominance.
Parameters
----------
objs : ndarray
Objective values with shape (pop_size, n_objs)
cons : ndarray or None
Constraint values with shape (pop_size, n_cons)
Returns
-------
fitness : ndarray
SPEA2 fitness values with shape (pop_size,). Lower is better;
values < 1 indicate non-dominated solutions.
"""
if cons is None:
return spea2_fitness(objs)
# Epsilon-constraint handling: violations below epsilon count as feasible
cv = np.sum(np.maximum(0, cons), axis=1)
cv[cv < self.epsilon] = 0
return spea2_fitness(objs, cv[:, None])
def _spea2_selection(self, objs, cons, N):
"""
Environmental selection for SPEA2 algorithm.
Parameters
----------
objs : ndarray
Objective values with shape (pop_size, n_objs)
cons : ndarray or None
Constraint values with shape (pop_size, n_cons)
N : int
Number of individuals to select
Returns
-------
selected_indices : ndarray
Indices of selected individuals (in original order)
selected_fitness : ndarray
Fitness values of selected individuals
"""
# Calculate fitness for all individuals
fitness = self._cal_fitness(objs, cons)
# Environmental selection: keep non-dominated solutions (fitness < 1)
next_selected = fitness < 1
if np.sum(next_selected) < N:
# Fill with the best dominated solutions by fitness
sorted_indices = np.argsort(fitness, kind='stable')
next_selected[sorted_indices[:N]] = True
elif np.sum(next_selected) > N:
# Truncate the non-dominated set by iteratively deleting the most crowded
candidates = np.where(next_selected)[0]
keep = spea2_truncation(objs[candidates], N)
next_selected = np.zeros_like(next_selected)
next_selected[candidates[keep]] = True
selected_indices = np.where(next_selected)[0]
selected_fitness = fitness[selected_indices]
return selected_indices, selected_fitness