"""
Nondominated Sorting Genetic Algorithm II (NSGA-II)
This module implements NSGA-II for multi-objective optimization problems.
References
----------
[1] Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II." IEEE transactions on evolutionary computation 6.2 (2002): 182-197.
Notes
-----
Author: Jiangtao Shen
Email: j.shen5@exeter.ac.uk
Date: 2025.10.23
Version: 1.0
"""
from tqdm import tqdm
import time
from ddmtolab.Methods.Algo_Methods.algo_utils import *
[docs]
class NSGA_II:
"""
Nondominated Sorting Genetic Algorithm II 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, 3]',
'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, save_data=True, save_path='./Data',
name='NSGA-II', disable_tqdm=True):
"""
Initialize NSGA-II 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)
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: 'NSGA-II')
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.save_data = save_data
self.save_path = save_path
self.name = name
self.disable_tqdm = disable_tqdm
[docs]
def optimize(self):
"""
Execute the NSGA-II 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)
# Perform initial non-dominated sorting for each task
front_no, crowd_dis = [], []
for i in range(nt):
_, front_i, crowd_i = nsga2_sort(objs[i], cons[i])
front_no.append(front_i)
crowd_dis.append(crowd_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 on front number, then crowding distance
# (PlatEMO: TournamentSelection(2,N,FrontNo,-CrowdDis))
matingpool = platemo_tournament_selection(2, n_per_task[i], front_no[i], -crowd_dis[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: sort and keep best n individuals
rank_i, front_i, crowd_i = nsga2_sort(objs[i], cons[i])
index = np.argsort(rank_i)[:n_per_task[i]]
objs[i], decs[i], cons[i], front_no[i], crowd_dis[i] = select_by_index(
index, objs[i], decs[i], cons[i], front_i, crowd_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