#!/usr/bin/env python
# Created by "Enes Cabbar AKÇA" in 2024
# Github: https://github.com/enescabbarakca29
# ------------------------------------------%
import numpy as np
from mealpy.optimizer import Optimizer
from mealpy.utils.opt_info import OptInfo
[docs]class OriginalBWO(Optimizer):
"""
The original version of: Beluga Whale Optimization (BWO)
Parameters
----------
epoch : int
Maximum number of iterations, default = 10000.
pop_size : int
Number of population size, default = 100.
References
~~~~~~~~~~
1. Zhong, Changting, Gang Li, and Zeng Meng. "Beluga whale optimization: A novel nature-inspired metaheuristic
algorithm." Knowledge-based systems 251 (2022): 109215. https://doi.org/10.1016/j.knosys.2022.109215
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy import FloatVar, BWO
>>>
>>> def objective_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict = {
>>> "bounds": FloatVar(lb=(-10.,) * 30, ub=(10.,) * 30, name="delta"),
>>> "minmax": "min",
>>> "obj_func": objective_function
>>> }
>>>
>>> model = BWO.OriginalBWO(epoch=1000, pop_size=50)
>>> g_best = model.solve(problem_dict)
>>> print(f"Solution: {g_best.solution}, Fitness: {g_best.target.fitness}")
>>> print(f"Solution: {model.g_best.solution}, Fitness: {model.g_best.target.fitness}")
"""
OPT_INFO = OptInfo(name="Beluga Whale Optimization", year=2022, difficulty="hard", kind="original")
def __init__(self, epoch: int = 10000, pop_size: int = 100, **kwargs: object) -> None:
super().__init__(**kwargs)
self.epoch = self.validator.check_int("epoch", epoch, [1, 100000])
self.pop_size = self.validator.check_int("pop_size", pop_size, [5, 10000])
self.set_parameters(["epoch", "pop_size"])
self.sort_flag = False
[docs] def evolve(self, epoch: int) -> None:
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration (starts from 0 or 1 depending on Mealpy loop)
"""
# Eq. (3): Bf = B0*(1 - T/(2*Tmax)), with B0 in (0,1) per individual
B0 = self.generator.random(self.pop_size)
Bf = B0 * (1.0 - epoch / (2.0 * self.epoch))
ndim = self.problem.n_dims
pop_new = []
# -------------------------
# Main move: Eq.4 or Eq.5
# -------------------------
for idx in range(self.pop_size):
rr = self.generator.choice(list(set(range(0, self.pop_size)) - {idx}))
pos_rr = self.pop[rr].solution
pos_ii = self.pop[idx].solution
if Bf[idx] > 0.5:
# ===================== Exploration (Eq. 4) =====================
r1, r2 = self.generator.random(2)
pj = self.generator.integers(0, ndim, size=ndim)
p1 = self.generator.integers(0, ndim, size=ndim)
base = pos_ii[pj]
diff = pos_ii[p1] - base
j_indices = np.arange(1, ndim + 1)
sin_val = np.sin(2.0 * np.pi * r2)
cos_val = np.cos(2.0 * np.pi * r2)
trig = np.where(j_indices % 2 == 0, sin_val, cos_val)
pos_new = base + diff * (1.0 + r1) * trig
else:
# ===================== Exploitation (Eq. 5) =====================
r3, r4 = self.generator.random(2)
C1 = 2.0 * r4 * (1.0 - epoch / self.epoch)
# Use built‑in Levy-flight function from Optimizer
# Beta=1.5 (Eq.6), multiplier=0.05 (scale), case=-1 returns multiplier * s only
LF = self.get_levy_flight_step(beta=1.5, multiplier=0.05, size=ndim, case=-1)
pos_new = r3 * self.g_best.solution - r4 * pos_ii + C1 * LF * (pos_rr - pos_ii)
# Bound control
pos_new = self.correct_solution(pos_new)
agent = self.generate_empty_agent(pos_new)
pop_new.append(agent)
# In sequential modes: evaluate and greedy-update immediately
if self.mode not in self.AVAILABLE_MODES:
agent.target = self.get_target(pos_new)
self.pop[idx] = self.get_better_agent(agent, self.pop[idx], self.problem.minmax)
# In parallel modes: evaluate batch and greedy-select
if self.mode in self.AVAILABLE_MODES:
pop_new = self.update_target_for_population(pop_new)
self.pop = self.greedy_selection_population(self.pop, pop_new, self.problem.minmax)
# -------------------------
# Whale fall (Eq. 8–10)
# -------------------------
# Eq. (10): Wf = 0.1 - 0.05*T/Tmax
Wf = 0.1 - 0.05 * (epoch / self.epoch)
# Eq. (9): Xstep = (ub - lb)*exp(-C2*T/Tmax), C2 = 2*Wf*n
C2 = 2.0 * Wf * self.pop_size
X_step = (self.problem.ub - self.problem.lb) * np.exp(-C2 * epoch / self.epoch)
# Sequential mode: evaluate per candidate
if self.mode not in self.AVAILABLE_MODES:
for idx in range(self.pop_size):
if float(self.generator.random()) < Wf:
rr = self.generator.choice(list(set(range(0, self.pop_size)) - {idx}))
r5, r6, r7 = self.generator.random(3)
cand = r5 * self.pop[idx].solution - r6 * self.pop[rr].solution + r7 * X_step
cand = self.correct_solution(cand)
agent_cand = self.generate_agent(cand)
self.pop[idx] = self.get_better_agent(agent_cand, self.pop[idx], self.problem.minmax)
# Parallel mode: batch-evaluate only the whale-fall candidates
else:
idxs = []
cand_agents = []
for idx in range(self.pop_size):
if float(self.generator.random()) < Wf:
rr = self.generator.choice(list(set(range(0, self.pop_size)) - {idx}))
r5, r6, r7 = self.generator.random(3)
cand = r5 * self.pop[idx].solution - r6 * self.pop[rr].solution + r7 * X_step
cand = self.correct_solution(cand)
idxs.append(idx)
cand_agents.append(self.generate_empty_agent(cand))
if len(cand_agents) > 0:
cand_agents = self.update_target_for_population(cand_agents)
for k, idx in enumerate(idxs):
self.pop[idx] = self.get_better_agent(cand_agents[k], self.pop[idx], self.problem.minmax)