Table 2 Collection of search operators utilized to obtain the tailored MH and their parameters variation, hyperparameters, and associated selector.

\(h_0\)

central_force_dynamic

–

gravity = 0.001, alpha = 0.01, beta = 1.5, dt = 1.0

All

\(h_1\)

central_force_dynamic

–

gravity = 0.001, alpha = 0.01, beta = 1.5, dt = 1.0

Greedy

\(h_2\)

differential_mutation

Mutation \(\textrm{Scheme}^{b_1}\)

num_rands = 1, factor = 1.0

All

\(h_3\)

differential_mutation

Mutation \(\textrm{Scheme}^{b_1}\)

num_rands = 1, factor = 1.0

Greedy

\(h_4\)

differential_mutation

Mutation \(\textrm{Scheme}^{b_2}\)

num_rands = 1, factor = 1.0

All

\(h_5\)

differential_mutation

Mutation \(\textrm{Scheme}^{b_2}\)

num_rands = 1, factor = 1.0

Greedy

\(h_6\)

firefly_dynamic

\(\textrm{Distribution}^{a_2}\)

alpha = 1.0, beta = 1.0, gamma = 100.0

All

\(h_7\)

firefly_dynamic

\(\textrm{Distribution}^{a_2}\)

alpha = 1.0, beta = 1.0, gamma = 100.0

Greedy

\(h_8\)

genetic_crossover

\(\textrm{PS}^{c_1}\), \(\textrm{CM}^{d_3}\)

mating_pool_factor = 0.4

All

\(h_{9}\)

genetic_crossover

\(\textrm{PS}^{c_1}\), \(\textrm{CM}^{d_3}\)

mating_pool_factor = 0.4

Greedy

\(h_{10}\)

genetic_crossover

\(\textrm{PS}^{c_3}\), \(\textrm{CM}^{d_3}\)

mating_pool_factor = 0.4

All

\(h_{11}\)

genetic_crossover

\(\textrm{PS}^{c_3}\), \(\textrm{CM}^{d_3}\)

mating_pool_factor = 0.4

Greedy

\(h_{12}\)

genetic_mutation

\(\textrm{Distribution}^{a_2}\)

scale = 1.0, elite_rate = 0.1, mutation_rate = 0.25

All

\(h_{13}\)

genetic_mutation

\(\textrm{Distribution}^{a_2}\)

scale = 1.0, elite_rate = 0.1, mutation_rate = 0.25

Greedy

\(h_{14}\)

gravitational_search

–

gravity = 1.0, alpha = 0.02

All

\(h_{15}\)

gravitational_search

–

gravity = 1.0, alpha = 0.02

Greedy

\(h_{16}\)

local_random_walk

\(\textrm{Distribution}^{a_1}\)

probability = 0.75, scale = 1.0

All

\(h_{17}\)

local_random_walk

\(\textrm{Distribution}^{a_1}\)

probability = 0.75, scale = 1.0

Greedy

\(h_{18}\)

random_sample

–

–

All

\(h_{19}\)

random_sample

–

–

Greedy

\(h_{20}\)

random_search

\(\textrm{Distribution}^{a_2}\)

scale = 1.0

Greedy

\(h_{21}\)

random_search

\(\textrm{Distribution}^{a_2}\)

scale = 0.01

Greedy

\(h_{22}\)

spiral_dynamic

–

radius = 0.9, angle = 22.5, sigma = 0.1

All

\(h_{23}\)

spiral_dynamic

–

radius = 0.9, angle = 22.5, sigma = 0.1

Greedy

\(h_{24}\)

swarm_dynamic

\(\textrm{Distribution}^{a_2}\), \(\textrm{SWA}^{e_1}\)

factor = 0.7, self_conf = 2.54, swarm_conf = 2.56

All

\(h_{25}\)

swarm_dynamic

\(\textrm{Distribution}^{a_2}\), \(\textrm{SWA}^{e_1}\)

factor =0.7, self_conf =2.54, swarm_conf =2.56

Greedy

\(h_{26}\)

swarm_dynamic

\(\textrm{Distribution}^{a_2}\), \(\textrm{SWA}^{e_2}\)

factor =1.0, self_conf =2.54, swarm_conf =2.56

All

\(h_{27}\)

swarm_dynamic

\(\textrm{Distribution}^{a_2}\), \(\textrm{SWA}^{e_2}\)

factor =1.0, self_conf =2.54, swarm_conf =2.56

Greedy

\(h_{28}\)

random_flight

\(\textrm{Distribution}^{a_3}\)

scale = 1.0, beta = 1.5

All

\(h_{29}\)

random_flight

\(\textrm{Distribution}^{a_3}\)

scale = 1.0, beta = 1.5

Greedy