An Evolutionary Dynamic Control Cuckoo Search Algorithm for Solving the Constrained Engineering Design Problems

Introduction

The process of obtaining the best solution for a given problem under the specified conditions is known as optimization. There are two types of mathematical optimization: (1) deterministic optimization and (2) stochastic optimization. The deterministic approaches search the space for the best potential solution using the problem's gradient information. The most successful deterministic methods are linear/nonlinear programming (Luenberger & Ye, 1984) and convex optimization (Boyd et al., 2004). The stochastic technique, on the other hand, uses a random probable answer that is checked by the statistical analysis to arrive at an optimal solution (Izonin et al., 2021), like the meta-heuristic algorithm that generates and uses random variables. These algorithms employ a global search strategy to find a global or near-global solution across the problem domain. Simple, gradient-free, adaptable, and problem-independent metaheuristic algorithms have always been desirable (Faramarzi, Heidarinejad, Stephens, et al., 2020). For easier reading, the symbols and abbreviations are provided in Table 1.

Symbols
	Abandoned chance		Best Fitness
	Number of Cuckoos		Worst fitness
	Problem dimension		A random number from the normal distribution
	Nest (solution)		Adaptive step size
	Upper boundaries		Maximum generation
	Lower boundaries		Chance factor
	Random number		Global best solution
	Generation	,	index
,	Step size	avg	Mean fitness
	Fitness value	std	Standard deviation
Abbreviations
ABC	Artificial Bee Colony	GOA	Grasshopper Optimisation Algorithm
ABO	Artificial Butterfly Optimization	GSA	Gravitational Search Algorithm
ACO	Ant Colony Optimization	GWO	Gray Wolf Optimizer
ACS	Adaptive Cuckoo Search	HBA	Honey Badger Algorithm
ALO	Ant Lion Optimizer	HFA	Human Felicity Algorithm
AOA	Arithmetic Optimization Algorithm	HGSO	Henry Gas Solubility Optimization
ASO	Atom Search Optimization	HHO	Harris Hawks Optimization
AVOA	African Vultures Optimization Algorithm	KHA	Krill Herd Algorithm
BBO	Biogeography-Based Optimization	LSA	Lightning Search Algorithm
BFOA	Bacterial Foraging Optimization Algorithm	MBO	Monarch Butterfly Optimization
BMO	Barnacles Mating Optimizer	MPA	Marine Predators Algorithm
BWO	Black Widow Optimization	MRFO	Manta Ray Foraging Optimization
CEC	Congress on Evolutionary Computation	PSO	Particle Swarm Optimization
ChOA	Chimp Optimization Algorithm	SA	Simulated Annealing
CROA	Coral Reefs Optimization Algorithm	SFO	Sailfish Optimizer
CS	Cuckoo Search	SI	Swarm Intelligence
CSA	Crow Search Algorithm	SMA	Slime Mould Algorithm
DCCS	Dynamic Control Cuckoo Search	SOA	Seagull Optimization Algorithm
DE	Differential Evolution	SSA	Squirrel Search Algorithm
EAs	Evolutionary Algorithms	TLBO	Teaching–Learning-Based Optimization
EO	Equilibrium Optimizer	VCS	Virus Colony Search
ESA	Electro-Search Algorithm	VPL	Volleyball Premier League
FA	Firefly Algorithm	WCA	Water Cycle Algorithm
FDA	Flow Direction Algorithm	WDO	Wind Driven Optimization
GA	Genetic Algorithm	WOA	Whale Optimization Algorithm