Mayfly optimization algorithm - Revision history

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	In [[mathematical optimization]], [[computer science]] and [[operations research]], the '''Mayfly Optimization Algorithm''' (MA) was developed by Dr. Zervoudakis K. and Prof. Dr. Tsafarakis S. to address both continuous and discrete optimization problems and is inspired from the flight behavior and the mating process of [[mayflies]]. It is a hybrid algorithmic structure of [[particle swarm optimization]], [[firefly algorithm]] and [[genetic algorithm]]. The processes of nuptial dance and random flight enhance the balance between the algorithm's exploration and exploitation properties and assist its escape from local optima. Its performance is superior to that of other popular metaheuristics like ~~[[Particle swarm optimization\|~~PSO]], [[Differential evolution\|DE]], ~~[[Genetic algorithm\|~~GA]] and ~~[[Firefly algorithm\|~~FA]], in terms of convergence rate and convergence speed.<ref>{{cite journal \|doi=10.1016/j.cie.2020.106559 \|title= A mayfly optimization algorithm \|journal= Computers & Industrial Engineering \|volume=145\|year=2020 \|last1= Zervoudakis \|first1= Konstantinos \|last2= Tsafarakis \|first2= Stelios }}</ref>		In [[mathematical optimization]], [[computer science]] and [[operations research]], the '''Mayfly Optimization Algorithm''' (MA) was developed by Dr. Zervoudakis K. and Prof. Dr. Tsafarakis S. to address both continuous and discrete optimization problems and is inspired from the flight behavior and the mating process of [[mayflies]]. It is a hybrid algorithmic structure of [[particle swarm optimization]], [[firefly algorithm]] and [[genetic algorithm]]. The processes of nuptial dance and random flight enhance the balance between the algorithm's exploration and exploitation properties and assist its escape from local optima. Its performance is superior to that of other popular metaheuristics like PSO, [[Differential evolution\|DE]], GA and FA, in terms of convergence rate and convergence speed.<ref>{{cite journal \|doi=10.1016/j.cie.2020.106559 \|title= A mayfly optimization algorithm \|journal= Computers & Industrial Engineering \|volume=145\|year=2020 \|last1= Zervoudakis \|first1= Konstantinos \|last2= Tsafarakis \|first2= Stelios }}</ref>

	==Introduction==		==Introduction==

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	MA pseudocode <ref>{{cite journal \|doi=10.1016/j.cie.2020.106559 \|title= A mayfly optimization algorithm \|journal= Computers & Industrial Engineering \|volume=145\|year=2020 \|last1= Zervoudakis \|first1= Konstantinos \|last2= Tsafarakis \|first2= Stelios }}</ref>		MA pseudocode <ref>{{cite journal \|doi=10.1016/j.cie.2020.106559 \|title= A mayfly optimization algorithm \|journal= Computers & Industrial Engineering \|volume=145\|year=2020 \|last1= Zervoudakis \|first1= Konstantinos \|last2= Tsafarakis \|first2= Stelios }}</ref>

	Objective function f(x), x=(x_1,…,x_d )^T		Objective function f(x), x=(x_1,…,x_d )^T
	Initialize the male mayfly population x_i (i=1,2,…,N) and velocities v_mi		Initialize the male mayfly population x_i (i=1,2,…,N) and velocities v_mi
	Initialize the female mayfly population y_i (i=1,2,…,M) and velocities v_fi		Initialize the female mayfly population y_i (i=1,2,…,M) and velocities v_fi
	Evaluate solutions		Evaluate solutions
	Find global best gbest		Find global best gbest
	Do While stopping criteria are not met		Do While stopping criteria are not met
	Update velocities and positions of males and females		Update velocities and positions of males and females
	Evaluate solutions		Evaluate solutions
	Rank the mayflies		Rank the mayflies
	Mate the mayflies		Mate the mayflies
	Evaluate offspring		Evaluate offspring
	Separate offspring to male and female randomly		Separate offspring to male and female randomly
	Replace worst solutions with the best new ones		Replace worst solutions with the best new ones
	Update pbest and gbest		Update pbest and gbest
	end while		end while

	===Multi Objective Mayfly Optimization Algorithm (MOMA)===		===Multi Objective Mayfly Optimization Algorithm (MOMA)===
	MOMA pseudocode<ref>{{cite journal \|doi=10.1016/j.cie.2020.106559 \|title= A mayfly optimization algorithm \|journal= Computers & Industrial Engineering \|volume=145\|year=2020 \|last1= Zervoudakis \|first1= Konstantinos \|last2= Tsafarakis \|first2= Stelios }}</ref>		MOMA pseudocode<ref>{{cite journal \|doi=10.1016/j.cie.2020.106559 \|title= A mayfly optimization algorithm \|journal= Computers & Industrial Engineering \|volume=145\|year=2020 \|last1= Zervoudakis \|first1= Konstantinos \|last2= Tsafarakis \|first2= Stelios }}</ref>

	Initialize the male mayfly population 𝑥𝑖		Initialize the male mayfly population 𝑥𝑖
	(𝑖 = 1,2, … , 𝑁) and velocities 𝑣𝑚𝑖		(𝑖 = 1,2, … , 𝑁) and velocities 𝑣𝑚𝑖
	Initialize the female mayfly population 𝑦𝑖		Initialize the female mayfly population 𝑦𝑖
	(𝑖 = 1,2, … , 𝑀) and velocities 𝑣𝑓𝑖		(𝑖 = 1,2, … , 𝑀) and velocities 𝑣𝑓𝑖
	Evaluate solutions using the predefined objective functions		Evaluate solutions using the predefined objective functions
	Store the nondominated solutions found in an external repository		Store the nondominated solutions found in an external repository
	Sort the mayflies		Sort the mayflies
	Do While stopping criteria are not met		Do While stopping criteria are not met
	Update velocities and positions of males and females		Update velocities and positions of males and females
	Evaluate solutions		Evaluate solutions
	~~'''~~If~~'''~~ a new mayfly dominates its personal best		If a new mayfly dominates its personal best
	Replace personal best with the new solution		Replace personal best with the new solution
	~~'''~~If~~'''~~ no one dominates the other		If no one dominates the other
	The new solution has a chance of 50% to replace the personal best		The new solution has a chance of 50% to replace the personal best
	Rank the mayflies		Rank the mayflies
	Mate the mayflies		Mate the mayflies
	Evaluate offspring		Evaluate offspring
	Separate offspring to male and female randomly		Separate offspring to male and female randomly
	~~'''~~If~~'''~~ an offspring dominates its same-sex parent		If an offspring dominates its same-sex parent
	Replace parent with the offspring		Replace parent with the offspring
	Insert all the new nondominated solutions found in the external repository		Insert all the new nondominated solutions found in the external repository
	Sort the nondominated solutions and truncate the repository if needed		Sort the nondominated solutions and truncate the repository if needed
	end while		end while

	== References ==		== References ==

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Moved page from wikipedia:en:Mayfly optimization algorithm (history)

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{{Article for deletion/dated|page=Mayfly optimization algorithm|timestamp=20220412032620|year=2022|month=April|day=12|substed=yes}}


{{Multiple issues|
{{notability|date=April 2021}}
{{primary sources|date=April 2021}}
{{Context|date=April 2022}}
}}
In [[mathematical optimization]], [[computer science]] and [[operations research]], the '''Mayfly Optimization Algorithm''' (MA) was developed by Dr. Zervoudakis K. and Prof. Dr. Tsafarakis S. to address both continuous and discrete optimization problems and is inspired from the flight behavior and the mating process of [[mayflies]]. It is a hybrid algorithmic structure of [[particle swarm optimization]], [[firefly algorithm]] and [[genetic algorithm]]. The processes of nuptial dance and random flight enhance the balance between the algorithm's exploration and exploitation properties and assist its escape from local optima. Its performance is superior to that of other popular metaheuristics like [[Particle swarm optimization|PSO]], [[Differential evolution|DE]], [[Genetic algorithm|GA]] and [[Firefly algorithm|FA]], in terms of convergence rate and convergence speed.<ref>{{cite journal |doi=10.1016/j.cie.2020.106559 |title= A mayfly optimization algorithm |journal= Computers & Industrial Engineering |volume=145|year=2020 |last1= Zervoudakis |first1= Konstantinos |last2= Tsafarakis |first2= Stelios }}</ref>

==Introduction==
The MA was developed to address both single objective and multi objective optimization problems.<ref>{{cite journal |doi=10.1016/j.cie.2020.106559 |title= A mayfly optimization algorithm |journal= Computers & Industrial Engineering |volume=145|year=2020 |last1= Zervoudakis |first1= Konstantinos |last2= Tsafarakis |first2= Stelios }}</ref> Since its first presentation the mayfly optimization algorithm has been used by researchers to address various optimization problems.<ref>{{cite journal |last1=Elsisi |first1=Mahmoud |last2=Tran |first2=Minh Quang |last3=Mahmoud |first3=Karar |last4=Lehtonen |first4=Matti |last5=Darwish |first5=Mohamed M.F. |title=Robust Design of ANFIS Based Blade Pitch Controller for Wind Energy Conversion Systems Against Wind Speed Fluctuations |journal=IEEE Access |date=2021 |doi=10.1109/ACCESS.2021.3063053|doi-access=free }}</ref><ref>{{cite journal |last1=Bhattacharyya |first1=Trinav |last2=Chatterjee |first2=Bitanu |last3=Singh |first3=Pawan Kumar |last4=Yoon |first4=Jin Hee |last5=Geem |first5=Zong Woo |last6=Sarkar |first6=Ram |title=Mayfly in Harmony: A New Hybrid Meta-heuristic Feature Selection Algorithm |journal=IEEE Access |date=2020 |doi=10.1109/access.2020.3031718|doi-access=free }}</ref><ref>{{cite journal |last1=Zhao |first1=J |last2=Gao |first2=Z |title=The improved mayfly optimization algorithm with Chebyshev map |journal=Journal of Physics: Conference Series |date=2020 |volume=1684 |issue=1 |doi=10.1088/1742-6596/1684/1/012075|doi-access=free }}</ref><ref>{{cite journal |last1=Ramasamy |first1=Krishnakumar |last2=Ravichandran |first2=Coimbatore Subramanian |title=Optimal design of renewable sources of PV/wind/FC generation for power system reliability and cost using MA‐RBFNN approach |journal=International Journal of Energy Research |date=2021 |doi=10.1002/er.6578}}</ref><ref>{{cite journal |last1=Liu |first1=Z |last2=Jiang |first2=P |last3=Wang |first3=J |last4=Zhang |first4=L |title=Ensemble Forecasting System for Short-Term Wind Speed Forecasting Based on Optimal Sub-Model Selection and Multi-Objective Version of Mayfly Optimization Algorithm |journal=Expert Systems with Applications |date=2021 |volume=177 |doi=10.1016/j.eswa.2021.114974}}</ref>

==Mayfly Optimization Algorithm pseudocodes==
Simplified Matlab codes are provided here: <ref>https://www.mathworks.com/matlabcentral/fileexchange/76902-a-mayfly-optimization-algorithm</ref><ref>https://www.mathworks.com/matlabcentral/fileexchange/85653-a-multiobjective-mayfly-optimization-algorithm</ref>
===Single Objective Mayfly Optimization Algorithm (MA)===
MA pseudocode <ref>{{cite journal |doi=10.1016/j.cie.2020.106559 |title= A mayfly optimization algorithm |journal= Computers & Industrial Engineering |volume=145|year=2020 |last1= Zervoudakis |first1= Konstantinos |last2= Tsafarakis |first2= Stelios }}</ref>

Objective function f(x), x=(x_1,…,x_d )^T
Initialize the male mayfly population x_i (i=1,2,…,N) and velocities v_mi
Initialize the female mayfly population y_i (i=1,2,…,M) and velocities v_fi
Evaluate solutions
Find global best gbest
Do While stopping criteria are not met
Update velocities and positions of males and females
Evaluate solutions
Rank the mayflies
Mate the mayflies
Evaluate offspring
Separate offspring to male and female randomly
Replace worst solutions with the best new ones
Update pbest and gbest
end while

===Multi Objective Mayfly Optimization Algorithm (MOMA)===
MOMA pseudocode<ref>{{cite journal |doi=10.1016/j.cie.2020.106559 |title= A mayfly optimization algorithm |journal= Computers & Industrial Engineering |volume=145|year=2020 |last1= Zervoudakis |first1= Konstantinos |last2= Tsafarakis |first2= Stelios }}</ref>

Initialize the male mayfly population 𝑥𝑖
(𝑖 = 1,2, … , 𝑁) and velocities 𝑣𝑚𝑖
Initialize the female mayfly population 𝑦𝑖
(𝑖 = 1,2, … , 𝑀) and velocities 𝑣𝑓𝑖
Evaluate solutions using the predefined objective functions
Store the nondominated solutions found in an external repository
Sort the mayflies
Do While stopping criteria are not met
Update velocities and positions of males and females
Evaluate solutions
'''If''' a new mayfly dominates its personal best
Replace personal best with the new solution
'''If''' no one dominates the other
The new solution has a chance of 50% to replace the personal best
Rank the mayflies
Mate the mayflies
Evaluate offspring
Separate offspring to male and female randomly
'''If''' an offspring dominates its same-sex parent
Replace parent with the offspring
Insert all the new nondominated solutions found in the external repository
Sort the nondominated solutions and truncate the repository if needed
end while

== References ==
{{reflist}}

[[Category:Optimization algorithms and methods]]
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