View source for List of metaphor-based metaheuristics

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[[File:Metaheuristics classification.svg|alt=A diagrammatic classification of metaheuristics|thumb|A diagram classifying the various kinds of metaheuristics]]
This is a chronologically ordered list of metaphor-based [[metaheuristics]] and [[swarm intelligence]] algorithms, sorted by decade of proposal.

== Algorithms ==
{{incomplete list|date=August 2016}}<!-- Is it possible to sort this list thematically rather than chronologically? ~Duckmather

I was thinking the same. ~Semanticing -->

=== 1980s-1990s ===

==== Simulated annealing (Kirkpatrick et al., 1983) ====
{{Main|Simulated annealing}}
[[File:3D TSP solved with simulated annealing 2.5 MB.gif|alt=animation of simulated annealing solving a 3D traveling salesman problem instance|thumb|Visualization of simulated annealing solving a three-dimensional [[travelling salesman problem]] instance on 120 points]]
Simulated annealing is a [[probabilistic algorithm]] inspired by [[Annealing (materials science)|annealing]], a heat treatment method in [[metallurgy]]. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For problems where finding the precise global optimum is less important than finding an acceptable local optimum in a fixed amount of time, simulated annealing may be preferable to alternatives such as [[gradient descent]].

The analogue of the slow cooling of annealing is a slow decrease in the probability of simulated annealing accepting worse solutions as it explores the solution space. Accepting worse solutions is a fundamental property of metaheuristics because it allows for a more extensive search for the optimal solution.

==== Ant colony optimization (ACO) (Dorigo, 1992) ====
{{Main|Ant colony optimization algorithms}}

The ant colony optimization algorithm is a [[probability|probabilistic]] technique for solving computational problems that can be reduced to finding good paths through [[Graph (discrete mathematics)|graph]]s. Initially proposed by [[Marco Dorigo]] in 1992 in his PhD thesis,<ref>{{cite book |first1=Alberto |last1=Colorni |first2=Marco |last2=Dorigo |first3=Vittorio |last3=Maniezzo |chapter=Distributed Optimization by Ant Colonies |pages=134–42 |chapter-url={{Google books|pWsNJkdZ4tgC|page=134|plainurl=yes}} |editor1-first=Francisco J. |editor1-last=Varela |editor2-first=Paul |editor2-last=Bourgine |year=1992 |title=Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life |publisher=MIT Press |isbn=978-0-262-72019-9 }}</ref><ref name="M. Dorigo, Optimization, Learning and Natural Algorithms">M. Dorigo, ''Optimization, Learning and Natural Algorithms'', PhD thesis, Politecnico di Milano, Italy, 1992.{{page needed|date=January 2018}}</ref> the first algorithm aimed to search for an optimal path in a graph based on the behavior of [[ants]] seeking a path between their [[ant colony|colony]] and a source of food. The original idea has since diversified to solve a wider class of numerical problems, and as a result, several problems{{Example needed|date=April 2022}} have emerged, drawing on various aspects of the behavior of ants. From a broader perspective, ACO performs a model-based search<ref>{{cite journal |doi=10.1023/B:ANOR.0000039526.52305.af |title=Model-Based Search for Combinatorial Optimization: A Critical Survey |journal=Annals of Operations Research |volume=131 |issue=1–4 |pages=373–95 |year=2004 |last1=Zlochin |first1=Mark |last2=Birattari |first2=Mauro |last3=Meuleau |first3=Nicolas |last4=Dorigo |first4=Marco |citeseerx=10.1.1.3.427 |s2cid=63137 }}</ref> and shares some similarities with the [[estimation of distribution algorithm]]s.

==== Particle swarm optimization (PSO) (Kennedy & Eberhart, 1995) ====
{{Main|Particle swarm optimization}}

Particle swarm optimization is a computational method that [[Mathematical optimization|optimizes]] a problem by [[iterative method|iteratively]] trying to improve a [[candidate solution]] with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, dubbed [[Point particle|particle]]s, and moving these particles around in the [[Optimization (mathematics)#Concepts and notation|search space]] according to simple [[formula|mathematical formulae]]{{Which|date=April 2022}} over the particle's [[Position (vector)|position]] and [[velocity]]. Each particle's movement is influenced by its local best known position but is also guided toward the best-known positions in the search space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions.

PSO is originally attributed to [[James Kennedy (social psychologist)|Kennedy]], [[Russell C. Eberhart|Eberhart]] and Shi<ref name=kennedy95particle/><ref name=shi98modified/> and was first intended for [[computer simulation|simulating]] [[social behaviour]]<ref name=kennedy97particle/> as a stylized representation of the movement of organisms in a bird [[Flocking (behavior)|flock]] or [[fish school]]. The algorithm was simplified, and it was observed to be performing optimization. The book by Kennedy and Eberhart<ref name=kennedy01swarm/> describes many philosophical aspects of PSO and [[swarm intelligence]]. An extensive survey of PSO applications is made by [[Riccardo Poli|Poli]].<ref name=poli07analysis/><ref name=poli08analysis/> A comprehensive review of theoretical and experimental works on PSO has been published by Bonyadi and Michalewicz.<ref name=bonyadi16survey/>

=== 2000s ===

==== Harmony search (HS) (Geem, Kim & Loganathan, 2001) ====
Harmony search is a phenomenon-mimicking [[metaheuristic]] introduced in 2001 by Zong Woo Geem, Joong Hoon Kim, and G. V. Loganathan<ref>{{cite journal |doi=10.1177/003754970107600201 |title=A New Heuristic Optimization Algorithm: Harmony Search |journal=Simulation |volume=76 |issue=2 |pages=60–8 |year=2016 |last1=Zong Woo Geem |last2=Joong Hoon Kim |last3=Loganathan |first3=G.V. |s2cid=20076748 }}</ref> and is inspired by the improvization process of jazz musicians. In the HS algorithm, a set of possible solutions is randomly generated (called Harmony memory). A new solution is generated by using all the solutions in the Harmony memory (rather than just two as used in GA) and if this new solution is better than the worst solution in Harmony memory, the worst solution gets replaced by this new solution. The effectiveness and advantages of HS have been demonstrated in various applications like design of municipal water distribution networks,<ref>{{cite journal |doi=10.1080/03052150500467430 |title=Optimal cost design of water distribution networks using harmony search |journal=Engineering Optimization |volume=38 |issue=3 |pages=259–277 |year=2006 |last1=Geem |first1=Zong Woo |s2cid=18614329 }}</ref> structural design,<ref>{{cite journal |doi=10.1080/0305215X.2012.704028 |title=Shape optimization of structures for frequency constraints by sequential harmony search algorithm |journal=Engineering Optimization |volume=45 |issue=6 |pages=627 |year=2013 |last1=Gholizadeh |first1=S. |last2=Barzegar |first2=A. |bibcode=2013EnOp...45..627G |s2cid=123589002 }}</ref> load dispatch problem in electrical engineering,<ref>{{cite journal |doi=10.1016/j.ijepes.2012.08.021 |title=An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems |journal=International Journal of Electrical Power & Energy Systems |volume=44 |pages=832–843 |year=2013 |last1=Wang |first1=Ling |last2=Li |first2=Ling-po }}</ref> multi-objective optimization,<ref>{{cite journal |doi=10.1109/TSG.2012.2237420 |title=An Improved Multi-Objective Harmony Search for Optimal Placement of DGs in Distribution Systems |journal=IEEE Transactions on Smart Grid |volume=4 |pages=557–567 |year=2013 |last1=Nekooei |first1=Komail |last2=Farsangi |first2=Malihe M. |last3=Nezamabadi-Pour |first3=Hossein |last4=Lee |first4=Kwang Y. |s2cid=12988437 }}</ref> rostering problems,<ref>{{cite journal |doi=10.1016/j.ins.2012.12.025 |title=A harmony search algorithm for nurse rostering problems |journal=Information Sciences |volume=233 |pages=126–140 |year=2013 |last1=Hadwan |first1=Mohammed |last2=Ayob |first2=Masri |last3=Sabar |first3=Nasser R. |last4=Qu |first4=Roug |citeseerx=10.1.1.298.6805 |s2cid=16569649 }}</ref> clustering,<ref>{{cite journal |doi=10.1109/TII.2013.2273739 |title=Real-Time Implementation of a Harmony Search Algorithm-Based Clustering Protocol for Energy-Efficient Wireless Sensor Networks |journal=IEEE Transactions on Industrial Informatics |volume=10 |pages=774–783 |year=2014 |last1=Hoang |first1=Duc Chinh |last2=Yadav |first2=Parikshit |last3=Kumar |first3=Rajesh |last4=Panda |first4=Sanjib Kumar |s2cid=3731612 }}</ref> and classification and feature selection.<ref>{{cite journal |doi=10.1109/TSMCB.2012.2193613 |pmid=22645272 |title=Feature Selection with Harmony Search |journal=IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics |volume=42 |issue=6 |pages=1509–23 |year=2012 |last1=Ren Diao |last2=Qiang Shen |s2cid=206794122 }}</ref><ref>{{cite journal |doi=10.1007/s00521-014-1766-y |title=Estimation of asphaltene precipitation from titration data: A hybrid support vector regression with harmony search |journal=Neural Computing and Applications |volume=26 |issue=4 |pages=789 |year=2014 |last1=Fattahi |first1=Hadi |last2=Gholami |first2=Amin |last3=Amiribakhtiar |first3=Mohammad Sadegh |last4=Moradi |first4=Siyamak |s2cid=16208680 }}</ref> A detailed survey on applications of HS can be found.<ref>{{Cite web |title=Harmony Search Algorithm |url=https://sites.google.com/a/hydroteq.com/www/ |access-date=23 April 2022 |website=sites.google.com}}</ref><ref>{{cite journal |doi=10.1016/j.engappai.2013.05.008 |title=A survey on applications of the harmony search algorithm |journal=Engineering Applications of Artificial Intelligence |volume=26 |issue=8 |pages=1818 |year=2013 |last1=Manjarres |first1=D. |last2=Landa-Torres |first2=I. |last3=Gil-Lopez |first3=S. |last4=Del Ser |first4=J. |last5=Bilbao |first5=M.N. |last6=Salcedo-Sanz |first6=S. |last7=Geem |first7=Z.W. }}</ref> and applications of HS in data mining can be found in.<ref>{{cite book |doi=10.1007/978-981-10-0451-3_77 |chapter=Applications of Harmony Search Algorithm in Data Mining: A Survey |title=Proceedings of Fifth International Conference on Soft Computing for Problem Solving |volume=437 |pages=863–74 |series=Advances in Intelligent Systems and Computing |year=2016 |last1=Assif Assad |last2=Deep |first2=Kusum |isbn=978-981-10-0450-6 }}</ref>

Dennis (2015) claimed that harmony search is a special case of the [[Evolution strategy|evolution strategies]] algorithm.<ref>{{cite journal |last1=Weyland |first1=Dennis |year=2015 |title=A critical analysis of the harmony search algorithm—How not to solve sudoku |journal=Operations Research Perspectives |volume=2 |pages=97–105 |doi=10.1016/j.orp.2015.04.001 |doi-access=free|hdl=10419/178253 |hdl-access=free }}</ref> However, Saka et al. (2016) argues that the structure of evolution strategies is different from that of harmony search.<ref>{{cite journal |last1=Saka |first1=M. |last2=Hasançebi |first2=O. |last3=Seem |first3=Z.W. |year=2016 |title=Metaheuristics in structural optimization and discussions on harmony search algorithm |url=https://www.sciencedirect.com/science/article/abs/pii/S2210650216000158 |journal=Swarm and Evolutionary Computation |volume=28 |pages=88–97 |doi=10.1016/j.swevo.2016.01.005}}</ref>

==== Artificial bee colony algorithm (Karaboga, 2005) ====
{{Main|Artificial bee colony algorithm}}

Artificial bee colony algorithm is a metaheuristic introduced by Karaboga in 2005<ref>{{cite journal |doi=10.4249/scholarpedia.6915 |title=Artificial bee colony algorithm |journal=Scholarpedia |volume=5 |issue=3 |pages=6915 |year=2010 |last1=Karaboga |first1=Dervis |bibcode=2010SchpJ...5.6915K |doi-access=free }}</ref> which simulates the foraging behaviour of [[honey bee]]s. The ABC algorithm has three phases: employed bee, onlooker bee and scout bee. In the employed bee and the onlooker bee phases, bees exploit the sources by local searches in the neighbourhood of the solutions selected based on deterministic selection in the employed bee phase and the [[Random selection|probabilistic selection]] in the onlooker bee phase. In the scout bee phase, which is analogous to bees abandoning exhausted food sources in the foraging process, solutions that are not beneficial anymore for search progress are abandoned, and new solutions are inserted instead to explore new regions in the search space. The algorithm has a well-balanced{{Weasel inline|date=April 2022}} exploration and exploitation ability.{{Clarify|date=April 2022}}

==== Bees algorithm (Pham, 2005) ====
{{Main|Bees algorithm}}

The bees algorithm was formulated by Pham and his co-workers in 2005<ref name="Pham & al, 2005">Pham DT, Ghanbarzadeh A, Koc E, Otri S, Rahim S and Zaidi M. The Bees Algorithm. Technical Note, Manufacturing Engineering Centre, Cardiff University, UK, 2005.{{page needed|date=September 2017}}</ref> and further refined in 2009.<ref name="Pham & Castellani, 2009">{{cite journal |doi=10.1243/09544062jmes1494 |title=The Bees Algorithm: Modelling foraging behaviour to solve continuous optimization problems |journal=Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science |volume=223 |issue=12 |pages=2919 |year=2009 |last1=Pham |first1=D T |last2=Castellani |first2=M |s2cid=111315200 }}</ref> Modelled on the foraging behaviour of [[honey bees]], the algorithm combines global explorative search with local exploitative search. A small number of artificial bees (scouts) explores randomly the solution space (environment) for solutions of high fitness (highly profitable food sources), whilst the bulk of the population search (harvest) the neighbourhood of the fittest solutions looking for the fitness optimum. A deterministic recruitment procedure which simulates the [[waggle dance]] of biological bees is used to communicate the scouts' findings to the foragers and distribute the foragers depending on the fitness of the neighbourhoods selected for local search. Once the search in the neighbourhood of a solution stagnates, the local fitness optimum is considered to be found, and the site is abandoned.

==== {{anchor|Imperialist competitive}} Imperialist competitive algorithm (Atashpaz-Gargari & Lucas, 2007) ====
{{Main|Imperialist competitive algorithm}}

The imperialist competitive algorithm (ICA), like most of the methods in the area of [[evolutionary computation]], does not need the gradient of the function in its optimization process. From a specific point of view, ICA can be thought of as the social counterpart of [[genetic algorithms]] (GAs). ICA is the mathematical model and the computer simulation of human [[Sociocultural evolution|social evolution]], while GAs is based on the [[biological evolution]] of species.

This algorithm starts by generating a set of random candidate solutions in the search space of the optimization problem. The generated random points are called the initial ''Countries''. Countries in this algorithm are the counterpart of ''Chromosome''s in GAs and ''Particle''s in [[Particle Swarm Optimization]] and it is an array of values of a candidate solution of optimization problem. The [[Loss function|cost function]] of the optimization problem determines the power of each country. Based on their power, some of the best initial countries (the countries with the least cost function value), become ''Imperialists'' and start taking control of other countries (called ''colonies'') and form the initial ''Empires''.<ref name="ica_en_2007_cnf_atashpaz_ica_ica">{{cite book |last1=Atashpaz-Gargari |first1=Esmaeil |title=2007 IEEE Congress on Evolutionary Computation |last2=Lucas |first2=Caro |year=2007 |isbn=978-1-4244-1339-3 |pages=4661–7 |chapter=Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition |doi=10.1109/CEC.2007.4425083 |s2cid=2736579}}</ref>

Two main operators of this algorithm are ''Assimilation'' and ''Revolution''. Assimilation makes the colonies of each empire get closer to the imperialist state in the space of socio-political characteristics (optimization search space). Revolution brings about sudden random changes in the position of some of the countries in the search space. During assimilation and revolution, a colony might reach a better position and then have a chance to take the control of the entire empire and replace the current imperialist state of the empire.<ref name=ica_en_2010_jnl_nazari_integrated_product_mix_outsourcing>{{cite journal |doi=10.1016/j.eswa.2010.04.081 |title=Solving the integrated product mix-outsourcing problem using the Imperialist Competitive Algorithm |journal=Expert Systems with Applications |volume=37 |issue=12 |pages=7615 |year=2010 |last1=Nazari-Shirkouhi |first1=S. |last2=Eivazy |first2=H. |last3=Ghodsi |first3=R. |last4=Rezaie |first4=K. |last5=Atashpaz-Gargari |first5=E. |s2cid=17563386 }}</ref>

''Imperialistic Competition'' is another part of this algorithm. All the empires try to win this game and take possession of colonies of other empires. In each step of the algorithm, based on their power, all the empires have a chance to take control of one or more of the colonies of the weakest empire.<ref name=ica_en_2007_cnf_atashpaz_ica_ica />

The algorithm continues with the mentioned steps (Assimilation, Revolution, Competition) until a stop condition is satisfied.

The above steps can be summarized as the below [[pseudocode]]:<ref name="ICA_2014_Survey">{{cite journal |last1=Hosseini |first1=Seyedmohsen |last2=Al Khaled |first2=Abdullah |year=2014 |title=A survey on the Imperialist Competitive Algorithm metaheuristic: Implementation in engineering domain and directions for future research |journal=Applied Soft Computing |volume=24 |pages=1078–1094 |doi=10.1016/j.asoc.2014.08.024}}</ref><ref name=ica_en_2010_jnl_nazari_integrated_product_mix_outsourcing />
 0) Define objective function: <math>f(\mathbf{x}), \quad \mathbf{x}=(x_1,x_2,\dots,x_d); \, </math>
 1) Initialization of the algorithm. Generate some random solution in the search space and create initial empires.
     2) Assimilation: Colonies move towards imperialist states in different in directions.
     3) Revolution: Random changes occur in the characteristics of some countries.
     4) Position exchange between a colony and Imperialist. A colony with a better position than the imperialist,
        has the chance to take the control of empire by replacing the existing imperialist.
     5) Imperialistic competition: All imperialists compete to take possession of colonies of each other.
     6) Eliminate the powerless empires. Weak empires lose their power gradually and they will finally be eliminated.
     7) If the stop condition is satisfied, stop, if not go to 2.
 8) End

==== {{anchor|River formation dynamics}} River formation dynamics (Rabanal, Rodríguez & Rubio, 2007) ====
River formation dynamics is based on imitating how water forms rivers by eroding the ground and depositing sediments (the drops act as the swarm). After drops transform the landscape by increasing/decreasing the altitude of places, solutions are given in the form of paths of decreasing altitudes. Decreasing gradients are constructed, and these gradients are followed by subsequent drops to compose new gradients and reinforce the best ones. This heuristic optimization method was proposed in 2007 by Rabanal et al.<ref>{{cite book |doi=10.1007/978-3-540-73554-0 |title=Unconventional Computation |volume=4618 |series=Lecture Notes in Computer Science |year=2007 |isbn=978-3-540-73553-3 |last1=Akl |first1=Selim G. |last2=Calude |first2=Cristian S. |last3=Dinneen |first3=Michael J. |last4=Rozenberg |first4=Grzegorz |last5=Todd Wareham |first5=H. |arxiv=0711.2964 }}</ref> The applicability of RFD to other NP-complete problems has been studied,<ref>{{cite book |doi=10.1007/978-3-642-00267-0_12 |chapter=Applying River Formation Dynamics to Solve NP-Complete Problems |title=Nature-Inspired Algorithms for Optimisation |volume=193 |pages=333–68 |series=Studies in Computational Intelligence |year=2009 |last1=Rabanal |first1=Pablo |last2=Rodríguez |first2=Ismael |last3=Rubio |first3=Fernando |isbn=978-3-642-00266-3 }}</ref> and the algorithm has been applied to fields such as routing<ref>{{cite journal |doi=10.1016/j.bjp.2013.11.015 |title=Smart data packet ad hoc routing protocol |journal=Computer Networks |volume=62 |pages=162–181 |year=2014 |last1=Amin |first1=Saman Hameed |last2=Al-Raweshidy |first2=H.S. |last3=Abbas |first3=Rafed Sabbar }}</ref> and robot navigation.<ref>{{cite journal |doi=10.4028/www.scientific.net/SSP.198.138 |title=Using River Formation Dynamics Algorithm in Mobile Robot Navigation |journal=Solid State Phenomena |volume=198 |pages=138–143 |year=2013 |last1=Redlarski |first1=Grzegorz |last2=Pałkowski |first2=Aleksander |last3=Dąbkowski |first3=Mariusz |s2cid=137020536 }}</ref> The main applications of RFD can be found at the survey Rabanal et al. (2017).<ref>{{cite journal |doi=10.1016/j.jocs.2017.08.002 |title=Applications of river formation dynamics |journal=Journal of Computational Science |volume=22 |pages=26–35 |year=2017 |last1=Rabanal |first1=Pablo |last2=Rodríguez |first2=Ismael |last3=Rubio |first3=Fernando |url=https://eprints.ucm.es/id/eprint/71694/1/mainJCS.pdf }}</ref>

==== {{anchor|Gravitational search algorithm}} Gravitational search algorithm (Rashedi, Nezamabadi-pour & Saryazdi, 2009) ====
The gravitational search algorithm is based on the [[law of gravity]] and the notion of mass interactions. The GSA algorithm uses the theory of [[Newtonian physics]] and its searcher [[Agent (artificial intelligence)|agents]] are the collection of masses. In GSA, there is an [[isolated system]] of masses. Using the gravitational force, every mass in the system can [[Action at a distance|see the situation]] of other masses. The gravitational force is therefore a way of transferring information between different masses.<ref>{{cite journal |doi=10.1016/j.ins.2009.03.004 |title=GSA: A Gravitational Search Algorithm |journal=Information Sciences |volume=179 |issue=13 |pages=2232 |year=2009 |last1=Rashedi |first1=Esmat |last2=Nezamabadi-Pour |first2=Hossein |last3=Saryazdi |first3=Saeid }}</ref> In GSA, agents are considered as objects and their performance is measured by their masses. All these objects attract each other by a [[gravity]] force, and this force causes movement of all objects towards the objects with heavier masses. Heavier masses correspond to better solutions of the problem. The [[Position (vector)|position]] of the agent corresponds to a solution of the problem, and its mass is determined using a fitness function. By lapse of time, masses are attracted by the heaviest mass, which would ideally present an optimum solution in the search space. The GSA could be considered as a small artificial world of masses obeying the Newtonian laws of gravitation and motion.<ref>{{Cite journal |last1=Rashedi |first1=Esmat |last2=Nezamabadi-pour |first2=Hossein |last3=Saryazdi |first3=Saeid |date=2009-06-13 |title=GSA: A Gravitational Search Algorithm |url=https://www.sciencedirect.com/science/article/pii/S0020025509001200 |journal=Information Sciences |series=Special Section on High Order Fuzzy Sets |language=en |volume=179 |issue=13 |pages=2232–2248 |doi=10.1016/j.ins.2009.03.004 |issn=0020-0255}}</ref> A multi-objective variant of GSA, called MOGSA, was proposed by Hassanzadeh et al. in 2010.<ref>{{cite book |doi=10.1109/CICSyN.2010.32 |chapter=A Multi-objective Gravitational Search Algorithm |title=2010 2nd International Conference on Computational Intelligence, Communication Systems and Networks |pages=7–12 |year=2010 |last1=Hassanzadeh |first1=Hamid Reza |last2=Rouhani |first2=Modjtaba |isbn=978-1-4244-7837-8 |s2cid=649636 }}</ref>

=== 2010s ===

==== Bat algorithm (Yang, 2010) ====
{{Main|Bat algorithm}}

Bat algorithm is a swarm-intelligence-based algorithm, inspired by the [[Animal echolocation|echolocation]] behavior of [[microbat]]s. BA automatically balances exploration (long-range jumps around the global search space to avoid getting stuck around one local maximum) with exploitation (searching in more detail around known good solutions to find local maxima) by controlling loudness and pulse emission rates of simulated bats in the multi-dimensional search space.<ref>{{cite book |doi=10.1007/978-3-642-12538-6_6 |chapter=A New Metaheuristic Bat-Inspired Algorithm |title=Nature Inspired Cooperative Strategies for Optimization (NICSO 2010) |volume=284 |pages=65–74 |series=Studies in Computational Intelligence |year=2010 |last1=Yang |first1=Xin-She |isbn=978-3-642-12537-9 |citeseerx=10.1.1.761.2708 |s2cid=14494281 }}</ref>

==== Spiral optimization (SPO) algorithm (Tamura & Yasuda 2011, 2016-2017) ====
{{Main|Spiral optimization algorithm}}
[[File:spo_movie4.gif|thumb|Spiral optimization algorithm]]

The spiral optimization algorithm, inspired by [[spiral]] phenomena in nature, is a multipoint search algorithm that has no objective function gradient. It uses multiple spiral models that can be described as deterministic dynamical systems. As search points follow logarithmic spiral trajectories towards the common center, defined as the current best point, better solutions can be found, and the common center can be updated.<ref>{{cite journal |doi=10.9746/jcmsi.9.134 |title=Spiral Optimization Algorithm Using Periodic Descent Directions |journal=SICE Journal of Control, Measurement, and System Integration |volume=9 |issue=3 |pages=134–43 |year=2016 |last1=Tamura |first1=Kenichi |last2=Yasuda |first2=Keiichiro |bibcode=2016JCMSI...9..134T |doi-access=free }}</ref>

==== Artificial swarm intelligence (Rosenberg, 2014) ====
Artificial swarm intelligence is a real-time closed-loop system of human users connected over the internet and structured in a framework modeled after natural swarms such that it evokes the group's collective wisdom as a unified emergent intelligence.<ref>{{Cite journal|last=Rosenberg|first=Louis|title=Artificial Swarm Intelligence, a Human-in-the-Loop Approach to A.I. |journal=Proceedings of the AAAI Conference on Artificial Intelligence |date=February 12, 2016 |url=https://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12087/12302 |volume=30 |doi=10.1609/aaai.v30i1.9833 |s2cid=8824332 |doi-access=free}}</ref><ref>{{Cite news|url=http://www.techrepublic.com/article/how-artificial-swarm-intelligence-uses-people-to-make-better-predictions-than-experts/|title=How 'artificial swarm intelligence' uses people to make better predictions than experts|last=Reese|first=Hope|date=Jan 22, 2016}}</ref> In this way, human swarms can answer questions, make predictions, reach decisions, and solve problems by collectively exploring a diverse set of options and converging on preferred solutions in synchrony. Invented by Dr. Louis Rosenberg in 2014, the ASI methodology has been noted for its ability to make accurate collective predictions that outperform the individual members of the swarm.<ref>{{cite book |doi=10.1109/SHBI.2015.7321685 |chapter=Human swarming, a real-time method for parallel distributed intelligence |title=2015 Swarm/Human Blended Intelligence Workshop (SHBI) |pages=1–7 |year=2015 |last1=Rosenberg |first1=Louis B. |isbn=978-1-4673-6522-2 |s2cid=15166767 }}</ref> In 2016, an Artificial Swarm Intelligence group from [[Unanimous A.I.]] was challenged by a reporter to predict the winners of the [[Kentucky Derby]]; it successfully picked the first four horses, in order, beating 540 to 1 odds.<ref>{{Cite web |last=Cuthbertson |first=Anthony |date=10 May 2016 |title=Artificial intelligence turns $20 into $11,000 in Kentucky Derby bet |url=https://www.newsweek.com/artificial-intelligence-turns-20-11000-kentucky-derby-bet-457783 |access-date=23 April 2022 |website=Newsweek |language=en}}</ref><ref>{{Cite news |last=Ohlheiser |first=Abby |date=2 June 2016 |title=What happened when an A.I. hive mind answered Reddit's burning politics questions |newspaper=Washington Post |url=https://www.washingtonpost.com/news/the-intersect/wp/2016/06/02/what-happened-when-an-ai-hive-mind-answered-reddits-burning-politics-questions/ |access-date=23 April 2022}}</ref>

== Self-tuning metaheuristics ==
Self-tuning metaheuristics have emerged as a significant advancement in the field of optimization algorithms in recent years, since fine tuning can be a very long and difficult process.<ref>{{Cite journal |last1=Huang |first1=Changwu |last2=Li |first2=Yuanxiang |last3=Yao |first3=Xin |date=2019 |title=A Survey of Automatic Parameter Tuning Methods for Metaheuristics |journal=IEEE Transactions on Evolutionary Computation |volume=24 |issue=2 |pages=201–216 |doi=10.1109/TEVC.2019.2921598 |issn=1089-778X|doi-access=free }}</ref> These algorithms differentiate themselves by their ability to autonomously adjust their parameters in response to the problem at hand, enhancing efficiency and solution quality. This self-tuning capability is particularly important in complex optimization scenarios where traditional methods may struggle due to rigid parameter settings.

== {{anchor|Criticism}} Criticism of the metaphor methodology ==
While individual metaphor-inspired metaheuristics have produced remarkably effective solutions to specific problems,<ref name="brownlee">Alexander Brownlee and John R. Woodward (2015). [http://theconversation.com/why-we-fell-out-of-love-with-algorithms-inspired-by-nature-42718 "Why we fell out of love with algorithms inspired by nature"]. ''[[The Conversation (website)|The Conversation]]''.</ref> metaphor-inspired metaheuristics in general have attracted criticism among researchers for hiding their lack of effectiveness or novelty behind elaborate metaphors.<ref name="brownlee" /><ref>Jerry Swan, Steven Adriaensen, Mohamed Bishr, Edmund K. Burke, John A. Clark, Patrick De Causmaecker, Juanjo Durillo, Kevin Hammond, Emma Hart, Colin G. Johnson, Zoltan A. Kocsis, Ben Kovitz, Krzysztof Krawiec, Simon Martin, J. J. Merelo, Leandro L. Minku, Ender Özcan, Gisele L. Pappa, Erwin Pesch, Pablo García-Sánchez, Andrea Schaerf, Kevin Sim, Jim E. Smith, Thomas Stützle, Stefan Voß, Stefan Wagner, Xin Yao. [http://www.cs.nott.ac.uk/~exo/docs/publications/research-agenda-metaheuristic.pdf "A Research Agenda for Metaheuristic Standardization"]. "Metaphors often inspire new metaheuristics, but without mathematical rigor, it can be hard to tell if a new metaheuristic is really distinct from a familiar one. For example, mathematically, 'Harmony search' turned out to be a simple variant of '[[Evolution Strategies]]' even though the metaphors that inspired them were quite different. Formally describing state, representation, and operators allows genuine novelty to be distinguished from minor variation."</ref> Kenneth Sörensen noted:<ref>{{cite journal |doi=10.1111/itor.12001 |title=Metaheuristics-the metaphor exposed |journal=International Transactions in Operational Research |volume=22 |pages=3–18 |year=2015 |last1=Sörensen |first1=Kenneth |citeseerx=10.1.1.470.3422 |s2cid=14042315 }}</ref>
<blockquote>
In recent years, the field of [[combinatorial optimization]] has witnessed a true tsunami of "novel" metaheuristic methods, most of them based on a metaphor of some natural or man-made process. The behavior of virtually any species of insects, the flow of water, musicians playing together – it seems that no idea is too far-fetched to serve as inspiration to launch yet another metaheuristic. [I] will argue that this line of research is threatening to lead the area of metaheuristics away from scientific rigor.
</blockquote>
Sörensen and [[Fred W. Glover|Glover]] stated:<ref>{{scholarpedia|title=Metaheuristics|urlname=Metaheuristics|curator=[[Fred W. Glover|Fred Glover]] and Kenneth Sörensen}}</ref>
<blockquote>
A large (and increasing) number of publications focuses on the development of (supposedly) new metaheuristic frameworks based on metaphors. The list of natural or man-made processes that has been used as the basis for a metaheuristic framework now includes such diverse processes as bacterial foraging, [[#River formation dynamics|river formation]], biogeography, musicians playing together, electromagnetism, [[#Gravitational search algorithm|gravity]], [[Imperialist competitive algorithm|colonization by an empire]], mine blasts, league championships, clouds, and so forth. An important subcategory is found in metaheuristics based on animal behavior. [[Ant colony optimization algorithms|Ants]], bees, [[Bat algorithm|bats]], wolves, cats, [[Firefly algorithm|fireflies]], eagles, dolphins, [[Shuffled frog leaping algorithm|frogs]], salmon, vultures, termites, flies, and many others, have all been used to inspire a "novel" metaheuristic. [...] As a general rule, publication of papers on metaphor-based metaheuristics has been limited to second-tier journals and conferences, but some recent exceptions to this rule can be found. Sörensen (2013) states that research in this direction is fundamentally flawed. Most importantly, the author contends that the novelty of the underlying metaphor does not automatically render the resulting framework "novel". On the contrary, there is increasing evidence that very few of the metaphor-based methods are new in any interesting sense.
</blockquote>
In response, [[Springer Science+Business Media|Springer]]'s ''Journal of Heuristics'' has updated their editorial policy to state:<ref>{{Cite web |title=Journal of Heuristic Policies on Heuristic Search Research |url=https://www.springer.com/cda/content/document/cda_downloaddocument/Journal+of+Heuristic+Policies+on+Heuristic+Search.pdf?SGWID=0-0-45-1483502-p35487524 |url-status=dead |archive-url=https://web.archive.org/web/20170709034524/https://www.springer.com/cda/content/document/cda_downloaddocument/Journal+of+Heuristic+Policies+on+Heuristic+Search.pdf?SGWID=0-0-45-1483502-p35487524 |archive-date=9 July 2017 |website=www.springer.com}}</ref>
<blockquote>
Proposing new paradigms is only acceptable if they contain innovative basic ideas, such as those that are embedded in classical frameworks like [[genetic algorithm]]s, [[tabu search]], and [[simulated annealing]]. The Journal of Heuristics avoids the publication of articles that repackage and embed old ideas in methods that are claimed to be based on metaphors of natural or manmade systems and processes. These so-called "novel" methods employ analogies that range from [[Intelligent water drops algorithm|intelligent water drops]], musicians playing jazz, [[Imperialist competitive algorithm|imperialist societies]], [[Shuffled frog leaping algorithm|leapfrogs]], kangaroos, all types of swarms and insects and even mine blast processes (Sörensen, 2013). If a researcher uses a metaphor to stimulate his or her own ideas about a new method, the method must nevertheless be translated into metaphor-free language, so that the strategies employed can be clearly understood, and their novelty is made clearly visible. (See items 2 and 3 below.) Metaphors are cheap and easy to come by. Their use to "window dress" a method is not acceptable."

[...] Implementations should be explained by employing standard optimization terminology, where a solution is called a "solution" and not something else related to some obscure metaphor (e.g., harmony, [[Firefly algorithm|flies]], [[bat algorithm|bats]], [[Imperialist competitive algorithm|countries]], etc.).

[...] The Journal of Heuristics fully endorses Sörensen's view that metaphor-based “novel” methods should not be published if they cannot demonstrate a contribution to their field. Renaming existing concepts does not count as a contribution. Even though these methods are often called “novel”, many present no new ideas, except for the occasional marginal variant of an already existing methodology. These methods should not take the journal space of truly innovative ideas and
research. Since they do not use the standard optimization vocabulary, they are unnecessarily difficult to understand.
</blockquote>

The policy of [[Springer Science+Business Media|Springer]]'s journal [[4OR - A Quarterly Journal of Operations Research]] states:<ref>{{Cite web |title=4OR – incl. Option to publish open access |url=https://www.springer.com/business+%26+management/operations+research/journal/10288 |access-date=23 April 2022 |website=www.springer.com}}</ref>
<blockquote>
The emphasis on scientific rigor and on innovation implies, in particular, that the journal does not publish articles that simply propose disguised variants of known methods without adequate validation (e.g., metaheuristics that are claimed to be "effective" on the sole basis of metaphorical comparisons with natural or artificial systems and processes). New methods must be presented in metaphor-free language by establishing their relationship with classical paradigms. Their properties must be established on the basis of scientifically compelling arguments: mathematical proofs, controlled experiments, objective comparisons, etc.
</blockquote>

The ACM Transactions on Evolutionary Learning Optimization and the [[Evolutionary Computation (journal)|Evolutionary Computation journal]] also include similar statements.<ref>{{Cite web |title=ACM Transactions on Evolutionary Learning and Optimization - Author Guidelines |url=https://dl.acm.org/journal/telo/author-guidelines |access-date=9 April 2024 |website=dl.acm.org/}}</ref><ref>{{Cite web |title=Evolutionary Computation - Submission Guidelines |url=https://direct.mit.edu/evco/pages/submission-guidelines |access-date=9 April 2024 |website=direct.mit.edu/evco/}}</ref>


== See also ==
* [[Conceptual metaphor]]
* [[Scientific community metaphor]]
* [[Table of metaheuristics]]

== Notes ==
{{reflist|2|refs=
<ref name=kennedy95particle>{{cite book |doi=10.1109/ICNN.1995.488968 |chapter=Particle swarm optimization |title=Proceedings of ICNN'95 - International Conference on Neural Networks |volume=4 |pages=1942–8 |year=1995 |last1=Kennedy |first1=J. |last2=Eberhart |first2=R. |isbn=978-0-7803-2768-9 |citeseerx=10.1.1.709.6654 |s2cid=7367791 }}</ref>

<ref name=kennedy97particle>{{cite book |doi=10.1109/ICEC.1997.592326 |chapter=The particle swarm: Social adaptation of knowledge |title=Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97) |pages=303–8 |year=1997 |last1=Kennedy |first1=J. |isbn=978-0-7803-3949-1 |s2cid=61487376 }}</ref>

<ref name=shi98modified>{{cite book |doi=10.1109/ICEC.1998.699146 |chapter=A modified particle swarm optimizer |title=1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360) |pages=69–73 |year=1998 |last1=Shi |first1=Y. |last2=Eberhart |first2=R. |isbn=978-0-7803-4869-1 |s2cid=16708577 }}</ref>

<ref name=kennedy01swarm>
{{cite book
|title=Swarm Intelligence
|last1=Kennedy
|first1=J.
|last2=Eberhart
|first2=R.C.
|year=2001
|publisher=Morgan Kaufmann
|isbn=978-1-55860-595-4
}}
</ref>

<ref name=poli07analysis>{{cite journal
|last=Poli
|first=R.
|url=http://cswww.essex.ac.uk/technical-reports/2007/tr-csm469.pdf
|title=An analysis of publications on particle swarm optimisation applications
|journal=Technical Report CSM-469
|publisher=Department of Computer Science, University of Essex, UK
|year=2007
|access-date=2016-08-31
|archive-url=https://web.archive.org/web/20110716231935/http://cswww.essex.ac.uk/technical-reports/2007/tr-csm469.pdf
|archive-date=2011-07-16
|url-status=dead
}}</ref>

<ref name=poli08analysis>{{cite journal |doi=10.1155/2008/685175 |title=Analysis of the Publications on the Applications of Particle Swarm Optimisation |journal=Journal of Artificial Evolution and Applications |volume=2008 |pages=1–10 |year=2008 |last1=Poli |first1=Riccardo |doi-access=free }}</ref>

<ref name=bonyadi16survey>{{cite journal |doi=10.1162/EVCO_r_00180 |pmid=26953883 |title=Particle Swarm Optimization for Single Objective Continuous Space Problems: A Review |journal=Evolutionary Computation |volume=25 |issue=1 |pages=1–54 |year=2017 |last1=Bonyadi |first1=Mohammad Reza |last2=Michalewicz |first2=Zbigniew |s2cid=8783143 }}</ref>
}}

== References ==

*{{cite book|first1=Kenneth|last1=Sörensen|first2=Marc|last2=Sevaux|first3=Fred|last3=Glover|editor-last1=Martí|editor-first1=Rafael|editor-last2=Panos|editor-first2=Pardalos|editor-last3=Resende|editor-first3=Mauricio|editor3-link=Mauricio Resende|isbn=978-3-319-07123-7|title=Handbook of Heuristics|chapter=A History of Metaheuristics|publisher=Springer|chapter-url=http://leeds-faculty.colorado.edu/glover/468%20-%20A%20History%20of%20Metaheuristics%20w%20Sorensen%20%26%20Sevaux.pdf|date=2017-01-16}}
*{{cite journal |doi=10.1111/itor.12001 |title=Metaheuristics-the metaphor exposed |journal=International Transactions in Operational Research |volume=22 |pages=3–18 |year=2015 |last1=Sörensen |first1=Kenneth |citeseerx=10.1.1.470.3422 |s2cid=14042315 }}
*{{cite book |doi=10.1145/2598394.2609841 |chapter=Metaheuristics in nature-inspired algorithms |title=Proceedings of the 2014 conference companion on Genetic and evolutionary computation companion - GECCO Comp '14 |pages=1419–22 |year=2014 |last1=Lones |first1=Michael A. |isbn=9781450328814 |citeseerx=10.1.1.699.1825 |s2cid=14997975 }}
*{{Cite journal |title=A Brief Review of Nature-Inspired Algorithms for Optimization |journal=Elektrotehniški Vestnik |last1=Fister |first1=Iztok |last2=Yang |first2=Xin-She |last3=Fister |first3=Iztok |last4=Brest |first4=Janez |last5=Fister |first5=Dušan |year=2013 |arxiv=1307.4186 }}

== External links ==
*[https://github.com/fcampelo/EC-Bestiary Evolutionary Computation Bestiary]{{snd}} a tongue-in-cheek account of all the weird metaphor-based metaheuristics out there in the wide world of academic publishing
*[https://thesciencematrix.com/Apps/metaheuristics/ The Science Matrix's List of Metaheuristic]{{Dead link|date=September 2021}}{{snd}} a complete list of metaheuristic algorithms filterable by name, author or year, providing a link to main publication of each algorithm

[[Category:Metaheuristics|*]]