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In [[computer science]], '''imperialist competitive algorithms''' are a type of computational method used to solve [[optimization problem]]s of different types.<ref name=ica_en_2007_cnf_atashpaz_ica_ica>{{cite conference
|last1= Atashpaz-Gargari
|first1= E.
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|first2= C
|title= Imperialist Competitive Algorithm: An algorithm for optimization inspired by imperialistic competition
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|year= 2007
|volume= 7
|pages= 4661–4666
|url=http://www.academia.edu/download/3930081/imperialistic_competitive_algorithm__ica__ieee_cec_2007.pdf
}}{{dead link|date=July 2022|bot=medic}}{{cbignore|bot=medic}}</ref><ref name=ICA_2014_Survey>{{cite journal
|last1= Hosseini
|first1=S.
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|volume=24
|pages=1078–1094
|doi=10.1016/j.asoc.2014.08.024
}}</ref> Like most of the methods in the area of [[evolutionary computation]], ICA 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 are based on the [[biological evolution]] of species.
== Metaphor ==
[[File:Imperialist-competitive-algorithm-flowchart.jpg|thumb|420px|Figure 1: Flowchart of Imperialist Competitive Algorithm (ICA)]]
Figure 1 shows the flowchart of the Imperialist Competitive Algorithm. This algorithm starts by generating a set of candidate random 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]] (PSO) and it is an array of values of a candidate solution of the 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 />
|last1= Nazari-Shirkouhi
|first1= S.
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== Algorithm ==
The above steps can be summarized as the below [[pseudocode]].<ref name=ICA_2014_Survey /><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
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,
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