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| In [[computer science]], '''Imperialist Competitive Algorithm (ICA)'''<ref name=ica_en_2007_cnf_atashpaz_ica_ica/> is a computational method that is used to solve [[optimization problem]]s of different types. Like most of the methods in the area of [[evolutionary computation]], ICA does not need the gradient of the function in its optimization process.
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| 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 [[social evolution]], while GAs are based on the [[biological evolution]] of species.
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| == Algorithm ==
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| [[File:Imperialist-competitive-algorithm-flowchart.jpg|thumb|420px|Figure 1: Flowchart of Imperialist Competitive Algorithm (ICA)]]
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| 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 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/>
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| 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 has the 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/>
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| ''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/>
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| Algorithm continues with the mentioned steps (Assimilation, Revolution, Competition) until a stop condition is satisfied.
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| == Pseudocode ==
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| The above steps can be summarized as the below [[pseudocode]].<ref name=ica_en_2010_jnl_nazari_integrated_product_mix_outsourcing/>
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| 0) Define objective function: <math>f(\mathbf{x}), \quad \mathbf{x}=(x_1,x_2,\dots,x_d); \, </math>
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| 1) Initialization of the algorithm. Generate some random solution in the search space and create initial empires.
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| 2) Assimilation: Colonies move towards imperialist states in different in directions.
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| 3) Revolution: Random changes occur in the characteristics of some countries.
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| 4) Position exchange between a colony and Imperialist. A colony with a better position than the imperialist,
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| has the chance to take the control of empire by replacing the existing imperialist.
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| 5) Imperialistic competition: All imperialists compete to take possession of colonies of each other.
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| 6) Eliminate the powerless empires. Weak empires lose their power gradually and they will finally be eliminated.
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| 7) If the stop condition is satisfied, stop, if not go to 2.
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| 8) End | |
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| == Variants ==
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| Like for [[Particle Swarm Optimization|PSO]], the first version of ICA was proposed for solving continuous optimization problems. Then in other works different variants of ICA were proposed for solving both discrete and continuous problems. For example Chaotic ICA is proposed by Duan, etal.<ref name=ica_en_2009_jnl_duan_template_matching_chaotic_ica/> and also a version of this algorithm for handling constrained optimization problems is proposed by Zhang, etal.<ref name=ica_en_2009_cnf_zhang_improved_ica_constrained_optimization/>
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| == Applications ==
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| ICA is used to solve different optimization problems in various areas of engineering and science. The following are some of the applications of this algorithm.
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| * Designing controller for industrial systems<ref name=ica_en_2008_en_conf_rajabioun_decentralized_pid_controller_design_mimo_evaporator/><ref name=ica_en_2008_jnl_atashpaz_ijicc_pid_mimo_distillation_column_process/><ref name=ica_en_2008_jnl_atashpaz_ijicc_pid_mimo_distillation_column_process/><ref name=ica_en_2007_cnf_atashpaz_optimal_pid_controller_isfs2007/><ref name=ica_en_2008_en_bchtr_rajabioun_nash_equilibrium_point_achievement/><ref name=ica_en_2009_jnl_atashpaz_decentralized_pid_controller_optimal_shrinkage_gershgorin_bands/>
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| * Designing Intelligent Recommender Systems<ref name=ica_en_2008_cnf_sepehrirad_recommender_systems/>
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| * Solving optimization problems in communication systems.<ref name=ica_en_2009_jnl_khabbazi_minimum_bit_error_rate_beamforming/><ref name=ica_2010_en_jnl_Alikhani_Evaluation_of_Image_Segmentation_Methods/><ref name=ica_2010_en_cnf_Sayadnavard_Wireless_sensor_network_localization/>
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| * Solving scheduling and production management problems<ref name=ica_en_2010_jnl_nazari_integrated_product_mix_outsourcing/><ref name=ica_en_2009_jnl_jolai_pareto_simulated_annealing_offline_scheduling_problem_with_rejection/><ref name=ica_en_2010_jnl_shokrollahpour_bi_criteria_flowshop/><ref name=ica_2010_en_jnl_Forouharfard_schedule_cross_docking_systems/><ref name=ica_2010_en_jnl_Karimi_scheduling_flexible_flow_shops_ica_electromagnetic/><ref name=ica_2010_en_jnl_Bagher_Balancing_of_stochastic_U_Type_assembly_lines/><ref name=ica_2010_en_jnl_Sarayloo_ica_Dynamic_Cell_Formation/>
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| * Training and analysis of Artificial Neural Networks<ref name=ica_en_2008_jnl_oskouyi_material_properties_characterization_sharp_indentation_test/><ref name=ica_en_2009_cnf_mahmoudi_ann_weights_optimization/>
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| * Nash Equilibrium Point Achievement<ref name=ica_en_2008_en_bchtr_rajabioun_nash_equilibrium_point_achievement/>
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| * Design and thermodynamic optimization of plate-fin heat exchangers<ref name=ica_moslem_2011/>
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| * and so on<ref name=ica_en_2010_jnl_lucas_linear_induction_motor/><ref name=ica_2010_en_jnl_omid_phev/><ref name=ica_2010_en_jnl_niknam_k_means_clustering/><ref name=ica_2010_en_jnl_mozafari_thin_interphase/>
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| == References ==
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| |title= Second law based optimization of a plate fin heat exchanger using Imperialist Competitive Algorithm
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| |title= Wireless sensor network localization using Imperialist Competitive Algorithm
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| |booktitle= 3rd IEEE International Conference on Computer Science and Information Technology
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| </ref>
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| <ref name=ica_en_2009_jnl_jolai_pareto_simulated_annealing_offline_scheduling_problem_with_rejection >
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| </ref>
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| |title= Solving the Integrated Product Mix-Outsourcing Problem by a Novel Meta-Heuristic Algorithm: Imperialist Competitive Algorithm
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| |year= 2010
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| |volume= 37
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| |issue= 12
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| |pages= 7615–7626
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| }}
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| </ref>
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| <ref name=ica_2010_en_jnl_Forouharfard_schedule_cross_docking_systems>
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| {{cite journal
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| |last2= Zandieh
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| |title= An imperialist competitive algorithm to schedule of receiving and shipping trucks in cross-docking systems
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| |journal= International Journal of Advanced Manufacturing Technology
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| |year= 2010
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| }}
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| </ref>
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| <ref name=ica_2010_en_jnl_Karimi_scheduling_flexible_flow_shops_ica_electromagnetic>
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| {{cite journal
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| |first1= N.
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| |last2= Zandieh
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| |first2= M.
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| |title= Group scheduling in flexible flow shops: A hybridised approach of imperialist competitive algorithm and electromagnetic-like mechanism
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| |journal= International Journal of Production Research
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| |year= 2010
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| |volume=
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| |issue=
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| |pages=
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| }}
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| </ref>
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| <ref name=ica_2010_en_jnl_Bagher_Balancing_of_stochastic_U_Type_assembly_lines>
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| {{cite journal
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| |last1= Bagher
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| |first1= M.
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| |last2= Zandieh
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| |first2= M.
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| |last3= Farsijani
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| |first3= H.
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| |title= Balancing of stochastic U-type assembly lines: an imperialist competitive algorithm
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| | |
| [[Category:Optimization algorithms and methods]]
| |
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