Generalized entropy index: Difference between revisions

Revision as of 21:21, 2 October 2013

In computer science, Imperialist Competitive Algorithm (ICA)^[1] is a computational method that is used to solve optimization problems 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.

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.

Algorithm

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 Chromosomes in GAs and Particles in Particle Swarm Optimization (PSO) and it is an array of values of a candidate solution of optimization problem. The 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.^[1]

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.^[2]

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.^[1]

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

Pseudocode

The above steps can be summarized as the below pseudocode.^[2]

0) Define objective function:  $f(\mathbf {x} ),\quad \mathbf {x} =(x_{1},x_{2},\dots ,x_{d});\,$ 
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

Variants

Like for 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.^[3] and also a version of this algorithm for handling constrained optimization problems is proposed by Zhang, etal.^[4]

Applications

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.

Designing controller for industrial systems^[5]^[6]^[6]^[7]^[8]^[9]
Designing Intelligent Recommender Systems^[10]
Solving optimization problems in communication systems.^[11]^[12]^[13]
Solving scheduling and production management problems^[2]^[14]^[15]^[16]^[17]^[18]^[19]
Training and analysis of Artificial Neural Networks^[20]^[21]
Nash Equilibrium Point Achievement^[8]
Design and thermodynamic optimization of plate-fin heat exchangers^[22]
and so on^[23]^[24]^[25]^[26]

References

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Generalized entropy index: Difference between revisions

Revision as of 21:21, 2 October 2013

Contents

Algorithm

Pseudocode

Variants

Applications

References

Navigation menu

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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.
+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.
+== Algorithm ==
+[[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 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/>
+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/>
+''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/>
+Algorithm continues with the mentioned steps (Assimilation, Revolution, Competition) until a stop condition is satisfied.
+== Pseudocode ==
+The above steps can be summarized as the below [[pseudocode]].<ref name=ica_en_2010_jnl_nazari_integrated_product_mix_outsourcing/>
+) Define objective function: <math>f(\mathbf{x}), \quad \mathbf{x}=(x_1,x_2,\dots,x_d); \, </math>
+) Initialization of the algorithm. Generate some random solution in the search space and create initial empires.
+) Assimilation: Colonies move towards imperialist states in different in directions.
+) Revolution: Random changes occur in the characteristics of some countries.
+) 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.
+) Imperialistic competition: All imperialists compete to take possession of colonies of each other.
+) Eliminate the powerless empires. Weak empires lose their power gradually and they will finally be eliminated.
+) If the stop condition is satisfied, stop, if not go to 2.
+) End
+== Variants ==
+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/>
+== Applications ==
+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.
+* 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/>
+* Designing Intelligent Recommender Systems<ref name=ica_en_2008_cnf_sepehrirad_recommender_systems/>
+* 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/>
+* 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/>
+* 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/>
+* Nash Equilibrium Point Achievement<ref name=ica_en_2008_en_bchtr_rajabioun_nash_equilibrium_point_achievement/>
+* Design and thermodynamic optimization of plate-fin heat exchangers<ref name=ica_moslem_2011/>
+* 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/>
+== References ==
+{{Reflist|refs=
+<ref name=ica_moslem_2011>
+{{cite conference
+|last1= Yousefi
+|first1= Moslem
+|last2= Mohammadi
+|first2= Hossein
+|title= Second law based optimization of a plate fin heat exchanger using Imperialist Competitive Algorithm
+|booktitle= International Journal of the Physical Sciences
+|year= 2011
+|volume= 6
+|pages= 4749–4759
+}}
+</ref>
+<ref name=ica_en_2007_cnf_atashpaz_ica_ica>
+{{cite conference
+|last1= Atashpaz-Gargari
+|first1= E.
+|last2= Lucas
+|first2= C
+|title= Imperialist Competitive Algorithm: An algorithm for optimization inspired by imperialistic competition
+|booktitle= IEEE Congress on Evolutionary Computation
+|year= 2007
+|volume= 7
+|pages= 4661–4666
+}}
+</ref>
+<ref name= ica_en_2009_jnl_duan_template_matching_chaotic_ica>
+{{cite journal
+|last1= Duan
+|first1=H.
+|last2=Xu
+|first2=C.
+|last3=Liu
+|first3=S.
+|last4=Shao
+|first4=S.
+|title=Template matching using chaotic imperialist competitive algorithm
+|journal=Pattern Recognition Letters
+|year=2009
+|volume=39
+|issue=6
+|pages=1362–1381
+}}
+</ref>
+<ref name=ica_en_2009_cnf_zhang_improved_ica_constrained_optimization>
+{{cite conference
+|last1=Zhang
+|first1=Yang
+|last2=Wang
+|first2=Yong
+|last3=Peng
+|first3=Cheng
+|title=Improved Imperialist Competitive Algorithm for Constrained Optimization
+|booktitle=Computer Science-Technology and Applications, IFCSTA
+|year=2009
+}}
+</ref>
+<ref name=ica_en_2008_en_conf_rajabioun_decentralized_pid_controller_design_mimo_evaporator>
+{{cite conference
+|last1=Rajabioun
+|first1=R.
+|last2=Hashemzadeh
+|first2=F.
+|last3=Atashpaz-Gargari
+|first3=E.
+|last4=Mesgari
+|first4=B.
+|last5=Rajaei Salmasi
+|first5=F.
+|title=Identification of a MIMO evaporator and its decentralized PID controller tuning using Colonial Competitive Algorithm
+|booktitle=In the proceeding of IFAC World Congress, Seoul, Korea
+|year=2008
+|pages=9952–9957
+}}
+</ref>
+<ref name=ica_en_2008_jnl_atashpaz_ijicc_pid_mimo_distillation_column_process>
+{{cite journal
+|last1= Atashpaz-Gargari
+|first1= E.
+|last2= Hashemzadeh
+|first2= F.
+|last3= Rajabioun
+|first3= R.
+|last4= Lucas
+|first4= C.
+|title= Colonial competitive algorithm: A novel approach for PID controller design in MIMO distillation column process
+|journal= International Journal of Intelligent Computing and Cybernetics
+|year= 2008
+|volume= 1
+|issue= 3
+|pages= 337–355
+}}
+</ref>
+<ref name=ica_en_2008_jnl_atashpaz_ijicc_pid_mimo_distillation_column_process>
+{{cite journal
+|last1= Gargari
+|first1= E.
+|last2= Hashemzadeh
+|first2= F.
+|last3= Rajabioun
+|first3= R.
+|last4= Lucas
+|first4= C.
+|title= Colonial competitive algorithm: A novel approach for PID controller design in MIMO distillation column process
+|journal= International Journal of Intelligent Computing and Cybernetics
+|year= 2008
+|volume=  1
+|pages= 337–355
+}}
+</ref>
+<ref name=ica_en_2007_cnf_atashpaz_optimal_pid_controller_isfs2007>
+{{cite conference
+|last1= Atashpaz-Gargari
+|first1= E.
+|last2= Lucas
+|first2= C.
+|title= Designing an optimal PID controller using Colonial Competitive Algorithm
+|booktitle= Proceeding of First Iranian Joint Congress on Intelligent and Fuzzy Systems
+|year= 2007
+}}
+</ref>
+<ref name=ica_en_2008_en_bchtr_rajabioun_nash_equilibrium_point_achievement>
+{{cite conference
+|last1= Rajabioun
+|first1= R.
+|last2= Atashpaz-Gargari
+|first2= E.
+|last3= Lucas
+|first3= C.
+|title= Colonial competitive algorithm as a tool for Nash equilibrium point achievement
+|booktitle= Computational Science and Its Applications–ICCSA
+|year= 2008
+|pages= 680–695
+}}
+</ref>
+<ref name=ica_en_2009_jnl_atashpaz_decentralized_pid_controller_optimal_shrinkage_gershgorin_bands>
+{{cite journal
+|last1= Atashpaz-Gargari
+|first1= E.
+|last2= Rajabioun
+|first2= R.
+|last3= Hashemzadeh
+|first3= F.
+|last4= R. Salmasi
+|first4= F.
+|title= A Decentralized PID controller based on Optimal Shrinkage of Gershgorin Bands and PID tuning Using Colonial Competitive Algorithm
+|journal= International Journal of Innovative Computing, Information and Control
+|year= 2009
+|volume=  5
+|issue=  10(A)
+}}
+</ref>
+<ref name=ica_en_2008_cnf_sepehrirad_recommender_systems>
+{{cite conference
+|last1= Sepehri Rad
+|first1= H.
+|last2= Lucas
+|first2= C.
+|title= Application of Imperialistic Competition Algorithm in recommender systems
+|booktitle= In 13th Int'l CSI Computer Conference (CSICC'08)
+|year= 2008
+}}
+</ref>
+<ref name=ica_en_2009_jnl_khabbazi_minimum_bit_error_rate_beamforming>
+{{cite journal
+|last1= Khabbazi
+|first1= Arash
+|last2= Atashpaz-Gargari
+|first2= Esmaeil
+|last3= Lucas
+|first3= Caro
+|title= Imperialist competitive algorithm for minimum bit error rate beamforming
+|journal= International Journal of Bio-Inspired Computation
+|year= 2009
+|volume= 1
+|issue= 1-2
+|pages= 125–133
+}}
+</ref>
+<ref name=ica_2010_en_jnl_Alikhani_Evaluation_of_Image_Segmentation_Methods>
+{{cite journal
+|last1= Alikhani koupaei
+|first1= Javad
+|last2= Abdechiri
+|first2= Marjan
+|title= An Optimization Problem for Evaluation of Image Segmentation Methods
+|journal= International Journal of Computer and Network Security
+|year= 2010
+|volume= 2
+|issue= 6
+}}
+</ref>
+<ref name=ica_2010_en_cnf_Sayadnavard_Wireless_sensor_network_localization>
+{{cite conference
+|last1= H. Sayadnavard
+|first1= Monireh
+|last2= T.  Haghighat
+|first2= Abolfazl
+|last3= Abdechiri
+|first3= Marjan
+|title= Wireless sensor network localization using Imperialist Competitive Algorithm
+|booktitle= 3rd IEEE International Conference on Computer Science and Information Technology
+|year= 2010
+}}
+</ref>
+<ref name=ica_en_2009_jnl_jolai_pareto_simulated_annealing_offline_scheduling_problem_with_rejection >
+{{cite journal
+|last1= Jolai
+|first1= F.
+|last2= Sangari
+|first2= M.
+|last3= Babaie
+|first3= M.
+|title= Pareto simulated annealing and colonial competitive algorithm to solve an offline scheduling problem with rejection
+|journal= Journal of Engineering Manufacture
+|year= 2010
+|volume= 224
+|issue= 7
+|pages= 1119–1131
+}}
+</ref>
+<ref name=ica_en_2010_jnl_shokrollahpour_bi_criteria_flowshop>
+{{cite journal
+|last1= Shokrollahpour
+|first1= E.
+|last2= Zandieh
+|first2= M.
+|last3= Dorri
+|first3= Behrouz
+|title= A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem
+|journal= International Journal of Production Research
+|year= 2010
+}}
+</ref>
+<ref name=ica_en_2010_jnl_nazari_integrated_product_mix_outsourcing>
+{{cite journal
+|last1= Nazari-Shirkouhi
+|first1= S.
+|last2= Eivazy
+|first2= H.
+|last3= Ghodsi
+|first3= R.
+|last4= Rezaie
+|first4= K.
+|last5= Atashpaz-Gargari
+|first5= E.
+|title= Solving the Integrated Product Mix-Outsourcing Problem by a Novel Meta-Heuristic Algorithm: Imperialist Competitive Algorithm
+|journal= Expert Systems with Applications
+|year= 2010
+|volume= 37
+|issue= 12
+|pages= 7615–7626
+}}
+</ref>
+<ref name=ica_2010_en_jnl_Forouharfard_schedule_cross_docking_systems>
+{{cite journal
+|last1= Forouharfard
+|first1= S.
+|last2= Zandieh
+|first2= M.
+|title= An imperialist competitive algorithm to schedule of receiving and shipping trucks in cross-docking systems
+|journal= International Journal of Advanced Manufacturing Technology
+|year= 2010
+}}
+</ref>
+<ref name=ica_2010_en_jnl_Karimi_scheduling_flexible_flow_shops_ica_electromagnetic>
+{{cite journal
+|last1= Karimi
+|first1= N.
+|last2= Zandieh
+|first2= M.
+|title= Group scheduling in flexible flow shops: A hybridised approach of imperialist competitive algorithm and electromagnetic-like mechanism
+|journal= International Journal of Production Research
+|year= 2010
+|volume=
+|issue=
+|pages=
+}}
+</ref>
+<ref name=ica_2010_en_jnl_Bagher_Balancing_of_stochastic_U_Type_assembly_lines>
+{{cite journal
+|last1= Bagher
+|first1= M.
+|last2= Zandieh
+|first2= M.
+|last3= Farsijani
+|first3= H.
+|title= Balancing of stochastic U-type assembly lines: an imperialist competitive algorithm
+|journal= International Journal of Advanced Manufacturing Technology
+|year= 2010
+|volume=
+|issue=
+|pages=
+}}
+</ref>
+<ref name=ica_2010_en_jnl_Sarayloo_ica_Dynamic_Cell_Formation>
+{{cite journal
+|last1= Sarayloo
+|first1= Fatemeh
+|last2= Tavakkoli-Moghaddam
+|first2= Reza
+|title= Imperialistic Competitive Algorithm for Solving a Dynamic Cell Formation Problem with Production Planning
+|journal= Advanced Intelligent Computing Theories and Applications, Lecture Notes in Computer Science
+|year= 2010
+|volume= 6215
+|issue=
+|pages= 266–276
+}}
+</ref>
+<ref name=ica_en_2008_jnl_oskouyi_material_properties_characterization_sharp_indentation_test>
+{{cite journal
+|last1= Biabangard-Oskouyi
+|first1= A.
+|last2= Atashpaz-Gargari
+|first2= E.
+|last3= Soltani
+|first3= N.
+|last4= Lucas
+|first4= C.
+|title= Application of Imperialist Competitive Algorithm for Material Properties Characterization from Sharp Indentation Test
+|journal= Int J Eng Simul
+|year= 2009
+|volume= 10
+|issue= 1
+|pages=
+}}
+</ref>
+<ref name=ica_en_2009_cnf_mahmoudi_ann_weights_optimization>
+{{cite conference
+|last1= T.
+|first1= Maryam
+|last2= F.
+|first2= Nafiseh
+|last3= L.
+|first3= Caro
+|last4= T.
+|first4= Fattaneh
+|title= Artificial Neural Network Weights Optimization based on Imperialist Competitive Algorithm
+|booktitle= Seventh International Conference on Computer Science and Information Technologies
+|year= 2009
+}}
+</ref>
+<ref name=ica_en_2008_en_bchtr_rajabioun_nash_equilibrium_point_achievement>
+{{cite journal
+|last1= Rajabioun
+|first1= R.
+|last2= Atashpaz-Gargari
+|first2= E.
+|last3= Lucas
+|first3= C.
+|title= Colonial Competitive Algorithm as a Tool for Nash Equilibrium Point Achievement
+|journal= Lecture Notes in Computer Science (LNCS)
+|year= 2008
+|pages= 680–695
+}}
+</ref>
+<ref name=ica_en_2010_jnl_lucas_linear_induction_motor>
+{{cite journal
+|last1= Lucas
+|first1= C.
+|last2= Nasiri-Gheidari
+|first2= Z.
+|last3= Tootoonchian
+|first3= F.
+|title= Application of an imperialist competitive algorithm to the design of a linear induction motor
+|journal= Energy Conversion and Management
+|year= 2010
+|volume= 51
+|issue= 7
+|pages= 1407–1411
+}}
+</ref>
+<ref name=ica_2010_en_jnl_omid_phev>
+{{cite journal
+|last1= Movahhedi
+|first1= Omid
+|last2= R. Salmasi
+|first2= Farzad
+|title= Optimal Design of Propulsion System with Adaptive Fuzzy Controller for a PHEV Based on Non-dominated Sorting Genetic and Colonial Competitive Algorithms
+|journal= International Review of Automatic Control
+|year= 2009
+}}
+</ref>
+<ref name=ica_2010_en_jnl_niknam_k_means_clustering>
+{{cite journal
+|last1= Niknam
+|first1= Taher
+|last2= Taherian Fard
+|first2= Elahe
+|last3= Pourjafarian
+|first3= Narges
+|last4= Rousta
+|first4= Alireza
+|title= An efficient hybrid algorithm based on modified imperialist competitive algorithm and K-means for data clustering
+|journal= Engineering Applications of Artificial Intelligence
+|year= 2010
+}}
+</ref>
+<ref name=ica_2010_en_jnl_mozafari_thin_interphase>
+{{cite journal
+|last1= Mozafari
+|first1= Hamid
+|last2= Abdi
+|first2= Behzad
+|last3= Ayob
+|first3= Amran
+|title= Optimization of Transmission Conditions for Thin Interphase Layer Based on Imperialist Competitive Algorithm
+|journal= International Journal on Computer Science and Engineering
+|year= 2010
+|volume= 2
+|issue= 7
+|pages= 2486–2490
+}}
+</ref>
+}}
+[[Category:Optimization algorithms and methods]]

Generalized entropy index: Difference between revisions

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