Skip to main content
SpringerLink
Log in

City councils evolution: a socio-inspired metaheuristic optimization algorithm

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

The supreme council of a city is usually formed by the evolution of councils from the smallest neighborhoods to the largest ones, regions, and finally the whole city. Council members of a region try to improve their performance to be selected as the boss of the council in the future election, and also a member of the larger region council. This fact motivates us to propose a socio-inspired metaheuristic optimization algorithm [named as city councils evolution (CCE)] inspired by the evolution of city councils. To analyze the effectiveness of CCE, it is applied to solve 20 general test functions and 29 benchmark functions from CEC 2017. Results of CCE are compared with the effectiveness of nine popular and new optimization algorithms belonging to different classes: SHADE and LSHADE-cnEpSin as optimization algorithms with high performance and winners of IEEE CEC competitions (2013 and 2017), and EO, BWO, PO, BMO, CHOA, AO, and WHO as newly developed algorithms (2020 and 2021). According to the average rank of Friedman test, for all 49 test functions, CCE outperforms EO, BWO, PO, BMO, CHOA, AO, and WHO by 65%, 95%, 64%, 68%, 80%, 74%, and 71%, respectively, whereas it is outperformed by SHADE and LSHADE-cnEpSin by 49% and 65%, respectively. Finally, the obtained results of solving real-world constrained optimization problems by the proposed algorithm show that it has better performance compared to some good algorithms in the literature. The source code of the CCE algorithm is publicly available at https://github.com/EinPira/City-Councils-Evolution-Algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Abbreviations

CCE:

City councils evolution

SHADE:

Success-history based adaptive DE

LSHADE-cnEpSin:

Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood

EO:

Equilibrium optimizer

BWO:

Black widow optimization algorithm

PO:

Political optimizer

BMO:

Barnacles mating optimizer

CHOA:

Chimp optimization algorithm

AO:

Aquila optimizer

WHO:

Wild horse optimizer

RMSE:

Root-mean-square error

ILS:

Iterated local search

SAA:

Simulated annealing algorithm

VSA:

Vortex search algorithm

TS:

Tabu search

GA:

Genetic algorithm

PSO:

Particle swarm optimization

ACO:

Ant colony optimization

MSSA:

Multi-objective salp swarm algorithm

MOEPO:

Multi-objective emperor penguin optimizer

MOGSABAT:

Multi-objective gravitational search algorithm and BAT algorithm

GP:

Genetic programming

DE:

Differential evolution

MA:

Memetic algorithm

BHA:

Black hole algorithm

GBO:

Gradient-based optimizer

TLBO:

Teaching–learning-based optimization

POA:

Parliamentary optimization algorithm

GPO:

Greedy politics optimization

ECO:

Election campaign optimization algorithm

TEO:

Thermal exchange optimization

WEO:

Water evaporation optimization

LSO:

Lightning search algorithm

OIO:

Optics inspired optimization

ECO:

Election campaign optimization algorithm

CS:

Cuckoo search

DE:

Dolphin echolocation

WOA:

Whale optimization algorithm

GWO:

Grey wolf optimizer

SSA:

Salp swarm algorithm

BA:

Bat algorithm

MBO:

Migrating birds optimization

GSO:

Group search optimizer

MFPA:

Modified flower pollination algorithm

HOA:

Horse herd optimization algorithm

GSA:

Gravitational search algorithm

BBC:

Big-bang crunch

GIO:

Gravitational interaction optimization

ANOVA:

One way analysis of variance

LGSI:

Ludo game-based swarm intelligence

MFO:

Moth flame optimization

GOA:

Grass-hopper optimization algorithm

SCA:

Sine cosine algorithm

GWO:

Gray wolf optimization

PRO:

Poor and rich optimization

SGO:

Social group optimization

PIC:

A performance improvement criterion

SN:

Smallest neighborhood

CT:

Councils tree

D:

A dimension of a given test function

N :

The population size

C :

An array with size N to implement the councils tree

h :

The height of the councils tree

crN :

The number of performance improvement criteria

max :

A function that returns the input with the highest fitness

α :

A random value and coefficients of two current solutions in the applied formula in the improve function

fit :

A fitness of an individual

d :

Number of council members

References

  • Abdel-Basset M, Abdel-Fatah L, Sangaiah AK (2018) Metaheuristic algorithms: a comprehensive review. Computational intelligence for multimedia big data on the cloud with engineering applications. Elsevier, Amsterdam, pp 185–231

    Google Scholar 

  • Abdel-Basset M, Mohamed R, Saber S, Askar SS, Abouhawwash M (2021) Modified flower pollination algorithm for global optimization. Mathematics 9(14):1661

    Google Scholar 

  • Abualigah L (2021) Group search optimizer: a nature-inspired meta-heuristic optimization algorithm with its results, variants, and applications. Neural Comput Appl 33(7):2949–2972

    Google Scholar 

  • Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-qaness MA, Gandomi AH (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250

    Google Scholar 

  • Ahmadianfar I, Bozorg-Haddad O, Chu X (2020) Gradient-based optimizer: a new metaheuristic optimization algorithm. Inf Sci 540:131–159

    MathSciNet  MATH  Google Scholar 

  • AlSattar HA, Zaidan AA, Zaidan BB, Bakar MA, Mohammed RT, Albahri OS, Alsalem MA, Albahri AS (2020) MOGSABAT: a metaheuristic hybrid algorithm for solving multi-objective optimisation problems. Neural Comput Appl 32(8):3101–3115

    Google Scholar 

  • Aragón VS, Esquivel SC, Coello CAC (2010) A modified version of a T-Cell algorithm for constrained optimization problems. Int J Numer Methods Eng 84(3):351–378

    MATH  Google Scholar 

  • Askari Q, Younas I, Saeed M (2020) Political optimizer: a novel socio-inspired meta-heuristic for global optimization. Knowl-Based Syst 195:105709

    Google Scholar 

  • Awad NH, Ali MZ, Suganthan PN (2017) Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. IEEE Congr Evol Comput (CEC) 2017:372–379. https://doi.org/10.1109/CEC.2017.7969336

    Article  Google Scholar 

  • Borji A (2007) A new global optimization algorithm inspired by parliamentary political competitions. In: Mexican international conference on artificial intelligence, pp 61–71

  • Cheng M-Y, Lien L-C (2012) Hybrid artificial intelligence-based PBA for benchmark functions and facility layout design optimization. J Comput Civ Eng 26(5):612–624

    Google Scholar 

  • Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203

    Google Scholar 

  • Coello Coello CA, Becerra RL (2004) Efficient evolutionary optimization through the use of a cultural algorithm. Eng Optim 36(2):219–236

    Google Scholar 

  • Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms. MIT Press, Cambridge

    MATH  Google Scholar 

  • Cui Z, Sun B, Wang G, Xue Y, Chen J (2017) A novel oriented cuckoo search algorithm to improve DV-Hop performance for cyber–physical systems. J Parallel Distrib Comput 103:42–52

    Google Scholar 

  • Dengiz B, Altiparmak F, Belgin O (2010) Design of reliable communication networks: a hybrid ant colony optimization algorithm. IIE Trans 42(4):273–287

    Google Scholar 

  • Doğan B, Ölmez T (2015) A new metaheuristic for numerical function optimization: vortex search algorithm. Inf Sci 293:125–145

    Google Scholar 

  • Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39

    Google Scholar 

  • dos Santos Coelho L (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37(2):1676–1683

    Google Scholar 

  • Duman E, Uysal M, Alkaya AF (2012) Migrating birds optimization: a new metaheuristic approach and its performance on quadratic assignment problem. Inf Sci 217:65–77

    MathSciNet  Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. In: Proceedings of the sixth international symposium on micro machine and human science, pp 39–43

  • Erol OK, Eksin I (2006) A new optimization method: big bang–big crunch. Adv Eng Softw 37(2):106–111

    Google Scholar 

  • Esfandyari S, Rafe V (2018) A tuned version of genetic algorithm for efficient test suite generation in interactive t-way testing strategy. Inf Softw Technol 94:165–185

    Google Scholar 

  • Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166

    Google Scholar 

  • Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190

    Google Scholar 

  • Flores JJ, López R, Barrera J (2011) Gravitational interactions optimization. In: International conference on learning and intelligent optimization, pp 226–237

  • Friedman M (1940) A comparison of alternative tests of significance for the problem of m rankings. Ann Math Stat 11(1):86–92

    MathSciNet  MATH  Google Scholar 

  • Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Google Scholar 

  • Glover F, Laguna M (1998) Tabu search. Handbook of combinatorial optimization. Springer, Berlin, pp 2093–2229

    Google Scholar 

  • Hayyolalam V, Kazem AAP (2020) Black widow optimization algorithm: a novel meta-heuristic approach for solving engineering optimization problems. Eng Appl Artif Intell 87:103249

    Google Scholar 

  • He X, Zhou Y (2018) Enhancing the performance of differential evolution with covariance matrix self-adaptation. Appl Soft Comput 64:227–243

    Google Scholar 

  • Hoffmann J, Nebel B (2001) The FF planning system: Fast plan generation through heuristic search. J Artif Intell Res 14:253–302

    MATH  Google Scholar 

  • Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Google Scholar 

  • Huang F, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356

    MathSciNet  MATH  Google Scholar 

  • Ito PK (1980) 7 Robustness of ANOVA and MANOVA test procedures. Handb Stat 1:199–236

    MATH  Google Scholar 

  • Kashan AH (2015) A new metaheuristic for optimization: optics inspired optimization (OIO). Comput Oper Res 55:99–125

    MathSciNet  MATH  Google Scholar 

  • Kaur H, Rai A, Bhatia SS, Dhiman G (2020) MOEPO: a novel multi-objective emperor penguin optimizer for global optimization: special application in ranking of cloud service providers. Eng Appl Artif Intell 96:104008

    Google Scholar 

  • Kaveh A, Bakhshpoori T (2016) Water evaporation optimization: a novel physically inspired optimization algorithm. Comput Struct 167:69–85

    Google Scholar 

  • Kaveh A, Dadras A (2017) A novel meta-heuristic optimization algorithm: thermal exchange optimization. Adv Eng Softw 110:69–84

    Google Scholar 

  • Kaveh A, Farhoudi N (2013) A new optimization method: dolphin echolocation. Adv Eng Softw 59:53–70

    Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, vol 4, pp 1942–1948

  • Khatri A, Gaba A, Rana KPS, Kumar V (2020) A novel life choice-based optimizer. Soft Comput 24(12):9121–9141

    Google Scholar 

  • Khishe M, Mosavi MR (2020) Chimp optimization algorithm. Expert Syst Appl 149:113338

    Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    MathSciNet  MATH  Google Scholar 

  • Kohli M, Arora S (2018) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Design Eng 5(4):458–472

    Google Scholar 

  • Korkmaz S, Ali NBH, Smith IF (2012) Configuration of control system for damage tolerance of a tensegrity bridge. Adv Eng Inform 26(1):145–155

    Google Scholar 

  • Koza JR, Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection, vol 1. MIT Press, Cambridge

    MATH  Google Scholar 

  • Krohling RA, dos Santos Coelho L (2006) Coevolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems. IEEE Trans Syst Man Cybern Part B (cybernetics) 36(6):1407–1416

    Google Scholar 

  • Kumar S, Datta D, Singh SK (2015) Black hole algorithm and its applications. Computational intelligence applications in modeling and control. Springer, Berlin, pp 147–170

    Google Scholar 

  • Kundu S, Parhi DR (2016) Navigation of underwater robot based on dynamically adaptive harmony search algorithm. Memet Comput 8(2):125–146

    Google Scholar 

  • Lagos-Eulogio P, Seck-Tuoh-Mora JC, Hernandez-Romero N, Medina-Marin J (2017) A new design method for adaptive IIR system identification using hybrid CPSO and DE. Nonlinear Dyn 88(4):2371–2389

    Google Scholar 

  • Lampinen J, Storn R (2004) Differential evolution. New optimization techniques in engineering. Springer, Berlin, pp 123–166

    Google Scholar 

  • Li X, Niu P, Li G, Liu J, Hui H (2015) Improved teaching-learning-based optimization algorithms for function optimization. In: 2015 11th international conference on natural computation (ICNC), pp 485–491

  • Lourenco H, Martin O, Stutzle T (2001) Iterated local search. In: Glover F, Kochenberger G (eds) “Handbook of Metaheuristics”. Kluwer. ISORMS 57, pp 321–353 (2002)

  • Lv W, He C, Li D, Cheng S, Luo S, Zhang X (2010) Election campaign optimization algorithm. Procedia Comput Sci 1(1):1377–1386

    Google Scholar 

  • McKight PE, Najab J (2010) Kruskal–Wallis test. In: The corsini encyclopedia of psychology, pp 1–1

  • Melvix JL (2014) Greedy politics optimization: metaheuristic inspired by political strategies adopted during state assembly elections. IEEE Int Adv Comput Conf (IACC) 2014:1157–1162

    Google Scholar 

  • MiarNaeimi F, Azizyan G, Rashki M (2021) Horse herd optimization algorithm: a nature-inspired algorithm for high-dimensional optimization problems. Knowl-Based Syst 213:106711. https://doi.org/10.1016/j.knosys.2020.106711

    Article  Google Scholar 

  • Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    Google Scholar 

  • Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Google Scholar 

  • Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  • Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513

    Google Scholar 

  • Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Google Scholar 

  • Mirjalili SZ, Mirjalili S, Saremi S, Faris H, Aljarah I (2018) Grasshopper optimization algorithm for multi-objective optimization problems. Appl Intell 48(4):805–820

    Google Scholar 

  • Mohanty PK, Parhi DR (2015) A new hybrid optimization algorithm for multiple mobile robots navigation based on the CS-ANFIS approach. Memet Comput 7(4):255–273

    Google Scholar 

  • Moosavi SHS, Bardsiri VK (2019) Poor and rich optimization algorithm: a new human-based and multi populations algorithm. Eng Appl Artif Intell 86:165–181

    Google Scholar 

  • Moscato P (1989) On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms. In: Caltech concurrent computation program, C3P Report, vol 826, p 1989

  • Naik A, Satapathy SC (2021) A comparative study of social group optimization with a few recent optimization algorithms. Complex Intell Syst 7(1):249–295

    Google Scholar 

  • Naruei I, Keynia F (2021) Wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems. Eng Comput 1–32

  • Ozkan O, Ermis M, Bekmezci I (2020) Reliable communication network design: the hybridisation of metaheuristics with the branch and bound method. J Oper Res Soc 71(5):784–799

    Google Scholar 

  • Pira E (2020) A novel approach to solve AI planning problems in graph transformations. Eng Appl Artif Intell 92:103684

    Google Scholar 

  • Pira E, Rafe V, Nikanjam A (2017) Deadlock detection in complex software systems specified through graph transformation using Bayesian optimization algorithm. J Syst Softw 131:181–200

    Google Scholar 

  • Pira E, Rafe V, Nikanjam A (2018) Searching for violation of safety and liveness properties using knowledge discovery in complex systems specified through graph transformations. Inf Softw Technol 97:110–134

    Google Scholar 

  • Rao R (2016) Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7(1):19–34

    Google Scholar 

  • Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315

    Google Scholar 

  • Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Google Scholar 

  • Ray T, Liew K-M (2003) Society and civilization: An optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4):386–396

    Google Scholar 

  • Richter S, Westphal M (2010) The LAMA planner: guiding cost-based anytime planning with landmarks. J Artif Intell Res 39:127–177

    MATH  Google Scholar 

  • Satapathy S, Naik A (2016) Social group optimization (SGO): a new population evolutionary optimization technique. Complex Intell Syst 2(3):173–203

    Google Scholar 

  • Sayed GI, Darwish A, Hassanien AE (2018) A new chaotic multi-verse optimization algorithm for solving engineering optimization problems. J Exp Theor Artif Intell 30(2):293–317

    Google Scholar 

  • Schönberger J (2020) A hybrid robust-stochastic optimization approach for the noise pollution routing problem with a heterogeneous vehicle fleet. In: Dynamics in logistics: proceedings of the 7th international conference LDIC 2020, Bremen, Germany, p 124

  • Shareef H, Ibrahim AA, Mutlag AH (2015) Lightning search algorithm. Appl Soft Comput 36:315–333

    Google Scholar 

  • Singh PR, Abd Elaziz M, Xiong S (2019) Ludo game-based metaheuristics for global and engineering optimization. Appl Soft Comput 84:105723

    Google Scholar 

  • Steven G (2002) Evolutionary algorithms for single and multicriteria design optimization. In: Osyczka A (eds) Structural and multidisciplinary optimization, vol 24, no 1. Springer, Berlin, pp 88–89. ISBN 3-7908-1418-01

  • Sulaiman MH, Mustaffa Z, Saari MM, Daniyal H (2020) Barnacles mating optimizer: a new bio-inspired algorithm for solving engineering optimization problems. Eng Appl Artif Intell 87:103330

    Google Scholar 

  • Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. IEEE Congr Evol Comput 2013:71–78

    Google Scholar 

  • Tirkolaee EB, Goli A, Faridnia A, Soltani M, Weber G-W (2020) Multi-objective optimization for the reliable pollution-routing problem with cross-dock selection using Pareto-based algorithms. J Clean Prod 276:122927

    Google Scholar 

  • Vaez SRH, Mehanpour H, Fathali MA (2020) Reliability assessment of truss structures with natural frequency constraints using metaheuristic algorithms. J Build Eng 28:101065

    Google Scholar 

  • Wang G-G, Cai X, Cui Z, Min G, Chen J (2017) High performance computing for cyber physical social systems by using evolutionary multi-objective optimization algorithm. IEEE Trans Emerg Top Comput 8(1):20–30

    Google Scholar 

  • Wilcoxon F (1992) Individual comparisons by ranking methods. Breakthroughs in statistics. Springer, Berlin, pp 196–202

    Google Scholar 

  • Yang X-S, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput

  • Yi J-H, Wang J, Wang G-G (2016) Improved probabilistic neural networks with self-adaptive strategies for transformer fault diagnosis problem. Adv Mech Eng 8(1):1687814015624832

    MathSciNet  Google Scholar 

  • Zhang JW, Wang GG (2012) Image matching using a bat algorithm with mutation. Appl Mech Mater 203:88–93

    Google Scholar 

Download references

Acknowledgements

We would like to thank Dr. Afshin Faramarzi and Dr. Ali Sadollah for providing us the Matlab codes of CEC 2017 test functions and the constrained version of the water cycle algorithm.

Author information

Authors and Affiliations

  1. Faculty of Information Technology and Computer Engineering, Azarbaijan Shahid Madani University, Tabriz, 5375171379, Iran

    Einollah Pira

Authors
  1. Einollah Pira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Einollah Pira.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pira, E. City councils evolution: a socio-inspired metaheuristic optimization algorithm. J Ambient Intell Human Comput 14, 12207–12256 (2023). https://doi.org/10.1007/s12652-022-03765-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-022-03765-5

Keywords

Search

Navigation