Mall optimization algorithm (MALL) based on human social behavior in commercial centers

Hadjiebrahim, Hamid; Toloie Eshlaghy, Abbas; Iranzadeh, Soleyman; Pourebrahimi, Alireza; Motadel, Mohammad Reza

doi:10.22075/ijnaa.2025.39047.5547

Mall optimization algorithm (MALL) based on human social behavior in commercial centers

Articles in Press

Document Type : Research Paper

Authors

Hamid Hadjiebrahim ¹

Abbas Toloie Eshlaghy ¹

Soleyman Iranzadeh ²

Alireza Pourebrahimi ³

Mohammad Reza Motadel ⁴

¹ Department of Industrial Management, Science and Research Branch, Islamic Azad University, Tehran, Iran

² Department of Industrial Management, Tabriz Branch, Islamic Azad University, Tabriz, Iran

³ Department of Industrial Management, Karaj Branch Islamic Azad University, Karaj, Iran

⁴ Department of Industrial Management, Central Tehran Branch, Islamic Azad University, Tehran, Iran

10.22075/ijnaa.2025.39047.5547

Abstract

This paper proposes a novel optimization algorithm inspired by human behavior in the shopping center called the Mall optimization algorithm (MALL), to solve challenging optimization problems. The MALL mimics the behavior of human factors present in a shopping mall including distributors of goods and services, sellers with non-commercial interests, new investors (from the group of sellers), and buyers and tourists (from the group of customers), each with specific behavior. The algorithm is evaluated on thirty well-known benchmark functions and ten challenging functions from CEC-C06 2019. The findings are compared with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Teaching Learning Based Optimization (TLBO). The results indicate that the MALL algorithm can provide highly competitive results compared to these expert meta-heuristic algorithms. Statistical analysis confirms the performance of local optima avoidance, exploration, exploitation, and convergence of this proposed algorithm. This article also addresses solving the known problem of supply chain management called the PLOT (Production, Logistics, Outbound, Transportation) system. Experimental results show that the proposed algorithm can be used to solve challenging problems with unknown search spaces.

Keywords

Optimization

Metaheuristics

Swarm-intelligence

human behavior-related algorithms

Supply chain management

[1] H.A. Abbass, MBO: Marriage in honey bees optimization‑ A haplometrosis polygynous swarming approach, Proc. 2001 Congr. Evol. Comput. (IEEE Cat. No. 01TH8546), IEEE, vol. 1, pp. 207-214, 2001.

[2] P. Agrawal, H.F. Abutarboush, T. Ganesh, and A.W. Mohamed, Metaheuristic Algorithms on Feature Selection: A Survey of One Decade of Research (2009‑2019), IEEE Access 9 (2021), 26766-26791.

[3] S.-A. Ahmadi, Human behavior‑based optimization: A novel metaheuristic approach to solve complex optimization problems, Neural Comput. Appl. 28 (2017), no. Suppl 1, 233-244.

[4] A. Ahmadi‑Javid, Anarchic Society Optimization: A human‑inspired method, IEEE Congr. Evol. Comput. (CEC), IEEE, 2011, pp. 2586-2592.

[5] A. Ahrari and A.A. Atai, Grenade explosion method‑ a novel tool for optimization of multimodal functions, Appl. Soft Comput. 10 (2010), no. 4, 1132-1140.

[6] B. Alatas, ACROA: artificial chemical reaction optimization algorithm for global optimization, Expert Syst. Appl. 38 (2011), no. 10, 13170-13180.

[7] E. Alba and B. Dorronsoro, The exploration/exploitation tradeoff in dynamic cellular genetic algorithms, IEEE Trans. Evol. Comput. 9 (2005), no. 2, 126-142.

[8] S. Arora and S. Singh, Butterfly optimization algorithm: A novel approach for global optimization, Soft Comput. 23 (2019), no. 3, 715-734.

[9] Q. Askari, M. Saeed, and I. Younas, Heap‑based optimizer inspired by corporate rank hierarchy for global optimization, Expert Syst. Appl. 161 (2020), 113702.

[10] A. Askarzadeh, Bird mating optimizer: An optimization algorithm inspired by bird mating strategies, Commun. Nonlinear Sci. Numer. Simul. 19 (2014), no. 4, 1213-1228.

[11] E. Atashpaz‑Gargari and C. Lucas, Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition, IEEE Congr. Evol. Comput., 2007, IEEE, pp. 4661-4667.

[12] M.A. Awadel‑Bayoumy, M. Rashad, M. Elsoud, and M. El‑Dosuky, Fafsa: Fast artificial fish swarm algorithm, Int. J. Inf. Sci. Intell. Syst. 2 (2013), no. 4, 60-70.

[13] B. Basturk, An artificial bee colony (ABC) algorithm for numeric function optimization, IEEE Swarm Intell. Symp., Indianapolis, IN, USA, 2006, vol. 2006, p. 12.

[14] M. Birattari, L. Paquete, T. Stützle, and K. Varrentrapp, Classification of Metaheuristics and Design of Experiments for the Analysis of Components, Tech. Rep. AIDA‑01‑05, Intellektik, Darmstadt Univ. Technol., Darmstadt, Germany, 2001.

[15] C. Blum, Ant colony optimization: Introduction and recent trends, Phys. Life Rev. 2 (2005), no. 4, 353-373.

[16] I. Boussaid, J. Lepagnot, and P. Siarry, A survey on optimization metaheuristics, Inform. Sci. 237 (2013), 82-117.

[17] V. Černý, Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm, J. Optim. Theory Appl. 45 (1985), 41-51.

[18] P. Civicioglu, Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm, Comput. Geosci. 46 (2012), 229-247.

[19] P. Civicioglu, Backtracking search optimization algorithm for numerical optimization problems, Appl. Math. Comput. 219 (2013), no. 15, 8121-8144.

[20] E. Cuevas, D. Oliva, D. Zaldivar, M. Pérez‑Cisneros, and H. Sossa, Circle detection using electro‑magnetism optimization, Inform. Sci. 182 (2012), no. 1, 40-55.

[21] Z. Cui and X. Cai, Using social cognitive optimization algorithm to solve nonlinear equations, 9th IEEE Int. Conf. Cogn. Inform. (ICCI'10), IEEE, 2010, pp. 199-203.

[22] C. Dai, W. Chen, Y. Song, and Y. Zhu, Seeker optimization algorithm: A novel stochastic search algorithm for global numerical optimization, J. Syst. Eng. Electron. 21 (2010), no. 2, 300-311.

[23] J. Derrac, S. García, D. Molina, and F. Herrera, A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms, Swarm Evol. Comput. 1 (2011), no. 1, 3-18.

[24] G. Dhiman and V. Kumar, Spotted hyena optimizer: A novel bio‑inspired based metaheuristic technique for engineering applications, Adv. Eng. Softw. 114 (2017), 48-70.

[25] G. Dhiman and V. Kumar, Emperor penguin optimizer: A bio‑inspired algorithm for engineering problems, Knowl.‑Based Syst. 159 (2018), 20-50.

[26] T.T. Dhivyaprabha, P. Subashini, and M. Krishnaveni, Synergistic fibroblast optimization: A novel nature‑inspired computing algorithm, Front. Inf. Technol. Electron. Eng. 19 (2018), no. 7, 815-833.

[27] J.G. Digalakis and K.G. Margaritis, On benchmarking functions for genetic algorithms, Int. J. Comput. Math. 77 (2001), no. 4, 481-506.

[28] M. Dorigo, M. Birattari, and T. Stützle, Ant colony optimization, IEEE Comput. Intell. Mag. 1 (2006), no. 4, 28-39.

[29] J. Dreo, J.-P. Aumasson, W. Tfaili, and P. Siarry, Adaptive learning search, a new tool to help comprehending metaheuristics, Int. J. Artif. Intell. Tools 16 (2007), no. 03, 483-505.

[30] H. Du, X. Wu, and J. Zhuang, Small‑world optimization algorithm for function optimization, Int. Conf. Nat. Comput., Springer, 2006, pp. 264-273.

[31] M.A. Eita and M.M. Fahmy, Group counseling optimization, Appl. Soft Comput. 22 (2014), 585-604.

[32] O.K. Erol and I. Eksin, A new optimization method: Big bang‑big crunch, Adv. Eng. Softw. 37 (2006), no. 6, 106-111.

[33] E. Fadakar and M. Ebrahimi, A new metaheuristic football game inspired algorithm, in 2016 1st Conf. Swarm Intell. Evol. Comput. (CSIEC), IEEE, 2016, pp. 6-11.

[34] T.A. Feo and M.G.C. Resende, A probabilistic heuristic for a computationally difficult set covering problem, Oper. Res. Lett. 8 (1989), no. 2, 67-71.

[35] T.A. Feo and M.G.C. Resende, Greedy randomized adaptive search procedures, J. Global Optim. 6 (1995), 109-133.

[36] M. Ferry, F3EA‑ A targeting paradigm for contemporary warfare, Aust. Army J. 10 (2013), no. 1, 49-64.

[37] A.H. Gandomi and A.H. Alavi, Krill herd: A new bio‑inspired optimization algorithm, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), no. 12, 4831-4845.

[38] H. Ghasemian, F. Ghasemian, and H. Vahdat‑Nejad, Human urbanization algorithm: A novel metaheuristic approach, Math. Comput. Simul. 178 (2020), 1-15.

[39] N. Ghorbani and E. Babaei, Exchange market algorithm, Appl. Soft Comput. 19 (2014), 177-187.

[40] F. Glover, Tabu search methods in artificial intelligence and operations research, ORSA Artif. Intell. 1 (1987), no. 2, 6.

[41] N. Hansen, S.D. Müller, and P. Koumoutsakos, Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA‑ES), Evol. Comput. 11 (2003), no. 1, 1-18.

[42] S. Harifi, M. Khalilian, J. Mohammadzadeh, and S. Ebrahimnejad, Emperor Penguins Colony: A new metaheuristic algorithm for optimization, Evol. Intell. 12 (2019), no. 2, 211-226.

[43] A. Hatamlou, Black hole: A new heuristic optimization approach for data clustering, Inform. Sci. 222 (2013), 175-184.

[44] J.H. Holland, Genetic algorithms, Sci. Am. 267 (1992), no. 1, 66-73.

[45] K. Hussain, M.N. Mohd Salleh, S. Cheng, and Y. Shi, Metaheuristic research: A comprehensive survey, Artif. Intell. Rev. 52 (2019), no. 4, 2191-2233.

[46] M. Jain, V. Singh, and A. Rani, A novel nature‑inspired algorithm for optimization: Squirrel search algorithm, Swarm Evol. Comput. 44 (2019), 148-175.

[47] V. Jayaraman and A. Ross, A simulated annealing methodology to distribution network design and management, Eur. J. Oper. Res. 144 (2003), no. 3, 629-645.

[48] A.H. Kashan, League championship algorithm: A new algorithm for numerical function optimization, in 2009 Int. Conf. Soft Comput. Pattern Recognit., IEEE, 2009, pp. 43-48.

[49] A.H. Kashan, R. Tavakkoli‑Moghaddam, and M. Gen, Find‑Fix‑Finish‑Exploit‑Analyze (F3EA) meta‑heuristic algorithm: An effective algorithm with new evolutionary operators for global optimization, Comput. Ind. Eng. 128 (2019), 192-218.

[50] A. Kaveh and A. Dadras, A novel meta‑heuristic optimization algorithm: Thermal exchange optimization, Adv. Eng. Softw. 110 (2017), 69-84.

[51] A. Kaveh and M. Khayatazad, A new meta‑heuristic method: Ray optimization, Comput. Struct. 112 (2012), 283-294.

[52] A. Kaveh and S. Talatahari, A novel heuristic optimization method: Charged system search, Acta Mech. 213 (2010), no. 3-4, 267-289.

[53] J. Kennedy and R. Eberhart, Particle swarm optimization, Proc. ICNN'95‑Int. Conf. Neural Netw., IEEE, 1995, vol. 4, pp. 1942-1948.

[54] S. Kirkpatrick, C.D. Gelatt Jr., and M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983), no. 4598, 671-680.

[55] J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, vol. 1, 1992.

[56] A.J. Kulkarni, I.P. Durugkar, and M. Kumar, Cohort intelligence: A self supervised learning behavior, IEEE Int. Conf. Syst. Man Cybern., IEEE, 2013, pp. 1396-1400.

[57] K.S. Lee and Z.W. Geem, A new meta‑heuristic algorithm for continuous engineering optimization: Harmony search theory and practice, Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 36-38, 3902-3933.

[58] H.R. Lourenço, O.C. Martin, and T. Stützle, Iterated local search, Handbook of Metaheuristics, Springer, 2003, pp. 320-353.

[59] X. Lu and Y. Zhou, A novel global convergence algorithm: bee collecting pollen algorithm, Int. Conf. Intell. Comput., Springer, 2008, pp. 518-525.

[60] W. Lv, C. He, D. Li, S. Cheng, S. Luo, and X. Zhang, Election campaign optimization algorithm, Procedia Comput. Sci. 1 (2010), no. 1, 1377-1386.

[61] S. Mirjalili, A.H. Gandomi, S.Z. Mirjalili, S. Saremi, H. Faris, and S.M. Mirjalili, Salp Swarm Algorithm: A bio‑inspired optimizer for engineering design problems, Adv. Eng. Softw. 114 (2017), 163-191.

[62] S. Mirjalili, S.M. Mirjalili, and A. Lewis, Grey wolf optimizer, Adv. Eng. Softw. 69 (2014), 46-61.

[63] N. Mladenovic, A variable neighborhood algorithm‑a new metaheuristic for combinatorial optimization, Papers presented at Optimization Days, 1995.

[64] N. Mladenovic, M. Drazic, V. Kovačevic‑Vujcic, and M. Cangalovic, General variable neighborhood search for the continuous optimization, Eur. J. Oper. Res. 191 (2008), no. 3, 753-770.

[65] F.F. Moghaddam, R.F. Moghaddam, and M. Cheriet, Curved Space Optimization: A Random Search Based on General Relativity Theory, arXiv preprint arXiv:1208.2214, 2012.

[66] R. Moghdani and K. Salimifard, Volleyball premier league algorithm, Appl. Soft Comput. 64 (2018), 161-185.

[67] A.W. Mohamed, A.A. Hadi, and A.K. Mohamed, Gaining‑sharing knowledge based algorithm for solving optimization problems: a novel nature‑inspired algorithm, Int. J. Mach. Learn. Cybern. (2019), 1-29.

[68] M. Molga and C. Smutnicki, Test functions for optimization needs, Test Funct. Optim. Needs 101 (2005), 48.

[69] N. Moosavian and B.K. Roodsari, Soccer league competition algorithm: A novel meta‑heuristic algorithm for optimal design of water distribution networks, Swarm Evol. Comput. 17 (2014), 14-24.

[70] A. Mucherino and O. Seref, Monkey search: a novel metaheuristic search for global optimization, AIP Conf. Proc., Amer. Inst. Phys., vol. 953, 2007, pp. 162-173.

[71] O. Olorunda and A.P. Engelbrecht, Measuring exploration/exploitation in particle swarms using swarm diversity, IEEE Congr. Evol. Comput. (IEEE World Congr. Comput. Intell.), IEEE, 2008, pp. 1128-1134.

[72] W.-T. Pan, A new fruit fly optimization algorithm: taking the financial distress model as an example, Knowl.‑Based Syst. 26 (2012), 69-74.

[73] P.C. Pinto, T.A. Runkler, and J.M.C. Sousa, Wasp swarm algorithm for dynamic MAX‑SAT problems, Int. Conf. Adapt. Nat. Comput. Algorithms, Springer, 2007, pp. 350-357.

[74] K.V. Price, N.H. Awad, M.Z. Ali, and P.N. Suganthan, Problem Definitions and Evaluation Criteria for the 100‑Digit Challenge Special Session and Competition on Single Objective Numerical Optimization, Tech. Rep., Nanyang Technol. Univ., Singapore, 2018.

[75] F. Ramezani and S. Lotfi, Social‑based algorithm (SBA), Appl. Soft Comput. 13 (2013), no. 5, 2837-2856.

[76] R. Rao, Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems, Int. J. Ind. Eng. Comput. 7 (2016), no. 1, 19-34.

[77] R.V. Rao, V.J. Savsani, and D.P. Vakharia, Teaching‑learning‑based optimization: A novel method for constrained mechanical design optimization problems, Comput.‑Aided Des. 43 (2011), no. 3, 303-315.

[78] E. Rashedi, H. Nezamabadi‑Pour, and S. Saryazdi, GSA: A gravitational search algorithm, Inform. Sci. 179 (2009), no. 13, 2232-2248.

[79] T. Ray and K.-M. Liew, Society and civilization: An optimization algorithm based on the simulation of social behavior, IEEE Trans. Evol. Comput. 7 (2003), no. 4, 386-396.

[80] I. Rechenberg, Evolution Strategy, Computational Intelligence: Imitating Life, J.M. Zurada, R.J. Marks II, and C. Goldberg, Eds., IEEE Press, Piscataway, NJ, 1994, pp. 147-169.

[81] R.G. Reynolds, An introduction to cultural algorithms, Proc. 3rd Annu. Conf. Evol. Program., World Scientific, 1994, pp. 131-139.

[82] M. Roth, Termite: A Swarm Intelligent Routing Algorithm for Mobile Wireless Ad‑Hoc Networks, Master's Thesis, Univ. Hamburg, Hamburg, Germany, 2005.

[83] H. Salimi, Stochastic fractal search: A powerful metaheuristic algorithm, Knowl.‑Based Syst. 75 (2015), 1-18.

[84] P. Savsani and V. Savsani, Passing vehicle search (PVS): A novel metaheuristic algorithm, Appl. Math. Model. 40 (2016), no. 5-6, 3951-3978.

[85] H. Shah‑Hosseini, Principal components analysis by the galaxy‑based search algorithm: A novel metaheuristic for continuous optimisation, Int. J. Comput. Sci. Eng. 6 (2011), no. 1-2, 132-140.

[86] Y. Shi, Brain storm optimization algorithm, Int. Conf. Swarm Intell., Springer, 2011, pp. 303-309.

[87] Y. Shiqin, J. Jianjun, and Y. Guangxing, A dolphin partner optimization, in 2009 WRI Global Congr. Intell. Syst., IEEE, vol. 1, pp. 124-128, 2009.

[88] D. Simon, Biogeography‑based optimization, IEEE Trans. Evol. Comput. 12 (2008), no. 6, 702-713.

[89] R. Storn and K. Price, Differential evolution‑ A simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim. 11 (1997), no. 4, 341-359.

[90] M.H. Sulaiman, Z. Mustaffa, M.M. Saari, and H. Daniyal, Barnacles mating optimizer: A new bio‑inspired algorithm for solving engineering optimization problems, Eng. Appl. Artif. Intell. 87 (2020), 103330.

[91] A. Tabari and A. Ahmad, A new optimization method: Electro‑Search algorithm, Comput. Chem. Eng. 103 (2017), 1-11.

[92] E.-G. Talbi, Metaheuristics: From Design to Implementation, John Wiley & Sons, 2009.

[93] A. Tharwat and T. Gabel, Parameters optimization of support vector machines for imbalanced data using social ski driver algorithm, Neural Comput. Appl. 32 (2020), 6925-6938.

[94] C. Voudouris and E. Tsang, Partial constraint satisfaction problems and guided local search, Proc., Practical Application of Constraint Technology (PACT'96), London, 1996, pp. 337-356.

[95] A.I. Wagan and M.M. Shaikh, A new metaheuristic optimization algorithm inspired by human dynasties with an application to the wind turbine micrositing problem, Appl. Soft Comput. 90 (2020), 106176.

[96] B. Webster and P.J. Bernhard, A local search optimization algorithm based on natural principles of gravitation, Report, Melbourne, FL. Florida Inst. Technol., 2003.

[97] D.H. Wolpert and W.G. Macready, No free lunch theorems for optimization, IEEE Trans. Evol. Comput. 1 (1997), no. 1, 67-82.

[98] Y. Xu, Z. Cui, and J. Zeng, Social emotional optimization algorithm for nonlinear constrained optimization problems, in Swarm, Evol., and Memetic Comput.: First Int. Conf. Swarm, Evol., and Memetic Comput., SEMCCO 2010, Chennai, India, December 16‑18, 2010. Proc. 1, Springer, 2010, pp. 583-590.

[99] X.-S. Yang, Firefly algorithm, stochastic test functions and design optimisation, Int. J. Bio‑Inspired Comput. 2 (2010), no. 2, 78-84.

[100] X.-S. Yang, A new metaheuristic bat‑inspired algorithm, Nature Inspired Cooperative Strategies for Optimization, Springer, 1994, pp. 65-74.

[101] X.-S. Yang, Test problems in optimization, arXiv preprint arXiv:1008.0549, 2010.

[102] X.-S. Yang and S. Deb, Cuckoo search via Lévy flights, World Congr. Nat. Biol. Inspired Comput. (NaBIC), IEEE, pp. 210-214, 2009.

[103] X. Yao, Y. Liu, and G. Lin, Evolutionary programming made faster, IEEE Trans. Evol. Comput. 3 (1999), no. 2, 82-102.

[104] L.M.Y. Zhang, C. Dahlmann, and Y. Zhang, Human‑inspired algorithms for continuous function optimization, IEEE Int. Conf. Intell. Comput. Intell. Syst., IEEE, 2009, vol. 1, pp. 318-321.