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Red deer algorithm (RDA): a new nature-inspired meta-heuristic

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Abstract

Nature has been considered as an inspiration of several recent meta-heuristic algorithms. This paper firstly studies and mimics the behavior of Scottish red deer in order to develop a new nature-inspired algorithm. The main inspiration of this meta-heuristic algorithm is to originate from an unusual mating behavior of Scottish red deer in a breading season. Similar to other population-based meta-heuristics, the red deer algorithm (RDA) starts with an initial population called red deers (RDs). They are divided into two types: hinds and male RDs. Besides, a harem is a group of female RDs. The general steps of this evolutionary algorithm are considered by the competition of male RDs to get the harem with more hinds via roaring and fighting behaviors. By solving 12 benchmark functions and important engineering as well as multi-objective optimization problems, the superiority of the proposed RDA shows in comparison with other well-known and recent meta-heuristics.

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  1. https://infosalamat.com/hospitals/hekmat-e-sari.

References

  • Arnaout JP (2016) Worm optimization for the traveling salesman problem. In: Heuristics, metaheuristics and approximate methods in planning and scheduling. Springer, Cham, pp 209–224

    Google Scholar 

  • Asaju LAB, Awadallah MA, Al-Betar MA, Khader AT (2015) Solving nurse rostering problem using artificial bee colony algorithm. In: ICIT 2015 the 7th international conference on information technology. pp 32–38

  • Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: Proceedings of the IEEE congress on evolutionary computation, Singapore, 25–28 September 2007. pp 4661–4667

  • Awadallah MA, Khader AT, Al-Betar MA, Bolaji ALA (2013) Global best harmony search with a new pitch adjustment designed for nurse rostering. J King Saud Univ Comput Inf Sci 25(2):145–162

    Google Scholar 

  • Awadallah MA, Al-Betar MA, Khader AT, Bolaji ALA, Alkoffash M (2017) Hybridization of harmony search with hill climbing for highly constrained nurse rostering problem. Neural Comput Appl 28(3):463–482

    Google Scholar 

  • Bailey RN, Garner KM, Hobbs MF (1997) Using simulated annealing and genetic algorithms to solve staff-scheduling problems. Asia Pac J Oper Res 14(2):27

    MathSciNet  MATH  Google Scholar 

  • Baker BM, Ayechew MA (2003) A genetic algorithm for the vehicle routing problem. Comput Oper Res 30(5):787–800

    MathSciNet  MATH  Google Scholar 

  • Barbarosoglu G, Ozgur D (1999) A tabu search algorithm for the vehicle routing problem. Comput Oper Res 26(3):255–270

    MathSciNet  MATH  Google Scholar 

  • Beheshti Z, Shamsuddin SMH (2013) A review of population-based meta-heuristic algorithms. Int J Adv Soft Comput Appl 5(1):1–35

    Google Scholar 

  • Ben-Arieh D, Gutin G, Penn M, Yeo A, Zverovitch A (2003) Process planning for rotational parts using the generalized travelling salesman problem. Int J Prod Res 41(11):2581–2596

    MATH  Google Scholar 

  • Blank DA, Ruckstuhl K, Yang W (2017) Development of juvenile goitered gazelle social behavior during the hiding period. Behav Proc 144:82–88

    Google Scholar 

  • Bullnheimer B, Hartl RF, Strauss C (1999) An improved ant system algorithm for thevehicle routing problem. Ann Oper Res 89:319–328

    MathSciNet  MATH  Google Scholar 

  • Burke EK, Curtois T, Post G, Qu R, Veltman B (2008) A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem. Eur J Oper Res 188(2):330–341

    MATH  Google Scholar 

  • Calvete HI, Galé C, Iranzo JA (2016) An improved evolutionary algorithm for the two-stage transportation problem with fixed charge at depots. OR Spectr 38(1):189–206

    MathSciNet  MATH  Google Scholar 

  • Chen L, Peng J, Zhang B (2017) Uncertain goal programming models for bicriteria solid transportation problem. Appl Soft Comput 51:49–59

    Google Scholar 

  • Cheraghalipour A, Hajiaghaei-Keshteli M, Paydar MM (2018) Tree growth algorithm (TGA): a novel approach for solving optimization problems. Eng Appl Artif Intell 72:393–414

    Google Scholar 

  • Clutton-Brock TH, Albon SD, Gibson RM, Guinness FE (1979) The logical stag: adaptive aspects of fighting in red deer (Cervus Elaphus L.). Anim Behav 27:211–225

    Google Scholar 

  • Crainic TG, Gajpal Y, Gendreau M (2015) Multi-zone multi-trip vehicle routing problem with time windows. INFOR Inf Syst Oper Res 53(2):49–67

    MathSciNet  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan TAMT (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Google Scholar 

  • Dong W, Zhou M (2017) A supervised learning and control method to improve particle swarm optimization algorithms. IEEE Trans Syst Man Cybern Syst 47(7):1135–1148

    Google Scholar 

  • Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cyber Part B (Cybernetics) 26(1):29–41

    Google Scholar 

  • Dowsland KA (1998) Nurse scheduling with tabu search and strategic oscillation. Eur J Oper Res 106(2–3):393–407

    MATH  Google Scholar 

  • Draa A (2015) On the performances of the flower pollination algorithm–qualitative and quantitative analyses. Appl Soft Comput 34:349–371

    Google Scholar 

  • El-Sherbiny MM, Alhamali RM (2013) A hybrid particle swarm algorithm with artificial immune learning for solving the fixed charge transportation problem. Comput Ind Eng 64(2):610–620

    Google Scholar 

  • Farley AA, Richardson KV (1984) Fixed charge problems with identical fixed charges. Eur J Oper Res 18(2):245–249

    MATH  Google Scholar 

  • Fathollahi-Fard AM, Hajiaghaei-Keshteli M (2016) Red Deer Algorithm (RDA); a new optimization algorithm inspired by Red Deers’ mating. In: IEEE International Conference on Industrial Engineering, pp 33–34

  • Fathollahi-Fard AM, Hajiaghaei-Keshteli M (2018) A stochastic multi-objective model for a closed-loop supply chain with environmental considerations. Appl Soft Comput 69:232–249

    Google Scholar 

  • Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2018) The social engineering optimizer (SEO). Eng Appl Artif Intell 72:267–293

    Google Scholar 

  • Fathollahi-Fard AM, Ranjbar-Bourani M, Cheikhrouhou N, Hajiaghaei-Keshteli M (2019) Novel modifications of social engineering optimizer to solve a truck scheduling problem in a cross-docking system. Comput Ind Eng 137:106103

    Google Scholar 

  • Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tian G, Li Z (2020) An adaptive Lagrangian relaxation-based algorithm for a coordinated water supply and wastewater collection network design problem. Inf Sci 512:1335–1359

    Google Scholar 

  • Feldmann M, Biskup D (2003) Single-machine scheduling for minimizing earliness and tardiness penalties by meta-heuristic approaches. Comput Ind Eng 44(2):307–323

    Google Scholar 

  • Fikar C, Hirsch P (2017) Home health care routing and scheduling: A review. Comput Oper Res 77:86–95

    MathSciNet  MATH  Google Scholar 

  • Fischetti M, González JJS, Toth P (1995) The symmetric generalized traveling salesman polytope. Networks 26(2):113–123

    MathSciNet  MATH  Google Scholar 

  • Fischetti M, Salazar González JJ, Toth P (1997) A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Oper Res 45(3):378–394

    MathSciNet  MATH  Google Scholar 

  • Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68

    Google Scholar 

  • Gendreau M, Hertz A, Laporte G (1994) A tabu search heuristic for the vehicle routing problem. Manage Sci 40(10):1276–1290

    MATH  Google Scholar 

  • Ghorbani N, Babaei E (2014) Exchange market algorithm. Appl Soft Comput 19:177–187

    Google Scholar 

  • Gonçalves TC, Valente JM, Schaller JE (2016) Metaheuristics for the single machine weighted quadratic tardiness scheduling problem. Comput Oper Res 70:115–126

    MathSciNet  MATH  Google Scholar 

  • Govindan K, Jafarian A, Nourbakhsh V (2015) Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic. Comput Oper Res 62:112–130

    MathSciNet  MATH  Google Scholar 

  • Gutjahr WJ, Rauner MS (2007) An ACO algorithm for a dynamic regional nurse-scheduling problem in Austria. Comput Oper Res 34(3):642–666

    MATH  Google Scholar 

  • Hajiaghaei-Keshteli M, Aminnayeri M (2013) Keshtel Algorithm (KA); a new optimization algorithm inspired by Keshtels’ feeding. In: Proceeding in IEEE conference on industrial engineering and management systems. pp 2249–2253

  • Hajiaghaei-Keshteli M, Fathollahi Fard AM, (2018) Sustainable closed-loop supply chain network design with discount supposition. Neural computing and applications (in press)

  • Hall NG, Kubiak W, Sethi SP (1991) Earliness–tardiness scheduling problems, II: deviation of completion times about a restrictive common due date. Oper Res 39(5):847–856

    MathSciNet  MATH  Google Scholar 

  • Han W, Xu J, Zhou M, Tian G, Wang P, Shen X, Hou E (2016) Cuckoo search and particle filter-based inversing approach to estimating defects via magnetic flux leakage signals. IEEE Trans Magn 52(4):1–11

    Google Scholar 

  • He S, Wu QH, Saunders JR (2009) Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE Trans Evol Comput 13(5):973–990

    Google Scholar 

  • Henrylab Al (1969) Record balancing problem-a dynamic programming solution of a generalized traveling salesman problem. Revue Francaise D Informatique De Recherche Operationnelle 3(NB 2):43

    Google Scholar 

  • Hiquebran DT, Alfa AS, Shapiro JA, Gittoes DH (1993) A revised simulated annealing and cluster-first route-second algorithm applied to the vehicle routing problem. Eng Optim 22(2):77–107

    Google Scholar 

  • Holland J (1975) Adaptation in natural and artificial systems: an introductory analysis with application to biology. Control and artificial intelligence

  • Hoogeveen JA, Van de Velde SL (1991) Scheduling around a small common due date. Eur J Oper Res 55(2):237–242

    MATH  Google Scholar 

  • Hosseini S, Al Khaled A (2014) A survey on the imperialist competitive algorithm metaheuristic: Implementation in engineering domain and directions for future research. Appl Soft Comput 24:1078–1094

    Google Scholar 

  • Hussain K, Salleh MNM, Cheng S, Shi Y (2018) Metaheuristic research: a comprehensive survey. Artificial intelligence review (in press)

  • James RJW (1997) Using tabu search to solve the common due date early/tardy machine scheduling problem. Comput Oper Res 24(3):199–208

    MathSciNet  MATH  Google Scholar 

  • Jiang X, Bai R, Atkin J, Kendall G (2017) A scheme for determining vehicle routes based on Arc-based service network design. INFOR Inf Syst Oper Res 55(1):16–37

    MathSciNet  Google Scholar 

  • Kar AK (2016) Bio inspired computing–A review of algorithms and scope of applications. Expert Syst Appl 59:20–32

    Google Scholar 

  • Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132

    MathSciNet  MATH  Google Scholar 

  • Kaveh A (2016) Advances in metaheuristic algorithms for optimal design of structures. Springer, Berlin

    MATH  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceeding of the IEEE international conference on neural networks, Perth, Australia. IEEE Service Center, Piscataway

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

    MathSciNet  MATH  Google Scholar 

  • Klose A (2008) Algorithms for solving the single-sink fixed-charge transportation problem. Comput Oper Res 35(6):2079–2092

    MathSciNet  MATH  Google Scholar 

  • Krause J, James R, Franks DW, Croft DP (eds) (2015) Animal social networks. Oxford University Press, Oxford

    Google Scholar 

  • Krishnanand KN, Ghose D (2005) Detection of multiple source locations using a glowworm metaphor with applications to collective robotics. In: Proceedings of the IEEE on swarm intelligence symposium, California, 8–10 June 2005. pp 84–91

  • Laporte G (1992) The vehicle routing problem: an overview of exact and approximate algorithms. Eur J Oper Res 59(3):345–358

    MathSciNet  MATH  Google Scholar 

  • Laporte G, Nobert Y (1983) Generalized travelling salesman problem through n sets of nodes: an integer programming approach. INFOR Inf Syst Oper Res 21(1):61–75

    MATH  Google Scholar 

  • Laporte G, Desrochers M, Nobert Y (1984) Two exact algorithms for the distance-constrained vehicle routing problem. Networks 14(1):161–172

    MATH  Google Scholar 

  • Laporte G, Asef-Vaziri A, Sriskandarajah C (1996) Some applications of the generalized travelling salesman problem. J Oper Res Soc 47(12):1461–1467

    MATH  Google Scholar 

  • Lee CY, Kim SJ (1995) Parallel genetic algorithms for the earliness-tardiness job scheduling problem with general penalty weights. Comput Ind Eng 28(2):231–243

    Google Scholar 

  • Liang J J, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer with local search. In: Proceedings of the IEEE congress on evolutionary computation, Edinburgh, UK, 2–4 September 2005. pp 522–528

  • Lipowski A, Lipowska D (2012) Roulette-wheel selection via stochastic acceptance. Phys A 391(6):2193–2196

    Google Scholar 

  • Lotfi MM, Tavakkoli-Moghaddam R (2013) A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl Soft Comput 13(5):2711–2726

    Google Scholar 

  • McComb KE (1991) Female choice for high roaring rates in red deer, Cervus elaphus. Anim Behav 41(1):79–88

    Google Scholar 

  • Mernik M, Liu SH, Karaboga D, Črepinšek M (2015) On clarifying misconceptions when comparing variants of the Artificial Bee Colony Algorithm by offering a new implementation. Inf Sci 291:115–127

    MathSciNet  MATH  Google Scholar 

  • Miller BL, Goldberg DE (1995) Genetic algorithms, tournament selection, and the effects of noise. Complex Syst 9(3):193–212

    MathSciNet  Google Scholar 

  • Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98

    Google Scholar 

  • Mirjalili S, Lewis A (2015) Novel performance metrics for robust multi-objective optimization algorithms. Swarm Evol Comput 21:1–23

    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, 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 

  • Molla-Alizadeh-Zavardehi S, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2011) Solving a capacitated fixed-charge transportation problem by artificial immune and genetic algorithms with a Prüfer number representation. Expert Syst Appl 38(8):10462–10474

    Google Scholar 

  • Molla-Alizadeh-Zavardehi S, Nezhad SS, Tavakkoli-Moghaddam R, Yazdani M (2013) Solving a fuzzy fixed charge solid transportation problem by metaheuristics. Math Comput Model 57(5):1543–1558

    MathSciNet  Google Scholar 

  • Moz M, Pato MV (2007) A genetic algorithm approach to a nurse rerostering problem. Comput Oper Res 34(3):667–691

    MATH  Google Scholar 

  • Nie Y, Wang B, Zhang X (2016) Hybrid harmony search algorithm for nurse rostering problem. In: Harmony search algorithm. Springer, Berlin, Heidelberg, pp 109–120

    Google Scholar 

  • Noon CE, Bean JC (1993) An efficient transformation of the generalized traveling salesman problem. INFOR Inf Syst Oper Res 31(1):39–44

    MATH  Google Scholar 

  • Pasha U, Hoff A, Hvattum LM (2016) Simple heuristics for the multi-period fleet size and mix vehicle routing problem. INFOR Inf Syst Oper Res 54(2):97–120

    MathSciNet  Google Scholar 

  • Rao R, Patel V (2013) Comparative performance of an elitist teaching-learning-based optimization algorithm for solving unconstrained optimization problems. Int J Ind Eng Comput 4(1):29–50

    Google Scholar 

  • Rego C, Roucairol C (1996) A parallel tabu search algorithm using ejection chains for the vehicle routing problem. In: Meta-heuristics. Springer, Boston, MA, pp 661–675

    Google Scholar 

  • Rodríguez-Espíndola O, Albores P, Brewster C (2018) Disaster preparedness in humanitarian logistics: A collaborative approach for resource management in floods. Eur J Oper Res 264(3):978–993

    MathSciNet  MATH  Google Scholar 

  • Sadeghi-Moghaddam S, Hajiaghaei-Keshteli M, Mahmoodjanloo M (2017) New approaches in metaheuristics to solve the fixed charge transportation problem in a fuzzy environment. Neural computing and applications (in press)

  • Samadi A, Mehranfar N, Fathollahi Fard AM, Hajiaghaei-Keshteli M (2018) Heuristic-based metaheuristic to address a sustainable supply chain network design problem. J Ind Prod Eng 35(2):102–117

    Google Scholar 

  • Sarasola B, Doerner KF, Schmid V, Alba E (2016) Variable neighborhood search for the stochastic and dynamic vehicle routing problem. Ann Oper Res 236(2):425–461

    MathSciNet  MATH  Google Scholar 

  • Saskena JP (1970) Mathematical model of scheduling clients through welfare agencies. J Can Oper Res Soc 8:185–200

    MathSciNet  Google Scholar 

  • Snyder LV, Daskin MS (2006) A random-key genetic algorithm for the generalized traveling salesman problem. Eur J Oper Res 174(1):38–53

    MathSciNet  MATH  Google Scholar 

  • Srivastava SS, Kumar S, Garg RC, Sen P (1969) Generalized traveling salesman problem through n sets of nodes. CORS J 7(2):97

    MathSciNet  MATH  Google Scholar 

  • Taguchi G (1986) Introduction to quality engineering: designing quality into products and processes (No. 658.562 T3)

  • Thouless CR, Guinness FE (1986) Conflict between red deer hinds: the winner always wins. Anim Behav 34(4):1166–1171

    Google Scholar 

  • Wang B, Xia X, Meng H, Li T (2017) Bad-scenario-set robust optimization framework with two objectives for uncertain scheduling systems. IEEE/CAA J Autom Sin 4(1):143–153

    MathSciNet  Google Scholar 

  • Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Google Scholar 

  • Wu TH, Yeh JY, Lee YM (2015) A particle swarm optimization approach with refinement procedure for nurse rostering problem. Comput Oper Res 54:52–63

    MathSciNet  MATH  Google Scholar 

  • Xie F, Jia R (2012) Nonlinear fixed charge transportation problem by minimum cost flow-based genetic algorithm. Comput Ind Eng 63(4):763–778

    Google Scholar 

  • Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84

    Google Scholar 

  • Yousefi M, Yusuff RM (2013) Minimising earliness and tardiness penalties in single machine scheduling against common due date using imperialist competitive algorithm. Int J Prod Res 51(16):4797–4804

    Google Scholar 

  • Zhao SZ, Suganthan PN, Das S (2010) Self-adaptive differential evolution with modified multi-trajectory search for CEC’2010 large scale optimization. In: Proceedings of the international conference on swarm, evolutionary, and memetic computing, Chennai, India, 16–18 December 2010

  • Zhou Y, Luo Q, Xie J, Zheng H (2016) A hybrid bat algorithm with path relinking for the capacitated vehicle routing problem. In: Metaheuristics and optimization in civil engineering. Springer, Cham, pp 255–276

    Google Scholar 

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Acknowledgements

The current paper is an extended version of our conference paper (Fathollahi-Fard and Hajiaghaei-Keshteli 2016) presented at the International Conference on Industrial Engineering (ICIE 2016) supported by the IEEE and held in Tehran on 15–16 January 2016.

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  1. Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran

    Amir Mohammad Fathollahi-Fard & Mostafa Hajiaghaei-Keshteli

  2. School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Reza Tavakkoli-Moghaddam

  3. Arts et Métiers Paris Tech, LCFC, Metz, France

    Reza Tavakkoli-Moghaddam

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  1. Amir Mohammad Fathollahi-Fard
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Correspondence to Mostafa Hajiaghaei-Keshteli.

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Fathollahi-Fard, A.M., Hajiaghaei-Keshteli, M. & Tavakkoli-Moghaddam, R. Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft Comput 24, 14637–14665 (2020). https://doi.org/10.1007/s00500-020-04812-z

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