Volleyball Premier League Algorithm

Abstract This article proposes a novel metaheuristic algorithm called Volleyball Premier League (VPL) inspired by the competition and interaction among volleyball teams during a season. It also mimics the coaching process during a volleyball match. To solve global optimization problems using the volleyball metaphor, there are terms such as substitution, coaching, and learning, which are captured in the VPL algorithm. The proposed algorithm is benchmarked on 23 well-known test functions, which are categorized into three groups, namely unimodal, multimodal and fixed-dimension multimodal functions. The solutions obtained using the VPL have been compared with other metaheuristic algorithms including Particle Swarm Optimization (PSO), Differential Evolution (DE), Genetic Algorithm (GA), Artificial Bee Colony (ABC), Firefly Algorithm (FA), Harmony Search (HS), Sin Cosine Algorithm (SCA), Soccer League Competition (SLC), and League Championship Algorithm (LCA). In addition, VPL has been used to solve three classical engineering design optimization problems. Results show that VPL algorithm possesses a strong capability to produce superior performance over the other well-known metaheuristic algorithms. The results of the experiments also show that the VPL is effectively applicable to solve problems with complex search space.

[1]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[2]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[3]  Conor Ryan,et al.  Grammatical evolution , 2007, GECCO '07.

[4]  Seyed Mohammad Mirjalili,et al.  Ions motion algorithm for solving optimization problems , 2015, Appl. Soft Comput..

[5]  A. Kaveh,et al.  Magnetic charged system search: a new meta-heuristic algorithm for optimization , 2012, Acta Mechanica.

[6]  Mohammad Bagher Ahmadi,et al.  An opposition-based algorithm for function optimization , 2015, Eng. Appl. Artif. Intell..

[7]  A. Roli,et al.  Metaheuristics for the Portfolio Selection Problem , 2008 .

[8]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[9]  Hamed Shah-Hosseini,et al.  Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation , 2011, Int. J. Comput. Sci. Eng..

[10]  Kathryn A. Dowsland,et al.  Simulated Annealing , 1989, Encyclopedia of GIS.

[11]  K. Lee,et al.  A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice , 2005 .

[12]  Petros Koumoutsakos,et al.  Optimization based on bacterial chemotaxis , 2002, IEEE Trans. Evol. Comput..

[13]  Min-Yuan Cheng,et al.  Symbiotic Organisms Search: A new metaheuristic optimization algorithm , 2014 .

[14]  Saeid Kazemzadeh Azad,et al.  Adaptive dimensional search: A new metaheuristic algorithm for discrete truss sizing optimization , 2015 .

[15]  M. Sayadi,et al.  A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems , 2010 .

[16]  Kousik Dasgupta,et al.  Load Balancing in Cloud Computing using Stochastic Hill Climbing-A Soft Computing Approach , 2012 .

[17]  Wansheng Tang,et al.  Monkey Algorithm for Global Numerical Optimization , 2008 .

[18]  Seyedali Mirjalili,et al.  SCA: A Sine Cosine Algorithm for solving optimization problems , 2016, Knowl. Based Syst..

[19]  Ardeshir Bahreininejad,et al.  Water cycle algorithm - A novel metaheuristic optimization method for solving constrained engineering optimization problems , 2012 .

[20]  Dervis Karaboga,et al.  A survey on the applications of artificial bee colony in signal, image, and video processing , 2015, Signal, Image and Video Processing.

[21]  Thomas Stützle,et al.  A beginner's introduction to iterated local search , 2001 .

[22]  Caro Lucas,et al.  Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition , 2007, 2007 IEEE Congress on Evolutionary Computation.

[23]  El-Ghazali Talbi,et al.  Metaheuristics - From Design to Implementation , 2009 .

[24]  Francisco Herrera,et al.  Real-Coded Memetic Algorithms with Crossover Hill-Climbing , 2004, Evolutionary Computation.

[25]  F. Merrikh Bayat,et al.  The runner-root algorithm: A metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature , 2015, Appl. Soft Comput..

[26]  Erik Valdemar Cuevas Jiménez,et al.  A swarm optimization algorithm inspired in the behavior of the social-spider , 2013, Expert Syst. Appl..

[27]  Rony Cueva,et al.  Double-relaxed GRASP Algorithm for Graphic Pattern Recognition in Forensic Odontology , 2011 .

[28]  Graham Kendall,et al.  A Tabu-Search Hyperheuristic for Timetabling and Rostering , 2003, J. Heuristics.

[29]  Hamid Salimi,et al.  Stochastic Fractal Search: A powerful metaheuristic algorithm , 2015, Knowl. Based Syst..

[30]  Andrew Lewis,et al.  The Whale Optimization Algorithm , 2016, Adv. Eng. Softw..

[31]  Fariborz Jolai,et al.  Lion Optimization Algorithm (LOA): A nature-inspired metaheuristic algorithm , 2016, J. Comput. Des. Eng..

[32]  Pin Luarn,et al.  A discrete version of particle swarm optimization for flowshop scheduling problems , 2007, Comput. Oper. Res..

[33]  Christian Blum,et al.  An Ant Colony Optimization Algorithm for Shop Scheduling Problems , 2004, J. Math. Model. Algorithms.

[34]  Carlos A. Coello Coello,et al.  An empirical study about the usefulness of evolution strategies to solve constrained optimization problems , 2008, Int. J. Gen. Syst..

[35]  Ali Ahrari,et al.  Grenade Explosion Method - A novel tool for optimization of multimodal functions , 2010, Appl. Soft Comput..

[36]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[37]  Xin Yao,et al.  Fast Evolutionary Programming , 1996, Evolutionary Programming.

[38]  Thomas Stützle,et al.  Ant Colony Optimization: Overview and Recent Advances , 2018, Handbook of Metaheuristics.

[39]  Hamed Shah-Hosseini,et al.  The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm , 2009, Int. J. Bio Inspired Comput..

[40]  A. Kaveh,et al.  An enhanced charged system search for configuration optimization using the concept of fields of forces , 2011 .

[41]  Seyedali Mirjalili,et al.  Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems , 2015, Neural Computing and Applications.

[42]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[43]  Victor O. K. Li,et al.  A social spider algorithm for global optimization , 2015, Appl. Soft Comput..

[44]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[45]  M. Fesanghary,et al.  An improved harmony search algorithm for solving optimization problems , 2007, Appl. Math. Comput..

[46]  E. Sandgren,et al.  Nonlinear Integer and Discrete Programming in Mechanical Design Optimization , 1990 .

[47]  Kalyanmoy Deb,et al.  Optimal design of a welded beam via genetic algorithms , 1991 .

[48]  Saeed Tavakoli,et al.  Improved Cuckoo Search Algorithm for Feed forward Neural Network Training , 2011 .

[49]  R. Reynolds,et al.  Using knowledge-based evolutionary computation to solve nonlinear constraint optimization problems: a cultural algorithm approach , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[50]  A. Gandomi Interior search algorithm (ISA): a novel approach for global optimization. , 2014, ISA transactions.

[51]  Richard F. Hartl,et al.  Pareto Ant Colony Optimization: A Metaheuristic Approach to Multiobjective Portfolio Selection , 2004, Ann. Oper. Res..

[52]  A. Kaveh,et al.  A novel heuristic optimization method: charged system search , 2010 .

[53]  Krzysztof Fleszar,et al.  New heuristics for one-dimensional bin-packing , 2002, Comput. Oper. Res..

[54]  Ibrahim Eksin,et al.  A new optimization method: Big Bang-Big Crunch , 2006, Adv. Eng. Softw..

[55]  Naser Moosavian,et al.  Soccer league competition algorithm: A novel meta-heuristic algorithm for optimal design of water distribution networks , 2014, Swarm Evol. Comput..

[56]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

[57]  Enrique Alba,et al.  Metaheuristic Procedures for Training Neural Networks (Operations Research/Computer Science Interfaces Series) , 2006 .

[58]  Cândida Ferreira Gene Expression Programming in Problem Solving , 2002 .

[59]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[60]  Piotr Oramus Improvements to Glowworm Swarm Optimization Algorithm , 2010, Comput. Sci..

[61]  Mohsen Ebrahimi Moghaddam,et al.  An image contrast enhancement method based on genetic algorithm , 2010, Pattern Recognit. Lett..

[62]  Shu-Cherng Fang,et al.  An Electromagnetism-like Mechanism for Global Optimization , 2003, J. Glob. Optim..

[63]  Mohammad-Reza Feizi-Derakhshi,et al.  Forest Optimization Algorithm , 2014, Expert Syst. Appl..

[64]  B. Kulkarni,et al.  An ant colony approach for clustering , 2004 .

[65]  C. Lucas,et al.  A novel numerical optimization algorithm inspired from weed colonization , 2006, Ecol. Informatics.

[66]  Christian Blum,et al.  Training feed-forward neural networks with ant colony optimization: an application to pattern classification , 2005, Fifth International Conference on Hybrid Intelligent Systems (HIS'05).

[67]  Ali Kaveh,et al.  Advances in Metaheuristic Algorithms for Optimal Design of Structures , 2014 .

[68]  D. Pham,et al.  THE BEES ALGORITHM, A NOVEL TOOL FOR COMPLEX OPTIMISATION PROBLEMS , 2006 .

[69]  Ali Kaveh Charged System Search Algorithm , 2014 .

[70]  Alex A. Freitas,et al.  A survey of evolutionary algorithms for data mining and knowledge discovery , 2003 .

[71]  E. Tsang,et al.  Guided Local Search , 2010 .

[72]  Afshin Ghanbarzadeh,et al.  the Bees Algorithm: a novel optimisation tool , 2007 .

[73]  Ling Wang,et al.  An effective co-evolutionary particle swarm optimization for constrained engineering design problems , 2007, Eng. Appl. Artif. Intell..

[74]  Taïcir Loukil,et al.  Solving multi-objective production scheduling problems using metaheuristics , 2005, Eur. J. Oper. Res..

[75]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .

[76]  Toshio Shoman,et al.  A modified convergence theorem for a random optimization method , 1977, Inf. Sci..

[77]  Carlos A. Coello Coello,et al.  Evolutionary Multi-Objective Optimization: Basic Concepts and Some Applications in Pattern Recognition , 2011, MCPR.

[78]  Thomas Bäck,et al.  A Survey of Evolution Strategies , 1991, ICGA.

[79]  Jeng-Shyang Pan,et al.  Cat swarm optimization , 2006 .

[80]  Conor Ryan,et al.  Grammatical evolution , 2001, IEEE Trans. Evol. Comput..

[81]  A. Kaveh,et al.  A new optimization method: Dolphin echolocation , 2013, Adv. Eng. Softw..

[82]  Morteza Haghir Chehreghani,et al.  Novel meta-heuristic algorithms for clustering web documents , 2008, Appl. Math. Comput..

[83]  Ali Kaveh,et al.  Colliding bodies optimization: A novel meta-heuristic method , 2014 .

[84]  Saeed Farzi Efficient Job Scheduling in Grid Computing with Modified Artificial Fish Swarm Algorithm , 2009 .

[85]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[86]  S. Deb,et al.  Elephant Herding Optimization , 2015, 2015 3rd International Symposium on Computational and Business Intelligence (ISCBI).

[87]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[88]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[89]  Xin-She Yang,et al.  Flower Pollination Algorithm for Global Optimization , 2012, UCNC.

[90]  Mislav Grgic,et al.  A Survey of Image Processing Algorithms in Digital Mammography , 2009, MMSP 2009.

[91]  E. Hopper,et al.  A Review of the Application of Meta-Heuristic Algorithms to 2D Strip Packing Problems , 2001, Artificial Intelligence Review.

[92]  Amir Hossein Alavi,et al.  Krill herd: A new bio-inspired optimization algorithm , 2012 .

[93]  R. Venkata Rao,et al.  Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems , 2011, Comput. Aided Des..

[94]  Mustafa Servet Kiran,et al.  TSA: Tree-seed algorithm for continuous optimization , 2015, Expert Syst. Appl..

[95]  Yves Crama,et al.  Simulated annealing for complex portfolio selection problems , 2003, Eur. J. Oper. Res..

[96]  Hussain Shareef,et al.  Lightning search algorithm , 2015, Appl. Soft Comput..

[97]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[98]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[99]  K. M. Ragsdell,et al.  Optimal Design of a Class of Welded Structures Using Geometric Programming , 1976 .

[100]  Jason Brownlee,et al.  Clever Algorithms: Nature-Inspired Programming Recipes , 2012 .

[101]  Yujun Zheng Water wave optimization: A new nature-inspired metaheuristic , 2015, Comput. Oper. Res..

[102]  Seyed Mohammad Mirjalili,et al.  The Ant Lion Optimizer , 2015, Adv. Eng. Softw..

[103]  Seyed Mohammad Mirjalili,et al.  Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm , 2015, Knowl. Based Syst..

[104]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[105]  Q. H. Wu,et al.  A heuristic particle swarm optimizer for optimization of pin connected structures , 2007 .

[106]  Abdolreza Hatamlou,et al.  Heart: a novel optimization algorithm for cluster analysis , 2014, Progress in Artificial Intelligence.

[107]  Peter Rossmanith,et al.  Simulated Annealing , 2008, Taschenbuch der Algorithmen.

[108]  Daniele Vigo,et al.  Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems , 1999, INFORMS J. Comput..

[109]  Ardeshir Bahreininejad,et al.  Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problems , 2013, Appl. Soft Comput..

[110]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[111]  Ali Husseinzadeh Kashan,et al.  League Championship Algorithm (LCA): An algorithm for global optimization inspired by sport championships , 2014, Appl. Soft Comput..

[112]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[113]  Laizhong Cui,et al.  Adaptive differential evolution algorithm with novel mutation strategies in multiple sub-populations , 2016, Comput. Oper. Res..

[114]  A. Kaveh,et al.  A new meta-heuristic method: Ray Optimization , 2012 .

[115]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[116]  Abdolreza Hatamlou,et al.  Black hole: A new heuristic optimization approach for data clustering , 2013, Inf. Sci..

[117]  Tamer Ölmez,et al.  A new metaheuristic for numerical function optimization: Vortex Search algorithm , 2015, Inf. Sci..

[118]  Pierre Hansen,et al.  Variable neighborhood search , 1997, Eur. J. Oper. Res..

[119]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[120]  Tung Khac Truong,et al.  Chemical reaction optimization with greedy strategy for the 0-1 knapsack problem , 2013, Appl. Soft Comput..

[121]  Kalyanmoy Deb,et al.  GeneAS: A Robust Optimal Design Technique for Mechanical Component Design , 1997 .

[122]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[123]  Michael A. Trick,et al.  Round robin scheduling - a survey , 2008, Eur. J. Oper. Res..

[124]  Dervis Karaboga,et al.  A novel clustering approach: Artificial Bee Colony (ABC) algorithm , 2011, Appl. Soft Comput..

[125]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[126]  Mostafa Hajiaghaei-Keshteli,et al.  Solving the integrated scheduling of production and rail transportation problem by Keshtel algorithm , 2014, Appl. Soft Comput..

[127]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

[128]  Ali Husseinzadeh Kashan,et al.  A new metaheuristic for optimization: Optics inspired optimization (OIO) , 2015, Comput. Oper. Res..

[129]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[130]  Siamak Talatahari,et al.  An improved ant colony optimization for constrained engineering design problems , 2010 .

[131]  Muzaffar Eusuff,et al.  Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization , 2006 .

[132]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[133]  Yu-Jun Zheng,et al.  Ecogeography-based optimization: Enhancing biogeography-based optimization with ecogeographic barriers and differentiations , 2014, Comput. Oper. Res..

[134]  Farshad Merrikh-Bayat,et al.  The runner-root algorithm , 2015 .