Is the Vehicle Routing Problem Dead? An Overview Through Bioinspired Perspective and a Prospect of Opportunities

Route planning is a research topic in artificial intelligence of paramount importance for a plethora of applications related to transportation and mobility. Problems related to the discovery of optimal routes have been at the core of hundreds of research studies reported to date in different scientific venues and tier-one journals. In this context, the vehicle routing problem (VRP) is arguably one of the most studied problems in this knowledge stream. Since its inception more than fifty years ago, manifold studies have been developed over decades of intense research efforts, proposing new realistic problem formulations and sophisticated algorithmic methods for its efficient solving. Such a vibrant activity has been propelled by the ever-growing needs and resource availability of the time being, which have spanned new challenging conditions for practical VRP problems. This is the main reason why this field of study, today, grasps more interest from the research community than ever. In this overview, we profoundly review the recent history and current status of the VRP and related variants. First, the important characteristics and variants of this problem are described in detail, followed by a systematic review of recent advances reported in the literature. We place special emphasis on bioinspired optimization algorithms published in the last years. On a closing note, the manuscript rounds up its literature overview with the envisioned status of this research area, exposed in the form of open challenges that still remain insufficiently addressed, and that should thus guide research efforts in the future.

[1]  Zhuo Fu,et al.  Tabu search algorithm for the distance-constrained vehicle routing problem with split deliveries by order , 2018, PloS one.

[2]  Yew-Soon Ong,et al.  Evolutionary Multitasking: A Computer Science View of Cognitive Multitasking , 2016, Cognitive Computation.

[3]  Reza Tavakkoli-Moghaddam,et al.  Efficiency of a multi-objective imperialist competitive algorithm: A bi-objective location-routing-inventory problem with probabilistic routes , 2014 .

[4]  Olli Bräysy,et al.  A Reactive Variable Neighborhood Search for the Vehicle-Routing Problem with Time Windows , 2003, INFORMS J. Comput..

[5]  Xin-She Yang,et al.  An Evolutionary Discrete Firefly Algorithm with Novel Operators for Solving the Vehicle Routing Problem with Time Windows , 2016, Nature-Inspired Computation in Engineering.

[6]  Hong Wang,et al.  Adaptive comprehensive learning bacterial foraging optimization and its application on vehicle routing problem with time windows , 2015, Neurocomputing.

[7]  Vijay Kumar,et al.  An Improved Firefly Algorithm for the Vehicle Routing Problem with Time Windows , 2018, 2018 International Conference on Advances in Computing, Communications and Informatics (ICACCI).

[8]  Nicos Christofides,et al.  An Algorithm for the Vehicle-dispatching Problem , 1969 .

[9]  Yuvraj Gajpal,et al.  Ant Colony Algorithm for Routing Alternate Fuel Vehicles in Multi-depot Vehicle Routing Problem , 2018, Decision Science in Action.

[10]  Eneko Osaba,et al.  A novel meta-heuristic based on soccer concepts to solve routing problems , 2013, GECCO '13 Companion.

[11]  Baozhen Yao,et al.  Improved artificial bee colony algorithm for vehicle routing problem with time windows , 2017, PloS one.

[12]  Ibrahim H. Osman,et al.  Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Methods for Vehicle Routing Problems with Time Windows , 1997 .

[13]  Zulaiha Ali Othman,et al.  Taguchi-based Parameter Setting of Cuckoo Search Algorithm for Capacitated Vehicle Routing Problem , 2016, ICML 2016.

[14]  A. Jabbarzadeh,et al.  Accelerated Cuckoo Optimization Algorithm for Capacitated Vehicle Routing Problem in Competitive Conditions , 2018 .

[15]  Kan Wu,et al.  A multiple colonies artificial bee colony algorithm for a capacitated vehicle routing problem and re-routing strategies under time-dependent traffic congestion , 2017, Comput. Ind. Eng..

[16]  Mohammad Saidi-Mehrabad,et al.  An Optimization Model for Heterogeneous Vehicle Routing and Scheduling Problem with Fixed Cost and Green Reverse Logistics Network Using Genetic Algorithm , 2019 .

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

[18]  Duc-Cuong Dang,et al.  Heuristic solutions for the vehicle routing problem with time windows and synchronized visits , 2016, Optim. Lett..

[19]  Ruey-Maw Chen,et al.  Neural-like encoding particle swarm optimization for periodic vehicle routing problems , 2019, Expert Syst. Appl..

[20]  Cinmayii Manliguez,et al.  Cuckoo search via Lévy flights for the capacitated vehicle routing problem , 2017, Journal of Industrial Engineering International.

[21]  Xin-She Yang,et al.  Bio-inspired computation: Where we stand and what's next , 2019, Swarm Evol. Comput..

[22]  Mansoureh Naderipour,et al.  A novel comprehensive macroscopic model for time-dependent vehicle routing problem with multi-alternative graph to reduce fuel consumption: A case study , 2016, Comput. Ind. Eng..

[23]  Hao Cai,et al.  Quantum Fireworks Evolutionary Algorithm for Vehicle Routing Problem in Supply Chain with Multiple Time Windows , 2018, 2018 2nd IEEE Advanced Information Management,Communicates,Electronic and Automation Control Conference (IMCEC).

[24]  Zhihua Cui,et al.  Monarch butterfly optimization , 2015, Neural Computing and Applications.

[25]  Leandro dos Santos Coelho,et al.  A Novel Metaheuristic Algorithm Inspired by Rhino Herd Behavior , 2018 .

[26]  James P. Kelly,et al.  The Impact of Metaheuristics on Solving the Vehicle Routing Problem: Algorithms, Problem Sets, and Computational Results , 1998 .

[27]  Liang Feng,et al.  Insights on Transfer Optimization: Because Experience is the Best Teacher , 2018, IEEE Transactions on Emerging Topics in Computational Intelligence.

[28]  GenMitsuo,et al.  A tutorial survey of job-shop scheduling problems using genetic algorithms, part II , 1996 .

[29]  Igor Skrjanc,et al.  New results in modelling derived from Bayesian filtering , 2010, Knowl. Based Syst..

[30]  Junli Wang,et al.  A Novel Hybrid Cuckoo Search Algorithm for Optimizing Vehicle Routing Problem in Logistics Distribution System , 2016 .

[31]  R. Sridharan,et al.  Design and development of a hybrid ant colony-variable neighbourhood search algorithm for a multi-depot green vehicle routing problem , 2017 .

[32]  Yew-Soon Ong,et al.  Multifactorial Evolution: Toward Evolutionary Multitasking , 2016, IEEE Transactions on Evolutionary Computation.

[33]  Daniele Vigo,et al.  Routing a Heterogeneous Fleet of Vehicles , 2008 .

[34]  Shin-Yu Lin,et al.  A simulated annealing heuristic for the open location-routing problem , 2015, Comput. Oper. Res..

[35]  Peng-Yeng Yin,et al.  Adaptive memory artificial bee colony algorithm for green vehicle routing with cross-docking , 2016 .

[36]  Ben Niu,et al.  SRBFOs for Solving the Heterogeneous Fixed Fleet Vehicle Routing Problem , 2015, ICIC.

[37]  Weibo Yang,et al.  An improved fireworks algorithm for the capacitated vehicle routing problem , 2018, Frontiers of Computer Science.

[38]  Ibrahim H. Osman,et al.  Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem , 1993, Ann. Oper. Res..

[39]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[40]  Patrick R. McMullen,et al.  Ant colony optimization techniques for the vehicle routing problem , 2004, Adv. Eng. Informatics.

[41]  Xiaohang Yue,et al.  Novel Ant Colony Optimization Methods for Simplifying Solution Construction in Vehicle Routing Problems , 2016, IEEE Transactions on Intelligent Transportation Systems.

[42]  Haibin Duan,et al.  Social-class pigeon-inspired optimization and time stamp segmentation for multi-UAV cooperative path planning , 2018, Neurocomputing.

[43]  Isa Nakhai Kamal Abadi,et al.  An efficient population-based simulated annealing algorithm for the multi-product multi-retailer perishable inventory routing problem , 2016, Comput. Ind. Eng..

[44]  B. Gillett,et al.  Multi-terminal vehicle-dispatch algorithm , 1976 .

[45]  Voratas Kachitvichyanukul,et al.  A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery , 2009, Comput. Oper. Res..

[46]  Magdalene Marinaki,et al.  Combinatorial neighborhood topology bumble bees mating optimization for the vehicle routing problem with stochastic demands , 2015, Soft Comput..

[47]  Ali Kaveh,et al.  A NOVEL META-HEURISTIC ALGORITHM: TUG OF WAR OPTIMIZATION , 2016 .

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

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

[50]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

[51]  Samy Bengio,et al.  The Vehicle Routing Problem with Time Windows Part II: Genetic Search , 1996, INFORMS J. Comput..

[52]  Yong Shi,et al.  A hybrid genetic algorithm for a home health care routing problem with time window and fuzzy demand , 2017, Expert Syst. Appl..

[53]  Javier Del Ser,et al.  Nature-inspired heuristics for the multiple-vehicle selective pickup and delivery problem under maximum profit and incentive fairness criteria , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[54]  Yongquan Zhou,et al.  A Hybrid Bat Algorithm with Path Relinking for the Capacitated Vehicle Routing Problem , 2013 .

[55]  Yongquan Zhou,et al.  A hybrid Cuckoo Search Algorithm-GRASP for Vehicle Routing Problem , 2013 .

[56]  Tom Van Woensel,et al.  Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts , 2019, Transp. Sci..

[57]  Robert A. Russell,et al.  Hybrid Heuristics for the Vehicle Routing Problem with Time Windows , 1995, Transp. Sci..

[58]  Salim Chikhi,et al.  Cooperative Parallel Metaheuristics based Penguin Optimization Search for Solving the Vehicle Routing Problem , 2016, Int. J. Appl. Metaheuristic Comput..

[59]  C. K. M. Lee,et al.  An Improved Artificial Bee Colony Algorithm for the Capacitated Vehicle Routing Problem , 2015, 2015 IEEE International Conference on Systems, Man, and Cybernetics.

[60]  A. Golmohammadi,et al.  A multi-objective location routing problem using imperialist competitive algorithm , 2016 .

[61]  Ferani E. Zulvia,et al.  Application of a fuzzy ant colony system to solve the dynamic vehicle routing problem with uncertain service time , 2016 .

[62]  Sai Ho Chung,et al.  Survey of Green Vehicle Routing Problem: Past and future trends , 2014, Expert Syst. Appl..

[63]  Lynda Ai Pin Tan The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

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

[65]  Ben Niu,et al.  Vehicle Routing Problem with Time Windows Based on Adaptive Bacterial Foraging Optimization , 2012, ICIC.

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

[67]  Eugene L. Lawler,et al.  The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1985 .

[68]  Vincent F. Yu,et al.  Symbiotic Organism Search (SOS) for Solving the Capacitated Vehicle Routing Problem , 2015 .

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

[70]  Magdalene Marinaki,et al.  A hybrid genetic - Particle Swarm Optimization Algorithm for the vehicle routing problem , 2010, Expert Syst. Appl..

[71]  Jörg Homberger,et al.  Two Evolutionary Metaheuristics For The Vehicle Routing Problem With Time Windows , 1999 .

[72]  Frédéric Semet,et al.  Rich vehicle routing problems: From a taxonomy to a definition , 2015, Eur. J. Oper. Res..

[73]  Yuan-biao Zhang,et al.  A Novel Algorithm to Solve the Vehicle Routing Problem with Time Windows: Imperialist Competitive Algorithm , 2011 .

[74]  Jan Dethloff,et al.  Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up , 2001, OR Spectr..

[75]  Xin-She Yang,et al.  A New Metaheuristic Bat-Inspired Algorithm , 2010, NICSO.

[76]  A. Perallos,et al.  Focusing on the Golden Ball Metaheuristic: An Extended Study on a Wider Set of Problems , 2014, TheScientificWorldJournal.

[77]  Yan Li,et al.  A green vehicle routing model based on modified particle swarm optimization for cold chain logistics , 2019, Ind. Manag. Data Syst..

[78]  Mazin Abed Mohammed,et al.  Solving vehicle routing problem by using improved genetic algorithm for optimal solution , 2017, J. Comput. Sci..

[79]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[80]  Werasak Kurutach,et al.  An Improved Golden Ball Algorithm for the Vehicle Routing Problem with Simultaneous Pickup and Delivery , 2018, 2018 IEEE/ACIS 17th International Conference on Computer and Information Science (ICIS).

[81]  Javier Del Ser,et al.  jMetalPy: a Python Framework for Multi-Objective Optimization with Metaheuristics , 2019, Swarm Evol. Comput..

[82]  Budi Santosa,et al.  Symbiotic organisms search and two solution representations for solving the capacitated vehicle routing problem , 2017, Appl. Soft Comput..

[83]  Can Berk Kalayci,et al.  An ant colony system empowered variable neighborhood search algorithm for the vehicle routing problem with simultaneous pickup and delivery , 2016, Expert Syst. Appl..

[84]  Seyed Hessameddin Zegordi,et al.  A Multi-Objective Imperialist Competitive Algorithm for Vehicle Routing Problem in Cross-docking Networks with Time Windows , 2018 .

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

[86]  Raman Maini,et al.  A hybrid of ant colony and firefly algorithms (HAFA) for solving vehicle routing problems , 2018, J. Comput. Sci..

[87]  Yosi Agustina Hidayat,et al.  A simulated annealing heuristic for the hybrid vehicle routing problem , 2017, Appl. Soft Comput..

[88]  Trong-The Nguyen,et al.  A Multi-Objective Optimal Vehicle Fuel Consumption Based on Whale Optimization Algorithm , 2017 .

[89]  Gilbert Laporte,et al.  Three multi-start data-driven evolutionary heuristics for the vehicle routing problem with multiple time windows , 2019, J. Heuristics.

[90]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[91]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

[92]  Iztok Fister,et al.  On Efficiently Solving the Vehicle Routing Problem with Time Windows Using the Bat Algorithm with Random Reinsertion Operators , 2018 .

[93]  Eneko Osaba,et al.  Design and Implementation of a Combinatorial Optimization Multi-population Meta-heuristic for Solving Vehicle Routing Problems , 2016, Int. J. Interact. Multim. Artif. Intell..

[94]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[95]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[96]  Chao Chen,et al.  Fresh seafood delivery routing problem using an improved ant colony optimization , 2019, Ann. Oper. Res..

[97]  Nitin Agrawal,et al.  AN Enhancement of whale optimization algorithm using ANN for routing optimization in Ad-hoc network , 2017 .

[98]  Abdelouahab Moussaoui,et al.  Penguins Search Optimization Algorithm (PeSOA) , 2013, IEA/AIE.

[99]  Zhenzhen Zhang,et al.  A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints , 2018, Eur. J. Oper. Res..

[100]  Liangjun Ke,et al.  A brain storm optimization approach for the cumulative capacitated vehicle routing problem , 2018, Memetic Comput..

[101]  Antonio J. Nebro,et al.  jMetal: A Java framework for multi-objective optimization , 2011, Adv. Eng. Softw..

[102]  Jiujun Cheng,et al.  Ant colony optimization with clustering for solving the dynamic location routing problem , 2016, Appl. Math. Comput..

[103]  Arun Kumar Sangaiah,et al.  An improved ant colony optimization for the multi-trip Capacitated Arc Routing Problem , 2018, Comput. Electr. Eng..

[104]  Shaoqiang Yu,et al.  An improved artificial bee colony algorithm for vehicle routing problem with time windows: A real case in Dalian , 2016 .

[105]  Feng Duan,et al.  Dynamic Vehicle Routing Problems with Enhanced Ant Colony Optimization , 2018 .

[106]  Richard W. Eglese,et al.  A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups , 2018, Comput. Oper. Res..

[107]  Manoj Kumar Tiwari,et al.  Multi-objective modeling of production and pollution routing problem with time window: A self-learning particle swarm optimization approach , 2016, Comput. Ind. Eng..

[108]  Ling Wei,et al.  Fitness-scaling adaptive genetic algorithm with local search for solving the Multiple Depot Vehicle Routing Problem , 2016, Simul..

[109]  R. Tavakkoli-Moghaddam,et al.  A hybrid simulated annealing for capacitated vehicle routing problems with the independent route length , 2006, Appl. Math. Comput..

[110]  Yasuhiro Tsujimura,et al.  A tutorial survey of job-shop scheduling problems using genetic algorithms, part II: hybrid genetic search strategies , 1999 .

[111]  Pedro Larrañaga,et al.  Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators , 1999, Artificial Intelligence Review.

[112]  Junguo Zhang,et al.  Adaptive Operator Quantum-Behaved Pigeon-Inspired Optimization Algorithm with Application to UAV Path Planning , 2018, Algorithms.

[113]  Kenneth Sörensen,et al.  Metaheuristics - the metaphor exposed , 2015, Int. Trans. Oper. Res..

[114]  Liying Zhao,et al.  Improved Harmony Search Algorithm for Truck Scheduling Problem in Multiple-Door Cross-Docking Systems , 2018 .

[115]  Michel Gendreau,et al.  An efficient variable neighborhood search heuristic for very large scale vehicle routing problems , 2007, Comput. Oper. Res..

[116]  David S.W. Lai,et al.  A Tabu Search Heuristic for the Heterogeneous Vehicle Routing Problem on a Multi-graph , 2016 .

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

[118]  Satvir Singh,et al.  Butterfly optimization algorithm: a novel approach for global optimization , 2018, Soft Computing.

[119]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[120]  Amir Hajjam El Hassani,et al.  An Improved Cuckoo Search for a Patient Transportation Problem with Consideration of Reducing Transport Emissions , 2018 .

[121]  Gilbert Laporte,et al.  Fifty Years of Vehicle Routing , 2009, Transp. Sci..

[122]  Ying Tan,et al.  Fireworks Algorithm for Optimization , 2010, ICSI.

[123]  Mohammad R. Akbari Jokar,et al.  A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem , 2016, Comput. Ind. Eng..

[124]  Jean-François Cordeau,et al.  VRP with Time Windows , 1999, The Vehicle Routing Problem.

[125]  Dan Wu,et al.  Brainstorming-Based Ant Colony Optimization for Vehicle Routing With Soft Time Windows , 2019, IEEE Access.

[126]  Milan Tuba,et al.  Unmanned Combat Aerial Vehicle Path Planning by Brain Storm Optimization Algorithm , 2018 .

[127]  Yongbo Li,et al.  An improved ant colony optimization algorithm for the multi-depot green vehicle routing problem with multiple objectives , 2019, Journal of Cleaner Production.

[128]  Ilya Pavlyukevich Lévy flights, non-local search and simulated annealing , 2007, J. Comput. Phys..

[129]  Javier Del Ser,et al.  A discrete water cycle algorithm for solving the symmetric and asymmetric traveling salesman problem , 2018, Appl. Soft Comput..

[130]  Chao Wang,et al.  A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup-delivery and time windows , 2015, Comput. Ind. Eng..

[131]  Baozhen Yao,et al.  An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot , 2016, Ann. Oper. Res..

[132]  Magdalene Marinaki,et al.  A Glowworm Swarm Optimization algorithm for the Vehicle Routing Problem with Stochastic Demands , 2016, Expert Syst. Appl..

[133]  Alex Van Breedam,et al.  Improvement heuristics for the Vehicle Routing Problem based on simulated annealing , 1995 .

[134]  Xin Chen,et al.  A hybrid algorithm combining glowworm swarm optimization and complete 2-opt algorithm for spherical travelling salesman problems , 2017, Appl. Soft Comput..

[135]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

[136]  Tarek Y. ElMekkawy,et al.  Hybridized ant colony algorithm for the Multi Compartment Vehicle Routing Problem , 2015, Appl. Soft Comput..

[137]  Kris Braekers,et al.  The vehicle routing problem: State of the art classification and review , 2016, Comput. Ind. Eng..

[138]  Wen-Chyuan Chiang,et al.  Simulated annealing metaheuristics for the vehicle routing problem with time windows , 1996, Ann. Oper. Res..

[139]  Michel Gendreau,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows , 1997, Transp. Sci..

[140]  Zhifeng Hao,et al.  Human-computer cooperative brain storm optimization algorithm for the two-echelon vehicle routing problem , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[141]  Shahaboddin Shamshirband,et al.  Gravitational Search Algorithm to Solve Open Vehicle Routing Problem , 2015, IBICA.

[142]  Xin-She Yang,et al.  An improved discrete bat algorithm for symmetric and asymmetric Traveling Salesman Problems , 2016, Eng. Appl. Artif. Intell..

[143]  Debasish Ghose,et al.  Glowworm swarm optimisation: a new method for optimising multi-modal functions , 2009, Int. J. Comput. Intell. Stud..

[144]  Stella Sofianopoulou,et al.  A Firefly Algorithm for the Heterogeneous Fixed Fleet VRP , 2019 .

[145]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[146]  Reza Tavakkoli-Moghaddam,et al.  Modified variable neighborhood search and genetic algorithm for profitable heterogeneous vehicle routing problem with cross-docking , 2019, Appl. Soft Comput..

[147]  Mitsuo Gen,et al.  A tutorial survey of job-shop scheduling problems using genetic algorithms—I: representation , 1996 .

[148]  Jean-François Cordeau,et al.  A parallel iterated tabu search heuristic for vehicle routing problems , 2012, Comput. Oper. Res..

[149]  Haibin Duan,et al.  Pigeon-inspired optimization: a new swarm intelligence optimizer for air robot path planning , 2014, Int. J. Intell. Comput. Cybern..

[150]  Vincent F. Yu,et al.  Solving the location-routing problem with simultaneous pickup and delivery by simulated annealing , 2016 .

[151]  Eneko Osaba,et al.  Golden ball: a novel meta-heuristic to solve combinatorial optimization problems based on soccer concepts , 2014, Applied Intelligence.

[152]  Marcus Ritt,et al.  An iterated tabu search for the multi-compartment vehicle routing problem , 2017, Comput. Oper. Res..

[153]  Francisco Herrera,et al.  SHADE with Iterative Local Search for Large-Scale Global Optimization , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

[154]  Gilbert Laporte,et al.  The vehicle routing problem: An overview of exact and approximate algorithms , 1992 .

[155]  Rong Chen,et al.  A Monarch Butterfly Optimization for the Dynamic Vehicle Routing Problem , 2017, Algorithms.

[156]  Adis Alihodzic Fireworks Algorithm with New Feasibility-Rules in Solving UAV Path Planning , 2016, 2016 3rd International Conference on Soft Computing & Machine Intelligence (ISCMI).

[157]  G. Laporte The traveling salesman problem: An overview of exact and approximate algorithms , 1992 .

[158]  Jesús Racero,et al.  Reducing pollutant emissions in a waste collection vehicle routing problem using a variable neighborhood tabu search algorithm: a case study , 2019, TOP.

[159]  Yuhui Shi,et al.  Brain Storm Optimization Algorithm , 2011, ICSI.

[160]  Ali Moudden,et al.  Adapted Bat Algorithm for Capacitated Vehicle Routing Problem , 2015 .

[161]  Rodrigo Linfati,et al.  A probabilistic granular tabu search for the distance constrained capacitated vehicle routing problem , 2018 .

[162]  Chao Wang,et al.  Solving vehicle routing problem with simultaneous pickup and delivery using parallel simulated annealing algorithm , 2015 .

[163]  Narges Norouzi,et al.  Evaluating of the particle swarm optimization in a periodic vehicle routing problem , 2015 .

[164]  Valeria Soto-Mendoza,et al.  Solving the open vehicle routing problem with capacity and distance constraints with a biased random key genetic algorithm , 2019, Comput. Ind. Eng..

[165]  Dominik Goeke,et al.  Granular tabu search for the pickup and delivery problem with time windows and electric vehicles , 2019, Eur. J. Oper. Res..

[166]  Richard F. Hartl,et al.  A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows , 2004, J. Heuristics.

[167]  Nicos Christofides,et al.  The vehicle routing problem , 1976, Revue française d'automatique, informatique, recherche opérationnelle. Recherche opérationnelle.

[168]  Gen-ke Yang,et al.  Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem , 2006 .

[169]  Erdal Aydemir,et al.  A Simulated Annealing Algorithm Based Solution Method for a Green Vehicle Routing Problem with Fuel Consumption , 2018, International Series in Operations Research & Management Science.

[170]  Baozhen Yao,et al.  Production , Manufacturing and Logistics An improved ant colony optimization for vehicle routing problem , 2008 .

[171]  Barrie M. Baker,et al.  A genetic algorithm for the vehicle routing problem , 2003, Comput. Oper. Res..

[172]  M. Goetschalckx,et al.  The vehicle routing problem with backhauls , 1989 .

[173]  Xin-She Yang,et al.  A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy , 2016, Soft Computing.

[174]  Jean-Yves Potvin,et al.  THE TRAVELING SALESMAN PROBLEM: A NEURAL NETWORK PERSPECTIVE , 1993 .

[175]  W. Hu,et al.  An improved flower pollination algorithm for optimization of intelligent logistics distribution center , 2019, Advances in Production Engineering & Management.

[176]  Salwani Abdullah,et al.  Modified artificial bee colony for the vehicle routing problems with time windows , 2016, SpringerPlus.

[177]  Panos M. Pardalos,et al.  A hybrid multi-objective genetic local search algorithm for the prize-collecting vehicle routing problem , 2019, Inf. Sci..

[178]  Cai Hao,et al.  Chaotic discrete bat algorithm for capacitated vehicle routing problem , 2019, Int. J. Auton. Adapt. Commun. Syst..

[179]  Panos M. Pardalos,et al.  Discrete firefly algorithm with compound neighborhoods for asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery , 2019, Appl. Soft Comput..

[180]  S. A. MirHassani,et al.  Reduction of carbon emissions in VRP by gravitational search algorithm , 2014 .

[181]  Richard F. Hartl,et al.  An improved Ant System algorithm for theVehicle Routing Problem , 1999, Ann. Oper. Res..

[182]  Iztok Fister,et al.  A Discrete and Improved Bat Algorithm for solving a medical goods distribution problem with pharmacological waste collection , 2019, Swarm Evol. Comput..

[183]  Han-Chieh Chao,et al.  Modified Discrete Glowworm Swarm Optimization Algorithm Based on Time Window Division for Multi-objective VRPTW , 2018 .

[184]  Antonio LaTorre,et al.  Multiple Offspring Sampling in Large Scale Global Optimization , 2012, 2012 IEEE Congress on Evolutionary Computation.

[185]  Vahid Kayvanfar,et al.  Enhanced intelligent water drops and cuckoo search algorithms for solving the capacitated vehicle routing problem , 2016, Inf. Sci..

[186]  Martin Desrochers,et al.  A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows , 1990, Oper. Res..

[187]  Hoong Chuin Lau,et al.  An artificial bee colony-based hybrid approach for waste collection problem with midway disposal pattern , 2019, Appl. Soft Comput..

[188]  Ali Moudden,et al.  A discrete Bat Algorithm for the vehicle routing problem with time windows , 2017, 2017 International Colloquium on Logistics and Supply Chain Management (LOGISTIQUA).

[189]  Limin Luo,et al.  Multi-strategy adaptive particle swarm optimization for numerical optimization , 2015, Eng. Appl. Artif. Intell..

[190]  Iztok Fister,et al.  Bioinspired Computational Intelligence and Transportation Systems: A Long Road Ahead , 2020, IEEE Transactions on Intelligent Transportation Systems.

[191]  Jing Shi,et al.  A multi-compartment vehicle routing problem with time windows for urban distribution - A comparison study on particle swarm optimization algorithms , 2019, Comput. Ind. Eng..

[192]  Ping Chen,et al.  A Hybrid Tabu Search Algorithm for a Real-World Open Vehicle Routing Problem Involving Fuel Consumption Constraints , 2018, Complex..

[193]  Paresh Tanna,et al.  Job Scheduling Heuristics and Simulation Tools in Cloud Computing Environment:A Survey , 2018 .

[194]  Gilbert Laporte,et al.  A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows , 2015, Comput. Oper. Res..

[195]  Sadoullah Ebrahimnejad,et al.  A green vehicle routing problem with time windows considering the heterogeneous fleet of vehicles: two metaheuristic algorithms , 2019, European J. of Industrial Engineering.

[196]  Mohamed Bensakhria,et al.  Efficient Golden-Ball Algorithm Based Clustering to solve the Multi-Depot VRP With Time Windows , 2018, Int. J. Appl. Evol. Comput..

[197]  Rui Wang,et al.  An Improved Flower Pollination Algorithm for Optimal Unmanned Undersea Vehicle Path Planning Problem , 2016, Int. J. Pattern Recognit. Artif. Intell..

[198]  Nasser R. Sabar,et al.  Meta-harmony search algorithm for the vehicle routing problem with time windows , 2015, Inf. Sci..

[199]  Javier Del Ser,et al.  A Harmony Search Approach for the Selective Pick-Up and Delivery Problem with Delayed Drop-Off , 2015, ICHSA.

[200]  Tantikorn Pichpibul,et al.  A new efficient and effective golden-ball-based technique for the capacitated vehicle routing problem , 2016, 2016 IEEE/ACIS 15th International Conference on Computer and Information Science (ICIS).

[201]  Juan Antonio Sicilia,et al.  An optimization algorithm for solving the rich vehicle routing problem based on Variable Neighborhood Search and Tabu Search metaheuristics , 2016, J. Comput. Appl. Math..

[202]  Angel A. Juan,et al.  Rich Vehicle Routing Problem , 2014, ACM Comput. Surv..

[203]  Farnaz Barzinpour,et al.  A multi-compartment capacitated arc routing problem with intermediate facilities for solid waste collection using hybrid adaptive large neighborhood search and whale algorithm , 2019, Waste management & research : the journal of the International Solid Wastes and Public Cleansing Association, ISWA.

[204]  W. Y. Szeto,et al.  An artificial bee colony algorithm for the capacitated vehicle routing problem , 2011, Eur. J. Oper. Res..

[205]  Hao Ding,et al.  Modified Artificial Bee Colony Algorithm for the Capacitated Vehicle Routing Problem , 2018, DEStech Transactions on Social Science, Education and Human Science.

[206]  Vincent F. Yu,et al.  A Simulated Annealing Heuristic for the Capacitated Green Vehicle Routing Problem , 2019, Mathematical Problems in Engineering.

[207]  Zhao Yang Dong,et al.  Electric Vehicle Route Optimization Considering Time-of-Use Electricity Price by Learnable Partheno-Genetic Algorithm , 2015, IEEE Transactions on Smart Grid.

[208]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[209]  Bruce L. Golden,et al.  The vehicle routing problem : latest advances and new challenges , 2008 .

[210]  Abdullah Konak,et al.  A genetic algorithm with exact dynamic programming for the green vehicle routing & scheduling problem , 2017 .

[211]  Omid Bozorg Haddad,et al.  Honey-Bees Mating Optimization (HBMO) Algorithm: A New Heuristic Approach for Water Resources Optimization , 2006 .

[212]  Jouhaina Chaouachi Siala,et al.  Discrete honeybee mating optimization algorithm for the routing of battery-operated automated guidance electric vehicles in personal rapid transit systems , 2016, Swarm Evol. Comput..

[213]  Qingfu Zhang,et al.  A Survey on Cooperative Co-Evolutionary Algorithms , 2019, IEEE Transactions on Evolutionary Computation.

[214]  Abdul Hanan Abdullah,et al.  Multiobjective Dynamic Vehicle Routing Problem and Time Seed Based Solution Using Particle Swarm Optimization , 2015, J. Sensors.

[215]  R. Yarinezhad,et al.  A New Routing Algorithm for Vehicular Ad-hoc Networks based on Glowworm Swarm Optimization Algorithm , 2019 .

[216]  Shahaboddin Shamshirband,et al.  OVRP_ICA: An Imperialist-Based Optimization Algorithm for the Open Vehicle Routing Problem , 2015, HAIS.

[217]  Wayan Firdaus Mahmudy,et al.  IMPROVED SIMULATED ANNEALING FOR OPTIMIZATION OF VEHICLE ROUTING PROBLEM WITH TIME WINDOWS (VRPTW) , 2014 .

[218]  Martin W. P. Savelsbergh,et al.  The General Pickup and Delivery Problem , 1995, Transp. Sci..