Abstract
Honey Bees Mating Optimization algorithm is a relatively new nature inspired algorithm. In this paper, this nature inspired algorithm is used in a hybrid scheme with other metaheuristic algorithms for successfully solving the Vehicle Routing Problem. More precisely, the proposed algorithm for the solution of the Vehicle Routing Problem, the Honey Bees Mating Optimization (HBMOVRP), combines a Honey Bees Mating Optimization (HBMO) algorithm with the Multiple Phase Neighborhood Search–Greedy Randomized Adaptive Search Procedure (MPNS–GRASP) and the Expanding Neighborhood Search (ENS) algorithm. Besides these two procedures, the proposed algorithm has, also, two additional main innovative features compared to other Honey Bees Mating Optimization algorithms concerning the crossover operator and the workers. Two sets of benchmark instances are used in order to test the proposed algorithm. The results obtained for both sets are very satisfactory. More specifically, in the fourteen classic instances proposed by Christofides, the average quality is 0.029% and in the second set with the twenty large scale vehicle routing problems the average quality is 0.40%.
Similar content being viewed by others
References
Abbass HA (2001a) A monogenous MBO approach to satisfiability. In: Proceeding of the international conference on computational intelligence for modelling, control and automation, CIMCA’2001, Las Vegas, NV, USA
Abbass HA (2001b) Marriage in honey-bee optimization (MBO): a haplometrosis polygynous swarming approach. In: The congress on evolutionary computation (CEC2001), Seoul, Korea, May 2001, pp 207–214
Afshar A, Bozog Haddad O, Marino MA, Adams BJ (2007) Honey-bee mating optimization (HBMO) algorithm for optimal reservoir operation. J Frankl Inst 344:452–462
Baker BM, Ayechew MA (2003) A genetic algorithm for the vehicle routing problem. Comput Oper Res 30(5):787–800
Baykasoglu A, Ozbakor L, Tapkan P (2007) Artificial bee colony algorithm and its application to generalized assignment problem. In: Chan FTS, Tiwari MK (eds) Swarm intelligence, focus on ant and particle swarm optimization. I-Tech Education and Publishing, Vienna, pp 113–144
Berger J, Barkaoui M (2003) A hybrid genetic algorithm for the capacitated vehicle routing problem. In: Proceedings of the genetic and evolutionary computation conference, Chicago, pp 646–656
Bodin L, Golden B, Assad A, Ball M (1983) The state of the art in the routing and scheduling of vehicles and crews. Comput Oper Res 10:63–212
Christofides N, Mingozzi A, Toth P (1979) The vehicle routing problem. In: Christofides N, Mingozzi A, Toth P, Sandi C (eds) Combinatorial optimization. Wiley, Chichester
Dantzig GB, Ramser JH (1959) The truck dispatching problem. Manag Sci 6(1):80–91
Dorigo M, Stutzle T (2004) Ant colony optimization. A Bradford book. The MIT Press, Cambridge
Drias H, Sadeg S, Yahi S (2005) Cooperative bees swarm for solving the maximum weighted satisfiability problem. In: IWAAN international work conference on artificial and natural neural networks, LNCS, vol 3512, pp 318–325
Fathian M, Amiri B, Maroosi A (2007) Application of honey bee mating optimization algorithm on clustering. Appl Math Comput. doi:10.1016/j.amc.2007.02.029
Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedure. J Glob Optim 6:109–133
Fisher ML (1995) Vehicle routing. In: Ball MO, Magnanti TL, Momma CL, Nemhauser GL (eds) Network routing, handbooks in operations research and management science, vol 8. North Holland, Amsterdam, pp 1–33
Garfinkel R, Nemhauser G (1972) Integer programming. Wiley, New York
Gendreau M, Hertz A, Laporte G (1994) A tabu search heuristic for the vehicle routing problem. Manag Sci 40:1276–1290
Gendreau M, Laporte G, Potvin J-Y (1997) Vehicle routing: modern heuristics. In: Aarts EHL, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, Chichester, pp 311–336
Gendreau M, Laporte G, Potvin J-Y (2002) Metaheuristics for the capacitated VRP. In: Toth P, Vigo D (eds) The vehicle routing problem, monographs on discrete mathematics and applications. Siam, Philadelphia, pp 129–154
Golden BL, Assad AA (1988) Vehicle routing: methods and studies. North Holland, Amsterdam
Golden BL, Wasil EA, Kelly JP, Chao IM (1998) The impact of metaheuristics on solving the vehicle routing problem: algorithms, problem sets, and computational results. In: Crainic TG, Laporte G (eds) Fleet management and logistics. Kluwer, Boston, pp 33–56
Haddad OB, Afshar A, Marino MA (2006) Honey-bees mating optimization (HBMO) algorithm: a new heuristic approach for water resources optimization. Water Resour Manag 20:661–680
Hansen P, Mladenovic N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130:449-467
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim. doi:10.1007/s10898-007-9149-x
Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8:687–697
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of 1995 IEEE international conference on neural networks, vol 4, pp 1942–1948
Laporte G, Gendreau M, Potvin J-Y, Semet F (2000) Classical and modern heuristics for the vehicle routing problem. Int Trans Oper Res 7:285–300
Li F, Golden B, Wasil E (2005) Very large-scale vehicle routing: new test problems, algorithms and results. Comput Oper Res 32(5):1165–1179
Lin S (1965) Computer solutions of the traveling salesman problem. Bell Syst Tech J 44:2245–2269
Marinakis Y, Migdalas A (2002) Heuristic solutions of vehicle routing problems in supply chain management. In: Pardalos PM, Migdalas A, Burkard R (eds) Combinatorial and global optimization. World Scientific, Singapore, pp 205–236
Marinakis Y, Migdalas A, Pardalos PM (2005) Expanding neighborhood GRASP for the traveling salesman problem. Comput Optim Appl 32:231–257
Marinakis Y, Migdalas A, Pardalos PM (2007a) A new bilevel formulation for the vehicle routing problem and a solution method using a genetic algorithm. J Glob Optim 38:555–580
Marinakis Y, Migdalas A, Pardalos PM (2007b) Multiple phase neighborhood search GRASP based on Lagrangean relaxation and random backtracking Lin Kernighan for the traveling salesman problem. J Comb Optim. doi:10.1007/s10878-007-9104-2
Marinakis Y, Migdalas A, Pardalos PM (2007c) Expanding neighborhood search—GRASP for the probabilistic traveling salesman problem. Optim Lett. doi:10.1007/s11590-007-0064-3
Marinakis Y, Marinaki M, Dounias G (2007d) A hybrid particle swarm optimization algorithm for the vehicle routing problem (submitted)
Mester D, Braysy O (2007) Active-guided evolution strategies for large-scale capacitated vehicle routing problems. Comput Oper Res 34(10):2964–2975
Osman IH (1993) Metastrategy simulated annealing and tabu search algorithms for combinatorial optimization problems. Ann Oper Res 41:421–451
Pham DT, Kog E, Ghanbarzadeh A, Otri S, Rahim S, Zaidi M (2006) The bees algorithm—a novel tool for complex optimization problems. In: IPROMS 2006 proceeding 2nd international virtual conference on intelligent production machines and systems. Elsevier, Oxford
Prins C (2004) A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Oper Res 31:1985–2002
Reimann M, Stummer M, Doerner K (2002) A savings based ant system for the vehicle routing problem. In: Proceedings of the genetic and evolutionary computation conference, New York, pp 1317–1326
Reimann M, Doerner K, Hartl RF (2004) D-ants: savings based ants divide and conquer the vehicle routing problem. Comput Oper Res 31(4):563–591
Resende MGC, Ribeiro CC (2003) Greedy randomized adaptive search procedures. In: Glover F, Kochenberger GA (eds) Handbook of metaheuristics. Kluwer, Boston, pp 219–249
Rochat Y, Taillard ED (1995) Probabilistic diversification and intensification in local search for vehicle routing. J Heuristics 1:147–167
Taillard ED (1993) Parallel iterative search methods for vehicle routing problems. Networks 23:661–672
Tarantilis CD (2005) Solving the vehicle routing problem with adaptive memory programming methodology. Comput Oper Res 32(9):2309–2327
Tarantilis CD, Kiranoudis CT (2002) BoneRoute: an adaptive memory-based method for effective fleet management. Ann Oper Res 115(1):227–241
Tarantilis CD, Kiranoudis CT, Vassiliadis VS (2002) A list based threshold accepting algorithm for the capacitated vehicle routing problem. Int J Comput Math 79(5):537–553
Teo J, Abbass HA (2003) A true annealing approach to the marriage in honey bees optimization algorithm. Int J Comput Intell Appl 3(2):199–211
Teodorovic D, Dell’Orco M (2005) Bee colony optimization—a cooperative learning approach to complex transportation problems. In: Advanced OR and AI methods in transportation, pp 51–60
Toth P, Vigo D (2002) The vehicle routing problem. Monographs on discrete mathematics and applications. Siam, Philadelphia
Wedde HF, Farooq M, Zhang Y (2004) BeeHive: an efficient fault-tolerant routing algorithm inspired by honey bee behavior. In: Dorigo M (ed) Ant colony optimization and swarm intelligence, LNCS 3172. Springer, Berlin, pp 83–94
Yang XS (2005) Engineering optimizations via nature-inspired virtual bee algorithms. In: Yang JM, Alvarez JR (eds) IWINAC 2005, LNCS 3562. Springer-Verlag, Berlin, pp 317–323
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marinakis, Y., Marinaki, M. & Dounias, G. Honey Bees Mating Optimization algorithm for large scale vehicle routing problems. Nat Comput 9, 5–27 (2010). https://doi.org/10.1007/s11047-009-9136-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-009-9136-x