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, Volume 21, Issue 1, pp 109–132 | Cite as

MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems

  • Angel A. Juan
  • Javier Faulin
  • Albert Ferrer
  • Helena R. Lourenço
  • Barry Barrios
Original Paper

Abstract

This paper discusses the use of probabilistic or randomized algorithms for solving vehicle routing problems with non-smooth objective functions. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods—both of exact and approximate nature—may fail to reach their full potential. The results obtained so far are promising enough to suggest that the idea of using biased probability distributions to randomize classical heuristics is a powerful one that can be successfully applied in a variety of cases.

Keywords

Randomized algorithms Combinatorial optimization Vehicle routing problem Biased random search Heuristics 

Mathematics Subject Classification (2000)

65K05 90C26 90C27 90C59 

References

  1. Al-Sultan KS (1995) A tabu search approach to the clustering problem. Pattern Recognit 28(9):1443–1451 CrossRefGoogle Scholar
  2. Bagirov AM, Yearwood J (2006) A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems. Eur J Oper Res 170:578–596 CrossRefGoogle Scholar
  3. Bagirov A, Lai DTH, Palaniswami M (2007) A nonsmooth optimization approach to sensor network localization. In: Palaniswami M, Marusic M, Law YW (eds) Proceedings of the 2007 international conference on intelligent sensors, sensor networks and information processing, pp 727–732 CrossRefGoogle Scholar
  4. Bauer J, Bektas T, Crainic TG (2010) Minimizing greenhouse gas emissions in intermodal freight transport: an application to rail service design. J Oper Res Soc 61:530–542 CrossRefGoogle Scholar
  5. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge Google Scholar
  6. Bresina JL (1996) Heuristic-biased stochastic sampling. In: Proceedings of the thirteenth national conference on artificial intelligence and the eighth innovative applications of artificial intelligence conference, vols 1–2, pp 271–278 Google Scholar
  7. Bullnheimer B, Hartl RF, Strauss C (1999) An improved ant system for the vehicle routing problem. Ann Oper Res 89:319–328 CrossRefGoogle Scholar
  8. Burkard RE, Çela E, Pardalos P, Pitsoulis LS (1998) The quadratic assignment problem. In: Du D-Z, Pardalos PM (eds) Handbook of combinatorial optimization, vol 3. Kluwer Academic, Dordrecht, pp 241–339 Google Scholar
  9. Carreto C, Baker B (2002) A GRASP interactive approach to the vehicle routing problem with backhauls. In: Ribeiro C, Hansen P (eds) Essays and surveys in metaheuristics. Kluwer Academic, Boston, pp 185–200 CrossRefGoogle Scholar
  10. Chaovalitwongse W, Kim D, Pardalos P (2003) GRASP with a new local search scheme for vehicle routing problems with time windows. J Comb Optim 7:179–207 CrossRefGoogle Scholar
  11. Chaves AA, Lorena LAN (2010) Clustering search algorithm for the capacitated centered clustering problem. Comput Oper Res 37(3):552–558 CrossRefGoogle Scholar
  12. Chiou SW (2007) A non-smooth optimization model for a two-tiered supply chain network. Inf Sci 177:5754–5762 CrossRefGoogle Scholar
  13. Chiou SW (2008) A non-smooth model for signalized road network design problems. Appl Math Model 32:1179–1190 CrossRefGoogle Scholar
  14. Clarke G, Wright J (1964) Scheduling of vehicles from a central depot to a number of delivery points. Oper Res 12(4):568–581 CrossRefGoogle Scholar
  15. Collet P, Rennard JP (2006) Stochastic optimization algorithms. In: Rennard JP (ed) Handbook of research on nature inspired computing for economics and management. Idea Group Reference, Hershey Google Scholar
  16. Cordeau JF, Gendreau M, Laporte G, Potvin JY, Semet F (2002) A guide to vehicle routing heuristics. J Oper Res Soc 53:512–522 CrossRefGoogle Scholar
  17. Cordeau JF, Gendreau M, Hertz A, Laporte G, Sormany JS (2004) New heuristics for the vehicle routing problem. In: Langevin A, Riopel D (eds) Logistics systems: design and optimization. Kluwer Academic, Dordrecht Google Scholar
  18. Christofides N, Mingozzi A, Toth P (1979) The vehicle routing problem. In: Christofides N, Mingozzi A, Toth P, Sandi L (eds) Combinatorial optimization. Wiley, Chichester, pp 315–338 Google Scholar
  19. Davis LD (1991) Handbook of genetic algorithms. Van Nostrand-Reinhold, New York, Google Scholar
  20. De Jong KA (2006) Evolutionary computation: a unified approach. MIT Press, Cambridge Google Scholar
  21. Derigs U, Metz A (1992) A matching-based approach for solving a delivery pick-up vehicle-routing problem with time constraints. OR Spektrum 14(2):91–106 CrossRefGoogle Scholar
  22. Derigs U, Li B, Vogel U (2010) Local search-based metaheuristics for the split delivery vehicle routing problem. J Oper Res Soc 61(9):1356–1364 Google Scholar
  23. Dorigo M, Stützle T (2010) Ant colony optimization: overview and recent advances. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. International series in operations research management science, vol 146, 2nd edn. Kluwer Academic, Dordrecht, pp 227–264 CrossRefGoogle Scholar
  24. Drezner Z, Hamacher H (eds) (2002) Facility location: applications and theory. Springer, New York Google Scholar
  25. Fagerholt K, Laporte G, Norstad I (2010) Reducing fuel emissions by optimizing speed on shipping routes. J Oper Res Soc 61:523–529 CrossRefGoogle Scholar
  26. Faulin J, Juan A (2008) The ALGACEA-1 method for the capacitated vehicle routing problem. Int Trans Oper Res 15:599–621 CrossRefGoogle Scholar
  27. Faulin J, Gilibert M, Juan A, Ruiz R, Vilajosana X (2008) SR-1: a simulation-based algorithm for the capacitated vehicle routing problem. In: Proceedings of the 2008 winter simulation conference, pp 2708–2716 CrossRefGoogle Scholar
  28. Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Glob Optim 6:109–133 CrossRefGoogle Scholar
  29. Festa P, Resende MGC (2002) GRASP: an annotated bibliography. In: Ribeiro CC, Hansen P (eds) Essays and surveys in metaheuristics, vol 15, pp 325–367 CrossRefGoogle Scholar
  30. Festa P, Resende MGC (2009a) An annotated bibliography of GRASP—Part I: Algorithms. Int Trans Oper Res 16:1–24 CrossRefGoogle Scholar
  31. Festa P, Resende MGC (2009b) An annotated bibliography of GRASP—Part II: Applications. Int Trans Oper Res 16:131–172 CrossRefGoogle Scholar
  32. Figliozzi MA (2011) The impacts of congestion on time-definitive urban freight distribution networks CO2 emission levels: Results from a case study in Portland, Oregon. Transp Res Part C 19(5):766–778 CrossRefGoogle Scholar
  33. Fisher ML, Jaikumar R (1981) A generalized assignment heuristic for vehicle routing. Networks 11:109–124 CrossRefGoogle Scholar
  34. Fleurent C, Glover F (1999) Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS J Comput 11(2):198–204 CrossRefGoogle Scholar
  35. Fogel LJ (1962) Autonomous automata. Ind Res 4:14–19 Google Scholar
  36. Funke B, Grunert T, Irnich S (2005) Local search for vehicle routing and scheduling problems: Review and conceptual integration. J Heuristics 11(4):267–306 CrossRefGoogle Scholar
  37. Gendreau M, Hertz A, Laporte G (1994) A tabu search heuristic for the vehicle routing problem. Manag Sci 40:1276–1290 CrossRefGoogle Scholar
  38. Gersht A, Shulman A (1989) Optimal routing in circuit switched communication. Networks 37:1203–1211 Google Scholar
  39. Gillet BE, Miller LR (1974) A heuristic algorithm for the vehicle dispatch problem. Oper Res 22:340–349 CrossRefGoogle Scholar
  40. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading Google Scholar
  41. Golden B, Raghavan S, Wasil EE (eds) (2008) The vehicle routing problem: latest advances and new challenges. Springer, New York Google Scholar
  42. Hamdan M, El-Hawary ME (2002) Hopfield-genetic approach for solving the routing problem. In: Computer networks. Proceedings of the 2002 IEEE Canadian conference on electrical and computer engineering, pp 823–827 Google Scholar
  43. Hansen P, Mladenovic N, Brimberg J, Moreno-Pérez JA (2010) Variable neighborhood search. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. International series in operations research & management science, vol 146, 2nd edn. Kluwer Academic, Dordrecht, pp 61–86 CrossRefGoogle Scholar
  44. Hashimoto H, Ibaraki T, Imahori S, Yagiura M (2006) The vehicle routing problem with flexible time windows and traveling times. Discrete Appl Math 154(16):2271–2290 CrossRefGoogle Scholar
  45. Hemamalini S, Simon SP (2010) Artificial bee colony algorithm for economic load dispatch problem with non-smooth cost functions. Electr Power Compon Syst, 38(7):786–803 CrossRefGoogle Scholar
  46. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor Google Scholar
  47. Hopfield JJ, Tank DW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52:21–43 Google Scholar
  48. Juan A, Faulin J, Ruiz R, Barrios B, Gilibert M, Vilajosana X (2009) Using oriented random search to provide a set of alternative solutions to the capacitated vehicle routing problem. In: Chinneck J, Kristjansson B, Saltzman M (eds) Operations research and cyber-infrastructure. Operations Research/Computer Science Interfaces Series, vol 47. Springer, New York, pp 331–346. ISBN: 978-0-387-88842-2 CrossRefGoogle Scholar
  49. Juan A, Faulin J, Jorba J, Riera D, Masip D, Barrios B (2010) On the use of Monte Carlo simulation, cache and splitting techniques to improve the Clarke and Wright savings heuristics. J Oper Res Soc 62(6):1085–1097 CrossRefGoogle Scholar
  50. Kant G, Jacks M, Aantjes C (2008) Coca-Cola enterprises optimizes vehicle routes for efficient product delivery. Interfaces 38:40–50 CrossRefGoogle Scholar
  51. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: 1995 IEEE international conference on neural networks proceedings, vols 1–6, pp 1942–1948 Google Scholar
  52. Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680 CrossRefGoogle Scholar
  53. Kontoravdis G, Bard J (1995) A GRASP for the vehicle routing problem with time windows. ORSA J Comput 7:10–23 CrossRefGoogle Scholar
  54. Kumares C, Labi S (2007) Transportation decision making: principles of project evaluation and programming. Wiley, Hoboken Google Scholar
  55. Laporte G (2009) Fifty years of vehicle routing. Transp Sci 43(4):408–416 CrossRefGoogle Scholar
  56. L’Ecuyer P (2006) Random number generation in simulation. Elsevier, Amsterdam Google Scholar
  57. Lin S, Lee Z, Ying K Lee C (2009) Applying hybrid meta-heuristics for capacitated vehicle routing problem. Expert Syst Appl 36(2):1505–1512 CrossRefGoogle Scholar
  58. Loiola EM, de Abreu NMM, Boaventura-Netto PO, Hahn P, Querido T (2007) A survey for the quadratic assignment problem. Eur J Oper Res 176(2):657–690 CrossRefGoogle Scholar
  59. Lokketangen A, Glover F (1998) Solving zero-one mixed integer programming problems using tabu search. Eur J Oper Res 106(2–3):624–658 CrossRefGoogle Scholar
  60. Lourenço HR, Martin O, Stützle T (2003) Iterated local search. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. International series in operations research management science. Kluwer Academic, Dordrecht, pp 321–353. Google Scholar
  61. Lourenço HR, Martin O, Stützle T (2010) Iterated local search: framework and applications. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. Publishers, international series in operations research management science, vol 146, 2nd edn. Kluwer Academic, Dordrecht, pp 363–397 CrossRefGoogle Scholar
  62. Lourenço HR, Ribeiro R (2011) Strategies for an integrated distribution problem. In: Montoya-Torres J, Juan A, Huaccho-Guatuco L, Faulin J, Rodríguez-Verján G (eds) Hybrid algorithms for service, computing and manufacturing systems: routing, scheduling and availability solutions. IGI Global Books, Hershey. ISBN: 978-1-61350-086-6 Google Scholar
  63. Mester D, Bräysy O (2007) Active-guided evolution strategies for the large-scale capacitated vehicle routing problems. Comput Oper Res 34:2964–2975 CrossRefGoogle Scholar
  64. Mladenovic N, Brimberg J, Hansen P, Moreno-Perez JA (2007) The p-median problem: A survey of meta-heuristic approaches. Eur J Oper Res 179(3):927–939 CrossRefGoogle Scholar
  65. Montoya-Torres J, Juan A, Huaccho-Guatuco L, Faulin J, Rodríguez-Verján G (eds) (2011) Hybrid algorithms for service, computing and manufacturing systems: routing and scheduling solutions. IGI Global, Hershey. ISBN: 978-1-61350-086-6 Google Scholar
  66. Muter I, Birbil SI, Sahin G (2010) Combination of metaheuristic and exact algorithms for solving set covering-type optimization problems. INFORMS J Comput 22(4):603–619 CrossRefGoogle Scholar
  67. Nawaz M, Enscore EE Jr, Ham I (1983) A heuristic algorithm for the m-machine, n-job flowshop sequencing problem. OMEGA, Int J Manag Sci 11(1):91–95 CrossRefGoogle Scholar
  68. Neyestani M, Farsangi MM, Nezamabani-Pour H (2010) A modified particle swarm optimization for economic dispatch with non-smooth cost functions. Eng Appl Artif Intell 23:1121–1126 CrossRefGoogle Scholar
  69. Nikolaev AG, Jacobson SH (2010) Simulated annealing. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. International series in operations research management science, vol 146, 2nd edn. Kluwer Academic, Dordrecht pp 1–40 CrossRefGoogle Scholar
  70. Oncan T (2007) A survey of the generalized assignment problem and its applications. INFOR 45(3):123–141 Google Scholar
  71. Oonsivilai A, Srisuruk W, Marungsri B, Kulworawanichpong T (2009) Tabu search approach to solve rou-ting issues in communication networks. In: World academy of science, engineering and technology, pp 1174–1177 Google Scholar
  72. Park JB, Lee KS, Shin JR, Lee KY (2005) A particle swarm optimization for economic dispatch with non-smooth cost functions. IEEE Trans Power Appar Syst 20:34–42 CrossRefGoogle Scholar
  73. Pinedo M (2008) Scheduling: theory, algorithms and systems. Springer, New York Google Scholar
  74. Pisinger D, Ropke S (2007) A general heuristic for vehicle routing problems. Comput Oper Res 34:2403–2435 CrossRefGoogle Scholar
  75. Poot A, Kant G, Wagelmans A (2002) A savings based method for real-life vehicle routing problems. J Oper Res Soc 53:57–68 CrossRefGoogle Scholar
  76. Potvin JY (2009) State-of-the art review evolutionary algorithms for vehicle routing. INFORMS J Comput 21(4):518–548 CrossRefGoogle Scholar
  77. Prais M e Ribeiro CC (2000) Variação de parâmetros em procedimientos GRASP. Investig Oper 9:1–20 Google Scholar
  78. Ramadurai V, Sichitiu ML (2003) Localization in wireless sensor networks: a probabilistic approach. In: International conference on wireless networks (ICWN03), pp 275–281 Google Scholar
  79. Reeves CR (2010) Genetic algorithms. In: Gendreau M, Potvin JY (eds) In: Handbook of metaheuristics. International series in operations research management science, vol 146, 2nd. edn. Kluwer Academic, Dordrecht, pp 109–140 CrossRefGoogle Scholar
  80. Resende MGC (2008) Metaheuristic hybridization with greedy randomized adaptive search procedures. In: Chen S-L, Raghavan S (eds) TutORials in operations research. INFORMS, pp 295–319 Google Scholar
  81. Resende M, Ribeiro C (2010) Greedy randomized adaptive search procedures: advances, hybridizations and applications. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. International series in operations research management science, vol 146, 2nd edn. Kluwer Academic, Dordrecht pp 27–264 Google Scholar
  82. Schlüter M, Egea JA, Banga JR (2009) Extended ant colony optimization for non-convex mixed integer nonlinear programming. Comput Oper Res 36(7):2217–2229 CrossRefGoogle Scholar
  83. Selim SZ, Al-Sultan KS (1991) A simulated annealing algorithm for the clustering problem. Pattern Recognit 24(10):1003–1008 CrossRefGoogle Scholar
  84. Suman B, Kumar P (2006) A survey of simulated annealing as a tool for single and multiobjective optimization. J Oper Res Soc 57(10):1143–1160 CrossRefGoogle Scholar
  85. Tarantilis CD, Kiranoudis CT (2002) Boneroute: an adaptative memory-based method for effective fleet management. Ann Oper Res 115:227–241 CrossRefGoogle Scholar
  86. Toscano R, Lyonnet P (2010) A new heuristic approach for non-convex optimization problems. Inf Sci 180(10):1955–1966 CrossRefGoogle Scholar
  87. Toth P, Vigo D (Eds) (2002) The vehicle routing problem. SIAM monographs on discrete mathematics and applications. SIAM, Philadelphia Google Scholar
  88. Urlings T, Ruiz R (2007) Local search in complex scheduling problems. In: Stutzle T, Birattari M, Hoos HH (eds) Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics. vol 4638, pp 202–206 CrossRefGoogle Scholar
  89. Vaisakh K, Srinivas LR (2011) Genetic evolving ant direction HDE for OPF with non-smooth cost functions and statistical analysis. Expert Syst Appl 38(3):2046–2062 CrossRefGoogle Scholar
  90. Wright S (1997) Primal-dual interior-point methods. SIAM, Philadelphia CrossRefGoogle Scholar
  91. Yang IT, Chou JS (2011) Multiobjective optimization for manpower assignment in consulting engineering firms. Appl Soft Comput 11(1):1183–1190 CrossRefGoogle Scholar
  92. Yang HT, Yang PC, Huang CL (1996) Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions. IEEE Trans Power Appar Syst 11:112–118 CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2011

Authors and Affiliations

  • Angel A. Juan
    • 1
  • Javier Faulin
    • 2
  • Albert Ferrer
    • 3
  • Helena R. Lourenço
    • 4
  • Barry Barrios
    • 5
  1. 1.Computer Science Dept.Open University of CataloniaBarcelonaSpain
  2. 2.Statistics and Operations Research Dept.Public University of NavarrePamplonaSpain
  3. 3.Applied Mathematics 1 Dept.Technical University of CataloniaBarcelonaSpain
  4. 4.Economics and Business Dept.Universitat Pompeu FabraBarcelonaSpain
  5. 5.Industrial Engineering and Management Science Dept.Northwestern UniversityEvanstonUSA

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