zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows. (English) Zbl 1231.90087
Summary: The vehicle routing problem with time windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.
90B06Transportation, logistics
90C27Combinatorial optimization
90C59Approximation methods and heuristics
90C29Multi-objective programming; goal programming
[1]Toth, P.; Vigo, D.: The vehicle routing problem, (2001)
[2]Dantzig, G. B.; Ramser, J. H.: The truck dispatching problem, Manage sci 6, No. 1, 80-91 (1956)
[3]Jozefowicz, N.; Semet, F.; Talbi, E. -G.: Multi-objective vehicle routing problems, Eur J oper res 189, 293-309 (2008) · Zbl 1148.90338 · doi:10.1016/j.ejor.2007.05.055
[4]Desrochers, M.; Desrosiers, J.; Solomon, M.: A new optimization algorithm for the vehicle routing problem with time windows, Oper res 40, No. 2, 342-354 (1992) · Zbl 0749.90025 · doi:10.1287/opre.40.2.342
[5]Cordeau, J. -F.; Desaulniers, G.; Desrosiers, J.; Solomon, M. M.; Soumis, F.: VRP with time windows, The vehicle routing problem, 157-193 (2001)
[6]Bräysy, O.; Gendreau, M.: Vehicle routing problem with time windows, part I: Route construction and local search algorithms, Transp sci 39, No. 1, 104-118 (2005)
[7]Bräysy, O.; Gendreau, M.: Vehicle routing problem with time windows, part II: Metaheuristics, Transp sci 39, No. 1, 119-139 (2005)
[8]Yu T, Davis L. An introduction to evolutionary computation in practice. In: Yu T, Davis L, Baydar CM, Roy R, editors. Evolutionary computation in practice, Studies in computational intelligence, vol. 88. Berlin, Germany: Springer; 2008. p. 1–8.
[9]Bräysy, O.; Dullaert, W.; Gendreau, M.: Evolutionary algorithms for the vehicle routing problem with time windows, J heuristics 10, No. 6, 587-611 (2004)
[10]Lenstra, J. K.; Kan, A. H. G.R.: Complexity of vehicle routing and scheduling problems, Networks 11, 221-227 (1981)
[11]Zitzler, E.; Laumanns, M.; Bleuler, S.: A tutorial on evolutionary multiobjective optimization, Metaheuristics for multiobjective optimisation, 3-38 (2004) · Zbl 1134.90491
[12]Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE trans evol comput 6, No. 2, 182-197 (2002)
[13]Zitzler E, Laumanns M, Thiele L. SPEA2: improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Zurich, Switzerland; 2001.
[14]Knowles, J. D.; Corne, D. W.: Approximating the nondominated front using the Pareto archived evolution strategy, Evol comput 8, No. 2, 149-172 (2000)
[15]Zitzler, E.; Künzli, S.: Indicator-based selection in multiobjective search, , 832-842 (2004)
[16]Zitzler, E.; Thiele, L.: Multiobjective optimization using evolutionary algorithms–a comparative case study, , 292-304 (1998)
[17]Zitzler, E.; Deb, K.; Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results, Evol comput 8, No. 2, 173-195 (2000)
[18]Deb, K.; Jain, S.: Running performance metrics for evolutionary multi-objective optimization, Proceedings of fourth Asia-Pacific conference on simulated evolution and learning, 13-20 (2002)
[19]Zitzler, E.; Thiele, L.; Laumanns, M.; Fonseca, C. M.; Da Fonseca, V. G.: Performance assesment of multiobjective optimizers: an analysis and review, IEEE trans evol comput 7, No. 2, 117-132 (2003)
[20]Knowles J, Thiele L, Zitzler E. A tutorial on the performance assessment of stochastic multiobjective optimizers. TIK Report 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich; 2006.
[21]Rahoual, M.; Kitoun, B.; Mabed, M. Hakim; Bachelet, V.; Benameur, F.: Multicriteria genetic algorithms for the vehicle routing problem with time windows, , 527-532 (2001)
[22]Srinivas, N.; Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms, Evol comput 2, No. 3, 221-248 (1994)
[23]Jung, S.; Moon, B. R.: A hybrid genetic algorithm for the vehicle routing problem with time windows, , 1309-1316 (2002)
[24]Zhu, K. Q.: A diversity-controlling adaptive genetic algorithm for the vehicle routing problem with time windows, , 176-183 (2003)
[25]Jozefowiez, N.; Semet, F.; Talbi, E. -G.: Enhancements of NSGA II and its application to the vehicle routing problem with route balancing, , 131-142 (2005)
[26]Murata, T.; Itai, R.: Multi-objective vehicle routing problems using two-fold EMO algorithms to enhance solution similarity on non-dominated solutions, Proceedings of third international conference on evolutionary multi-criteria optimization, lecture notes in computer science 3410, 885-896 (2005) · Zbl 1109.90304 · doi:10.1007/b106458
[27]Le Bouthillier, A.; Crainic, T. G.: A cooperative parallel metaheuristic for vehicle routing with time windows, Comput oper res 32, 1685-1708 (2005) · Zbl 1074.90006 · doi:10.1016/j.cor.2003.11.023
[28]Glover, F. W.; Laguna, M.: Tabu search, (1998)
[29]Homberger, J.; Gehring, H.: A two-phase hybrid metaheuristic for the vehicle routing problem with time windows, Eur J oper res 162, 220-238 (2005) · Zbl 1132.90378 · doi:10.1016/j.ejor.2004.01.027
[30]Beyer, H. -G.; Schwefel, H. -P.: Evolution strategies–a comprehensive introduction, Nat comput 1, No. 1, 3-52 (2002) · Zbl 1014.68134 · doi:10.1023/A:1015059928466
[31]Tan, K. C.; Chew, Y. H.; Lee, L. H.: A hybrid multiobjective evolutionary algorithm for solving vehicle routing problem with time windows, Comput optim appl 34, No. 1, 115-151 (2006) · Zbl 1111.90022 · doi:10.1007/s10589-005-3070-3
[32]Ombuki, B.; Ross, B. J.; Hanshar, F.: Multi-objective genetic algorithms for vehicle routing problem with time windows, Appl intell 24, No. 1, 17-30 (2006)
[33]Zitzler, E.; Laumanns, M.; Thiele, L.: SPEA 2: improving the strength Pareto evolutionary algorithm for multiobjective optimization, Evolutionary methods for design optimisation and control, 19-26 (2002)
[34]Garcia-Najera A, Bullinaria JA. A multi-objective density restricted genetic algorithm for the vehicle routing problem with time windows, in: Proceedings of 2008 UK workshop on computational intelligence, 2008.
[35]Garcia-Najera, A.; Bullinaria, J. A.: Bi-objective optimization for the vehicle routing problem with time windows: using route similarity to enhance performance, Proceedings of fifth international conference on evolutionary multi-criterion optimization, lecture notes in computer science 5467, 275-289 (2009)
[36]Garcia-Najera A. Preserving population diversity for the multi-objective vehicle routing problem with time windows. In: GECCO 2009 graduate student workshop, ACM; 2009. p. 2689–92.
[37]Sörensen, K.: Distance measures based on the edit distance for permutation-type representations, J heuristics 13, No. 1, 35-47 (2007)
[38]Garcia-Najera, A.; Bullinaria, J. A.: Comparison of similarity measures for the multi-objective vehicle routing problem with time windows, , 579-586 (2009)
[39]Eiben, A. E.; Smith, J. E.: Introduction to evolutionary computing, (2003)
[40]Goldberg DE, Deb K. A comparative analysis of selection schemes used in genetic algorithms. In: Foundations of genetic algorithms. Morgan Kaufmann; 1991. p. 69–93.
[41]Solomon, M. M.: Algorithms for the vehicle routing and scheduling problems with time window constraints, Oper res 35, No. 2, 254-265 (1987) · Zbl 0625.90047 · doi:10.1287/opre.35.2.254
[42]Pisinger, D.; Ropke, S.: A general heuristic for vehicle routing problems, Comput oper res 34, No. 8, 2403-2435 (2007) · Zbl 1144.90318 · doi:10.1016/j.cor.2005.09.012