A multiphase dynamic programming algorithm for the shortest path problem with resource constraints
The shortest path problem with resource constraints (SPPRC) finds a least cost path between two nodes in a network while respecting constraints on resource consumption. The problem is mainly used as a subproblem inside column generation for crew scheduling and vehicle routing problems. The standard...
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| Vydáno v: | European journal of operational research Ročník 315; číslo 2; s. 470 - 483 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.06.2024
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | The shortest path problem with resource constraints (SPPRC) finds a least cost path between two nodes in a network while respecting constraints on resource consumption. The problem is mainly used as a subproblem inside column generation for crew scheduling and vehicle routing problems. The standard approach for the subproblems is based on dynamic programming (DP). This class of methods is generally effective in practice when there are only a few resources, but it seems to be time-consuming for huge instances with many resources. To handle this issue, we propose a new exact primal algorithm called the multiphase dynamic programming algorithm (MPDPA) to solve the SPPRC in acyclic networks. The proposed approach splits the state-space into small disjoint subspaces. These subspaces are sequentially explored in several iterations, where each iteration builds on the previous ones, to reduce the dimension of the subspaces to explore and to quickly generate better paths. Computational experiments on vehicle and crew scheduling instances show the excellent performance of our approach compared to the standard DP method. On the one hand, MPDPA returns optimal solutions while achieving time reduction factors between 1.44 and 3.59 on average compared to DP. On the other hand, MPDPA is able to generate feasible paths with up to 90% of the optimal cost in less than 10% of the time required by standard DP. This feature is useful in column generation and may greatly reduce the computational effort, because we can stop the MPDPA solution process once columns with sufficiently negative reduced costs are obtained.
•New primal exact algorithm for the shortest path problem with resource constraints.•New generalized formulation to split the search space into disjoint subspaces.•Sets of feasible paths of nonincreasing costs leading to optimality are generated.•Learning techniques from the previous iterations are embedded.•Extensive experiments on simultaneous vehicle and crew scheduling problem instances. |
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| AbstractList | The shortest path problem with resource constraints (SPPRC) finds a least cost path between two nodes in a network while respecting constraints on resource consumption. The problem is mainly used as a subproblem inside column generation for crew scheduling and vehicle routing problems. The standard approach for the subproblems is based on dynamic programming (DP). This class of methods is generally effective in practice when there are only a few resources, but it seems to be time-consuming for huge instances with many resources. To handle this issue, we propose a new exact primal algorithm called the multiphase dynamic programming algorithm (MPDPA) to solve the SPPRC in acyclic networks. The proposed approach splits the state-space into small disjoint subspaces. These subspaces are sequentially explored in several iterations, where each iteration builds on the previous ones, to reduce the dimension of the subspaces to explore and to quickly generate better paths. Computational experiments on vehicle and crew scheduling instances show the excellent performance of our approach compared to the standard DP method. On the one hand, MPDPA returns optimal solutions while achieving time reduction factors between 1.44 and 3.59 on average compared to DP. On the other hand, MPDPA is able to generate feasible paths with up to 90% of the optimal cost in less than 10% of the time required by standard DP. This feature is useful in column generation and may greatly reduce the computational effort, because we can stop the MPDPA solution process once columns with sufficiently negative reduced costs are obtained.
•New primal exact algorithm for the shortest path problem with resource constraints.•New generalized formulation to split the search space into disjoint subspaces.•Sets of feasible paths of nonincreasing costs leading to optimality are generated.•Learning techniques from the previous iterations are embedded.•Extensive experiments on simultaneous vehicle and crew scheduling problem instances. |
| Author | Himmich, Ilyas El Hallaoui, Issmail Soumis, François |
| Author_xml | – sequence: 1 givenname: Ilyas surname: Himmich fullname: Himmich, Ilyas email: i.himmich@insea.ac.ma organization: GERAD et École Polytechnique de Montréal Département de Mathématiques et Génie Industriel, Montreal, Quebec H3C 3A7, Canada – sequence: 2 givenname: Issmail surname: El Hallaoui fullname: El Hallaoui, Issmail email: issmail.elhallaoui@gerad.ca organization: GERAD et École Polytechnique de Montréal Département de Mathématiques et Génie Industriel, Montreal, Quebec H3C 3A7, Canada – sequence: 3 givenname: François surname: Soumis fullname: Soumis, François email: francois.soumis@gerad.ca organization: GERAD et École Polytechnique de Montréal Département de Mathématiques et Génie Industriel, Montreal, Quebec H3C 3A7, Canada |
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| Cites_doi | 10.1287/trsc.35.3.286.10153 10.1002/net.3230100403 10.1016/j.cor.2012.07.008 10.1002/net.21511 10.1016/S0377-2217(96)00195-6 10.1016/j.disopt.2006.05.007 10.3138/infor.45.4.239 10.1002/net.3230190402 10.1016/0377-2217(88)90034-3 10.1287/opre.1110.0975 10.1016/j.ejor.2014.11.003 10.1287/trsc.2014.0582 10.1287/ijoc.1110.0456 10.1002/net.20292 10.1016/j.ejor.2006.10.012 10.1080/03155986.1988.11732063 10.1287/trsc.34.3.312.12298 10.1016/j.ejor.2004.09.052 10.1007/s11590-014-0742-x 10.1002/net.20247 10.1002/net.21960 10.1002/net.10090 10.1016/j.trb.2006.12.001 10.1002/net.3230040304 |
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| Keywords | Column generation Dynamic programming Shortest path problem with resource constraints Transportation |
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| References | Feillet, Gendreau, Rousseau (b17) 2007; 45 Lozano, Duque, Medaglia (b22) 2016; 50 Halpern, Priess (b19) 1974; 4 Di Puglia Pugliese, Guerriero (b14) 2013; 62 Irnich, Desaulniers (b21) 2005 Zabarankin, Uryasev, Pardalos (b30) 2001 Muhandiramge, Boland (b25) 2009; 53 Haase, Desaulniers, Desrosiers (b18) 2001; 35 Xue, G. (2000). Primal–dual algorithms for computing weight-constrained shortest paths and weight-constrained minimum spanning trees. In Santos, Coutinho-Rodrigues, Current (b28) 2007; 41 (pp. 271–277). Lozano, Medaglia (b23) 2013; 40 Desrochers, Soumis (b11) 1988; 35 Desrosiers, Dumas, Solomon, Soumis (b13) 1995; vol. 8 Desaulniers, Villeneuve (b7) 2000; 34 Baldacci, Mingozzi, Roberti (b1) 2011; 59 Desaulniers (b8) 1997; 97 Desrochers, Soumis (b10) 1988; 26 Duque, Lozano, Medaglia (b16) 2015; 242 Beasley, Christofides (b3) 1989; 19 Handler, Zang (b20) 1980; 10 Carlyle, Royset, Wood (b6) 2008; 52 Baldacci, Mingozzi, Roberti (b2) 2011; 24 Lübbecke (b24) 2010 Desrochers (b9) 1986 Nagih, Soumis (b26) 2006; 172 Dumitrescu, Boland (b15) 2003; 42 Cabrera, Medaglia, Lozano, Duque (b5) 2020; 76 Righini, Salani (b27) 2006; 3 Bolívar, Lozano, Medaglia (b4) 2014; 8 Desrosiers (b12) 2010 Zhu, Wilhelm (b31) 2007; 183 Haase (10.1016/j.ejor.2023.11.047_b18) 2001; 35 Di Puglia Pugliese (10.1016/j.ejor.2023.11.047_b14) 2013; 62 Duque (10.1016/j.ejor.2023.11.047_b16) 2015; 242 Desrochers (10.1016/j.ejor.2023.11.047_b9) 1986 Dumitrescu (10.1016/j.ejor.2023.11.047_b15) 2003; 42 Cabrera (10.1016/j.ejor.2023.11.047_b5) 2020; 76 Carlyle (10.1016/j.ejor.2023.11.047_b6) 2008; 52 Righini (10.1016/j.ejor.2023.11.047_b27) 2006; 3 Feillet (10.1016/j.ejor.2023.11.047_b17) 2007; 45 Irnich (10.1016/j.ejor.2023.11.047_b21) 2005 Desaulniers (10.1016/j.ejor.2023.11.047_b8) 1997; 97 Zabarankin (10.1016/j.ejor.2023.11.047_b30) 2001 Lozano (10.1016/j.ejor.2023.11.047_b22) 2016; 50 Halpern (10.1016/j.ejor.2023.11.047_b19) 1974; 4 Zhu (10.1016/j.ejor.2023.11.047_b31) 2007; 183 Desrosiers (10.1016/j.ejor.2023.11.047_b13) 1995; vol. 8 Lübbecke (10.1016/j.ejor.2023.11.047_b24) 2010 Desrosiers (10.1016/j.ejor.2023.11.047_b12) 2010 Santos (10.1016/j.ejor.2023.11.047_b28) 2007; 41 Beasley (10.1016/j.ejor.2023.11.047_b3) 1989; 19 Bolívar (10.1016/j.ejor.2023.11.047_b4) 2014; 8 Baldacci (10.1016/j.ejor.2023.11.047_b2) 2011; 24 Desrochers (10.1016/j.ejor.2023.11.047_b10) 1988; 26 Nagih (10.1016/j.ejor.2023.11.047_b26) 2006; 172 Baldacci (10.1016/j.ejor.2023.11.047_b1) 2011; 59 Desaulniers (10.1016/j.ejor.2023.11.047_b7) 2000; 34 Desrochers (10.1016/j.ejor.2023.11.047_b11) 1988; 35 10.1016/j.ejor.2023.11.047_b29 Handler (10.1016/j.ejor.2023.11.047_b20) 1980; 10 Lozano (10.1016/j.ejor.2023.11.047_b23) 2013; 40 Muhandiramge (10.1016/j.ejor.2023.11.047_b25) 2009; 53 |
| References_xml | – reference: Xue, G. (2000). Primal–dual algorithms for computing weight-constrained shortest paths and weight-constrained minimum spanning trees. In – volume: 42 start-page: 135 year: 2003 end-page: 153 ident: b15 article-title: Improved preprocessing, labeling and scaling algorithm for the weight-constrained shortest path problem publication-title: Networks – volume: 45 start-page: 239 year: 2007 end-page: 256 ident: b17 article-title: New refinements for the solution of vehicle routing problems with branch and price publication-title: INFOR. Information Systems and Operational Research – volume: 172 start-page: 500 year: 2006 end-page: 514 ident: b26 article-title: Nodal aggregation of resource constraints in shortest path problem publication-title: EJOR – volume: 183 start-page: 564 year: 2007 end-page: 577 ident: b31 article-title: Three-stage approaches for optimizing some variations of the resource constrained shortest-path sub-problem in a column generation context publication-title: EJOR – volume: 50 start-page: 348 year: 2016 end-page: 357 ident: b22 article-title: An exact algorithm for the elementary shortest path problem with resource constraints publication-title: Transportation Science – volume: 52 start-page: 256 year: 2008 end-page: 270 ident: b6 article-title: Lagrangean relaxation and enumeration for solving constrained shortest-path problems publication-title: Networks – year: 2010 ident: b12 article-title: GENCOL: Une équipe et un logiciel d’optimisation – volume: 40 start-page: 378 year: 2013 end-page: 384 ident: b23 article-title: On an exact method for the constrained shortest path problem publication-title: Computers & Operations Research – volume: 62 start-page: 183 year: 2013 end-page: 200 ident: b14 article-title: A survey of resource constrained shortest path problems: Exact solution approaches publication-title: Networks – volume: 59 start-page: 1269 year: 2011 end-page: 1283 ident: b1 article-title: New route relaxation and pricing strategies for the vehicle routing problem publication-title: Operations Research – volume: 76 start-page: 128 year: 2020 end-page: 146 ident: b5 article-title: An exact bidirectional pulse algorithm for the constrained shortest path publication-title: Networks – volume: 34 start-page: 312 year: 2000 end-page: 319 ident: b7 article-title: The shortest path problem with time windows and linear waiting costs publication-title: Transportation Science – volume: 26 start-page: 191 year: 1988 end-page: 212 ident: b10 article-title: A generalized permanent labeling algorithm for the shortest path problem with time windows publication-title: INFOR. Information Systems and Operational Research – reference: (pp. 271–277). – volume: 19 start-page: 379 year: 1989 end-page: 394 ident: b3 article-title: An algorithm for the resource constrained shortest path problem publication-title: Networks – volume: 35 start-page: 242 year: 1988 end-page: 254 ident: b11 article-title: A reoptimization algorithm for the shortest path problem with time windows publication-title: European Journal of Operational Research – volume: 3 start-page: 255 year: 2006 end-page: 273 ident: b27 article-title: Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints publication-title: Discrete Optimization – volume: 41 start-page: 756 year: 2007 end-page: 771 ident: b28 article-title: An improved solution algorithm for the constrained shortest path problem publication-title: Transportation Research Part B – volume: 10 start-page: 293 year: 1980 end-page: 309 ident: b20 article-title: A dual algorithm for the constrained shortest path problem publication-title: Networks – volume: vol. 8 start-page: 35 year: 1995 end-page: 139 ident: b13 article-title: Time constrained routing and scheduling publication-title: Network routing, handbook in operations research and management science – volume: 97 start-page: 245 year: 1997 end-page: 259 ident: b8 article-title: Crew pairing at air france publication-title: European Journal of Operational Research – volume: 4 start-page: 241 year: 1974 end-page: 253 ident: b19 article-title: Shortest paths with time constraints on moving and parking publication-title: Networks – start-page: 1 year: 2010 end-page: 14 ident: b24 article-title: Column generation publication-title: Wiley Encyclopedia of Operations Research and Management Science – volume: 35 start-page: 286 year: 2001 end-page: 303 ident: b18 article-title: Simultaneous vehicle and crew scheduling in urban mass transit systems publication-title: Transportation Science – volume: 242 start-page: 788 year: 2015 end-page: 797 ident: b16 article-title: An exact method for the biobjective shortest path problem for large-scale road networks publication-title: European Journal of Operational Research – volume: 8 start-page: 2155 year: 2014 end-page: 2172 ident: b4 article-title: Acceleration strategies for the weight constrained shortest path problem with replenishment publication-title: Optimization Letters – start-page: 271 year: 2001 end-page: 303 ident: b30 article-title: Optimal risk path algorithms publication-title: Cooperative control and optimization – volume: 24 start-page: 356 year: 2011 end-page: 371 ident: b2 article-title: New state-space relaxations for solving the traveling salesman problem with time windows publication-title: INFORMS Journal on Computing – year: 1986 ident: b9 article-title: La fabrication d’horaires de travail pour les conducteurs d’autobus par une méthode de génération de colonnes – start-page: 33 year: 2005 end-page: 65 ident: b21 article-title: Shortest path problems with resource constraints – volume: 53 start-page: 358 year: 2009 end-page: 381 ident: b25 article-title: Simultaneous solution of lagrangean dual problems interleaved with preprocessing for the weight constrained shortest path problem publication-title: Networks – volume: 35 start-page: 286 year: 2001 ident: 10.1016/j.ejor.2023.11.047_b18 article-title: Simultaneous vehicle and crew scheduling in urban mass transit systems publication-title: Transportation Science doi: 10.1287/trsc.35.3.286.10153 – volume: 10 start-page: 293 year: 1980 ident: 10.1016/j.ejor.2023.11.047_b20 article-title: A dual algorithm for the constrained shortest path problem publication-title: Networks doi: 10.1002/net.3230100403 – volume: 40 start-page: 378 issue: 1 year: 2013 ident: 10.1016/j.ejor.2023.11.047_b23 article-title: On an exact method for the constrained shortest path problem publication-title: Computers & Operations Research doi: 10.1016/j.cor.2012.07.008 – volume: 62 start-page: 183 issue: 3 year: 2013 ident: 10.1016/j.ejor.2023.11.047_b14 article-title: A survey of resource constrained shortest path problems: Exact solution approaches publication-title: Networks doi: 10.1002/net.21511 – volume: 97 start-page: 245 issue: 2 year: 1997 ident: 10.1016/j.ejor.2023.11.047_b8 article-title: Crew pairing at air france publication-title: European Journal of Operational Research doi: 10.1016/S0377-2217(96)00195-6 – ident: 10.1016/j.ejor.2023.11.047_b29 – volume: vol. 8 start-page: 35 year: 1995 ident: 10.1016/j.ejor.2023.11.047_b13 article-title: Time constrained routing and scheduling – volume: 3 start-page: 255 year: 2006 ident: 10.1016/j.ejor.2023.11.047_b27 article-title: Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints publication-title: Discrete Optimization doi: 10.1016/j.disopt.2006.05.007 – volume: 45 start-page: 239 issue: 4 year: 2007 ident: 10.1016/j.ejor.2023.11.047_b17 article-title: New refinements for the solution of vehicle routing problems with branch and price publication-title: INFOR. Information Systems and Operational Research doi: 10.3138/infor.45.4.239 – year: 2010 ident: 10.1016/j.ejor.2023.11.047_b12 – volume: 19 start-page: 379 issue: 4 year: 1989 ident: 10.1016/j.ejor.2023.11.047_b3 article-title: An algorithm for the resource constrained shortest path problem publication-title: Networks doi: 10.1002/net.3230190402 – volume: 35 start-page: 242 year: 1988 ident: 10.1016/j.ejor.2023.11.047_b11 article-title: A reoptimization algorithm for the shortest path problem with time windows publication-title: European Journal of Operational Research doi: 10.1016/0377-2217(88)90034-3 – volume: 59 start-page: 1269 issue: 5 year: 2011 ident: 10.1016/j.ejor.2023.11.047_b1 article-title: New route relaxation and pricing strategies for the vehicle routing problem publication-title: Operations Research doi: 10.1287/opre.1110.0975 – volume: 242 start-page: 788 issue: 3 year: 2015 ident: 10.1016/j.ejor.2023.11.047_b16 article-title: An exact method for the biobjective shortest path problem for large-scale road networks publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2014.11.003 – volume: 50 start-page: 348 issue: 1 year: 2016 ident: 10.1016/j.ejor.2023.11.047_b22 article-title: An exact algorithm for the elementary shortest path problem with resource constraints publication-title: Transportation Science doi: 10.1287/trsc.2014.0582 – volume: 24 start-page: 356 issue: 3 year: 2011 ident: 10.1016/j.ejor.2023.11.047_b2 article-title: New state-space relaxations for solving the traveling salesman problem with time windows publication-title: INFORMS Journal on Computing doi: 10.1287/ijoc.1110.0456 – volume: 53 start-page: 358 year: 2009 ident: 10.1016/j.ejor.2023.11.047_b25 article-title: Simultaneous solution of lagrangean dual problems interleaved with preprocessing for the weight constrained shortest path problem publication-title: Networks doi: 10.1002/net.20292 – volume: 183 start-page: 564 issue: 2 year: 2007 ident: 10.1016/j.ejor.2023.11.047_b31 article-title: Three-stage approaches for optimizing some variations of the resource constrained shortest-path sub-problem in a column generation context publication-title: EJOR doi: 10.1016/j.ejor.2006.10.012 – start-page: 1 year: 2010 ident: 10.1016/j.ejor.2023.11.047_b24 article-title: Column generation – volume: 26 start-page: 191 year: 1988 ident: 10.1016/j.ejor.2023.11.047_b10 article-title: A generalized permanent labeling algorithm for the shortest path problem with time windows publication-title: INFOR. Information Systems and Operational Research doi: 10.1080/03155986.1988.11732063 – volume: 34 start-page: 312 issue: 3 year: 2000 ident: 10.1016/j.ejor.2023.11.047_b7 article-title: The shortest path problem with time windows and linear waiting costs publication-title: Transportation Science doi: 10.1287/trsc.34.3.312.12298 – start-page: 33 year: 2005 ident: 10.1016/j.ejor.2023.11.047_b21 – volume: 172 start-page: 500 issue: 2 year: 2006 ident: 10.1016/j.ejor.2023.11.047_b26 article-title: Nodal aggregation of resource constraints in shortest path problem publication-title: EJOR doi: 10.1016/j.ejor.2004.09.052 – volume: 8 start-page: 2155 issue: 8 year: 2014 ident: 10.1016/j.ejor.2023.11.047_b4 article-title: Acceleration strategies for the weight constrained shortest path problem with replenishment publication-title: Optimization Letters doi: 10.1007/s11590-014-0742-x – start-page: 271 year: 2001 ident: 10.1016/j.ejor.2023.11.047_b30 article-title: Optimal risk path algorithms – volume: 52 start-page: 256 year: 2008 ident: 10.1016/j.ejor.2023.11.047_b6 article-title: Lagrangean relaxation and enumeration for solving constrained shortest-path problems publication-title: Networks doi: 10.1002/net.20247 – volume: 76 start-page: 128 issue: 2 year: 2020 ident: 10.1016/j.ejor.2023.11.047_b5 article-title: An exact bidirectional pulse algorithm for the constrained shortest path publication-title: Networks doi: 10.1002/net.21960 – volume: 42 start-page: 135 issue: 3 year: 2003 ident: 10.1016/j.ejor.2023.11.047_b15 article-title: Improved preprocessing, labeling and scaling algorithm for the weight-constrained shortest path problem publication-title: Networks doi: 10.1002/net.10090 – volume: 41 start-page: 756 issue: 7 year: 2007 ident: 10.1016/j.ejor.2023.11.047_b28 article-title: An improved solution algorithm for the constrained shortest path problem publication-title: Transportation Research Part B doi: 10.1016/j.trb.2006.12.001 – volume: 4 start-page: 241 issue: 3 year: 1974 ident: 10.1016/j.ejor.2023.11.047_b19 article-title: Shortest paths with time constraints on moving and parking publication-title: Networks doi: 10.1002/net.3230040304 – year: 1986 ident: 10.1016/j.ejor.2023.11.047_b9 |
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| SubjectTerms | Column generation Dynamic programming Shortest path problem with resource constraints Transportation |
| Title | A multiphase dynamic programming algorithm for the shortest path problem with resource constraints |
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