Arc Routing, Vehicle Routing, and Turn Penalties Thibaut Vidal Departamento de Inform´ atica, Pontif´ ıcia Universidade Cat´ olica do Rio de Janeiro Rua Marquˆ es de S˜ ao Vicente, 225 - G´ avea, Rio de Janeiro - RJ, 22451-900, Brazil vidalt@inf.puc-rio.br Seminar Bologna, May 31 th , 2016
Contents 1 Node and edge routing problems 2 Combined neighborhoods for arc routing problems Methodology Cutting off complexity: memories + bidirectional search Cutting off complexity: moves filtering via LBs 3 Problem generalizations 4 Very large neighborhoods 5 Computational experiments Integration into two state-of-the-art metaheuristics Comparison with previous literature CARP – To reduce or not to reduce Problems with turn penalties and delays at intersections 6 Conclusions/Perspectives Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 0 / 54 >
Contents 1 Node and edge routing problems 2 Combined neighborhoods for arc routing problems Methodology Cutting off complexity: memories + bidirectional search Cutting off complexity: moves filtering via LBs 3 Problem generalizations 4 Very large neighborhoods 5 Computational experiments Integration into two state-of-the-art metaheuristics Comparison with previous literature CARP – To reduce or not to reduce Problems with turn penalties and delays at intersections 6 Conclusions/Perspectives Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 0 / 54 >
Challenges • Capacitated Vehicle Routing Problem • Consider: ◮ n customers, with demands q i ◮ Complete distance matrix c ij ◮ Homogeneous fleet of m vehicles with capacity Q , located at a single depot • Find: ◮ Least-distance delivery routes ◮ Servicing all customers ◮ Respecting capacity limits Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 1 / 54 >
Challenges 64 64 161 114 • Arc routing for home delivery, 95 96 2 112 113 63 snow plowing, refuse collection, 97 111 94 139 21 21 109 postal services, among others. 91 66 51 110 198 42 79 48 69 202 • Lead to additional challenges: 78 29 29 3 3 3 154 9 9 9 49 13 13 50 155 68 138 5 5 5 10 10 45 ⇒ Deciding on travel directions for 189 services on edges ⇒ Shortest path between services are conditioned by service orientations (may also need to include some additional aspects such as turn penalties or delays at intersections). Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 2 / 54 >
Challenges • Arc routing for home delivery, snow plowing, refuse collection, Sequencing Assignment postal services, among others. • Lead to additional challenges: ⇒ Deciding on travel directions for Service services on edges Orientations ⇒ Shortest path between services are conditioned by service orientations (may also need to include some Shortest additional aspects such as turn Paths penalties or delays at intersections). Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 3 / 54 >
A question of neighborhood • Most recent CARP heuristics rely on Assignment Sequencing several enumerative neighborhood classes to optimize assignment, sequencing and service Service orientation decisions Orientations ◮ See, e.g. Brand˜ ao and HEURISTIC SEARCH Eglese (2008); Usberti et al. (2013); Dell’Amico DYNAMIC et al. (2016)... PROGRAMMING Shortest ◮ Shortest paths between Each solution Paths node extremities have evaluation in O(1) been pre-processed once the shortest ◮ Three decision classes are paths are known heuristically addressed ⇒ This is, however, not the only option. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 4 / 54 >
A question of neighborhood • Most recent CARP heuristics rely on Assignment Sequencing several enumerative neighborhood classes to optimize assignment, sequencing and service Service orientation decisions Orientations ◮ See, e.g. Brand˜ ao and HEURISTIC SEARCH Eglese (2008); Usberti et al. (2013); Dell’Amico DYNAMIC et al. (2016)... PROGRAMMING Shortest ◮ Shortest paths between Each solution Paths node extremities have evaluation in O(1) been pre-processed once the shortest ◮ Three decision classes are paths are known heuristically addressed ⇒ This is, however, not the only option. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 4 / 54 >
A question of neighborhood • Most recent CARP heuristics rely on Assignment Sequencing several enumerative neighborhood classes to optimize assignment, sequencing and service Service orientation decisions Orientations ◮ See, e.g. Brand˜ ao and HEURISTIC SEARCH Eglese (2008); Usberti et al. (2013); Dell’Amico DYNAMIC et al. (2016)... PROGRAMMING Shortest ◮ Shortest paths between Each solution Paths node extremities have evaluation in O(1) been pre-processed once the shortest ◮ Three decision classes are paths are known heuristically addressed ⇒ This is, however, not the only option. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 4 / 54 >
A question of neighborhood • In Beullens et al. (2003) and Muyldermans et al. (2005), O ( n ) Assignment Sequencing dynamic-programming HEURISTIC SEARCH based optimization of service orientations: DYNAMIC Service PROGRAMMING • Combined in Irnich Evaluation of each Orientations (2008) with the solution in O(n) neighborhood of Balas and Simonetti (2001), leading to promising Shortest Paths results on mail delivery applications. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 5 / 54 >
A question of neighborhood • In Beullens et al. (2003) and Muyldermans et al. (2005), O ( n ) Assignment Sequencing dynamic-programming HEURISTIC SEARCH based optimization of service orientations: DYNAMIC Service PROGRAMMING • Combined in Irnich Evaluation of each Orientations (2008) with the solution in O(n) neighborhood of Balas and Simonetti (2001), leading to promising Shortest Paths results on mail delivery applications. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 5 / 54 >
A question of neighborhood • Also the search space of giant tours (Lacomme et al., 2001, 2004; Assignment Sequencing Ramdane-Cherif, 2002) • Evaluating a solution takes O ( n 2 ) operations (or O ( n ) with a faster Service HEURISTIC SEARCH Orientations Split algorithm, see In the space of DYNAMIC Vidal 2016) “ giant tours ” PROGRAMMING Evaluation of each • Because of this higher solution in O(n²) complexity, such Shortest Paths solution representation is rarely used in a LS. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 6 / 54 >
A question of neighborhood • Also the search space of giant tours (Lacomme et al., 2001, 2004; Assignment Sequencing Ramdane-Cherif, 2002) • Evaluating a solution takes O ( n 2 ) operations (or O ( n ) with a faster Service HEURISTIC SEARCH Orientations Split algorithm, see In the space of DYNAMIC Vidal 2016) “ giant tours ” PROGRAMMING Evaluation of each • Because of this higher solution in O(n²) complexity, such Shortest Paths solution representation is rarely used in a LS. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 6 / 54 >
A question of neighborhood • Also the search space of giant tours (Lacomme et al., 2001, 2004; Assignment Sequencing Ramdane-Cherif, 2002) • Evaluating a solution takes O ( n 2 ) operations (or O ( n ) with a faster Service HEURISTIC SEARCH Orientations Split algorithm, see In the space of DYNAMIC Vidal 2016) “ giant tours ” PROGRAMMING Evaluation of each • Because of this higher solution in O(n²) complexity, such Shortest Paths solution representation is rarely used in a LS. Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 6 / 54 >
A question of neighborhood Sequencing Assignment • Finally, the search HEURISTIC SEARCH space used in Wøhlk in the space of giant tours (2003, 2004), also Service (without evoked in orientation) Orientations Ramdane-Cherif DYNAMIC (2002): PROGRAMMING O(n²) per solution Shortest evaluation Paths Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 7 / 54 >
A question of neighborhood • Transferring several decision classes into exact dynamic-programming based components. • This is a structural problem decomposition: Efficient exact methods, such as bi- directional dynamic programming or integer programming on restricted formulations Decision used to derive other decisions set x 1 Difficult combinatorial Heuristic search, optimization problem e.g., local search with several families on a decision set of decisions Decision set x 2 Introduction Neighborhoods Generalizations Larger Neighborhoods Experiments Conclusions References 8 / 54 >
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