Valid inequalities and branch-and-cut algorithm for the pickup and delivery traveling salesman problem with multiple stacks

Pereira, Armando Honorio; Mateus, Geraldo Robson; Urrutia, Sebastián

doi:10.1016/j.ejor.2021.07.051

Cited by 6 publications

(4 citation statements)

References 30 publications

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“…They proved new optimal solutions for several benchmark instances, and optimal solutions previously known in the literature are solved more efficiently. Finally, Pereira et al (2022) proposes a procedure of valid inequalities and exact algorithms to solve the PDTSPMS. They also propose a new ILP formulation and new valid inequalities as the foundation for a B&C algorithm.…”

Section: Literature Reviewmentioning

confidence: 99%

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A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

Mardones

Gatica

Contreras‐Bolton

2022

Int Trans Operational Res

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This paper addresses the double traveling salesman problem with partial last‐in‐first‐out (LIFO) loading constraints. A vehicle picks up items in the pickup area and loads them into its container, a horizontal stack. Once all the pickup operations are done, the vehicle can deliver the items to the delivery area because pickup‐and‐delivery areas are geographically separated. Additionally, the loading and unloading operations also follow a partial LIFO policy. The aim is to find a Hamiltonian cycle that satisfies the loading and unloading policy described above in order to minimize the distance traveled by the vehicle in both areas and the cost of the rearrangements that are performed across the routes. The state‐of‐the‐art algorithm finds good solutions to the existing instances. However, finding good‐quality solutions in large instances requires longer computing times. Therefore, we propose an iterated local search that considers two additional components to the classical components, the intensification and restart procedure. The first helps in a more thorough examination of promising neighborhoods, while the second helps in the complete diversity of the solutions in the hopes of escaping the local optima. Moreover, a new unique decoding approach for the solution representation is proposed to effectively generate feasible solutions. The proposed algorithm's performance is evaluated on an existing set of instances and in two new additional sets of larger instances that are proposed. The computational results obtained on the three test sets show that the proposed algorithm outperforms the state‐of‐the‐art algorithm in terms of computing time required to find good‐quality solutions.

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Section: Literature Reviewmentioning

confidence: 99%

“…Finally, Pereira et al. (2022) proposes a procedure of valid inequalities and exact algorithms to solve the PDTSPMS. They also propose a new ILP formulation and new valid inequalities as the foundation for a B&C algorithm.…”

Section: Literature Reviewmentioning

confidence: 99%

A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

Mardones

Gatica

Contreras‐Bolton

2022

Int Trans Operational Res

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“…The total length of the route is 7542, the calculation time was 1.45 s and the circuitous route passes through positions 1, 49, 32, 45, 19, 41, 8, 9, 10, 43, 33, 51, 11, 52, 14, 13, 47, 26, 27, 28, 12, 25, 4, 6, 15, 5, 24, 48, 38, 37, 40, 39, 36, 35, 34, 44, 46, 16, 29, 50, 20, 23, 30, 2, 7, 42, 21, 17, 3, 18, 31, 22, 1. The optimal route can be seen in Figure 4. Finally, GAMS for the kroA100.tsp benchmark stopped the computation at 1000.02 s by exceeding the time limit, but the intermediate result of the path length 21282 and its traversal through positions 1,47,93,28,67,58,61,51,87,25,81,69,64,40,54,2,44,50,73,68,85,82,95,13,76,33,37,5,52,78,96,39,30,48,100,41,71,14,3,43,46,29,34,83,…”

Section: Tsp Implementation In Gamsmentioning

confidence: 99%

“…However, there are also approaches based on deterministic methods such as cutting plane [35], branch and bound [36] and branch and cut [37,38].…”

Section: Introductionmentioning

confidence: 99%

The Assignment Problem and Its Relation to Logistics Problems

Šeda

2022

Algorithms

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The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations is one of the aims of this paper. For some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with the informally derived MIP model and the traveling salesman problem are used to present the limits of the software’s applicability.

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Dynamic pickup and delivery problem with transshipments and LIFO constraints

Xiao-feng

Wei

2023

Computers & Industrial Engineering

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Valid inequalities and branch-and-cut algorithm for the pickup and delivery traveling salesman problem with multiple stacks

Cited by 6 publications

References 30 publications

A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

The Assignment Problem and Its Relation to Logistics Problems

Dynamic pickup and delivery problem with transshipments and LIFO constraints

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