Curve Reconstruction, the Traveling Salesman Problem, and Menger's Theorem on Length

The whale optimization algorithm is a new type of swarm intelligence bionic optimization algorithm, which has achieved good optimization results in solving continuous optimization problems. However, it has less application in discrete optimization problems. A variable neighborhood discrete whale optimization algorithm for the traveling salesman problem (TSP) is studied in this paper. The discrete code is designed first, and then the adaptive weight, Gaussian disturbance, and variable neighborhood search strategy are introduced, so that the population diversity and the global search ability of the algorithm are improved. The proposed algorithm is tested by 12 classic problems of the Traveling Salesman Problem Library (TSPLIB). Experiment results show that the proposed algorithm has better optimization performance and higher efficiency compared with other popular algorithms and relevant literature.

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An Iterated Local Search for the Traveling Salesman Problem with Pickup, Delivery and Handling Costs

2020 39th International Conference of the Chilean Computer Science Society (SCCC) ◽

10.1109/sccc51225.2020.9281164 ◽

2020 ◽

Author(s):

Carlos Rey ◽

Paolo Toth ◽

Daniele Vigo

Keyword(s):

Local Search ◽

Traveling Salesman Problem ◽

Iterated Local Search ◽

Traveling Salesman ◽

The Traveling Salesman Problem

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An Optimal Algorithm for the Traveling Salesman Problem with Time Windows

Operations Research ◽

10.1287/opre.43.2.367 ◽

1995 ◽

Vol 43 (2) ◽

pp. 367-371 ◽

Cited By ~ 171

Author(s):

Yvan Dumas ◽

Jacques Desrosiers ◽

Eric Gelinas ◽

Marius M. Solomon

Keyword(s):

Traveling Salesman Problem ◽

Optimal Algorithm ◽

Time Windows ◽

Traveling Salesman ◽

The Traveling Salesman Problem

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Dynamic Shortest Paths Methods for the Time-Dependent TSP

Algorithms ◽

10.3390/a14010021 ◽

2021 ◽

Vol 14 (1) ◽

pp. 21

Author(s):

Christoph Hansknecht ◽

Imke Joormann ◽

Sebastian Stiller

Keyword(s):

Column Generation ◽

Traveling Salesman Problem ◽

Shortest Path ◽

Valid Inequalities ◽

Shortest Paths ◽

Traveling Salesman ◽

Time Dependent ◽

Full Generality ◽

Branching Rule ◽

The Traveling Salesman Problem

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

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