Improving the state-of-the-art in the Traveling Salesman Problem: An Anytime Automatic Algorithm Selection

2022 ◽  
Vol 187 ◽  
pp. 115948
Author(s):  
Isaías I. Huerta ◽  
Daniel A. Neira ◽  
Daniel A. Ortega ◽  
Vicente Varas ◽  
Julio Godoy ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
State Of The Art ◽  
The State ◽  
Traveling Salesman ◽  
Algorithm Selection ◽  
Automatic Algorithm Selection ◽  
The Traveling Salesman Problem ◽  
Automatic Algorithm

scholarly journals Exact Methods for the Traveling Salesman Problem with Drone

2021 ◽  
Vol 55 (2) ◽  
pp. 315-335
Author(s):  
Roberto Roberti ◽  
Mario Ruthmair
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
The State ◽  
Set Partitioning ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Branch And Price ◽  
Last Mile ◽  
The Traveling Salesman Problem

Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and a drone are teamed up to serve a set of customers. This combination of truck and drone can exploit the benefits of both vehicle types: the truck has a large capacity but usually low travel speed in urban areas; the drone is faster and not restricted to street networks, but its range and carrying capacity are limited. We propose a compact mixed-integer linear program (MILP) for several TSP-D variants that is based on timely synchronizing truck and drone flows; such an MILP is easy to implement but nevertheless leads to competitive results compared with the state-of-the-art MILPs. Furthermore, we introduce dynamic programming recursions to model several TSP-D variants. We show how these dynamic programming recursions can be exploited in an exact branch-and-price approach based on a set partitioning formulation using ng-route relaxation and a three-level hierarchical branching. The proposed branch-and-price can solve instances with up to 39 customers to optimality outperforming the state-of-the-art by more than doubling the manageable instance size. Finally, we analyze different scenarios and show that even a single drone can significantly reduce a route’s completion time when the drone is sufficiently fast.

scholarly journals Solve traveling salesman problem using EMF-CE algorithm

2020 ◽  
Author(s):  
Meng Luo ◽  
Shiliang Gu
Keyword(s):  
Local Search ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
Search Algorithm ◽  
Feedback Regulation ◽  
Critical Value ◽  
Traveling Salesman ◽  
Online Library ◽  
The Traveling Salesman Problem ◽  
Algorithm Implementation

<p>In this paper, a novel search algorithm that based on the Contraction-Expansion algorithm and integrated three operators Exchange, Move, and Flip (EMF-CE) is proposed for the traveling salesman problem (TSP). EMF-CE uses a negative exponent function to generate critical value as the feedback regulation of algorithm implementation. Also, combined Exchange Step, Move step with Flip step and constitute of more than twenty combinatorial optimizations of program elements. It has been shown that the integration of local search operators can significantly improve the performance of EMF-CE for TSPs. We test small and medium scale (51-1000 cities) TSPs were taken from the TSPLIB online library. The experimental results show the efficiency of the proposed EMF-CE for addressing TSPs compared to other state-of-the-art algorithms.</p>

scholarly journals A Multi-objective Version of the Lin-Kernighan Heuristic for the Traveling Salesman Problem

2018 ◽  
Vol 25 (1) ◽  
pp. 48
Author(s):  
Emerson Bezerra De Carvalho ◽  
Elizabeth Ferreira Gouvêa Goldbarg ◽  
Marco Cesar Goldbarg
Keyword(s):  
Local Search ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
Symmetric Case ◽  
Traveling Salesman ◽  
Weighted Sum ◽  
Pareto Dominance ◽  
Multi Objective ◽  
The Traveling Salesman Problem ◽  
Single Objective

The Lin and Kernighan’s algorithm for the single objective Traveling Salesman Problem (TSP) is one of the most efficient heuristics for the symmetric case. Although many algorithms for the TSP were extended to the multi-objective version of the problem (MTSP), the Lin and Kernighan’s algorithm was still not fully explored. Works that applied the Lin and Kernighan’s algorithm for the MTSP were driven to weighted sum versions of the problem. We investigate the LK from a Pareto dominance perspective. The multi-objective LK was implemented within two local search schemes and applied to 2 to 4-objective instances. The results  showed that the proposed algorithmic variants obtained better results than a state-of-the-art algorithm.

scholarly journals Solve traveling salesman problem using EMF-CE algorithm

2020 ◽  
Author(s):  
Meng Luo ◽  
Shiliang Gu
Keyword(s):  
Local Search ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
Search Algorithm ◽  
Feedback Regulation ◽  
Critical Value ◽  
Traveling Salesman ◽  
Online Library ◽  
The Traveling Salesman Problem ◽  
Algorithm Implementation

<p>In this paper, a novel search algorithm that based on the Contraction-Expansion algorithm and integrated three operators Exchange, Move, and Flip (EMF-CE) is proposed for the traveling salesman problem (TSP). EMF-CE uses a negative exponent function to generate critical value as the feedback regulation of algorithm implementation. Also, combined Exchange Step, Move step with Flip step and constitute of more than twenty combinatorial optimizations of program elements. It has been shown that the integration of local search operators can significantly improve the performance of EMF-CE for TSPs. We test small and medium scale (51-1000 cities) TSPs were taken from the TSPLIB online library. The experimental results show the efficiency of the proposed EMF-CE for addressing TSPs compared to other state-of-the-art algorithms.</p>

scholarly journals Solve traveling salesman problem using EMF-CE algorithm

2020 ◽  
Author(s):  
Meng Luo ◽  
Shiliang Gu
Keyword(s):  
Local Search ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
Search Algorithm ◽  
Feedback Regulation ◽  
Critical Value ◽  
Traveling Salesman ◽  
Online Library ◽  
The Traveling Salesman Problem ◽  
Algorithm Implementation

<p>In this paper, a novel search algorithm that based on the Contraction-Expansion algorithm and integrated three operators Exchange, Move, and Flip (EMF-CE) is proposed for the traveling salesman problem (TSP). EMF-CE uses a negative exponent function to generate critical value as the feedback regulation of algorithm implementation. Also, combined Exchange Step, Move step with Flip step and constitute of more than twenty combinatorial optimizations of program elements. It has been shown that the integration of local search operators can significantly improve the performance of EMF-CE for TSPs. We test small and medium scale (51-1000 cities) TSPs were taken from the TSPLIB online library. The experimental results show the efficiency of the proposed EMF-CE for addressing TSPs compared to other state-of-the-art algorithms.</p>

scholarly journals Developing Programming Tools to Handle Traveling Salesman Problem by the Three Object-Oriented Languages

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Hassan Ismkhan ◽  
Kamran Zamanifar
Keyword(s):  
Traveling Salesman Problem ◽  
State Of The Art ◽  
Hybrid Genetic Algorithm ◽  
Object Oriented ◽  
Traveling Salesman ◽  
Abstract Data Type ◽  
Programming Tools ◽  
Abstract Data ◽  
The Traveling Salesman Problem ◽  
Object Oriented Languages

The traveling salesman problem (TSP) is one of the most famous problems. Many applications and programming tools have been developed to handle TSP. However, it seems to be essential to provide easy programming tools according to state-of-the-art algorithms. Therefore, we have collected and programmed new easy tools by the three object-oriented languages. In this paper, we present ADT (abstract data type) of developed tools at first; then we analyze their performance by experiments. We also design a hybrid genetic algorithm (HGA) by developed tools. Experimental results show that the proposed HGA is comparable with the recent state-of-the-art applications.

scholarly journals Improved CP-Based Lagrangian Relaxation Approach with an Application to the TSP

2021 ◽  
Author(s):  
Raphaël Boudreault ◽  
Claude-Guy Quimper
Keyword(s):  
Lagrangian Relaxation ◽  
State Of The Art ◽  
Optimization Technique ◽  
Search Space ◽  
The State ◽  
Traveling Salesman ◽  
Resolution Time ◽  
Lagrangian Multipliers ◽  
The Traveling Salesman Problem ◽  
New Algorithms

CP-based Lagrangian relaxation (CP-LR) is an efficient optimization technique that combines cost-based filtering with Lagrangian relaxation in a constraint programming context. The state-of-the-art filtering algorithms for the WeightedCircuit constraint that encodes the traveling salesman problem (TSP) are based on this approach. In this paper, we propose an improved CP-LR approach that locally modifies the Lagrangian multipliers in order to increase the number of filtered values. We also introduce two new algorithms based on the latter to filter WeightedCircuit. The experimental results on TSP instances show that our algorithms allow significant gains on the resolution time and the size of the search space when compared to the state-of-the-art implementation.

Sign in / Sign up

Export Citation Format

Share Document