scholarly journals THE TRAVELING SALESMAN PROBLEM WITH MULTI-VISIT DRONE

2021 ◽  
Vol 37 (4) ◽  
pp. 465-493
Author(s):  
Quang Minh Ha ◽  
Duy Manh Vu ◽  
Xuan Thanh Le ◽  
Minh Ha Hoang
Keyword(s):  
Traveling Salesman Problem ◽  
Positive Impact ◽  
Iterated Local Search ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Solution Quality ◽  
Benchmark Instances ◽  
Time Optimal ◽  
The Traveling Salesman Problem ◽  
First Time

This paper deals with the Traveling Salesman Problem with Multi-Visit Drone (TSP-MVD) in which a truck works in collaboration with a drone that can serve up to q > 1 customers consecutively during each sortie. We propose a Mixed Integer Linear Programming (MILP) formulation and a metaheuristic based on Iterated Local Search to solve the problem. Benchmark instances collected from the literature of the special case with q = 1 are used to test the performance of our algorithms. The obtained results show that our MILP model can solve a number of instances to optimality. This is the first time optimal solutions for these instances are reported. Our ILS performs better other algorithms in terms of both solution quality and running time on several class of instances. The numerical results obtained by testing the methods on new randomly generated instances show again the effectiveness of the methods as well as the positive impact of using the multi-visit drone.

scholarly journals Heuristic Approaches to Solve Traveling Salesman Problem

2015 ◽  
Vol 15 (2) ◽  
pp. 390
Author(s):  
Malik Muneeb Abid ◽  
Iqbal Muhammad
Keyword(s):  
Exact Solution ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Solution Quality ◽  
Heuristic Approaches ◽  
The Traveling Salesman Problem

This paper provides the survey of the heuristics solution approaches for the traveling salesman problem (TSP). TSP is easy to understand, however, it is very difficult to solve. Due to complexity involved with exact solution approaches it is hard to solve TSP within feasible time. That’s why different heuristics are generally applied to solve TSP. Heuristics to solve TSP are presented here with detailed algorithms. At the end, comparison among selected approaches shows the efficiency of approaches in terms of solution quality and time consumed to solve TSP.

scholarly journals ISLAND MIGRATION MODEL WITH PARALLEL MUTATION STRATEGIES FOR COMPUTING THE TRAVELING SALESMAN PROBLEM ON MULTICOMPUTER PLATFORM

2014 ◽  
pp. 96-102
Author(s):  
Plamenka I. Borovska ◽  
Subhi A. Bahudaila ◽  
Milena K. Lazarova
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Coarse Grained ◽  
Mutation Rates ◽  
Solution Quality ◽  
Suggested Approach ◽  
Mutation Strategy ◽  
The Traveling Salesman Problem ◽  
The Impact

This paper investigates the efficiency of a model of parallel genetic computation of the traveling salesman problem with circular periodic chromosomes migration. The parallel model is verified by MPI-based program implementation on a multicomputer platform. The correlation of the application and architectural spaces has been investigated by exploring the impact of the scalability of the application and the parallel machine size over the efficiency of the parallel system. Performance profiling, evaluation and analysis have been made for different numbers of cities and different sizes of the multicomputer platform. The paper also investigates the impact of the mutation strategy on the solution quality of coarse-grained parallel genetic algorithm with circular periodic migration for the traveling salesman problem. We propose an approach to improve the quality of solution by applying parallel variable mutation rates for the local evolutions in the concurrent processes. A series of experiments has been carried out with parallel fixed and variable mutation rates in order to estimate the efficiency of the suggested approach. The best quality solutions have been obtained for the strategy with parallel fixed mutation rates.

scholarly journals Exact and Heuristic Algorithms for the Carrier–Vehicle Traveling Salesman Problem

2020 ◽  
Author(s):  
Güneş Erdoğan ◽  
E. Alper Yıldırım
Keyword(s):  
Structural Properties ◽  
Traveling Salesman Problem ◽  
Heuristic Algorithms ◽  
Iterated Local Search ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
High Quality ◽  
Optimization Formulation ◽  
New Formulation ◽  
Carrier Vehicle

This paper presents new structural properties for the carrier–vehicle traveling salesman problem. The authors provide a new mixed-integer second-order conic optimization formulation, with associated optimality cuts based on the structural properties, and an iterated local search (ILS) algorithm. Computational experiments on instances from the literature demonstrate the superiority of the new formulation to the existing models and algorithms in the literature, and the high-quality solutions found by the ILS algorithm.

scholarly journals An Improved Ant Colony Optimization Based on an Adaptive Heuristic Factor for the Traveling Salesman Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Pengzhen Du ◽  
Ning Liu ◽  
Haofeng Zhang ◽  
Jianfeng Lu
Keyword(s):  
Traveling Salesman Problem ◽  
Large Scale ◽  
Traveling Salesman ◽  
Local Optimum ◽  
Solution Quality ◽  
Movement Strategies ◽  
Comparison Algorithms ◽  
Adaptive Heuristic ◽  
The Traveling Salesman Problem ◽  
Local Optimizer

The traveling salesman problem (TSP) is a typical combinatorial optimization problem, which is often applied to sensor placement, path planning, etc. In this paper, an improved ACO algorithm based on an adaptive heuristic factor (AHACO) is proposed to deal with the TSP. In the AHACO, three main improvements are proposed to improve the performance of the algorithm. First, the k-means algorithm is introduced to classify cities. The AHACO provides different movement strategies for different city classes, which improves the diversity of the population and improves the search ability of the algorithm. A modified 2-opt local optimizer is proposed to further tune the solution. Finally, a mechanism to jump out of the local optimum is introduced to avoid the stagnation of the algorithm. The proposed algorithm is tested in numerical experiments using 39 TSP instances, and results shows that the solution quality of the AHACO is 83.33% higher than that of the comparison algorithms on average. For large-scale TSP instances, the algorithm is also far better than the comparison algorithms.

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.

New Genetic Operator (Jump Crossover) for the Traveling Salesman Problem

2016 ◽  
pp. 1739-1752 ◽  
Author(s):  
Hicham El Hassani ◽  
Said Benkachcha ◽  
Jamal Benhra
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Methods ◽  
Search Space ◽  
Traveling Salesman ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Hard Problems ◽  
The Traveling Salesman Problem ◽  
Np Hard Problems

Inspired by nature, genetic algorithms (GA) are among the greatest meta-heuristics optimization methods that have proved their effectiveness to conventional NP-hard problems, especially the traveling salesman problem (TSP) which is one of the most studied supply chain management problems. This paper proposes a new crossover operator called Jump Crossover (JMPX) for solving the travelling salesmen problem using a genetic algorithm (GA) for near-optimal solutions, to conclude on its efficiency compared to solutions quality given by other conventional operators to the same problem, namely, Partially matched crossover (PMX), Edge recombination Crossover (ERX) and r-opt heuristic with consideration of computational overload. The authors adopt a low mutation rate to isolate the search space exploration ability of each crossover. The experimental results show that in most cases JMPX can remarkably improve the solution quality of the GA compared to the two existing classic crossover approaches and the r-opt heuristic.

scholarly journals Dynamic Flying Ant Colony Optimization (DFACO) for Solving the Traveling Salesman Problem

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1837 ◽  
Author(s):  
Dahan ◽  
El Hindi ◽  
Mathkour ◽  
AlSalman
Keyword(s):  
Ant Colony Optimization ◽  
Traveling Salesman Problem ◽  
Service Selection ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Neighboring Node ◽  
Solution Quality ◽  
Web Service Selection ◽  
The Traveling Salesman Problem

This paper presents an adaptation of the flying ant colony optimization (FACO) algorithm to solve the traveling salesman problem (TSP). This new modification is called dynamic flying ant colony optimization (DFACO). FACO was originally proposed to solve the quality of service (QoS)-aware web service selection problem. Many researchers have addressed the TSP, but most solutions could not avoid the stagnation problem. In FACO, a flying ant deposits a pheromone by injecting it from a distance; therefore, not only the nodes on the path but also the neighboring nodes receive the pheromone. The amount of pheromone a neighboring node receives is inversely proportional to the distance between it and the node on the path. In this work, we modified the FACO algorithm to make it suitable for TSP in several ways. For example, the number of neighboring nodes that received pheromones varied depending on the quality of the solution compared to the rest of the solutions. This helped to balance the exploration and exploitation strategies. We also embedded the 3-Opt algorithm to improve the solution by mitigating the effect of the stagnation problem. Moreover, the colony contained a combination of regular and flying ants. These modifications aim to help the DFACO algorithm obtain better solutions in less processing time and avoid getting stuck in local minima. This work compared DFACO with (1) ACO and five different methods using 24 TSP datasets and (2) parallel ACO (PACO)-3Opt using 22 TSP datasets. The empirical results showed that DFACO achieved the best results compared with ACO and the five different methods for most of the datasets (23 out of 24) in terms of the quality of the solutions. Further, it achieved better results compared with PACO-3Opt for most of the datasets (20 out of 21) in terms of solution quality and execution time.

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