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 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 Traveling-Salesman-Problem Algorithm Based on Simulated Annealing and Gene-Expression Programming

Information ◽  
2018 ◽  
Vol 10 (1) ◽  
pp. 7 ◽  
Author(s):  
Ai-Hua Zhou ◽  
Li-Peng Zhu ◽  
Bin Hu ◽  
Song Deng ◽  
Yan Song ◽  
...  
Keyword(s):  
Gene Expression ◽  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Heuristic Algorithms ◽  
Gene Expression Programming ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Np Hard Problem ◽  
Convergence Performance ◽  
The Traveling Salesman Problem

The traveling-salesman problem can be regarded as an NP-hard problem. To better solve the best solution, many heuristic algorithms, such as simulated annealing, ant-colony optimization, tabu search, and genetic algorithm, were used. However, these algorithms either are easy to fall into local optimization or have low or poor convergence performance. This paper proposes a new algorithm based on simulated annealing and gene-expression programming to better solve the problem. In the algorithm, we use simulated annealing to increase the diversity of the Gene Expression Programming (GEP) population and improve the ability of global search. The comparative experiments results, using six benchmark instances, show that the proposed algorithm outperforms other well-known heuristic algorithms in terms of the best solution, the worst solution, the running time of the algorithm, the rate of difference between the best solution and the known optimal solution, and the convergent speed of algorithms.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 82-92 ◽  
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

scholarly journals Solving Dynamic Traveling Salesman Problem Using Dynamic Gaussian Process Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Stephen M. Akandwanaho ◽  
Aderemi O. Adewumi ◽  
Ayodele A. Adebiyi
Keyword(s):  
Gaussian Process ◽  
Traveling Salesman Problem ◽  
Nearest Neighbor ◽  
Gaussian Process Regression ◽  
Predictive Distribution ◽  
Iterated Local Search ◽  
Traveling Salesman ◽  
Computational Time ◽  
Nonstationary Covariance ◽  
Nonstationary Conditions

This paper solves the dynamic traveling salesman problem (DTSP) using dynamic Gaussian Process Regression (DGPR) method. The problem of varying correlation tour is alleviated by the nonstationary covariance function interleaved with DGPR to generate a predictive distribution for DTSP tour. This approach is conjoined with Nearest Neighbor (NN) method and the iterated local search to track dynamic optima. Experimental results were obtained on DTSP instances. The comparisons were performed with Genetic Algorithm and Simulated Annealing. The proposed approach demonstrates superiority in finding good traveling salesman problem (TSP) tour and less computational time in nonstationary conditions.

scholarly journals Genetiniai algoritmai komivojažieriaus uždaviniui: negatyvieji ir pozityvieji aspektai*

2009 ◽  
Vol 50 ◽  
pp. 173-180
Author(s):  
Alfonsas Misevičius ◽  
Andrius Blažinskas ◽  
Jonas Blonskis ◽  
Vytautas Bukšnaitis
Keyword(s):  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem ◽  
Traveling Salesman ◽  
High Quality ◽  
Genetic Search ◽  
Local Improvement ◽  
Effi Ciency ◽  
The Traveling Salesman Problem

Šiame straipsnyje nagrinėjami klausimai, susiję su genetinių algoritmų taikymu, sprendžiant gerai žinomą kombinatorinio optimizavimo uždavinį – komivojažieriaus uždavinį (KU) (angl. traveling salesman problem). Svarstoma, jog genetinio algoritmo efektyvumui didelę įtaką turi uždavinio specifi nės savybės, todėl labai svarbu kūrybiškai sudaryti genetinį algoritmą konkrečiam sprendžiamam uždaviniui. Pateikiami eksperimentų, atliktų su realizuotu genetiniu algoritmu, rezultatai, iliustruojantys skirtingų veiksnių įtaką rezultatų kokybei. Konstatuojama, kad tinkamas genetinių operatorių ir lokaliojo individų (sprendinių) gerinimo derinimas leidžia gerokai padidinti genetinės paieškos efektyvumą.On the Genetic Algorithms for the Traveling Salesman Problem: Negative and Positive AspectsAlfonsas Misevičius, Andrius Blažinskas, Jonas Blonskis, Vytautas Bukšnaitis SummaryIn this paper, we discuss some issues related to the application of genetic algorithms (GAs) to the well-known combinatorial optimization problem – the traveling salesman problem (TSP). The results obtained from the experiments with the different variants of the genetic algorithm are presented as well. Based on these results, it is concluded that the effi ciency of the genetic search is much infl uenced by both the specifi c nature of the problem and the features of the algorithm itself. In particular, it should be emphasized that the incorporation of the (postcrossover) procedures for the local improvement of offspring has one of the crucial roles in obtaining high-quality solutions.

Intelligent Ant Colony System for Traveling Salesman Problem and Clustering

2011 ◽  
pp. 18-42
Author(s):  
Shu-Chuan Chu ◽  
Jeng-Shyang Pan
Keyword(s):  
Ant Colony Optimization ◽  
Traveling Salesman Problem ◽  
Data Clustering ◽  
Heuristic Algorithms ◽  
Computation Time ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
K Nearest Neighbor ◽  
Ant Colony Systems

Processes that simulate natural phenomena have successfully been applied to a number of problems for which no simple mathematical solution is known or is practicable. Such meta-heuristic algorithms include genetic algorithms, particle swarm optimization and ant colony systems and have received increasing attention in recent years. This work parallelizes the ant colony systems and introduces the communication strategies so as to reduce the computation time and reach the better solution for traveling salesman problem. We also extend ant colony systems and discuss a novel data clustering process using Constrained Ant Colony Optimization (CACO). The CACO algorithm extends the ant colony optimization algorithm by accommodating a quadratic distance metric, the Sum of K Nearest Neighbor Distances (SKNND) metric, constrained addition of pheromone and a shrinking range strategy to improve data clustering. We show that the CACO algorithm can resolve the problems of clusters with arbitrary shapes, clusters with outliers and bridges between clusters

Team Orienteering with Time-Varying Profit

2021 ◽  
Author(s):  
Qinxiao Yu ◽  
Yossiri Adulyasak ◽  
Louis-Martin Rousseau ◽  
Ning Zhu ◽  
Shoufeng Ma
Keyword(s):  
Valid Inequalities ◽  
Iterated Local Search ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Orienteering Problem ◽  
Time Varying ◽  
High Quality ◽  
Hybrid Heuristic ◽  
Team Orienteering Problem ◽  
Team Orienteering

This paper studies the team orienteering problem, where the arrival time and service time affect the collection of profits. Such interactions result in a nonconcave profit function. This problem integrates the aspect of time scheduling into the routing decision, which can be applied in humanitarian search and rescue operations where the survival rate declines rapidly. Rescue teams are needed to help trapped people in multiple affected sites, whereas the number of people who could be saved depends as well on how long a rescue team spends at each site. Efficient allocation and scheduling of rescue teams is critical to ensure a high survival rate. To solve the problem, we formulate a mixed-integer nonconcave programming model and propose a Benders branch-and-cut algorithm, along with valid inequalities for tightening the upper bound. To solve it more effectively, we introduce a hybrid heuristic that integrates a modified coordinate search (MCS) into an iterated local search. Computational results show that valid inequalities significantly reduce the optimality gap, and the proposed exact method is capable of solving instances where the mixed-integer nonlinear programming solver SCIP fails in finding an optimal solution. In addition, the proposed MCS algorithm is highly efficient compared with other benchmark approaches, whereas the hybrid heuristic is proven to be effective in finding high-quality solutions within short computing times. We also demonstrate the performance of the heuristic with the MCS using instances with up to 100 customers. Summary of Contribution: Motivated by search and rescue (SAR) operations, we consider a generalization of the well-known team orienteering problem (TOP) to incorporate a nonlinear time-varying profit function in conjunction with routing and scheduling decisions. This paper expands the envelope of operations research and computing in several ways. To address the scalability issue of this highly complex combinatorial problem in an exact manner, we propose a Benders branch-and-cut (BBC) algorithm, which allows us to efficiently deal with the nonconcave component. This BBC algorithm is computationally enhanced through valid inequalities used to strengthen the bounds of the BBC. In addition, we propose a highly efficient hybrid heuristic that integrates a modified coordinate search into an iterated local search. It can quickly produce high-quality solutions to this complex problem. The performance of our solution algorithms is demonstrated through a series of computational experiments.

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