An exact -constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits

2009 ◽  
Vol 194 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Jean-François Bérubé ◽  
Michel Gendreau ◽  
Jean-Yves Potvin
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem ◽  
Exact Constraint ◽  
Constraint Method

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 Branch and Bound Algorithm for the Traveling Salesman Problem is not a Direct Type Algorithm

2020 ◽  
Vol 27 (1) ◽  
pp. 72-85
Author(s):  
Aleksandr N. Maksimenko
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Clique Number ◽  
Traveling Salesman ◽  
Branch And Bound Algorithm ◽  
Combinatorial Optimization Problems ◽  
Type Algorithm ◽  
The Traveling Salesman Problem

In this paper, we consider the notion of a direct type algorithm introduced by V. A. Bondarenko in 1983. A direct type algorithm is a linear decision tree with some special properties. the concept of a direct type algorithm is determined using the graph of solutions of a combinatorial optimization problem. ‘e vertices of this graph are all feasible solutions of a problem. Two solutions are called adjacent if there are input data for which these and only these solutions are optimal. A key feature of direct type algorithms is that their complexity is bounded from below by the clique number of the solutions graph. In 2015-2018, there were five papers published, the main results of which are estimates of the clique numbers of polyhedron graphs associated with various combinatorial optimization problems. the main motivation in these works is the thesis that the class of direct type algorithms is wide and includes many classical combinatorial algorithms, including the branch and bound algorithm for the traveling salesman problem, proposed by J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel in 1963. We show that this algorithm is not a direct type algorithm. Earlier, in 2014, the author of this paper showed that the Hungarian algorithm for the assignment problem is not a direct type algorithm. ‘us, the class of direct type algorithms is not so wide as previously assumed.

scholarly journals PARALLEL TEMPERING FOR THE TRAVELING SALESMAN PROBLEM

2009 ◽  
Vol 20 (04) ◽  
pp. 539-556 ◽  
Author(s):  
CHIAMING WANG ◽  
JEFFREY D. HYMAN ◽  
ALLON PERCUS ◽  
RUSSEL CAFLISCH
Keyword(s):  
Simulated Annealing ◽  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Minimum Distance ◽  
Optimization Problems ◽  
Optimization Method ◽  
Traveling Salesman ◽  
Parallel Tempering ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

We explore the potential of parallel tempering as a combinatorial optimization method, applying it to the traveling salesman problem. We compare simulation results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performance of the two methods. We find that a straightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulations are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems.

Microcanonical Optimization Applied to the Traveling Salesman Problem

1998 ◽  
Vol 09 (01) ◽  
pp. 133-146 ◽  
Author(s):  
Alexandre Linhares ◽  
José R. A. Torreão
Keyword(s):  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Physics ◽  
Traveling Salesman ◽  
Tabu Search Algorithm ◽  
Combinatorial Optimization Problems ◽  
Microcanonical Annealing ◽  
The Traveling Salesman Problem

Optimization strategies based on simulated annealing and its variants have been extensively applied to the traveling salesman problem (TSP). Recently, there has appeared a new physics-based metaheuristic, called the microcanonical optimization algorithm (μO), which does not resort to annealing, and which has proven a superior alternative to the annealing procedures in various applications. Here we present the first performance evaluation of μO as applied to the TSP. When compared to three annealing strategies (simulated annealing, microcanonical annealing and Tsallis annealing), and to a tabu search algorithm, the microcanonical optimization has yielded the best overall results for several instances of the euclidean TSP. This confirms μO as a competitive approach for the solution of general combinatorial optimization problems.

scholarly journals ОГЛЯД ЗАВДАНЬ МАРШРУТИЗАЦІЇ, ЩО ЗВОДЯТЬСЯ ДО ЗАДАЧІ КОМІВОЯЖЕРА

2020 ◽  
pp. 152-159
Author(s):  
Ольга Борисовна Маций
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Information Technologies ◽  
Traveling Salesman ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Np Complete ◽  
Modern Information ◽  
The Traveling Salesman Problem

The solution to the problem of improving the management of the transport process depends not only on the level of modernization of vehicles and the degree of use of modern information technologies, but also on the choice of routes that reduce the cost of transporting goods and passengers. Actual working conditions of vehicles in road networks put forward a number of tasks for optimizing closed routes, which are based on the classic routing problem (VRP - Vehicle Routing Problem).VRP is one of the generalizations of the hard-to-solve traveling salesman problem. The traveling salesman task is NP-complete. It refers to the main tasks of combinatorial optimization and, forming a continuously replenished set of applications and generalizations, remains an urgent research topic. An exact solution to the traveling salesman problem can be found only by reducing the enumeration of the type of branches and boundaries, which are not always applicable in operational planning by vehicle traffic. Therefore, the development of new and improvement of currently known methods for solving routing problems, reducible to the traveling salesman problem, and their software implementation is both a theoretical and practically important problem.The article considers the class of routing problems reducible to the traveling salesman problem. It is shown that optimization tasks for closed routes (routing problems), which are an important part of transport logistics, occupy key positions in the management of the processes of moving goods and passengers with the support of modern information technologies. An obvious feature that combines the considered list of routing problems (the symmetric traveling salesman problem, the problem of packing in containers, the school bus problem) is that they are formulated as generalizations or variants of the NP-complete traveling salesman problem with restrictions that narrow the scope of feasible solutions. The strongest restrictions become insufficient solvability conditions, stimulating interest in the study of combinatorial optimization problems associated with the traveling salesman problem.

Research on MPI-Based Parallel Max-Min Ant System

2012 ◽  
Vol 198-199 ◽  
pp. 1321-1326 ◽  
Author(s):  
Yu Liu ◽  
Guo Dong Wu
Keyword(s):  
Combinatorial Optimization ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
Computation Time ◽  
Traveling Salesman ◽  
Ant System ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

When solving large scale combinatorial optimization problems, Max-Min Ant System requires long computation time. MPI-based Parallel Max-Min Ant System described in this paper can ensure the quality of the solution, as well as reduce the computation time. Numerical experiments on the multi-node cluster system show that when solving the traveling salesman problem, MPI-based Parallel Max-Min Ant System can get better computational efficiency.

scholarly journals Opposition-Based Ant Colony Optimization Algorithm for the Traveling Salesman Problem

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1650
Author(s):  
Zhaojun Zhang ◽  
Zhaoxiong Xu ◽  
Shengyang Luan ◽  
Xuanyu Li ◽  
Yifei Sun
Keyword(s):  
Ant Colony Optimization ◽  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
Combinatorial Optimization Problems ◽  
Opposition Based Learning ◽  
The Traveling Salesman Problem

Opposition-based learning (OBL) has been widely used to improve many swarm intelligent optimization (SI) algorithms for continuous problems during the past few decades. When the SI optimization algorithms apply OBL to solve discrete problems, the construction and utilization of the opposite solution is the key issue. Ant colony optimization (ACO) generally used to solve combinatorial optimization problems is a kind of classical SI optimization algorithm. Opposition-based ACO which is combined in OBL is proposed to solve the symmetric traveling salesman problem (TSP) in this paper. Two strategies for constructing opposite path by OBL based on solution characteristics of TSP are also proposed. Then, in order to use information of opposite path to improve the performance of ACO, three different strategies, direction, indirection, and random methods, mentioned for pheromone update rules are discussed individually. According to the construction of the inverse solution and the way of using it in pheromone updating, three kinds of improved ant colony algorithms are proposed. To verify the feasibility and effectiveness of strategies, two kinds of ACO algorithms are employed to solve TSP instances. The results demonstrate that the performance of opposition-based ACO is better than that of ACO without OBL.

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

2012 ◽  
pp. 342-352
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Exact Algorithms ◽  
Traveling Salesman ◽  
Routing Problem ◽  
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 Reinforcement learning for the traveling salesman problem with refueling

2021 ◽  
Author(s):  
André L. C. Ottoni ◽  
Erivelton G. Nepomuceno ◽  
Marcos S. de Oliveira ◽  
Daniela C. R. de Oliveira
Keyword(s):  
Reinforcement Learning ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Autonomous Vehicle ◽  
Route Planning ◽  
Potential Method ◽  
Traveling Salesman ◽  
Q Learning ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

AbstractThe traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems. Many methods derived from TSP have been applied to study autonomous vehicle route planning with fuel constraints. Nevertheless, less attention has been paid to reinforcement learning (RL) as a potential method to solve refueling problems. This paper employs RL to solve the traveling salesman problem With refueling (TSPWR). The technique proposes a model (actions, states, reinforcements) and RL-TSPWR algorithm. Focus is given on the analysis of RL parameters and on the refueling influence in route learning optimization of fuel cost. Two RL algorithms: Q-learning and SARSA are compared. In addition, RL parameter estimation is performed by Response Surface Methodology, Analysis of Variance and Tukey Test. The proposed method achieves the best solution in 15 out of 16 case studies.

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