Traveling salesman path problems
نویسندگان
چکیده
In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem, in which the objective is to find a minimum cost walk from the source to destination visiting all cities at least once. We first characterize traveling salesman walk perfect graphs, graphs for which the convex hull of incidence vectors of traveling salesman walks can be described by linear inequalities. We show these graphs have a description by way of forbidden minors and also characterize them constructively. We also address the asymmetric traveling salesman path problem and give a factor O( √ n)-approximation algorithm for this problem.
منابع مشابه
New Heuristic Algorithms for Solving Single-Vehicle and Multi-Vehicle Generalized Traveling Salesman Problems (GTSP)
Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...
متن کاملSolving the Multiple Traveling Salesman Problem by a Novel Meta-heuristic Algorithm
The multiple traveling salesman problem (MTSP) is a generalization of the famous traveling salesman problem (TSP), where more than one salesman is used in the solution. Although the MTSP is a typical kind of computationally complex combinatorial optimization problem, it can be extended to a wide variety of routing problems. This paper presents an efficient and evolutionary optimization algorith...
متن کاملSolving Traveling Salesman Problem based on Biogeography-based Optimization and Edge Assembly Cross-over
Biogeography-Based Optimization (BBO) algorithm has recently been of great interest to researchers for simplicity of implementation, efficiency, and the low number of parameters. The BBO Algorithm in optimization problems is one of the new algorithms which have been developed based on the biogeography concept. This algorithm uses the idea of animal migration to find suitable habitats for solvin...
متن کاملAn Approach for Solving Traveling Salesman Problem
In this paper, we introduce a new approach for solving the traveling salesman problems (TSP) and provide a solution algorithm for a variant of this problem. The concept of the proposed method is based on the Hungarian algorithm, which has been used to solve an assignment problem for reaching an optimal solution. We introduced a new fittest criterion for crossing over such problems, and illu...
متن کاملA Hybrid Modified Meta-heuristic Algorithm for Solving the Traveling Salesman Problem
The traveling salesman problem (TSP) is one of the most important combinational optimization problems that have nowadays received much attention because of its practical applications in industrial and service problems. In this paper, a hybrid two-phase meta-heuristic algorithm called MACSGA used for solving the TSP is presented. At the first stage, the TSP is solved by the modified ant colony s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Program.
دوره 113 شماره
صفحات -
تاریخ انتشار 2008