Weconsider theRailwayTravelingSalesmanProblem (RTSP) in which a salesman using the railway network wishes to visit a certain number of cities to carry out his/her business, starting and ending at the same city, and having as goal to minimize the overall time of the journey. RTSP is an NP-hard problem. Although it is related to the Generalized Asymmetric Traveling Salesman Problem, in this paper...

This note aims to give an application of entropy to the analysis of algorithms, using Shearer’s entropy lemma to bound the running time of Bellman’s dynamic programming solution to the traveling salesman problem. The original venue for this material was my course Randommised algorithms (2008) at Lund University. 1. The Traveling Salesman Problem Given a weighted graph like

Theoretical computer science has given birth to a very intriguing and fascinating class of problems known as Nondeterministic Polynomial-time (NP) complete problems. Among their captivating properties are their computational complexity despite often deceptively simple formulations. An example of this is the ubiquitous Traveling Salesman Problem (TSP). This problem has had an uncontested popular...

by Howard Kleiman

The TSP, VRP and OP problems with time constraints have one common sub-problem – the task of finding the minimum route duration for a given order of customers. While much work has been done on routing and scheduling problems with time windows, to this date only few articles considered problems with multiple time windows. Moreover, since the assumption of constant travel time between two locatio...

The multiple Traveling Salesman Problem (mTSP) is a complex combinatorial optimization problem, which is a generalization of the well-known Traveling Salesman Problem (TSP), where one or more salesmen can be used in the solution. The optimization task can be described as follows: given a fleet of vehicles, a common depot and several requests by the customers, find the set of routes with overall...

In this paper, we extend the classical multiple traveling salesman problem (mTSP) by imposing a minimal number of nodes that a traveler must visit as a side condition. We consider single and multidepot cases and propose integer linear programming formulations for both, with new bounding and subtour elimination constraints. We show that several variations of the multiple salesman problem can be ...

We allow representing and reasoning in the presence of nested multiple aggregates over multiple variables and nested multiple aggregates over functions involving multiple variables in answer sets, precisely, in answer set optimization programming and in answer set programming. We show the applicability of the answer set optimization programming with nested multiple aggregates and the answer set...