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

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 object...

While it was known for a long time how to transform an asymmetric traveling salesman problem on the complete graph with n vertices into a symmetric traveling salesman problem on an incomplete graph with 2n vertices, no method was available until recently for using this correspondence to derive facets of the symmetric traveling salesman polytope from facets of the asymmetric one. In this paper w...

This paper presented a mixed integer programming for integrated scheduling and process planning. The presented process plan included some orders with precedence relations similar to Multiple Traveling Salesman Problem (MTSP), which was categorized as an NP-hard problem. These types of problems are also called advanced planning because of simultaneously determining the appropriate sequence and m...

The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performan...

The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performan...

In the single objective period traveling salesman problem (SOPTSP), each of given n cities has to be visited by the traveling salesman a fixed number of times according to some allowable day combinations over a given m day planning period with the objective to minimize the total traveling distance over the whole period. The existing solution methods for the SOPTSP always generate a set of unbal...

In this paper, we deal with the Time-Dependent Traveling Salesman Problem with Time Windows (TDTSPTW ). Firstly, we prove that under special conditions the TDTSPTW can be solved as an Asymmetric Traveling Salesman Problem with Time Windows (ATSPTW ), with suitable-defined time windows and (constant) travel times. Secondly, we show that, if the special conditions do not hold, the ATSPTW optimal ...

Abstract In industrial production, parallel robot is often used for sorting, battery clamp divided into two structures, the classification and multi-target sorting problems. The motion path of end-effector planned, overall practical problem transformed a similar traveling salesman problem. improved genetic algorithm proposed to optimize time sequence, optimized shortens 10.23% total distance on...

The subject of this work is the new idea of blocks for the cyclic flow shop problem with setup times, using multiple patterns with different sizes determined for each machine constituting optimal schedule of cities for the traveling salesman problem (TSP). We propose to take advantage of the Intel Xeon Phi parallel computing environment during so-called ’blocks’ determination basing on patterns...