1 Although the bottleneck traveling salesman problem has not apparently been discussed before, the closely related bottleneck assignment problem has been discussed and solved by 0. Gross, "The bottleneck assignment problem," the RAND Corporation P-1630, March 6, 1959. 2 See Kruskal, J. B., "On the shortest spanning subtree of a graph and the travelling salesman problem," Proc. Amer. Math. Soc.,...

We study the online version of the Prize-Collecting Traveling Salesman Problem (PCTSP), a generalization of the Traveling Salesman Problem (TSP). In the TSP, the salesman has to visit a set of cities while minimizing the length of the overall tour. In the PCTSP, each city has a given weight and penalty, and the goal is to collect a given quota of the weights of the cities while minimizing the l...

In the online traveling salesman problem requests for visits to cities (points in a metric space) arrive online while the salesman is traveling. The salesman moves at no more than unit speed and starts and ends his work at a designated origin. The objective is to find a routing for the salesman which finishes as early as possible. Performance of algorithms is measured through their competitive ...

We consider online versions of the Traveling Salesman Problem (TSP) in Euclidean space, where the natural offline problem is the classical TSP with (city) release dates (a city release date is the time after which the city must be served). We analyze in turn the non-negative real line R+, the real line R and finally the general case R. The first part of the paper analyzes the version of the onl...

In this paper we will deal with the sequencing and routing problem of order pickers in conventional multi-parallel-aisle warehouse systems. For this NP-hard Steiner Travelling Salesman Problem exact algorithms only exist for warehouses with at most three cross aisles. We propose a new approach were the problem of routing order pickers in multiple-block warehouses is translated into a classical ...

Genetic Algorithms are the population based search and optimization technique that mimic the process of natural evolution. Different crossover and mutation operators exist to solve the problem that involves large population size. Example of such a problem is travelling sales man problem, which is having a large set of solution. In this paper we will discuss different mutation operators that hel...