Online Traveling Salesman Problems with Service Flexibility
The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem. We are concerned here with online versions of this problem defi ned on metric spaces. One novel aspect in the paper is the introduction of a sound theoretical model to incorporate "yes-no" decisions...
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| Format: | Article |
| Language: | en_US |
| Published: |
Wiley
2011
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| Online Access: | http://hdl.handle.net/1721.1/62212 https://orcid.org/0000-0002-8585-6566 |
| Summary: | The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization
problem. We are concerned here with online versions of this problem defi ned on metric
spaces. One novel aspect in the paper is the introduction of a sound theoretical model
to incorporate "yes-no" decisions on which requests to serve, together with an online
strategy to visit the accepted requests.
In order to do so, we assume that there is a penalty for not serving a request.
Requests for visit of points in the metric space are revealed over time to a server,
initially at a given origin, who must decide in an online fashion which requests to serve
in order to minimize the time to serve all accepted requests plus the sum of the penalties
associated with the rejected requests.
We first look at the special case of the non-negative real line. After providing a polynomial time algorithm for the online version of the problem, we propose and prove the
optimality of a 2-competitive polynomial time online algorithm based on re-optimization
approaches. We also consider the impact of advanced information (lookahead) on this
optimal competitive ratio. We then consider the generalizations of these results to the
case of the real line. We show that the previous algorithm can be extended to an optimal 2-competitive online algorithm. Finally we consider the case of a general metric
space and propose an original c-competitive online algorithm, where ....
We also give a polynomial-time (1:5p + 1)-competitive online algorithm which uses a
polynomial-time -approximation for the online problem. |
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