Paper Info
Title
Hardness results for the probabilistic traveling salesman problem with deadlines
Abstract
The Probabilistic Traveling Salesman Problem with Deadlines (PTSPD) is a Stochastic Vehicle Routing Problem considering time dependencies. Even the evaluation of the objective function is considered to be a computationally demanding task. So far there is no evaluation method known that guarantees a polynomial runtime, but on the other hand there are also no hardness results regarding the PTSPD objective function. In our work we show that the evaluation of the objective function of the PTSPD, even for Euclidean instances, is #P-hard. In fact, we even show that computing the probabilities, with which deadlines are violated is #P-hard. Based on this result we additionally show that the decision variant of the Euclidean PTSPD, the optimization variant of the Euclidean PTSPD and delta evaluation in reasonable local search neighborhoods is #P-hard.
Year
DOI
Venue
2012
10.1007/978-3-642-32147-4_35
ISCO
Keywords
Field
DocType
delta evaluation,evaluation method,optimization variant,salesman problem,hardness result,euclidean ptspd,stochastic vehicle routing problem,objective function,ptspd objective function,decision variant,euclidean instance
Probabilistic traveling salesman problem,Mathematical optimization,Vehicle routing problem,Polynomial,Local search (optimization),Euclidean geometry,Mathematics,Computational complexity theory
Conference
Citations 
PageRank 
References 
6
0.52
16
Authors
3
Name
Order
Citations
PageRank
Dennis Weyland11088.43
Roberto Montemanni264344.25
Luca Maria Gambardella37926726.40