Vehicle routing with time windows
Operations Research
A tabu search heuristic for the multi-depot vehicle routing problem
Computers and Operations Research
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
SIAM Journal on Computing
Aggregation for the probabilistic traveling salesman problem
Computers and Operations Research - Anniversary focused issue of computers & operations research on tabu search
Computational complexity of stochastic programming problems
Mathematical Programming: Series A and B
Runtime reduction techniques for the probabilistic traveling salesman problem with deadlines
Computers and Operations Research
Probabilistic Traveling Salesman Problem with Deadlines
Transportation Science
New Approximation-Based Local Search Algorithms for the Probabilistic Traveling Salesman Problem
Computer Aided Systems Theory - EUROCAST 2009
Estimation-based metaheuristics for the probabilistic traveling salesman problem
Computers and Operations Research
Introduction to Stochastic Programming
Introduction to Stochastic Programming
Computers and Operations Research
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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.