Machine Learning and the Traveling Repairman

Details Machine Learning and the Traveling Repairman Machine Learning and the Traveling Repairman

2011-04-27

arxiv.org/abs/1104.5061v1

Mathematics

Optimization and Control

41 pages, 15 figures

Scientific paper

The goal of the Machine Learning and Traveling Repairman Problem (ML&TRP) is to determine a route for a "repair crew," which repairs nodes on a graph. The repair crew aims to minimize the cost of failures at the nodes, but as in many real situations, the failure probabilities are not known and must be estimated. We introduce two formulations for the ML&TRP, where the first formulation is sequential: failure probabilities are estimated at each node, and then a weighted version of the traveling repairman problem is used to construct the route from the failure cost. We develop two models for the failure cost, based on whether repeat failures are considered, or only the first failure on a node. Our second formulation is a multi-objective learning problem for ranking on graphs. Here, we are estimating failure probabilities simultaneously with determining the graph traversal route; the choice of route influences the estimated failure probabilities. This is in accordance with a prior belief that probabilities that cannot be well-estimated will generally be low. It also agrees with a managerial goal of finding a scenario where the data can plausibly support choosing a route that has a low operational cost.

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