Tim Holzmann
Current Research
SOLVING DISCRETE MULTI-OBJECTIVE OPTIMIZATION PROBLEMS USING MODIFIED AUGMENTED WEIGHTED TCHEBYCHEV SCALARIZATIONS
Authors: Tim Holzmann and J. Cole Smith
Abstract: In this paper we present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem. We contribute a generating algorithm that will, without supervision, generate the entire non-dominated set for any number of objectives. To our knowledge, this is the first generating method for general discrete multi-objective problems that uses a variant of the Tchebychev norm. In a computational study, our algorithm's running times are comparable to previously published algorithms.
THE SHORTEST PATH INTERDICTION PROBLEM WITH AUGMENTATION (SPIP-A)
Authors:
Tim Holzmann and J. Cole Smith
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Abstract:
We consider the shortest path interdiction problem with augmentation. As in standard interdiction problems, there exist two agents, a leader and a follower, playing a Stackelberg game. The leader seeks to maximize the follower's minimum cost by removing (or interdicting) certain arcs from the network. The follower may augment the network after the interdiction by constructing additional arcs. The leader is aware of which arcs may be augmented by the follower, but is unaware of how many additional arcs the follower may add. The effectiveness of an interdiction action is given by the length of a shortest path using only uninterdicted arcs and arcs augmented after the interdiction. We employ a multiobjective optimization model for this problem, with each objective corresponding to a different limit on the number of arcs that the defender can augment. We provide mathematical optimization techniques to compute the Pareto-optimal frontier.