# Inverse Multi-objective Shortest Path Problem Under the Bottleneck Type Weighted Hamming Distance

Abstract : Given a network $G(N,\!A,\!C)$ and a directed path $P^0$ from the source node s to the sink node t, an inverse multi-objective shortest path problem is to modify the cost matrix C so that $P^0$ becomes an efficient path and the modification is minimized. In this paper, the modification is measured by the bottleneck type weighted Hamming distance and is proposed an algorithm to solve the inverse problem. Our proposed algorithm can be applied for some other inverse multiobjective problem. As an example, we will mention how the algorithm is used to solve the inverse multi-objective minimum spanning tree problem under the bottleneck type weighted Hamming distance.
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https://hal.inria.fr/hal-01760645
Contributor : Hal Ifip <>
Submitted on : Friday, April 6, 2018 - 3:08:14 PM
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Mobarakeh Karimi, Massoud Aman, Ardeshir Dolati. Inverse Multi-objective Shortest Path Problem Under the Bottleneck Type Weighted Hamming Distance. 2nd International Conference on Topics in Theoretical Computer Science (TTCS), Sep 2017, Tehran, Iran. pp.34-40, ⟨10.1007/978-3-319-68953-1_4⟩. ⟨hal-01760645⟩

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