The Multiobjective Shortest Path Problem Is NP-Hard, or Is It?

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10173)


To show that multiobjective optimization problems like the multiobjective shortest path or assignment problems are hard, we often use the theory of \(\mathbf {NP} \)-hardness. In this paper we rigorously investigate the complexity status of some well-known multiobjective optimization problems and ask the question if these problems really are \(\mathbf {NP} \)-hard. It turns out, that most of them do not seem to be and for one we prove that if it is \(\mathbf {NP} \)-hard then this would imply \(\mathbf {P} = \mathbf {NP} \) under assumptions from the literature. We also reason why \(\mathbf {NP} \)-hardness might not be well suited for investigating the complexity status of intractable multiobjective optimization problems.


Multiobjective Optimization Knapsack Problem Multiobjective Optimization Problem Single Objective Problem Travel Salesperson Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author especially thanks Paolo Serafini for a very kind and indepth discussion of this topic. Also many thanks to Kathrin Klamroth and Michael Stiglmayr for many fruitful discussions on the complexity of multiobjective combinatorial optimization problems.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceTU DortmundDortmundGermany

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