In this paper, we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an existing algorithm for the single-objective problem to multi-objective optimization. We propose also an enhancement to accelerate the algorithm, even for the single-objective case, and we develop a faster version for special multi-objective instances. Second, we introduce a deterministic multi-objective problem with sum and bottleneck functions, which provides a superset of the robust efficient solutions. Based on this, we develop a label setting algorithm to solve the multi-objective uncertain shortest path problem. We compare both approaches on instances of the multi-objective uncertain shortest path problem originating from hazardous material transportation.

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Keywords Combinatorial optimization, Multi-objective robust optimization, Multiple objective programming, Robust optimization, Shortest path problem
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Journal European Journal of Operational Research
Raith, A, Schmidt, M.E, Schöbel, A, & Thom, L. (Lisa). (2018). Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty. European Journal of Operational Research. doi:10.1016/j.ejor.2017.12.018