Uncertain multiobjective orienteering problem and its application to UAV reconnaissance mission planning.

Orienteering problem is gradually prevalent in the recent decade, but studies considering both uncertainty and multiobjective are still at low pace. In this paper, the uncertain multiobjective orienteering problem (UMOOP) is modeled based on uncertainty theory, in which objective functions contain uncertain vectors. Firstly, the Kataoka criterion and the 'worst-case-oriented' philosophy are adopted, and the UMOOP is transformed into a deterministic problem alpha-UMOOP with a series of chance constrains. On this basis, concept of efficient solution with belief degree is defined. Secondly, two assumptions are introduced to deal with the uncertain vectors, and a deterministic equivalent form D-UMOOP can be obtained. It is theoretically proved that efficient solutions to D-UMOOP are equivalent to the efficient solutions with belief degrees to the UMOOP. Additionally, since the D-UMOOP is NP-hard, a discrete multiobjective bat algorithm is designed with the discrete updating process and the multiobjective local search strategy. Finally, an application is presented to the unmanned aerial vehicle (UAV) reconnaissance mission planning problem, which is modeled as uncertain biobjective orienteering problems, and tackled by the theoretical result and algorithm in this paper. The studies provide a new way for multiple attribute and uncertain decision-making problems.