Exact Solution of Problems in UAV Guidance and Communications Probablistic and Discrete Mathematical Models

Project: Research project

Project Details

Description

Problems associated with UAVs are considered challenging optimization problems. There is a huge literature available and due to their heavy use in practice there must be implementations that have proven to work in a sufficiently reliable and effective way. It is the goal of this project to contribute to two types of approaches, probabilistic methods and discrete optimization formulations. The latter includes models that have integer or binary variables.
Based on our prior research involving partially observable Markov decision processes, the corresponding approach to UAV guidance including for multi-target tracking will be considered but different from the existing literature, provably optimal solutions will be sought. This can be accomplished with some effort even if the underlying optimization problem is not convex. We had been able to convexify
a closely related directional sensor problem before and this will be the first goal. It is undoubtedly of value to solve interesting cases to optimality, providing a benchmark for the large variety of heuristic methods deployed.
A basic UAV guidance model will be treated first followed by extensions as outlined in a recent survey article. This will be done partly in collaboration with experts who had already been our coauthors on directional sensor work.
Discrete optimization problems that are extremely challenging are the quadratic assignment problems. They arise in communications, both for the index assignment problem in coding or modulation methods but also, for example, as multi-objective QAPs, in UAV communications. Other models from UAV guidance have a related form. Porting a sophisticated program which exactly solved a difficult previously unsolved 3d QAP from communications to the 2d case and further augmenting it, a tool will be prepared which will allow to solve previously unsolved cases of practical interest of size 32 and up. This is remarkable since only
few special instances of this size, mostly of academic interest, have been solved and that with a huge effort. One key characteristic of our approach is exploitation of symmetry present in the problem. Initial results have already shown that this is more efficient than the highly perfected commercial software for discrete optimization. Subsequently, related models will be considered partly in coordination with our collaborator on the QAP problem but also with experts in the area of UAV guidance and communications.
StatusFinished
Effective start/end date9/30/159/30/18

Funding

  • DOD-USAF: Air Force Research Labs (AFRL): $373,712.00

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