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Space mission planning and spacecraft design are tightly coupled and need to be considered together for optimal performance; however, this integrated optimization problem results in a large-scale Mixed-Integer Nonlinear Programming (MINLP) problem, which is challenging to solve. In response to this challenge, this paper proposes a new solution approach to this MINLP problem by iterative solving a set of coupled subproblems via the augmented Lagrangian coordination approach following the philosophy of Multi-disciplinary Design Optimization (MDO). The proposed approach leverages the unique structure of the problem that enables its decomposition into a set of coupled subproblems of different types: a Mixed-Integer Quadratic Programming (MIQP) subproblem for mission planning and one or more Nonlinear Programming (NLP) subproblem(s) for spacecraft design. Since specialized MIQP or NLP solvers can be applied to each subproblem, the proposed approach can efficiently solve the otherwise intractable integrated MINLP problem. An automatic and effective method to find an initial solution for this iterative approach is also proposed so that the optimization can be performed without the need for a user-defined initial guess. In the demonstration case study, a human lunar exploration mission sequence is optimized with a subsystem-level parametric spacecraft design model. Compared to the state-of-the-art method, the proposed formulation can obtain a better solution with a shorter computational time even without parallelization. For larger problems, the proposed solution approach can also be easily parallelizable and thus is expected to be further advantageous and scalable.
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Fast Globally Optimal Catalog Matching using MIQCP
Abstract We propose a novel exact method to solve the probabilistic catalog matching problem faster than previously possible. Our new approach uses mixed integer programming and introduces quadratic constraints to shrink the problem by multiple orders of magnitude. We also provide a method to use a feasible solution to dramatically speed up our algorithm. This gain in performance is dependent on how close to optimal the feasible solution is. Also, we are able to provide good solutions by stopping our mixed integer programming solver early. Using simulated catalogs, we empirically show that our new mixed integer program with quadratic constraints is able to be set up and solved much faster than previous large linear formulations. We also demonstrate our new approach on real-world data from the Hubble Source Catalog. This paper is accompanied by publicly available software to demonstrate the proposed method.
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- PAR ID:
- 10465674
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astronomical Journal
- Volume:
- 166
- Issue:
- 4
- ISSN:
- 0004-6256
- Format(s):
- Medium: X Size: Article No. 174
- Size(s):
- Article No. 174
- Sponsoring Org:
- National Science Foundation
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