Integer Programming as a General Solution Methodology for Path-Based Optimization in Robotics: Principles and Best Practices
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The resolution of many robotics problems demands the optimization of certain reward (or cost) over a huge number of candidate paths. In this paper, we describe an integer programming (IP) solution methodology for path-based optimization problems that is both easy to apply (in two simple steps) and frequently high-performance in terms of the computation time and the achieved optimality. We demonstrate the generality of our approach through the application to three challenging path-based optimization problems: multi-robot path planning (MPP), minimum constraint removal (MCR), and reward collection problems (RCPs). In the process, in addition to providing basic working IP models, we describe best practices (which include many generic heuristics) that lead to significant performance boosts. Associated simulation experiments show that the approach can efficiently produce (near-)optimal solutions for problems with large state spaces, complex constraints, and complicated objective functions.
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