# Integer Programming as a General Solution Methodology for Path-Based Optimization in Robotics: Principles, Best Practices, and Applications

## TL;DR

This paper presents a general, easy-to-apply integer programming methodology for solving complex path-based optimization problems in robotics, demonstrating high efficiency and optimality across multiple challenging applications.

## Contribution

The paper introduces a simple two-step IP solution approach applicable to various path-based problems and proposes two new robotics problems solvable with this method.

## Key findings

- Efficiently produces near-optimal solutions for large, complex problems.
- Demonstrates applicability to multi-robot path planning, constraint removal, and reward collection.
- Introduces two new robotics problems solved effectively with the proposed methodology.

## Abstract

Integer programming (IP) has proven to be highly effective in solving many path-based optimization problems in robotics. However, the applications of IP are generally done in an ad-hoc, problem specific manner. In this work, after examined a wide range of path-based optimization problems, we describe an IP solution methodology for these problems that is both easy to apply (in two simple steps) and 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). Associated experiments show that the approach can efficiently produce (near-)optimal solutions for problems with large state spaces, complex constraints, and complicated objective functions. In conjunction with the proposition of the IP methodology, we introduce two new and practical robotics problems: multi-robot minimum constraint removal (MMCR) and multi-robot path planning (MPP) with partial solutions, which can be quickly and effectively solved using our proposed IP solution pipeline.