Deploying autonomous sonobuoys optimally on a linear array via assignment problem

Abstract

A sonobuoy is an underwater acoustic sensor primarily deployed by airdrop. An acoustic sensor plays a significant role in conducting anti-submarine warfare for detecting underwater sounds. As a future underwater acoustic sensor, sonobuoy is expected to have an ability of self-movement, i.e., autonomous sonobuoy. In this study, we consider an optimal linear array deployment of autonomous sonobuoys when detecting an unknown underwater sound, assuming that the initial locations of sonobuoys are random in a specified operational area. Deploying sonobuoys from the initial locations onto a specific line requires to first determine the line and positions on that line. Under the interval equivalence between two adjacent sonobuoys, we propose two lines, one that is perpendicular from the underwater sound source location and the other based on the linear regression analysis using the initial locations of sonobuoys. With these two lines onto which sonobuoys will be deployed, we provide two optimization models, total distance minimization and maximum distance minimization, which turn out to be assignment and bottleneck assignment problems, respectively, with nonlinear cost coefficients in the objectives. Due to non-convexity of the objectives, we solve these problems for a fixed interval repetitively as a linear program and integer program, respectively. Computational results show that regression-based line provides higher solution qualities for both problems. Finally, we suggest an approximate interval in a heuristic manner, which guarantees a highly near-optimality as the number of sonobuoys increases. Our results may support a decision-making and provide practitioners with insight on more variety of effective use of autonomous sonobuoys.