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On the surface of a sphere, we take as inputs two points, neither of them contained in any of a number of spherical polygon obstacles, and quickly find the shortest route connecting these two points while avoiding any obstacle. The WetRoute method presented here has been adopted by the US Navy for several applications. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 374–385, 2016

© 2009 Wiley Periodicals, Inc. Naval Research Logistics 58: 281–295, 2011 The article of record as published may be located at http://dx.doi.org/DOI 10.1002/nav.20377

The U.S. Coast Guard, Customs and Border Patrol, Marine Corps, and Navy have deployed several hundred port patrol vessels to protect waterways, U.S. Navy ships and other high-value assets in ports world-wide. Each vessel has an armed crew of four, is relatively fast, and features a surface search radar, radios, and a machine gun. These vessels coordinate surveillance patrols in groups of two or four. We developed a mathematical model for advantageously positioning these vessels, and possibly shore-based radar too, to minimize the probability that an intelligent adversary in one or more speedboats will evade detection while mounting an attack. Attackers can use elevated obstructions to evade radar detection in their attack paths, and ports feature many such restrictions to navigation and observation. A key, but realistic assumption complicates planning: the attackers will be aware of defensive positions and capabilities in advance of mounting their attack. The defender-attacker optimization suggests plans here for a fictitious port, the port of Hong Kong, and the U.S. Navy Fifth Fleet Headquarters in Bahrain. In these cases, the defender can almost certainly detect any attack, even though the attacker, observing defender prepositioning, plans clever, and evasive attack tracks. Published 2011 Wiley Periodicals, Inc.† Naval Research Logistics, 2011