Solving multistatic sonar location problems with mixed-integer programming

A multistatic sonar system consists of one or more sources that are able to emit underwater sound, and receivers that listen to the reflected sound waves. Knowing the speed of sound in water, the time when the sound was sent from a source, and the arrival time of the sound at one or more receivers,...

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Vydáno v:	Optimization and engineering Ročník 21; číslo 1; s. 273 - 303
Hlavní autoři:	Fügenschuh, Armin R., Craparo, Emily M., Karatas, Mumtaz, Buttrey, Samuel E.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.03.2020 Springer Nature B.V
Témata:	Coasts Control Engineering Environmental Management Equipment costs Financial Engineering Integer programming Integers Mathematics Mathematics and Statistics Nonlinear equations Operations Research/Decision Theory Optimization Receivers Research Article Sonar Sound propagation Sound waves Systems Theory Underwater acoustics Linearization of quadratic terms Mixed-Integer nonlinear programming Exact methods Network design problems Multistatic sonar systems
ISSN:	1389-4420, 1573-2924
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Abstract	A multistatic sonar system consists of one or more sources that are able to emit underwater sound, and receivers that listen to the reflected sound waves. Knowing the speed of sound in water, the time when the sound was sent from a source, and the arrival time of the sound at one or more receivers, it is possible to determine the location of surrounding objects. The propagation of underwater sound is a complex phenomenon that depends on various attributes of the water (density, pressure, temperature, and salinity) and the emitted sound (pulse length and volume), as well as the reflection properties of the water’s surface. These effects can be approximated by nonlinear equations. Furthermore, natural obstacles in the water, such as the coastline, need to be taken into consideration. Given an area of the ocean that should be endowed with a sonar system for surveillance, this paper formulates two natural sensor placement problems. In the first, the goal is to maximize the area covered by a fixed number of sources and receivers. In the second, the goal is to cover the entire area with a minimum-cost set of equipment. For each problem, this paper considers two different sensor models: definite range (“cookie-cutter”) and probabilistic. It thus addresses four problem variants using integer nonlinear formulations. Each variant can be reformulated as an integer linear program in one of several ways; this paper discusses these reformulations, then compares them numerically using a test bed from coastlines around the world and a state-of-the-art mixed-integer program solver (IBM ILOG CPLEX).
AbstractList	A multistatic sonar system consists of one or more sources that are able to emit underwater sound, and receivers that listen to the reflected sound waves. Knowing the speed of sound in water, the time when the sound was sent from a source, and the arrival time of the sound at one or more receivers, it is possible to determine the location of surrounding objects. The propagation of underwater sound is a complex phenomenon that depends on various attributes of the water (density, pressure, temperature, and salinity) and the emitted sound (pulse length and volume), as well as the reflection properties of the water’s surface. These effects can be approximated by nonlinear equations. Furthermore, natural obstacles in the water, such as the coastline, need to be taken into consideration. Given an area of the ocean that should be endowed with a sonar system for surveillance, this paper formulates two natural sensor placement problems. In the first, the goal is to maximize the area covered by a fixed number of sources and receivers. In the second, the goal is to cover the entire area with a minimum-cost set of equipment. For each problem, this paper considers two different sensor models: definite range (“cookie-cutter”) and probabilistic. It thus addresses four problem variants using integer nonlinear formulations. Each variant can be reformulated as an integer linear program in one of several ways; this paper discusses these reformulations, then compares them numerically using a test bed from coastlines around the world and a state-of-the-art mixed-integer program solver (IBM ILOG CPLEX).
Author	Fügenschuh, Armin R. Buttrey, Samuel E. Craparo, Emily M. Karatas, Mumtaz
Author_xml	– sequence: 1 givenname: Armin R. surname: Fügenschuh fullname: Fügenschuh, Armin R. email: fuegenschuh@b-tu.de organization: Brandenburgische Technische Universität Cottbus-Senftenberg – sequence: 2 givenname: Emily M. surname: Craparo fullname: Craparo, Emily M. organization: Operations Research Department, Naval Postgraduate School – sequence: 3 givenname: Mumtaz surname: Karatas fullname: Karatas, Mumtaz organization: Industrial Engineering Department, National Defense University, Naval Academy, Industrial Engineering Department, Bahcesehir University – sequence: 4 givenname: Samuel E. surname: Buttrey fullname: Buttrey, Samuel E. organization: Operations Research Department, Naval Postgraduate School
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CitedBy_id	crossref_primary_10_1007_s10479_020_03892_2 crossref_primary_10_1016_j_oceaneng_2023_116655 crossref_primary_10_3390_s25134139 crossref_primary_10_1016_j_eswa_2023_121985 crossref_primary_10_1016_j_comnet_2021_108041 crossref_primary_10_1109_ACCESS_2021_3134173 crossref_primary_10_5194_essd_16_4529_2024 crossref_primary_10_1016_j_comnet_2021_108416 crossref_primary_10_1016_j_cor_2021_105439 crossref_primary_10_1016_j_cor_2024_106637 crossref_primary_10_1109_JSEN_2024_3508742 crossref_primary_10_1016_j_ejor_2025_08_003
Cites_doi	10.1016/j.orl.2004.05.001 10.2514/4.862137 10.1016/j.orl.2004.03.005 10.1287/opre.15.6.1171 10.1287/opre.22.1.180 10.1016/j.dam.2007.12.008 10.1287/opre.50.6.956.345 10.1007/s10107-004-0529-4 10.1287/mnsc.22.4.455 10.1002/nav.21746 10.1002/j.1538-7305.1957.tb01515.x 10.1287/opre.40.1.S109 10.1016/j.ejor.2018.02.006 10.1007/BF01589101 10.1007/s10236-011-0483-7 10.1080/01621459.1937.10503522 10.1029/2008GC00233 10.1145/2491288.2491305 10.1109/WSC.2015.7408244 10.23919/OCEANS.2009.5422114
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SubjectTerms	Coasts Control Engineering Environmental Management Equipment costs Financial Engineering Integer programming Integers Mathematics Mathematics and Statistics Nonlinear equations Operations Research/Decision Theory Optimization Receivers Research Article Sonar Sound propagation Sound waves Systems Theory Underwater acoustics
Title	Solving multistatic sonar location problems with mixed-integer programming
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