Given a water-terrain area of interest (waterways, ports, etc.), this paper attempts to efficiently allocate underwater sonars to achieve a reasonable amount of coverage within a limited budget. Coverage is defined as the capability of sonars to detect threats. Though total coverage is desired, priority is given to the criticality/importance attached to the location of an area of interest on a grid-based system. Unlike other works in the literature, the developed model takes into consideration uncertainty inherent in the detection probability of sonars. Apart from issues of sonar reliability, underwater terrain, with its changing conditions, is bound to affect detection probabilities. While taking into consideration the specific physics of sonars in the model development, the model also adopts a hexagonal grid-based system to ensure more efficient placement of sonars. Based on an initially proposed mixed-integer program, a robust optimization model also is proposed to take care of uncertainties. With smaller scale problems, the model works adequately within a relatively short time period. However, large scale problems require extensive memory, taking much longer. As such, a heuristic is proposed as an alternative to the proposed model. Experimental results indicate the heuristic works effectively under most circumstances and performs less effectively under a few limited scenarios.


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