Various recent events have shown the enormous importance of maritime search-and-rescue missions. By reducing the time to find floating victims at sea, the number of casualties can be reduced. A major improvement can be achieved by employing autonomous aerial systems for autonomous search missions, allowed by the recent rise in technological development. In this context, the need for efficient search trajectory planning methods arises. The objective is to maximize the probability of detecting the target at a certain time k, which depends on the estimation of the position of the target. For stationary target search, this is a function of the observation at time k. When considering the target movement, this is a function of all previous observations up until time k. This is the main difficulty arising in solving moving target search problems when the duration of the search mission increases. We present an intermediate result for the single searcher single target case towards an efficient algorithm for longer missions with multiple aerial vehicles. Our primary aim in the development of this algorithm is to disconnect the networks of the target and platform, which we have achieved by applying Benders decomposition. Consequently, we solve two much smaller problems sequentially in iterations. Between the problems, primal and dual information is exchanged. To the best of our knowledge, this is the first approach utilizing dual information within the category of moving target search problems. We show the applicability in computational experiments and provide an analysis of the results. Furthermore, we propose well-founded improvements for further research towards solving real-life instances with multiple searchers.
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