Optimal Discrete Search with a Map.

有效的搜索策略在广泛的现实世界中是必要的。马来西亚航空公司370航班的搜寻失败，耗资超过2亿澳元。因此，重要的是要了解如何以最有效的方式使用如此大量的资金，即使将来发生类似的情况。搜索行为不仅可能非常昂贵，而且不能及时找到搜索目标的风险可能更高。例如，在自然灾害发生后，救援队越早找到失踪人员，该人员的生存机会就越大。经典搜索问题假设搜索目标隐藏在多个不同位置中的一个，并且在搜索正确位置时存在已知的发现概率。在这种情况下，可以通过将搜索过程建模为多臂强盗来找到搜索位置的最佳可能顺序。这是一个受到老虎机启发的经过充分研究的数学模型，其中做出了一系列决定以最大化某些奖励。在现有的文献中，大多数搜索模型假设这些位置可以在瞬间之间移动，并且没有额外的成本。这个假设极大地简化了问题，但在许多实际应用中并不成立。在这个博士学位的过程中，我们的目标是开发和评估搜索策略的有效性，包括在不同地点之间旅行的时间或财务成本。与海军研究生院（蒙特雷，美国）合作。

Effective search strategies are necessary in a wide range of real-world situations. The unsuccessful search for Malaysian Airlines flight 370 cost more than two hundred million Australian dollars. It is therefore important to understand how such large amounts of money can be used in the most efficient way possible were a similar even to happen in the future. Not only can the act of searching be very expensive but the risk of not finding the target of the search in time can be even more costly. For example, the earlier a rescue squad can find a missing person after a natural disaster the greater that person's chances of survival.The classical search problem assumes that the target of the search is hidden in one of multiple distinct locations and that when searching the correct location there is a known probability of discovery. In this case, the best possible order to search the locations can be found by modelling the search process as a multi-armed bandit. This is a well-studied mathematical model inspired by slot machines where a series of decisions are made to maximise some reward. In the existing literature, most search models assume that these locations can be moved between instantaneously and at no additional cost. This assumption massively simplifies the problem but doesn't hold in many real-world applications. Over the course of this PhD, our aim is to develop and evaluate the effectiveness of search strategies that incorporate the time or financial costs of traveling between locations.In partnership with Naval Postgraduate School (Monterey, US).