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In this work, the optimal sensor displacement problem in wireless sensor networks is addressed. It is assumed that a network, consisting of independent, collaborative and mobile nodes, is available. Starting from an initial configuration, the aim is to define a specific sensors displacement, which allows the network to achieve high performance, in terms of energy consumption and travelled distance. To mathematically represent the problem under study, different innovative optimization models are proposed and defined, by taking into account different performance objectives. An extensive computational phase is carried out in order to assess the behaviour of the developed models in terms of solution quality and computational effort. A comparison with distributed approaches is also given, by considering different scenarios.