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Localization is one of the most fundamental problems in wireless sensor networks, since the locations of the sensor nodes are critical to both network operations and most application level tasks. A GPS-free localization scheme for wireless sensor networks is presented in this paper. First, we develop a standardized clustering-based approach for the local coordinate system formation wherein a multiplication factor is introduced to regulate the number of master and slave nodes and the degree of connectivity among master nodes. Second, using homogeneous coordinates, we derive a transformation matrix between two Cartesian coordinate systems to efficiently merge them into a global coordinate system and effectively overcome the flip ambiguity problem. The algorithm operates asynchronously without a centralized controller; and does not require that the location of the sensors be known a priori. A set of parameter-setting guidelines for the proposed algorithm is derived based on a probability model and the energy requirements are also investigated. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results. We also compare the performance of the proposed algorithm under a variety multiplication factor, node density and node communication radius scenario. Experiments show that our algorithm outperforms existing mechanisms in terms of accuracy and convergence time.

A B S T R A C TMulti-task optimization algorithm is an emergent paradigm which solves multiple self-contained tasks simultaneously. It is thought that multi-factorial evolutionary algorithm (MFEA) can be seen as a novel multi-population algorithm, wherein each population is represented independently and evolved for the selected task only. However, the theoretical and experimental evidence to this conclusion is not very convincing and especially, the coincidence relation between MFEA and multi-population evolution model is ambiguous and inaccurate. This paper aims to make an in-depth analysis of this relationship, and to provide more theoretical and experimental evidence to support the idea. In this paper, we clarify several key issues unsettled to date, and design a novel across-population crossover approach to avoid population drift. Then MFEA and its variation are reviewed carefully in view of multi-population evolution model, and the coincidence relation between them are concluded. MFEA is completely recoded along with this idea and tested on 25 multi-task optimization problems. Experimental results illustrate its rationality and superiority. Furthermore, we analyze the contribution of each population to algorithm performance, which can help us design more efficient multi-population algorithm for multi-task optimization. MTO paradigm [6]. If the optimization tasks happen to bear some commonality or complementarity, then the inclusion of knowledge transfer often leads to significant performance improvements relative to conventional EAs alone.

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