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In this paper, in the absence of any constraint qualifications, we develop sequential necessary and sufficient optimality conditions for a constrained multiobjective fractional programming problem characterizing a Henig proper efficient solution in terms of the $\epsilon$-subdifferentials and the subdifferentials of the functions. This is achieved by employing a sequential Henig subdifferential calculus rule of the sums of $m \ (m\geq 2)$ proper convex vector valued mappings with a composition of two convex vector valued mappings. In order to present an example illustrating the main results of this paper, we establish the classical optimality conditions under Moreau-Rockafellar qualification condition. Our main results are presented in the setting of reflexive Banach space in order to avoid the use of nets.

The wireless sensor networks (WSNs) is a power constrained system, since nodes run on limited power batteries which shorten its lifespan.The main challenge facing us in the design and conception of Wireless Sensor Networks (WSNs) is to find the best way to extend their life span. The clustering algorithm is a key technique used to increase the scalability and life span of the network in general. In this paper, we propose and evaluate a distributed energy-efficient clustering algorithm for WSNs. This heterogeneous-energy protocol is a new clustering algorithm to decrease probability of failure nodes and in which we introduce the node's remaining energy so as to determine the cluster heads. We study the impact of heterogeneity of nodes on WSNs that are hierarchically clustered. Finally, simulation results show that the proposed algorithm increases the life span of the whole network and performs better than LEACH and EEHC according to the metric:first node dies., Comment: 7 pages, 8 Figures