Mobile ad hoc networks are infrastructure less communication networks that are spontaneously created by a number of mobile devices. Due to the highly fluctuating topology of such networks, finding the optimal configuration of communication protocols is a complex and crucial task. Additionally, different objectives must be usually considered. Small changes in the values of the parameters directly affects the performance of the protocol, promoting one objective while reducing another. Therefore, multi-objective optimisation is needed for fine tuning the protocol. In this work, we propose a novel parallel multi-objective local search that optimises an energy efficient broadcasting algorithm in terms of coverage, energy used, broadcasting time, and network resources. The proposed method looks for appropriate values for a set of 5 variables that markedly influence the behavior of the protocol to provide accurate tradeoff configurations in a reasonable short execution time. The new proposed algorithm is validated versus two efficient multi-objective evolutionary algorithms from the state of the art, offering comparable quality results in much shorter times.