Contribution for crossover and mutation for degree constrained minimum spanning tree problem (d-MSTP)

In this article, we are interested in managing engineering design of ad hoc wireless network. We have to design topology of such networks to guarantee all nodes cover. So, spanning tree concept is applied to design and optimise the tree with the constraint of the degree (d-MSTP) of the multipoint relay (MPR). The first part relates the previous work and the specification of the proposed crossing and mutation operators. The new operators provide the locality and complete heredity. We target to generate only valid solutions without intermediate stages such as detection's cycle and elimination's cycle. The encoding used is edges-set. In the second part, we develop an optimisation application-based genetic algorithm applying our new operators. Simulation's parameters are small and large complete graph. We give simulation's results vs. Zou et al.'s results. We conclude, the fitness value is improved and the search space is reduced.