The factorial hidden Markov modeling framework, has been proposed in the literature as an effective approach for intermittent fault diagnosis applications. Moreover, the dynamic multiple fault diagnosis problem (DMFD) with non-ideal tests is computationally challenging. Several methodologies have been introduced for the solution of the DMFD problem, namely: the Lagrangian relaxation algorithm, the deterministic simulated annealing and the block coordinate ascent. However, to the best of our knowledge, no evolutionary algorithm including analysis of DMFD characteristics has ever been attempted. This research paper, presents a probability first memetic algorithm (PFMA) for solving the DMFD combinatorial optimization problem, by considering input probability matrices. PFMA improves the performance of the genetic algorithm, with less computational cost. This is achieved by exploiting input probability information, using a local search strategy and a crossover operator. Computational results show that the proposed algorithm finds the optimal solutions on small-scale stochastic synthesis models. Additionally, high-quality solutions are obtained on medium and large-scale cases. The algorithm has been tested successfully on a real-world application. The experimental results highlight the efficiency of the genetic algorithm, following a reasonable local search strategy, towards the solution of an NP-hard combinatorial optimization problem.