This paper explores, with numerical case studies, the performance of an optimization algorithm that is a variant of EPSO, the Evolutionary Particle Swarm Optimization method. EPSO is already a hybrid approach that may be seen as a PSO with self-adaptive weights or an Evolutionary Programming approach with a self-adaptive recombination operator. The new hybrid DEEPSO retains the self-adaptive properties of EPSO but borrows the concept of rough gradient from Differential Evolution algorithms. The performance of DEEPSO is compared to a well-performing EPSO algorithm in the optimization of problems of the fixed cost type, showing consistently better results in the cases presented.