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The parallelism provided by low cost environments as multi-core and GPU processors has encouraged the design of algorithms that can utilize it. In the last time, the GPU approach constitutes an environment of proven successful progress in the implementation of different bio-inspired algorithms without major additional costs of performance. Among these techniques, the Firefly Algorithm (FA) is a recent method based on the flashing light of fireflies. As a population-based algorithm with operations without a high level of divergence, it is well suited as a highly parallelizable model on GPU. In this work we describe the design of a Discrete Firefly Algorithm (GPU-DFA) to solve permutation combinatorial problems. Two well-known permutation optimization problems (Travelling Salesman Problem and DNA Fragment Assembling Problem) were employed in order to test GPU-DFA. We have evaluated numerical …