•A novel adaptive hybrid evolutionary firefly algorithm (AHEFA) for shape and size optimization of truss structures under multiple frequency constraints is proposed.•This algorithm is a hybridization of the differential evolution (DE) algorithm and the firefly algorithm (FA).•The AHEFA significantly improves the convergence rate and the solution accuracy.•Six numerical examples are examined for the validity of the present algorithm. This paper presents a novel adaptive hybrid evolutionary firefly algorithm (AHEFA) for shape and size optimization of truss structures under multiple frequency constraints. This algorithm is a hybridization of the differential evolution (DE) algorithm and the firefly algorithm (FA). An automatically adapted parameter is utilized to select an appropriate mutation scheme for an effective trade-off between the global and local search abilities. An elitist technique is applied to the selection phase to choose the best individuals. Accordingly, the convergence rate is significantly improved with the high solution accuracy. Six numerical examples are examined for the validity of the present algorithm.