The firefly algorithm (FA) is proposed as a heuristic algorithm, inspired by natural phenomena. The FA has attracted a lot of attention due to its effectiveness in dealing with various global optimization problems. However, it could easily fall into a local optimal value or suffer from low accuracy when solving high-dimensional optimization problems. To improve the performance of the FA, this paper adds the self-adaptive logarithmic inertia weight to the updating formula of the FA, and proposes the introduction of a minimum attractiveness of a firefly, which greatly improves the convergence speed and balances the global exploration and local exploitation capabilities of FA. Additionally, a step-size decreasing factor is introduced to dynamically adjust the random step-size term. When the dimension of a search is high, the random step-size becomes very small. This strategy enables the FA to explore solution more accurately. This improved FA (LWFA) was evaluated with ten benchmark test functions under different dimensions (D = 10, 30, and 100) and with standard IEEE CEC 2010 benchmark functions. Simulation results show that the performance of improved FA is superior comparing to the standard FA and other algorithms, i.e., particle swarm optimization, the cuckoo search algorithm, the flower pollination algorithm, the sine cosine algorithm, and other modified FA. The LWFA also has high performance and optimal efficiency for a number of optimization problems.