Since the convergence speed of the Firefly Algorithm (FA) is slow, and the solution accuracy of the FA is low, an improved Firefly Algorithm with Uniform local search and Variable step size (UVFA) was proposed. Firstly, uniform local search was established by the uniform design theory to accelerate convergence and to enhance exploitation ability. Secondly, search step size was dynamically tuned by using the variable step size strategy to balance exploration and exploitation. Finally, uniform local search and variable step size were fused. The results of simulation tests on twelve benchmark functions show that the objective function mean of UVFA was significantly better than FA, WSSFA (Wise Step Strategy for Firefly Algorithm), VSSFA (Variable Step Size Firefly Algorithm) and Uniform local search Firefly Algorithm (UFA), and the time complexity was obviously reduced. UVFA is good at solving low dimensional and high dimensional problems, and has good robustness.

A new method of large-scale optimization based on divide-and-conquer strategy was proposed. Firstly, based on the principle of additive separability, an improved variable grouping method was proposed. The randomly accessing point method was used to check the correlation between all variables in pairs. At the same time, by making full use of the interdependency information of learning, the large groups of separable variables were re-grouped. Secondly, a new subcomponent optimizer was designed based on an improved differential evolution algorithm to enhance the subspace optimization performance. Finally, this two kinds of improvements were introduced to co-evolutionary framework to construct a DECC-NDG-CUDE (Cooperative differential evolution with New Different Grouping and enhancing Differential Evolution with Commensal learning and Uniform local search) algorithm. Two experiments of grouping and optimization were made on 10 large-scale optimization problems. The experimental results show the interdependency between variables can be effectively identified by the new method of grouping, and the performance of DECC-NDG-CUDE is better than two state-of-the-art algorithms DECC-D (Differential Evolution with Cooperative Co-evolution and differential Grouping) and DECCG (Differential Evolution with Cooperative Co-evolution and Random Grouping).