Underestimation-Assisted Global-Local Cooperative Differential Evolution and the Application to Protein Structure Prediction

Various mutation strategies show distinct advantages in differential evolution (DE). The cooperation of multiple strategies in the evolutionary process may be effective. This article presents an underestimation-assisted global and local cooperative DE to simultaneously enhance the effectiveness and efficiency. In the proposed algorithm, two phases, namely, the global exploration and the local exploitation, are performed in each generation. In the global phase, a set of trial vectors is produced for each target individual by employing multiple strategies with strong exploration capability. Afterward, an adaptive underestimation model with an self-adapted slope control parameter is proposed to evaluate these trial vectors, the best of which is selected as the candidate. In the local phase, the better-based strategies guided by individuals that are better than the target individual are designed. For each individual accepted in the global phase, multiple trial vectors are generated by using these strategies and filtered by the underestimation value. The cooperation between the global and local phases includes two aspects. First, both of them concentrate on generating better individuals for the next generation. Second, the global phase aims to locate promising regions quickly while the local phase serves as a local search for enhancing convergence. Moreover, a simple mechanism is designed to determine the parameter of DE adaptively in the searching process. Finally, the proposed approach is applied to predict the protein 3-D structure. The experimental studies on classical benchmark functions, CEC test sets, and protein structure prediction problem show that the proposed approach is superior to the competitors.