Lamarckian evolution explains how an individual's ability of learning can help to guide the evolutionary process. Performing a local search is regarded as a learning process for an individual. We propose the concept of re-learning based on Lamarckian evolution. After all individuals have learned, the local search information is then collected for a second learning process using approximation techniques. Under the situation of using quadratic approximation, we mathematically analyze the basic algorithm developed under this concept. We also develop a novel algorithm based on the basic algorithm and the analysis results. The experimental results show that the algorithm can provide a more reliable and efficient performance on high dimensional multimodal problems. © 2000 IEEE.