Application of chaotic theory in differential evolution algorithms

Previous researches have shown that hybrid differential evolution (DE) algorithms incorporated with chaotic sequences are effective in solving single objective optimization problem. Based on these pioneering efforts, this paper extends the hybrid chaotic DE to solve multi-objective optimization problems (MOPs). First, various application of chaotic sequence in DE are studied in detail, and different hybrid chaotic DE algorithms are compared and analyzed in order to find one general chaotic DE. Then, the performances and effectiveness of various hybrid chaotic DE algorithms existed in related literature are examined based upon five benchmark constraint MOPs. The comparative study shows that the hybrid DE with chaotic migration outperformed the hybrid DE with chaotic self-adaptive control parameters F and CR setting. The results also demonstrated that the hybrid chaotic DE is not effective for solving MOPs, while it is successful and competitive for solving single objective optimization problem.