Application of chaotic theory in differential evolution algorithms

Abstract

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.

Determination of an effective implementation of the differential evolution method to power shortage minimization

“…Although, the standard DE method is often inferior to its modifications with various improvements, the authors decided to conduct additional research to determine the most appropriate methods for models of PSM. This work touches on the issue of the efficiency of calculating nonlinear models with quadratic losses using various implementations of the Differential Evolution method, including different mutation strategies [13][14][15][16][17][18][19][20]. This study will allow us to determine the most appropriate method of variation of the DE, including the specific mutation strategy.…”

The Effects of Using Chaotic Map on Improving the Performance of Multiobjective Evolutionary Algorithms

“…Comparisons of different chaotic maps in improving the effects of COAs for solving single objective problems are common, but it is rare in solving multiobjective optimization problems (MOPs). Yu et al [11] revealed that COA is not effective for solving MOPs, whereas the experiments in Alatas and Akin [12] showed the opposite. The results on these foregoing researches demonstrate that COAs are successful and competitive for solving single objective optimization problem, but effects of COAs on solving MOPs are not consistent.…”