School of Electronic Information Engineering, Jiujiang University, Jiujiang 332005, China.
College of Information Management, Jiangxi University of Finance and Ecomomics, Nanchang 330013, China.
Comput Intell Neurosci. 2021 Oct 29;2021:8930980. doi: 10.1155/2021/8930980. eCollection 2021.
Differential evolution (DE) is a robust algorithm of global optimization which has been used for solving many of the real-world applications since it was proposed. However, binomial crossover does not allow for a sufficiently effective search in local space. DE's local search performance is therefore relatively poor. In particular, DE is applied to solve the complex optimization problem. In this case, inefficiency in local research seriously limits its overall performance. To overcome this disadvantage, this paper introduces a new local search scheme based on Hadamard matrix (HLS). The HLS improves the probability of finding the optimal solution through producing multiple offspring in the local space built by the target individual and its descendants. The HLS has been implemented in four classical DE algorithms and jDE, a variant of DE. The experiments are carried out on a set of widely used benchmark functions. For 20 benchmark problems, the four DE schemes using HLS have better results than the corresponding DE schemes, accounting for 80%, 75%, 65%, and 65% respectively. Also, the performance of jDE with HLS is better than that of jDE on 50% test problems. The experimental results and statistical analysis have revealed that HLS could effectively improve the overall performance of DE and jDE.
差分进化（DE）是一种强大的全局优化算法，自提出以来，已被用于解决许多实际问题。然而，二项交叉运算在局部空间中不能进行足够有效的搜索。因此，DE 的局部搜索性能相对较差。特别是，当 DE 应用于解决复杂的优化问题时，局部搜索效率低下严重限制了其整体性能。为了克服这一缺点，本文提出了一种基于 Hadamard 矩阵（HLS）的新局部搜索方案。HLS 通过在目标个体及其后代构建的局部空间中生成多个后代，提高了找到最优解的概率。HLS 已在四个经典的 DE 算法和 jDE（DE 的一个变体）中实现。实验在一组广泛使用的基准函数上进行。对于 20 个基准问题，使用 HLS 的四个 DE 方案的结果均优于相应的 DE 方案，分别占 80%、75%、65%和 65%。此外，使用 HLS 的 jDE 的性能在 50%的测试问题上优于 jDE。实验结果和统计分析表明，HLS 可以有效提高 DE 和 jDE 的整体性能。
