Abstract Differential evolution (DE) is known as a strong and simple optimization method able to work with non-differential, nonlinear, and multimodal functions. This paper proposes a modified differential evolution (MDE) algorithm for solving a high dimensional nonlinear optimization problem. The issue is finding maximum likelihood estimation (MLE) for the parameters of a non-homogeneous Poisson process (NHPP) software reliability model. We make two modifications to DE: a mutation scheme based on a new affine combination of three points for increasing the exploration power of the algorithm, and another is a uniform scaling crossover scheme to increase the exploitation ability of the algorithm. The performance of the proposed scheme is empirically validated using five software reliability models on three software failure datasets. Analysis of research findings indicates that the proposed scheme enhances the convergence speed of the DE algorithm, and preserves the quality of the solution. A comparison with two other peer algorithms is also shown the superiority of the proposed algorithm.

中文翻译：

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基于改进差分进化算法的软件可靠性模型参数优化

摘要 差分进化 (DE) 被认为是一种强大而简单的优化方法，能够处理非差分、非线性和多模态函数。本文提出了一种用于解决高维非线性优化问题的修正差分进化 (MDE) 算法。问题是为非齐次泊松过程 (NHPP) 软件可靠性模型的参数找到最大似然估计 (MLE)。我们对DE进行了两个修改：一种是基于新的三点仿射组合的变异方案，以增加算法的探索能力，另一种是统一缩放交叉方案，以增加算法的开发能力。所提出方案的性能使用三个软件故障数据集上的五个软件可靠性模型进行了实证验证。对研究结果的分析表明，所提出的方案提高了DE算法的收敛速度，并保持了解的质量。与其他两种对等算法的比较也显示了所提出算法的优越性。