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首页> 外文期刊>Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on >On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum
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On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

机译：一类具有唯一全局最优解的连续函数的微分演化的收敛性

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摘要

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.
机译：差分演化（DE）可以说是当前关注的最强大的随机实参数优化算法之一。自1990年代中期成立以来，DE一直在科学和工程学各个领域的现实世界优化问题中找到许多成功的应用。本文朝着规范DE（DE / rand / 1 / bin）算法的收敛性分析迈出了重要的第一步。首先考虑DE型突变，交叉和选择机制，为试验解决方案的概率密度函数（PDF）得出时间递归关系。然后，通过应用Lyapunov稳定性定理的概念，表明随着时间接近无穷大，假定狄拉克三角洲分布的形状，试验解的PDF狭窄地集中在目标函数的全局最优值附近。通过构造基于PDF的Lyapunov函数并显示其随时间单调减少，可以建立总体PDF的渐近收敛行为。该分析适用于一类具有唯一全局最优值（但可能具有多个局部最优值）的连续和实值目标函数。理论结果已通过相关的计算机模拟得到证实。

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