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Optimizing functionals using Differential Evolution
Engineering Applications of Artificial Intelligence ( IF 8 ) Pub Date : 2020-11-13 , DOI: 10.1016/j.engappai.2020.104086
K.B. Cantún-Avila , D. González-Sánchez , S. Díaz-Infante , F. Peñuñuri

Metaheuristic algorithms are typically used for optimizing a function f:AR, where A is a subset of RN. Nevertheless, many real-life problems require A to be a set of functions which makes f a functional. In this paper, we present a methodology to address the optimization of functionals by using the evolutionary algorithm known as Differential Evolution. Unlike traditional techniques where continuity and differentiability assumptions are required to solve some associated differential equations—like calculus of variations, Pontryagin’s principle or dynamic programming, the optimization is carried out directly on the functional without the need of any of the assumptions mentioned before. Lagrangians involving derivatives are considered, these derivatives are computed implementing Automatic Differentiation with dual numbers. To the best of our knowledge, this is the first time that a metaheuristic optimization approach has been applied to directly optimize a broad variety of functionals. The effectiveness of our methodology is validated by solving two problems. The first problem is related to the implementation of quarantine and isolation in SARS epidemics and the second validation problem deals with the well-known brachistochrone curve problem. The results of both validation problems are in outstanding agreement with those obtained with the application of traditional techniques, specifically with the Forward–Backward-Sweep method in the first problem, and with the calculus of variations for the latter problem. We also found that interpolation may be employed to solve the large scale global optimization problems arisen in the optimization of functionals.



中文翻译:

使用差分进化优化功能

元启发式算法通常用于优化功能 F一种[R,在哪里 一种 是...的子集 [Rñ。然而,许多现实生活中的问题需要一种 成为一组功能 F功能。在本文中,我们提出了一种通过使用称为差分进化的进化算法来解决功能优化的方法。与传统的技术需要连续性和微分假设来解决一些相关的微分方程(例如变化演算,蓬特里亚金的原理或动态编程)不同,该优化直接在函数上进行,而无需前面提到的任何假设。考虑了涉及导数的拉格朗日函数,这些导数是通过实现具有双数的自动微分来计算的。据我们所知,这是第一次将元启发式优化方法直接用于优化各种功能。通过解决两个问题验证了我们方法论的有效性。第一个问题与SARS流行病中隔离和隔离的实施有关,第二个验证问题涉及众所周知的腕足动物曲线曲线问题。这两个验证问题的结果与传统技术的应用,特别是第一个问题中的前向-后退-扫描方法,以及后一个问题的变化演算,都取得了显着的一致性。我们还发现,可以采用插值法来解决在函数优化中出现的大规模全局优化问题。第一个问题与SARS流行病中隔离和隔离的实施有关,第二个验证问题涉及众所周知的腕足动物曲线曲线问题。这两个验证问题的结果与传统技术的应用,特别是第一个问题中的前向-后退-扫描方法,以及后一个问题的变化演算,都取得了显着的一致性。我们还发现,可以采用插值法来解决在函数优化中出现的大规模全局优化问题。第一个问题与SARS流行病中隔离和隔离的实施有关,第二个验证问题涉及众所周知的腕足动物曲线曲线问题。这两个验证问题的结果与传统技术的应用,特别是第一个问题中的前向-后退-扫描方法,以及后一个问题的变化演算,都取得了显着的一致性。我们还发现,可以采用插值法来解决在函数优化中出现的大规模全局优化问题。以及针对后一个问题的变化演算。我们还发现,可以采用插值法来解决在函数优化中出现的大规模全局优化问题。以及针对后一个问题的变化演算。我们还发现,可以采用插值法来解决在函数优化中出现的大规模全局优化问题。

更新日期:2020-11-13
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