Evolutionary computation, an alternative solution to nonlinear optimization problems

Francisco J. Espinosa Garcia, Ricardo Tapia Herrera, Tonatiuh Cortés Hernández, J. A. Meda Campaña
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Abstract

Analytical and numerical methods have been applied to solve problems in engineering. However, in some practical cases, they usually fail when there is a certain degree of complexity, for instance, when there is a certain lack of information about the elements of the system and when the unknowns are functions. These types of problems are often called nonlinear optimization problems. As an alternative to solving them, evolutionary computation methods are usually implemented, although they do not generate an exact solution, and provide a series of approximations that are generally feasible. In this context, the objective of this work is to briefly highlight the most typical characteristics of these type of algorithms, some advantages, and the importance of its use today. Due to the wide variety of existing methods, it would become complex to explain all of them in detail, so only a description of the differential evolution (DE) algorithm will be made because it is one of the most used and because there is current research that seeks to improve its performance.
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进化计算:非线性优化问题的另一种解决方案
分析和数值方法一直被用于解决工程问题。然而,在某些实际情况下,当问题具有一定的复杂性时,例如,当系统元素的信息存在一定的缺失以及未知数为函数时,这些方法通常会失效。这类问题通常被称为非线性优化问题。作为解决这些问题的替代方法,通常会采用进化计算方法,尽管这些方法不会生成精确的解决方案,但会提供一系列近似值,这些近似值通常是可行的。在这种情况下,这项工作的目的是简要强调这类算法最典型的特点、一些优势及其在当今应用的重要性。由于现有方法种类繁多,对所有方法进行详细说明将变得十分复杂,因此我们将只对微分进化(DE)算法进行说明,因为它是使用最多的算法之一,而且目前的研究也在努力提高其性能。
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