帕累托最优

帕累托最优(中文8000字,英文5000字)
摘  要
在过去的20年里，进化算法已经成功用于解决2个或更多个目标(称为“多目标”)的问题。这个领域被称为“进化多目标优化”，已成为一个非常活跃的研究领域，该领域上升到各式各样的算法、技术来维持多样性、选择机制、归档和应用方案,以及其他重要的贡献。在本文中，我们将提供一个通用的概述,强调在这个领域中已经发展起来的主要研究成果，以及它的研究趋势和未来的挑战。
1  介绍
两个或更多目标（称之为“多目标”）的问题在工程和许多学科中普遍存在。解决这样的问题是困难的，因为他们的目标往往相互之间有冲突,这样就有必要给出一个最优的新概念。
十九世纪末，一个最优概念在经济学中已经发展起来。后来，这个最优概念在运筹学中被正式介绍并开始应用于解决多目标问题。在过去的几年，这项研究区域增长到几乎成为一个单独的运筹学分支来进行研究。
 20 years of Evolutionary Multi-Objective
Optimization:What Has Been Done and What
 Remains To Be Done
Abstract
  Evolutionary algorithms have been successfully used to solve problem with 2 or more objective functions (called "multi-objective")during the last 20 years. This filed is now called "Evolutionary Multi-Optimization" and has become a very active research area, giving rise to a wide variety of algorithms, techniques to maintain diversity, selection mechanisms, archiving schemes, and applications, among other important contribution.  In this paper, we will provide a general overview of this area, emphasizing the main research findings that have shaped the field, as well as its research trends its future challenges.
1 Introduction
  Problems with two or more objectives (called "multi-objective" or "multi-criteria") are very common in engineering and many other disciplines. The solution of such problems is difficult because their objectives tend to be in conflict with each other, which makes necessary a new notion of optimality.