优化的新趋势

Czeslaw Smutnicki
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引用次数: 2

摘要

近年来,用于解决控制、规划、设计和管理问题中产生的优化任务的方法已经完全改变了。单峰、凸、可微标量目标函数的情况已经从实验室中消失了,因为已经开发出了许多令人满意的有效方法。在战场上仍然有一些困难的情况:多模态,多标准,不可微,np困难,离散,具有巨大的维度。这些由行业和市场产生的实际任务,给寻求全局最优带来了严重的麻烦。产生这些问题的主要原因是:局部极值基数大,极值次数呈指数级;维度诅咒;np困难;缺乏可微性。不幸的是,已知的“经典”精确解方法在如此困难的工作条件下被认为是相当弱的。自八十年代初以来,人们观察到近似方法的迅速发展,这种方法不受局部极值的影响。事实上,这些方法的实践先于合适的理论的发展,而理论的形成通常比创造方法的时间点晚10-15年。这就是为什么我们现在观察到20多种受自然启发的不同方法,如果包括并行计算环境,则超过30种。本文提出的方法,方法和趋势观察到现代优化的关键调查,重点是自然启发的技术推荐的特别困难的问题。根据所述优化任务的类别和目标函数的类别,讨论了方法的适用性。给出了这些算法的数值性质和理论性质。我们自己最新的非常有效的建议也提供。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
New trends in optimization
Approaches used to solve optimization tasks generated in problems of control, planning, designing and management have completely changed during recent years. Cases with unimodal, convex, differentiable scalar goal functions have disappeared from research labs, because a lot of satisfactory efficient methods were developed. On the battle square there have remained hard cases: multimodal, multi-criteria, non-differentiable, NP-hard, discrete, with huge dimensionality. These practical tasks, generated by industry and market, have caused serious troubles in seeking global optimum. Main reasons of these troubles are recognized as: huge cardinality of local extremes frequently with the exponential number of extremes; curse of dimensionality; NP-hardness; lack of differentiability. Unfortunately, known “classical” exact solution methods have considered as rather weak in so hard conditions of the work. From the beginning of eighties have been observed fast development of approximate methods, resistant to local extremes. In fact, practice of these methods antecede development of the suitable theory, which has been formed usually 10–15 years later than the time moment of creating the approach. That's why we observe now more than 20 different approaches inspired by Nature and more than 30 if we include parallel computing environments. The paper presents critical survey of methods, approaches and trends observed in modern optimization, focusing on nature-inspired techniques recommended for particularly hard problems. Applicability of the methods, depending the class of stated optimization task and classes of goal function, have been discussed. Numerical as well theoretical properties of these algorithms are shown. Newest our own very efficient proposals are also provided.
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