Ersatz function method for minimizing a finite-valued function on a compact set
Ersatz function method for minimizing a finite-valued function on a compact set
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用于最小化紧集上的有限值函数的 Ersatz 函数方法
DOI：
10.1134/s0965542514020110
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发表时间：
2014
影响因子：
0.7
通讯作者：
A. I. Ryabikov
中科院分区：
文献类型：
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作者：
A. I. Ryabikov
提出了一种求解连续变量和函数取大的有限值集的最优化问题的方法。这种类型的问题出现在离散时间动态系统的控制规则的多准则建设，其性能标准与违反对系统的要求的数量相一致。该规则依赖于一个有限的参数集，其容许值集定义了容许控制规则的集合。一个例子是选择一个控制规则的水库级联的问题。该优化方法是基于解决一个修改后的问题，其中的原始功能被替换为一个连续的eruption函数。证明了原函数与误差函数的平均极小值之间的关系定理。用幂律误差函数求解最优化问题，确定了指数对解的质量的影响。实验表明，该方法产生的溶液具有相当高的质量。
A method is proposed for solving optimization problems with continuous variables and a function taking a large finite set of values. Problems of this type arise in the multicriteria construction of a control rule for a discrete-time dynamical system whose performance criteria coincide with the number of violations of requirements imposed on the system. The rule depends on a finite set of parameters whose set of admissible values defines a collection of admissible control rules. An example is the problem of choosing a control rule for a cascade of reservoirs. The optimization method is based on solving a modified problem in which the original function is replaced by a continuous ersatz function. A theorem on the relation between the average-minimal values of the original and ersatz functions is proved. Optimization problems are solved with power-law ersatz functions, and the influence exerted by the exponent on the quality of the solution is determined. It is experimentally shown that the solutions produced by the method are of fairly high quality.