This article aims to develop mathematical methods and algorithms that automatically build nonlinear models of planning and management of economic objects based on the use of empirical samples (observations). We call the relevant new information technology "Building Optimization Models from Data (BOMD)". The offered technology BOMD allows to obtain an objective control models that reflect the real economic processes. This is its main advantage over commonly employed subjective approach to management. To solve the problems posed in the article, the methods of artificial intelligence were used, in particular, the training of neural networks and construction of decision trees. If the learning sample contains simultaneously the values of the objective function and the values of characteristic function of constraints, it is proposed to use an approach based on the training of two neural networks: NN1 — for the synthesis of the objective function and NN2 — for the synthesis of the approximating characteristic function of constraints (instead of a neural network NN2, a decision tree can be used). The solution of the problem presented by such synthesized neural model may end up finding, generally speaking, a local conditional extremum. To find the global extremum of the multiextremal neural objective function, a heuristic algorithm based on a preliminary classification of the search area by using the decision tree is developed. Presented in the paper approach to an extraction of conditionally optimization model from the data for the case when there is no information on the points not belonging to the set of admissible solutions is fundamentally novel. In this case, a heuristic algorithm for approximating the region of admissible solutions based on the allocation of regular (non-random) empty segments of the search area is developed.

中文翻译：

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BOMD：从数据构建优化模型（基于神经网络的方法）

本文旨在开发数学方法和算法，这些方法和算法可根据经验样本（观测值）自动构建经济对象计划和管理的非线性模型。我们将相关的新信息技术称为“根据数据构建优化模型（BOMD）”。提供的技术BOMD允许获得反映真实经济过程的客观控制模型。这是其相对于常用的主观管理方法的主要优势。为了解决本文提出的问题，使用了人工智能方法，特别是神经网络的训练和决策树的构建。如果学习样本同时包含目标函数的值和约束的特征函数的值，建议使用一种基于两个神经网络训练的方法：NN1-用于综合目标函数，NN2-用于综合约束的近似特征函数（代替神经网络NN2，决策树可以使用）。一般说来，由这种合成的神经模型提出的问题的解决方案可能最终找到局部条件极值。为了找到多极神经目标函数的全局极值，开发了一种基于启发式算法的基于搜索区域的初步分类的决策树。本文提出的方法是从数据中提取条件优化模型，这种情况下，如果没有关于不属于可容许解集的点的信息，则从根本上讲是新颖的。