BOMD: Building Optimization Models from Data (Neural Networks based Approach)

Vladimir Donskoy; Vladimir Donskoy

doi:10.3934/QFE.2019.4.608

Quantitative Finance and Economics

2019, Volume 3, Issue 4: 608-623. doi: 10.3934/QFE.2019.4.608

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Research article Special Issues

BOMD: Building Optimization Models from Data (Neural Networks based Approach)

Vladimir Donskoy ^,

Department of Mathematics & Computer Science, V.I. Vernadsky Crimean Federal University, Simferopol, 295007, Russia

Received: 27 July 2019 Accepted: 19 September 2019 Published: 30 September 2019
JEL Codes: C45, D22, D83, M11

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.
- intelligent economic management,
- model extraction,
- sample,
- neural network,
- decision tree
Citation: Vladimir Donskoy. BOMD: Building Optimization Models from Data (Neural Networks based Approach)[J]. Quantitative Finance and Economics, 2019, 3(4): 608-623. doi: 10.3934/QFE.2019.4.608

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Abstract

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.

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