Intelligent optimization based on machine learning: state of art and perspectives (a survey)

This survey focuses on the following problem: it is necessary, observing the behaviour of the object, automatically figure out how to improve (optimize) the quality of his functioning and to identify constraints to the improvement of this quality. In other words, build the objective function (or set of objective functions in multiobjective case) and constraints — i.e. the mathematical model of optimization — by mean machine learning. We present the main developed to date methods and algorithms that enable the automatic construction of mathematical models of planning and management objects by the use of arrays of precedents. The construction of empirical optimization models by reliable case information allows us to obtain an objective control model that reflects real-world processes. This is their main advantage compared to the traditional, subjective approach to the construction of control models. Relevant to the task a set of mathematical methods and information technologies called “Extraction optimization models from data”, “BOMD: Building Optimization Models from Data”, “Building Models from Data”, “The LION Way: Learning plus Intelligent Optimization”, “Data-Driven Optimization”. The incompleteness of information and uncertainty are understood in different ways. Significantly different are the problem settings — deterministic, stochastic, parametric, mixed. Therefore, the consideration of a wider range of tasks leads to a variety of (primarily statistical) and other formulations of the problem and interpretations of uncertainty and incompleteness of initial information. The survey contains the following sections:

• Empirical synthetic of pseudoBoolean models;
• Empirical linear models with real variables;
• Empirical neural network optimization models;
• Iterative models;
• Models, including statistical statements;
• Problems, associated with the lack of the training set of points not belonging to the region of feasible solutions.