Abstract
The article presents four main chapters that allow you to formulate an optimization task and choose a method for solving it from static and dynamic optimization methods to single-criterion and multi-criteria optimization. In the group of static optimization methods, the methods are without constraints and with constraints, gradient and non-gradient and heuristic. Dynamic optimization methods are divided into basic - direct and indirect and special. Particular attention has been paid to multi-criteria optimization in single-object approach as static and dynamic optimization, and multi-object optimization in game control scenarios. The article shows not only the classic optimization methods that were developed many years ago, but also the latest in the field, including, but not limited to, particle swarms.
Highlights
The main goal of optimization is to implement the object control process in the best way
The optimization task consists in determining the values of state variables x* at which the control goal function F*(x*) takes the minimum or maximum value [4,5,6]
The static optimization task can be formulated as finding the optimal value of the x* variable that minimizes or maximizes the goal control function as an optimal control quality index F(x) in the form of a relationship: F(x) = f(x) for x = x1, x2, ..., xn
Summary
The main goal of optimization is to implement the object control process in the best way. The mathematical description of the process formulated for the purposes of its optimization is its model. Optimization is as good as the mathematical model is adequate (Fig. 1). The function F(x) means the assessment of the quality of the object's operation or the course of the control process and takes the name of the function of the control purpose or control quality index, and x are the decision variables or variables of the control process state [1,2,3]. The optimization task consists in determining the values of state variables x* at which the control goal function F*(x*) takes the minimum or maximum value [4,5,6]. The values of the components of the state vector x cannot be arbitrary and are subject to various restrictions.
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