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A. V. Panteleev and M. M. S. Karane
16.1 Introduction
The scope of multi-agent algorithms [1] is quite wide, and at present, such algorithms
are more and more often used to solve various kinds of optimization problems. This is
due to the fact that multi-agent algorithms are in no way inferior to existing classical
methods, and even vice versa quite often surpass them. They make it possible to solve
problems of greater dimension much more successfully or if restrictions are imposed
on the system. The advantage of multi-agent algorithms also lies in the fact that it is
not necessary to have information about the behavior of a function or its properties.
Multi-agent methods are used in many fields, such as the theory of optimal control
[2–5] for optimizing a criterion or in machine learning for tuning and training neural
networks [6].
The principle of operation of multi-agent algorithms consists in the formation of
a group of agents on the solution search set, and depending on the specific algorithm,
a set of actions is carried out on the agents that lead group of agents to answer the
task.
The purpose of this work is to develop a multi-agent algorithms and their application in order to find the optimal open-loop control. This requires a formation of more
general algorithm, which will include multi-agent algorithms. Another purpose is to
find the optimal open-loop control in two ways: by decomposing the control into a
system of basis functions and representing the control in relay form with a certain
set of switching points.
The novelty of this approach is the use of multi-agent algorithms to search for
optimal program control. Each multi-agent algorithm is based on new ideas for
finding the optimal solution. The novelty of the hybrid multi-agent method of interpolation search [7] is the use of interpolation curves, which allows to adapt the locally
changing structure of the level surfaces of the objective function. In the multi-agent
method based on the use of linear regulators of agent movement control, four types
of optimal program control with full feedback on the state vector are searched at the
stages of the algorithm. For each control, its own criterion is optimized.
In addition, before applying multi-agent algorithms, one should investigate their
effectiveness on a standard set of test functions [8, 9] of two variables in order to
identify the most suitable ranges of parameter values. Using them, it is possible to
solve applied problems with great success. In [7], for the hybrid multi-agent method
of interpolation search, a detailed analysis of the efficiency is given, and the best
algorithm parameters are established.
The chapter is organized as follows. Section 16.2 provides a description of multiagent methods. Application of multi-agent methods for optimal open-loop control
problems is given in Sect. 16.3. Section 16.4 concludes the chapter.
A. V. Panteleev and M. M. S. Karane
16.1 Introduction
The scope of multi-agent algorithms [1] is quite wide, and at present, such algorithms
are more and more often used to solve various kinds of optimization problems. This is
due to the fact that multi-agent algorithms are in no way inferior to existing classical
methods, and even vice versa quite often surpass them. They make it possible to solve
problems of greater dimension much more successfully or if restrictions are imposed
on the system. The advantage of multi-agent algorithms also lies in the fact that it is
not necessary to have information about the behavior of a function or its properties.
Multi-agent methods are used in many fields, such as the theory of optimal control
[2–5] for optimizing a criterion or in machine learning for tuning and training neural
networks [6].
The principle of operation of multi-agent algorithms consists in the formation of
a group of agents on the solution search set, and depending on the specific algorithm,
a set of actions is carried out on the agents that lead group of agents to answer the
task.
The purpose of this work is to develop a multi-agent algorithms and their application in order to find the optimal open-loop control. This requires a formation of more
general algorithm, which will include multi-agent algorithms. Another purpose is to
find the optimal open-loop control in two ways: by decomposing the control into a
system of basis functions and representing the control in relay form with a certain
set of switching points.
The novelty of this approach is the use of multi-agent algorithms to search for
optimal program control. Each multi-agent algorithm is based on new ideas for
finding the optimal solution. The novelty of the hybrid multi-agent method of interpolation search [7] is the use of interpolation curves, which allows to adapt the locally
changing structure of the level surfaces of the objective function. In the multi-agent
method based on the use of linear regulators of agent movement control, four types
of optimal program control with full feedback on the state vector are searched at the
stages of the algorithm. For each control, its own criterion is optimized.
In addition, before applying multi-agent algorithms, one should investigate their
effectiveness on a standard set of test functions [8, 9] of two variables in order to
identify the most suitable ranges of parameter values. Using them, it is possible to
solve applied problems with great success. In [7], for the hybrid multi-agent method
of interpolation search, a detailed analysis of the efficiency is given, and the best
algorithm parameters are established.
The chapter is organized as follows. Section 16.2 provides a description of multiagent methods. Application of multi-agent methods for optimal open-loop control
problems is given in Sect. 16.3. Section 16.4 concludes the chapter.