Optimization of generalized multi-purpose systems

The article expands the definition of multi-purpose system that was previously implemented by the author. Multi-purpose system is defined as a collection of elements that react to external impacts by reassigning parts of the impact between the members of the collection in an optimal way. It is assumed that the vector of the impact is always scalar, every element of the system is able to react to any kind of separate impact autonomously, without any interaction with other elements of the system. The article considers the model of the generalized multi-purpose system, where these restrictions are removed. The model described in the article allows for limited impact reaction of the system’s elements. The possibility of joint response for impact for the elements of the system is considered. A multi-criteria methods of evaluation the system’s performance is proposed. Accurate algorithms of optimization of integrated and guaranteeing systems based on the model of a mixed linear programming are proposed. Given the high dimensionality of the numerically solved tasks for the optimization problems, precise and heuristic methods for the dimensionality reduction are proposed. A variety of tasks, such as designing of objects and systems of objects, standardization and unification, arrangement of items, services and others can be solved by means of optimization of the generalized multi-purpose systems.