Simulation in Graphs Search for Optimal Solutions of Design Problems of Technical Systems

Abstract

The article is devoted to solving for the optimum to the tasks on projection of technical systems regardless of their functional purpose. In the introduction necessity of such problem definition and of its solving is grounded. For teleological task solving search using of graph theory is offered. For that a new concept of n-partite graphs is entered. A theorem on simple circuits (routes) of such graphs is defined, which are formed by prescribed subset integration of empty graphs (zero-graphs); top points of them are regulated in the design parameters of technical system. It is proved that total number of such routes is determined by the product of element numbers in subset empty graphs. It is shown that each of these routes is one of the states of the technical system. It is elaborated entry algorithm of block matrix routes for n-partite graphs as well as for elements of block matrices.  As an illustrative example of the offered technique the problem on cinematic synthesis of articulated lever for-bar linkages mechanism is considered. Variation strategy for the free parameter quantities of the system is worked out. Also it is shown how substantially.