Problem of trace – one of the most labor-consuming in a common problem of automation of design of REA. It is connected with several factors, in particular with variety of ways of constructive and technological realization of connections, specific criteria of optimization and restriction are applied to each of which at the algorithmic solution of a task. From the mathematical point of view trace – the most difficult problem of a choice from huge number of versions of the optimum decision.
Shortcomings are labor input of a method and complexity of its realization (selection of coefficients for power communications); need of fixation of location of some number of constructive elements on a payment for prevention of big unevenness of their placement on separate sites of a payment.
All cells of an assembly field subdivide on busy and free. Cells in which the conductors constructed on the previous steps are already located are considered busy or there are assembly conclusions of elements, and also the cells corresponding to border of a payment and sites forbidden for making of conductors. Every time when carrying out the new route it is possible to use only free cells which number in process of carrying out routes is reduced.
Iterative algorithms have the structure similar to the iterative algorithms of configuration considered earlier. For improvement of initial placement of elements on a payment enter iterative process of shift into them places of couples of elements.
In other words as splittings parts of set of G into columns are considered, if any part from this set not empty; for any two parts crossing of a set of edges can be not empty; association of all parts is equal in accuracy column G.
The main idea of algorithm consists in a choice of such lines and columns which shift leads to concentration in diagonal cages of a matrix of R maximum numbers of elements. Let's construct a rectangular matrix of W = || wi, j || nix(n-ni) in which lines are defined by tops from a great number of I, and columns – of a great number of V. On crossing of k of a line (and q of a column is an element
The main objective of trace is formulated as follows: according to the set scheme of connections to lay necessary conductors on the plane (a payment, a crystal, etc.) to realize the set technical connections taking into account in advance set restrictions. The main are restrictions on width of conductors and the minimum distances between them.
The specified process proceeds until the set of X1 does not contain n of elements or accession of the next unallotted top of xj to a piece of G1(X1,U will not lead to violation of restriction on the number of external connections of a piece equal
where αjε – a contiguity matrix element initially column G (X, U); δ (xg) – the relative weight of top of xg, G1(X1,U equal to an increment of number of external edges of a piece at inclusion of top of xg in a set of X1; E – a set of indexes of the tops included in the formed piece of the count on the previous steps of algorithm; m – the most admissible number of external relations of separately taken piece with all remained.
The algorithms using consecutive process of fixing of elements in positions are the most high-speed now. However on quality of the received decision consecutive algorithms concede to the iterative. Therefore they are used usually for receiving initial placement of elements on a payment.
If the adjusting sizes of all elements placed on a payment are identical, the element chosen on the next step fix in that position from among unoccupied, for which value of criterion function taking into account earlier placed Rl-1 elements minimum. In particular, if criterion of an optimality is the minimum of the total weighed length of connections,
On a matrix of contiguity of the initial count | αhp|NxN where by N – number of tops of the initial count (at great value of N for reduction of volume of random access memory of the COMPUTER it is used not a matrix of contiguity, but its code realization), we determine local degrees of tops.
Algorithms of heuristic type. These algorithms are partially based on heuristic reception of search of a way in a labyrinth. Thus each connection is carried out on the shortest way, bypassing the obstacles which are found on the way.