In this paper, the crystal plan is formed by the recursive use of a "guillotine cut". To set the plan means to set the structure of the binary tree of the cuts, i.e. sequence of binary cuts; for internal tree vertices, to indicate the type of the cut H or V; to number the leaves of the tree and indicate the orientation of the modules. The structure of the binary tree of the cuts can be set using the Polish expression on the base of the alphabet A = {M, TR}, where the set of letters M = {mi|i = 1, 2, ..., nМ} corresponds to the leaves of the section tree (regions), and the set R = {H, V} corresponds to the cuts. We propose a way and methods for solving the problems of planning VLSI based on a modified ant colony. The task of synthesizing the section tree of the plan with the choice of types of sections, identification and orientation of the modules in the work is reduced to the task of forming a modified Polish expression with the identification of elements on the composite model of the solution space, including many alternative vertices. To keep the collective evolutionary memory during the life of the ant population and to form the solution of the problem, we use the complete graph G = (X, U) with alternative vertex states. Each vertex may be in one of two alternative states, i.e., α or β, corresponding to the orientation of the module or the type of the cut. The task of synthesizing the Polish expression is formulated as the task of finding the least-cost route on the solution search graph G = (X, U). A distinctive feature is that when building a route, simultaneously with the choice of the vertex xi∈ X, the state of this vertex is selected. The time complexity of the algorithm is O(n2). Experiments have shown that for large dimensions, the time indicators of the developed algorithm exceed those of the compared algorithms with the best values of the objective function.
Combining dynamic programming with filtering to solve a four-stage two-dimensional guillotine-cut bounded knapsack problem
