Компьютерная оптимизация размещения элементов электронных цепей

Abstract

The problem of optimal placement of elements of electrical and electronic circuits is considered. The minimum weighted length of the connections is selected as the criterion. The scheme is defined by a matrix of connections. We consider a fixed set of element positions and a distance matrix based on an orthogonal metric. This problem is a variant of the general mathematical model, called the quadratic assignment problem. The geometric limitation of the problem is that no more than one element is placed in one cell. Combinatorial analogs of the Gauss-Seidel method, the genetic algorithm, and the corresponding hybrid methods for solving the quadratic assignment problem with optimal placement of electronic equipment elements are developed and implemented on a computer. A series of computational experiments was conducted, which showed satisfactory computational qualities of the proposed methods. The proposed computational method, which is a combinatorial analog of the method of coordinate descent and one of the variants of the general approach based on paired permutations, is characterized by the best computational qualities among the methods studied in the article. According to well-known studies, the genetic algorithm is obviously no worse than the Monte Carlo method. The research conducted in the article shows that the method of penalty functions in the problem of placement and for the case of a genetic algorithm is ineffective. Therefore, it is of interest to consider permutations without repetitions as individuals of the population. This circumstance is taken into account at the stages of selection and mutation: at these stages, the standard calculations according to the genetic algorithm are supplemented by the procedure of paired rearrangements of genes in the chromosome. The article provides a detailed description of the program for the implementation of the genetic method on a computer.