The optimization of placing electronic components by a modified alternating-variable descent method
The problem of optimal placement of elements of electrical and electronic circuits is considered. The minimum weighted connection length is selected as the criterion. A computational method is proposed that is a modification of the coordinate descent method and one of the variants of the General approach based on pair permutations. The scheme is defined by the connection matrix. 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. Geometric restriction of the problem - no more than one element can be placed in one cell. It is stated that approaches based on paired and similar permutations are economical, and the method of the penalty function leads to" ditching " and is ineffective. A modified coordinate descent method is described, which is a variant of the pair permutation method, in which pairs are selected based on the coordinate descent method. In the proposed version of the coordinate descent method, two coordinates are changed simultaneously at one stage of calculations (and not one, as in the usual optimization method). one of the coordinates is used for the usual trial step, and the other is used for correction, returning to the acceptable area. Next, the value of the target function is calculated at the found point and compared with the previously reached value. If the value has improved, the found point becomes the new starting point. Otherwise, a step is made on a different coordinate with simultaneous correction of the vector of item position numbers (return to the allowed area). The experience of using the modified method in solving the problem of placing EVA elements has shown its significant advantages in comparison with other known methods, for example, the genetic algorithm, as well as the method of penalty functions. An example of calculations using the proposed method is considered. The connection matrix was set analytically. First, the initial approximation was searched by the Monte Carlo method (10,000 iterations), after which the local optimum was calculated using a modified method of coordinate descent in the permutation space without repetitions (a limit of 100 iterations was set). The initial value of the coordinate step is equal to the size of the permutation, then at each iteration it was reduced by 1 to the minimum possible value of 1. The advantage of this method is that there is no penalty function. The search is performed automatically in the permutation space without repetitions. Computational experiments have shown high computational qualities of the proposed method.