Truss optimization using eigenvectors of the covariance matrix

Abstract

In this paper, by combining eigenvectors of the covariance matrix and random normal distribution, a new method has been presented to solve optimization problems. This method has been inspired by CMA-ES method and has been named eigenvectors of covariance matrix (ECM). ECM generates some solutions in each stage; then it assigns a value to all solutions by utilizing a dynamic penalty function. The best solution in each stage is selected as the answer of optimization problem and ECM tries to push towards a better point. According to the penalty function, the solutions with no violation along with the solutions with little violation are considered as good solutions and named desirable data. By utilizing desirable data, a square matrix is formed and its covariance matrix can be calculated. The eigenvectors of the covariance matrix are orthogonal and they show directions of distribution of desirable points that have been chosen before. We can hopefully get a better answer by moving from the best current answer towards the points which are distributed normally and randomly around the weighted combination of eigenvectors. To ensure the validity and accuracy of ECM method, weights of six truss structures have been optimized through this method and the results have been compared with previous studies.