An Algorithm for Optimum Structural Design without Line Search

Abstract : In this paper, a new optimization algorithm for optimal design of engineering systems is presented. The main feature of the new algorithm is that it does not rely on one dimensional search to compute a step size at any design iteration. Implication of the feature is that algorithm requires evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of constraints for such systems is very expensive. The reason for the high cost is that many constraints for such design problems are implicit functions of design variables. Thus their evaluation requires solution for a high dimensional finite element model for the system. The new algorithm is based on finding upper and lower bounds on the optimum cost and is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general purpose computer code GRP2 is developed. The code is used to solve several small scale problems to gain experience and insight into the algorithm. Numerical experience with examples is discussed. It is shown that the algorithm has substantial potential for applications in optimal design of engineering systems. (Author)