Move limits definition in structural optimization with sequential linear programming. Part I: Optimization algorithm

A variety of numerical methods have been proposed in literature in purpose to deal with the complexity and nonlinearity of structural optimization problems. In practical design, sequential linear programming (SLP) is very popular because of its inherent simplicity and because linear solvers (e.g. Simplex) are easily available. However, SLP performance is sensitive to the definition of proper move limits for the design variables which task itself often involves considerable heuristics. This research presents a new SLP algorithm (LESLP-linearization error sequential linear programming) that implements an advanced technique for defining the move limits. The LESLP algorithm is formulated so to overcome the traditional limitations of the SLP method. The new algorithm is successfully tested in weight minimization problems of truss structures with up to hundreds of design variables and thousands of constraints: sizing and configuration problems are considered. Optimization problems of non-truss structures are also presented. The key-ideas of LESLP and the discussion on numerical efficiency of the new algorithm are presented in a two-part paper. The first part concerns the basics of the LESLP formulation and provides potential users with a guide to programming LESLP on computers. In a companion paper, the numerical efficiency, advantages and drawbacks of LESLP are discussed and compared to those of other SLP algorithms recently published or implemented in commercial software packages.