ASSESSING ACHIEVED SAVINGS USING OPTIMIZED TRUSSES WITH CARDINALITY CONSTRAINTS

Abstract

This research presents the additional benefits gained when using cardinality constraints in just sizing and combined sizing and shape optimization to find solutions with minimal weight while using a set number of different cross-sections allowed in the design. When limiting the number of cross-sections, an optimal solution can result in a structure with a reasonable number of different types of stock needed, unlike an approach which is unconstrained in this regard. This creates a more practical solution, which reduces the complexity of the solution and more resembles an experience-driven design, but with a lower overall weight than analytical solutions due to the optimization methods’ ability to explore practically the entire search space for a minimal weight solution. This limitation has adverse effects on the design. The downside is that the weight of the resulting structure is higher than the global optimum (one which disregards the number of different types or sizes of cross-sections used). However, it means that there are fewer different bar stock dimensions to be ordered, and less waste is created once the necessary pieces are cut from standard bar stock. The example used for these purposes is a typical optimization problem of a 17-bar truss with various numbers of different cross-sections used. The optimal solutions for this example were made using original software developed by the authors for the purposes of previously published research. Standard, available, bar stock dimensions were used in the optimization process in order to best resemble a real-world application. The results illustrate the added benefits of including fewer different bar stock types and the accompanying savings, which are indirectly created using this method.