Cost-Optimal Design and Support Vector Regression

This paper presented the use of the Lagrange multiplier method (LMM) for cost optimumdesign of singly and doubly reinforced rectangular concrete beams, under designconstraints. The first part of the study is the basic definitions of LMM and someformulae, which require for the optimum design of the beams. Three numerical exampleswere solved using the LMM, in different situations. Typically, parameters such as thewidth of the beam (b), externally applied ultimate moment (Mu), the compressivestrength of concrete (F'c) and yield strength of steel (Fy) are considered as determinedparameters. The aim is to attain the optimal values of the area of tension (As) and the areaof compression steel (A's), effective depth of the beam (dopt) and the minimum cost of theobjective function (Cmin). In addition, numerical problems analyzed and solved by thestandard design method with Good and reliable results have been obtained. The results ofthe LMM were compared with the results of the standard design method, and thiscomparison showed that the LMM could successfully be used to minimize the cost of thereinforced concrete beams without the need for repeated trials. As result, the proposedapproach is a powerful, suitable, effective and reliable method for optimum design ofpractical engineering problems. At the final section this paper, the support vectorregression (SVR) was trained with design data, which obtained from the optimal designformulas. After successful trials, SVR predicted with the high accuracy and better results,the parameters previously acquire their optimal values by the LMM.

Keywords:

Optimal design , singly reinforced concrete beams , doubly reinforced concrete beams , LMM , standard design method.