Nonlinear Mixed‐Discrete Structural Optimization

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Abstract
This paper presents a solution code for mixed‐discrete variable optimization. An optimization algorithm comprising two different techniques, discrete steepest descent and rotating coordinate directions, originally proposed for all discrete optimization, is extended. The extensions have been done in such a way that continuous variables are treated as discrete variables while keeping their continuous nature in the analysis. Several example problems have been solved, three of which are reported. Each example problem is different in nature and in degree of nonlinearity from others. All three example problems reached or almost reached the global optimum. All the practical difficulties (resolution valley, overshooting the optimum, etc.) usually encountered in the discrete or mixed‐discrete optimization are believed to be overcome by the solution code presented herein. The present solution code can effectively be applied to a variety of problems. Details of each technique with the necessary extension and modifications are described.