Abstract
Several structural design problems that involve continuous and discrete variables are very challenging because of the combinatorial and non-convex characteristics of the problems. Although the deterministic optimization approach theoretically guarantees to find the global optimum, it usually leads to a significant burden in computational time. This article studies the deterministic approach for globally solving mixed–discrete structural optimization problems. An improved method that symmetrically reduces the number of constraints for linearly expressing signomial terms with pure discrete variables is applied to significantly enhance the computational efficiency of obtaining the exact global optimum of the mixed–discrete structural design problem. Numerical experiments of solving the stepped cantilever beam design problem and the pressure vessel design problem are conducted to show the efficiency and effectiveness of the presented approach. Compared with existing methods, this study introduces fewer convex terms and constraints for transforming the mixed–discrete structural problem and uses much less computational time for solving the reformulated problem to global optimality.
Highlights
Various problems that contain continuous and discrete variables arise in practical structural design applications; the mixed–discrete structural optimization (MDSO) problems have attracted increasing attention from researchers and practitioners in the last few decades
The focus of this article is on the deterministic optimization approach for globally solving the MDSO problems that can be formulated as signomial geometric programming problems with mixed–discrete variables, such as the stepped cantilever beam design problem, the spring design problem, and the pressure vessel design problem
For treating pure discrete signomial terms in the MDSO problems, Tsai and Lin [18] proposed a linear transformation by using a logarithmic number of extra binary variables and constraints
Summary
Various problems that contain continuous and discrete variables arise in practical structural design applications; the mixed–discrete structural optimization (MDSO) problems have attracted increasing attention from researchers and practitioners in the last few decades. Lin and Tsai [17] provided a complete survey of research on optimization approaches for the MDSO problems with signomial geometric functions, and proposed a deterministic method to solve the MDSO problems with signomial geometric functions by using convex transformations, linearization methods, and range reduction mechanisms. For treating pure discrete signomial terms in the MDSO problems, Tsai and Lin [18] proposed a linear transformation by using a logarithmic number of extra binary variables and constraints. Reduces the number of convex terms generated in reformulating the MDSO problems: Compared with the Lin and Tsai [17] method that converts the pure discrete signomial terms to convex terms and linearizes the inverse transformation functions, this study directly linearizes the pure discrete signomial terms.
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