Solution of structural optimization problems by piecewise linearization

Abstract

Summary. Structural optimization problems tend to be nonlinear and often also nonconvex. In this paper it is proposed to reduce a general class of such problems to linear programming problems through piecewise linearization. They can then be solved by the highly effective linear programming computer codes currently available.1. Introduction. Structural optimization problems tend to be nonlinear and often also non-convex. However, as stated e.g. by Morris in [1], they can frequently be cast in a form where both the objective function and the constraints are fractions of polynomials in the design variables. Such problems can readily be piecewise linearized, and a global optimum can be found through mixed integer programming. If the problem is convex, the linearization results in a linear programming problem without integer variables.Linear programming codes are now commercially available which can solve problems with a large number of variables within a reasonably short time. Thus piecewise linearization represents a solution technique which should be seriously considered for a large class of structural optimization problems.