Bilevel Approach of a Decomposed Topology Optimization Problem

In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed on non-overlapping sub-domains. In this paper, we consider the resulting problem as multilevel one and show that it can be written as one level proble

An Attempt to Solve Decomposed Topology Optimization Problem Based Multicriteria Approach

Copyright c ○ 2014 K. Atani, A. Makrizi and B. Radi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper deals with decomposed topology optimization problem (DTOP) written in [6] as a bilevel programming problem (BPP). The BPP are often known to be hard to solve in practice. Due to the effectiveness and efficiency of multicriteria techniques to solve industrial problems, several authors have attempted to establish a link between bilevel programming and multicriteria optimization [4]. For this reason, a finite element discretization procedure is described for DTOP, and the discrete problem is solved using multicriteria techniques. In this context, we define an order relation such that the optimal solutions of BPP are the nondominated points with respect to this order relation. To achieve this outcome, we construct two convex cones, given the nondominated points with respect to the order relation induced by the cones, we prove that their preimage are nondominated with respect to the first order relation cited above, and are also solution to the BPP