The Branch and Cut Method in the PLATO-N Project

We present the multiple load structural topology design problems with discrete design variables which are considered in the PLATO-N project. For the considered class of problems a global optimization method based on the concept of branch and cut is developed and implemented. In the method a large number of continuous relaxations are solved. Strong continuous relaxations are obtained by removing certain complicating constraints. Using duality results these relaxations are reformulated into programs which can be efficiently solved within the branch and cut search tree. We also present an algorithm for generating cuts to strengthen the quality of the relaxations. The branch and cut method is used to solve a benchmark example which can be used to validate other methods and heuristics. 2. Keywords: Topology optimization, branch and cut, stress constraints, reformulations, relaxations. In this work we consider structural topology optimization problems in which the design variables are chosen from a finite set of given values. The optimal design problems are modeled as non-convex mixed 0–1 optimization problems. In the PLATO-N ∗ project we are interested in two particular problems from the field of optimal structural topology design. The first problem is a minimum weight problem wit

Phase-Field Relaxation of Topology Optimization with Local Stress Constraints

We introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase-field method. The starting point of the relaxation is a reformulation of the material problem involving linear and 0–1 constraints only. The 0–1 constraints are then relaxed and approximated by a Cahn-Hilliard type penalty in the objective functional, which yields convergence of minimizers to 0–1 designs as the penalty parameter decreases to zero. A major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter. The relaxation scheme yields a large-scale optimization problem with a high number of linear inequality constraints. We discretize the problem by finite elements and solve the arising finite-dimensional programming problems by a primal-dual interior point method. Numerical experiments for problems with stress constraints based on different criteria indicate the success and robustness of the new approach