Evaluation of combinatorial algorithms for optimizing highly nonlinear structural problems

Abstract

Optimizing highly nonlinear structural problems can be very challenging due to the large number of parameters. Classical compliance minimization does not work for such problems. Common optimization algorithms also do not find good solutions. This work evaluates both commonly used optimization algorithms and algorithms not yet used in topology optimization. The algorithms are evaluated using a simple nonlinear problem: minimizing the end displacement of a cantilever beam fixed on one side and loaded by gravity. The global optimum for a coarse mesh grid is computed by simulating nearly 60 million possible topology designs using a Brute-Force search. We use this benchmark to evaluate the computational cost and objective values of known and newly developed optimization methods. The known methods are binary-coded Genetic Algorithm, Simulated Annealing, and Free Shape Optimization. The Reduced Variable Neighborhood Search (RVNS) has not yet been applied to topology optimization. We provide two implementations of RVNS: Breadth-First Search with a limited search depth (BFSL) and with an optional restriction for the size of the simultaneously modified area (TBFSL). According to the benchmark, TBFSL is the most efficient approach. For the optimization on a finer mesh grid, TBFSL is combined with a multi-grid approach to further increase efficiency.