Multiobjective Evolutionary Topology Optimization Algorithm Using Quadtree Encoding

A multiobjective high-degree-of-freedom design optimization algorithm that enables topological changes in design is proposed for multiobjective aerodynamic design optimization. In this method, a design is encoded using a regional quadtree, which is often used in computer graphics to increase the speed and save memory in image processing. The optimization problem is solved using multiobjective genetic programming with new crossover, mutation, regularization, and decoding operators designed to handle the evolution of the quadtree structure efficiently and properly. The proposed algorithm is evaluated by solving two multiobjective airfoil shape reproduction problems. The results show that the proposed method can represent typical airfoil shapes with different topologies more efficiently than the conventional evolutionary algorithm.