A New Approach to Topology Optimization with Genetic Algorithm and Parameterization Level Set Function

Abstract

In this paper, a new approach to topology optimization using the parameterized level set function and genetic algorithm optimization methods is presented. The impact of a number of parameters describing the level set function in the representation of the model was examined. Using the B-spline interpolation function, the number of variables describing the level set function was decreased, enabling the application of evolutionary methods (genetic algorithms) in the topology optimization process. The traditional level set method is performed by using the Hamilton–Jacobi transport equation, which implies the use of gradient optimization methods that are prone to becoming stuck in local minima. Furthermore, the resulting optimal shapes are strongly dependent on the initial solution. The proposed topology optimization procedure, written in MATLAB R2013b, utilizes a genetic algorithm for global optimization, enabling it to locate the global optimum efficiently. To assess the acceleration and convergence capabilities of the proposed topology optimization method, a new genetic algorithm penalty operator was tested. This operator addresses the slow convergence issue typically encountered when the genetic algorithm optimization procedure nears a solution. By penalizing similar individuals within a population, the method aims to enhance convergence speed and overall performance. In complex examples (3D), the method can also function as a generator of good initial solutions for faster topology optimization methods (e.g., level set) that rely on such initial solutions. Both the proposed method and the traditional methods have their own advantages and limitations. The main advantage is that the proposed method is a global search method. This makes it robust against entrapment in local minima and independent of the initial solution. It is important to note that this evolutionary approach does not necessarily perform better in terms of convergence speed compared to gradient-based or other local optimization methods. However, once the global optimum has been found using the genetic algorithm, convergence can be accelerated using a faster local method such as gradient-based optimization. The application and usefulness of the method were tested on typical 2D cantilever beams and Michell beams.