An Adaptive Reference Vector-Guided Evolutionary Algorithm Using Growing Neural Gas for Many-Objective Optimization of Irregular Problems

Most reference vector-based decomposition algorithms for solving multiobjective optimization problems may not be well suited for solving problems with irregular Pareto fronts (PFs) because the distribution of predefined reference vectors may not match well with the distribution of the Pareto-optimal solutions. Thus, the adaptation of the reference vectors is an intuitive way for decomposition-based algorithms to deal with irregular PFs. However, most existing methods frequently change the reference vectors based on the activeness of the reference vectors within specific generations, slowing down the convergence of the search process. To address this issue, we propose a new method to learn the distribution of the reference vectors using the growing neural gas (GNG) network to achieve automatic yet stable adaptation. To this end, an improved GNG is designed for learning the topology of the PFs with the solutions generated during a period of the search process as the training data. We use the individuals in the current population as well as those in previous generations to train the GNG to strike a balance between exploration and exploitation. Comparative studies conducted on popular benchmark problems and a real-world hybrid vehicle controller design problem with complex and irregular PFs show that the proposed method is very competitive.