A new weight vectors generation method for R2 indicator based evolutionary multiobjective optimization algorithm

In multi-objective optimization problems (MOPs), set-based performance indicators are commonly used to assess the convergence and diversity of Pareto front approximation. Performance indicators can be used as the selection strategies. The selection strategy of indicator based evolutionary multi-objective algorithms (EMOAs) is guided by a general preference information, which maps objectives into a single contribution value by means of a set of utility functions. R2-EMOA is one of the most important indicator-based algorithms to solve MOPs. We use fast R2-ranking to rank the individuals of EMOAs. This paper suggests a new weight generator strategy, which is based on direction angles, for MOPs. Our main purpose is to explore the relationship among direction angles, weight vectors and direction vectors. Our proposed weight generator scheme is incorporated to two different search engines, resulting in two new EMOAs, named IR2-MOGA and IR2-MODE. The performance of our proposed method is validated and compared with other R2-EMOAs on a number of unconstraint benchmark problems. Experimental results demonstrate that our algorithms can significantly improve the convergence and diversity of R2-EMOA.