The IGD+ Indicator and Reference Vector Guided Evolutionary Algorithm for Many-objective Optimization Problems

Performance indicators are suitable for the environmental selection in evolutionary multi-objective evolutionary algorithms (EAs). Balancing convergence and diversity is very important for performance indicators based evolutionary algorithms. Recently, the modified inverted generational distance, named IGD+ indicator, is popular to solve optimization problems with two or three objectives due to its better characteristics that the indicator can obtain the weak Pareto dominance solutions. However, only adopting the selection mechanism based on the IGD+ indicator in high dimensional objective space, is no longer enough to guarantee the candidate solutions a good diversity. In order to address this issue, we employ the reference vector to assist the IGD+ indicator for solving many-objective EAs. It is the first time to combine the IGD+ indicator and the selection based on the objective space partition. Experimental results have been conducted on the DTLZ test instances which show that our algorithm has achieved a competitive performance for multi-objective and many-objective optimization.