An Indicator-Guided Many-Objective Evolutionary Algorithm with Adaptive Mapping Distance

The shape of the Pareto Front (PF) has a significant influence on maintaining population diversity, which makes it challenging for most algorithms to effectively balance the population convergence and diversity when solving many-objective optimization problems (MaOPs). Therefore, this paper proposes an indicator-guided many-objective evolutionary algorithm with adaptive mapping distance, termed MaOEA-IAMD. In this algorithm, an adaptive mapping distance calculation strategy is designed to maintain population diversity. This strategy estimates the PF curvature using the Newton–Raphson method, and maps individuals onto the PF based on the obtained curvature information, thereby calculating the adaptive mapping distance between two individuals to measure their similarity in search direction. Meanwhile, we develop a select-replacement strategy by using the binary additive epsilon indicator and the adaptive mapping distance to balance the population convergence and diversity. In addition, a knee points-based classification mutation strategy is designed to generate high-quality offspring, further improving the search efficiency of MaOEA-IAMD. We compare MaOEA-IAMD with six state-of-the-art algorithms on 21 benchmark test problems and 2 real-world optimization problems. The experimental results demonstrate the competitiveness and effectiveness of the proposed algorithm.