MaOEA-PGTS: A Probabilistic Flow-Guided Two-Stage Strategy for Many-Objective Optimization

Many-objective evolutionary algorithms (MaOEAs) often suffer a loss of selection pressure, hindering efficient exploration of Pareto-optimal regions. To address this problem, this paper proposes a probabilistic flow-guided two-stage strategy for many-objective optimization (MaOEA-PGTS). MaOEA-PGTS divides evolution into an exploratory phase and a convergence phase, and dynamically balances diversity and convergence via probabilistic-flow control. In the first stage, candidate solutions are classified into optimal, intermediate, and worst streams using a probabilistic-flow strategy. Each stream is assigned a performance-based probability weight, which is dynamically adjusted via the Poisson cumulative distribution function. In the second stage, the algorithm employs an adaptive thresholding mechanism is employed to reduce the probability of missegregation between solution streams. Finally, the algorithm integrates a normally distributed probability density function to optimize the selection of individuals during the selection process and further maintain inter-population balance. MaOEA-PGTS is tested against seven state-of-the-art algorithms (Two_Arch2, IBEA, NSGA-III, MOEA/D, AGE-II, MOPSO, CMOPSO) on standard many-objective optimization problems, specifically the DTLZ and WFG test functions. Experimental results show that MaOEA-PGTS significantly outperforms the comparison algorithms in terms of both convergence and diversity metrics.