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It is critical to maintain significant convergence and diversity in many-objective optimization problems (MaOPs) for the performance of many-objective evolutionary algorithms (MaOEAs). However, some issues pose serious challenges to MaOEAs, such as the intensification of the conflict between convergence and diversity, and the lack of Pareto selection pressure. To address the above issues, we propose a cooperative-competitive two-stage game mechanism assisted many-objective evolutionary algorithms (MaOEA-GM). The algorithm is divided into two stages, such as competition and cooperative. In competitive game stage, a strategy pool is constructed, including angle penalty distance strategy and favorable convergence strategy. In addition, a new game utility function is designed to balance convergence and diversity. This method promotes the selection of genetically superior parents for inheritance, so that the population can quickly approach the true Pareto front. In cooperative game stage, individuals choose their preferred environmental selection mechanism by voting. The final scheme is determined using the criterion of minority obedience to the majority, thereby increasing the algorithm Pareto selection pressure. Experimental results demonstrate that compared with five advanced MaOEAs, The MaOEA-GM algorithm has not only preponderance in convergence and diversity indicators, but also higher competitiveness in solving MaOPs. [ABSTRACT FROM AUTHOR]

Multi-objective optimization problems with interval parameter (IMOPs) are among the most critical optimization problems in practical applications. However, in contrast to deterministic multi-objective optimization, few studies have addressed IMOPs. Moreover, the uncertainty in such problems makes the convergence and diversity of the algorithm more challenging. Therefore, this paper proposes an interval multi-objective optimization algorithm based on elite genetic strategy (EG-IMOEA). First, existing interval dominance relations cannot comprehensively determine which of the two intervals is better when their midpoints are equal but their upper and lower limits are unequal. Therefore, a conditional-based interval confidence dominance relation is proposed that considers both the average level of convergence and value of the minimum lower limit of intervals. The interval crowding distance (ICD) applied to multiple objectives is then defined to evaluate the solutions more completely. Furthermore, an elite genetic strategy for crossover and mutation is proposed to generate better offspring. The proposed algorithm was evaluated on nine benchmark test problems and compared with the typical algorithm as well as state-of-the-art algorithms. The results showed that this algorithm outperformed the comparison algorithms in terms of convergence, diversity, imprecision, and uniform distribution. [ABSTRACT FROM AUTHOR]