Particle swarm optimization (PSO) is a type of swarm intelligence algorithm that is frequently used to resolve specific global optimization problems due to its rapid convergence and ease of operation. However, PSO still has certain deficiencies, such as a poor trade-off between exploration and exploitation and premature convergence. Hence, this paper proposes a dual-stage hybrid learning particle swarm optimization (DHLPSO). In the algorithm, the iterative process is partitioned into two stages. The learning strategy used at each stage emphasizes exploration and exploitation, respectively. In the first stage, to increase population variety, a Manhattan distance based learning strategy is proposed. In this strategy, each particle chooses the furthest Manhattan distance particle and a better particle for learning. In the second stage, an excellent example learning strategy is adopted to perform local optimization operations on the population, in which each particle learns from the global optimal particle and a better particle. Utilizing the Gaussian mutation strategy, the algorithm’s searchability in particular multimodal functions is significantly enhanced. On benchmark functions from CEC 2013, DHLPSO is evaluated alongside other PSO variants already in existence. The comparison results clearly demonstrate that, compared to other cutting-edge PSO variations, DHLPSO implements highly competitive performance in handling global optimization problems.

The Differential Evolution (DE) algorithm, which is an efficient optimization algorithm, has been used to solve various optimization problems. In this paper, adaptive dimensional learning with a tolerance framework for DE is proposed. The population is divided into an elite subpopulation, an ordinary subpopulation, and an inferior subpopulation according to the fitness values. The ordinary and elite subpopulations are used to maintain the current evolution state and to guide the evolution direction of the population, respectively. The inferior subpopulation learns from the elite subpopulation through the dimensional learning strategy. If the global optimum is not improved in a specified number of iterations, a tolerance mechanism is applied. Under the tolerance mechanism, the inferior and elite subpopulations implement the restart strategy and the reverse dimensional learning strategy, respectively. In addition, the individual status and algorithm status are used to adaptively adjust the control parameters. To evaluate the performance of the proposed algorithm, six state-of-the-art DE algorithm variants are compared on the benchmark functions. The results of the simulation show that the proposed algorithm outperforms other variant algorithms regarding function convergence rate and solution accuracy.