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The differential evolution (DE) algorithm is widely regarded as one of the most influential evolutionary algorithms for addressing complex optimization problems. However, the fixed mutation strategy limits the adaptive ability of DE, and the lack of utilization of historical information limits the optimization ability of DE. In this paper, an indicator-based self-learning differential evolution algorithm (ISDE) is proposed. A jump out mechanism based on deep reinforcement learning is adopted to control the mutation intensity of the population. The neural network in the jump out mechanism is designed as a decision maker. The mutation intensity of the population is controlled by the neural network, and the neural network are trained by a double deep Q network algorithm based on the continuous data generated during the evolution process. A population range indicator (PRI) is utilized to describe individual differences in the population. A diversity maintenance mechanism is designed to maintain individual differences according to the value of PRI. The experimental results reveal that the comprehensive performance of ISDE is superior to comparison algorithms on CEC 2017 real-parameter numerical optimization. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) and Estimation of distribution algorithm (EDA) exhibit complementary superiority in solving complex continuous optimization and engineering problems. The design of appropriate strategies coordinated with the two algorithms to balance exploration and exploitation is conducive to obtaining high-precision solutions. A knowledge-driven co-evolutionary algorithm assisted by a cross-regional interactive learning mechanism (KCACIL) is proposed to achieve a comprehensive collaboration between the algorithms, diverse strategies, and cross-regional individuals. Various elite-guided mutation strategies and a self-feedback strategy based on successful experience in light of implicit knowledge are devoted to fulfilling self-learning and cross-regional interactive learning to accomplish individual collaboration and knowledge transfer in the three regions. Reinforcement learning based on ε − g r e e d y and simulated annealing is employed as feedback on the cross-regional individual information to promote the collaboration between opposition-based learning, interaction learning mechanism, and the revised strategy of inferior solutions with small Q values and high distance density. The dynamic self-adaptive adjustment strategies of multiple parameters are adopted to balance diversity and convergence. KCACIL is verified on the CEC 2014, 2017, 2020 benchmark test suites, and engineering applications. Experimental results indicate KCACIL is superior to the state-of-the-art comparison algorithms. • A knowledge-driven comprehensive co-evolutionary algorithm is proposed. • Cross-regional interactive learning with adaptive parameters is introduced. • A collaboration of strategies guided by reinforcement learning is implemented. • The learning mechanisms based on intra-regional implicit knowledge are designed. • Two improvement strategies of solutions specific to the phenomenon are employed. [ABSTRACT FROM AUTHOR]