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Many-objective optimization problems (MaOPs) are challenging tasks involving optimizing many conflicting objectives simultaneously. Decomposition-based many-objective evolutionary algorithms have effectively maintained a balance between convergence and diversity in recent years. However, these algorithms face challenges in accurately approximating the complex geometric structure of irregular Pareto fronts (PFs). In this paper, an information entropy-driven evolutionary algorithm based on reinforcement learning (RL-RVEA) for many-objective optimization with irregular Pareto fronts is proposed. The proposed algorithm leverages reinforcement learning to guide the evolution process by interacting with the environment to learn the shape and features of PF, which adaptively adjusts the distribution of reference vectors to cover the PFs structure effectively. Moreover, an information entropy-driven adaptive scalarization approach is designed in this paper to reflect the diversity of nondominated solutions, which facilitates the algorithm to balance multiple competing objectives adaptively and select solutions efficiently while maintaining individual diversity. To verify the effectiveness of the proposed algorithm, the RL-RVEA compared with seven state-of-the-art algorithms on the DTLZ, MaF, and WFG test suites and four real-world MaOPs. The results of the experiments demonstrate that the suggested algorithm provides a novel and practical method for addressing MaOPs with irregular PFs. • A novel RL-RVEA addresses many-objective optimization with irregular pareto fronts. • A reinforcement learning-based adaptive reference vector to guide the direction of convergence. • A scalarization approach preserves the diversity of solutions for next generation. • The RL-RVEA outperforms seven advanced many-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow problem, called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution operator in a single algorithmic framework. Additionally, an adaptive method is proposed to update the number of solutions evolved by each DE operator based on both the diversity of the population and the quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%. • Development of an adaptive method (AM) for optimizing diversity and solution quality. • Innovative constraint handling approach, progressively adding constraints for improved performance. • Incorporation of intermittent renewable energy models for realistic problem solving. • Extensive validation on IEEE 30-bus and IEEE 118-bus networks, outperforming state-of-the-art algorithms in cost, loss, and environmental impact reduction. [ABSTRACT FROM AUTHOR]

This paper introduces a novel surrogate-assisted multi-objective nutcracker optimization algorithm. This algorithm is built upon the recently proposed nutcracker optimization algorithm, drawing inspiration from the behaviours observed in Clark's nutcrackers. The algorithm is developed based on two distinct behaviours exhibited by these birds. To comprehensively evaluate the performance of the proposed algorithm, a dual-pronged approach is adopted. On the one hand, a set of artificial test problems is employed to scrutinize the algorithm's capabilities, while on the other hand, a set of real-world problems is considered to assess its practical efficacy. The results of the proposed algorithm are evaluated in comparison to existing baseline algorithms and state-of-the-art algorithms, using well-recognized performance metrics, both qualitatively and quantitatively. The obtained results provide convincing evidence of the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Combinatorial optimization problems (COPs) play an important role in both industrial production and theoretical research. As a classical class of optimization algorithms, evolutionary algorithms have shown good performance in COPs. However, as the size of the problem increases, it becomes difficult for evolutionary algorithms to produce satisfactory solutions within the specified time. In recent years, neural network algorithms have been applied to solve COPs and have shown superior effects. Inspired by this, this paper proposes a new algorithm based on graph structure for solving COPs. Through relaxation, COPs are transformed into their corresponding continuous optimization problems. The output state of our algorithm is converted to a discrete solution by approximation method. Compared with previous algorithms, our algorithm can not only solve COPs with general form such as binary quadratic programming (BQP), but also solve COPs with special form, which greatly expands the application scope of neural network algorithms. In addition, our algorithm can be embedded into other problem frameworks such as solving multi-objective combinatorial optimization problem (MOCOP) through scalarization method. A new penalty function is added to the objective function, which enables our algorithm to overcome the inconsistency between the optimal solution of the original problem and the corresponding continuous problem, so that our algorithm can perform well on various problems. Several numerical simulations are used to illustrate the effectiveness of our algorithm in solving COPs. Experimental results show that our algorithm can effectively solve COPs with general form and has a shorter solving time compared to traditional evolutionary algorithms. [ABSTRACT FROM AUTHOR]