Decomposition-based evolutionary algorithm with dual adjustments for many-objective optimization problems?

Balancing the convergence and diversity of solutions is a pivotal task for many-objective optimization problems (MaOPs). The decomposition-based evolutionary algorithm has demonstrated great potential in solving MaOPs in the past years. However, its performance degrades when MaOPs have complex Pareto fronts (PFs). Inspired by its pros and cons, this paper proposes a decomposition-based evolutionary algorithm adopting dual adjustments to address MaOPs with irregular PFs. First, an MaOP is divided into a set of subproblems by the distance between weight vectors. Each subproblem selects an appropriate solution from its region, using the specified scalarizing function. Then, the first adjustment updates all the scalarizing functions for each weight vector, where a strategy integrating history information is used to promote the accuracy of the adjustment. Sequentially, the second adjustment updates weight vectors based on the population distribution, which simulates and modifies the value function of reinforcement learning to intensify the rationality of updates. Note that the excitation frequencies of two adjustments are adaptive. Additionally, we design fine-tuning introducing reminding solutions to enhance exploitation. Finally, numerous experiments demonstrate that the proposed algorithm performs better or is equivalent to five state-of-the-art algorithms on 150 test instances and one practical problem .