A dynamic evolution of graph structure-based algorithm for multi-modal multi-objective optimization - Yan, Pengguo; Tian, Ye; Liu, Yu (Swarm and evolutionary computation, 2025)
In the field of multi-modal multi-objective optimization problems (MMOPs), the challenge lies in simultaneously identifying multiple Pareto-optimal solution sets within the decision space and accurately locating the Pareto front in the objective space. Therefore, it is particularly important to develop a method that can effectively represent and utilize the complex relationships and dependencies between variables. Considering that graph structures have unique advantages in capturing complex relationships and dependencies, it is necessary to explore graph-theoretic methods to solve the problem. Inspired by this, a dynamic evolution of graph structure-based algorithm is proposed in this paper. Specifically, a historical data-driven graph generation strategy is proposed to construct the initial population as graph-structured data. Then, the node2vec strategy is applied to perform random walks based on the weights on the edges, avoiding repeating the same mistakes in the search process, to enable more rapid and effective population evolution on the graph. Furthermore, a dynamic modal-labeling mechanism based on an adaptive density-based spatial clustering of applications with noise of the graph structure is proposed to prevent the mixing of information from different modalities while enabling the timely detection and optimization of initially unrecognized modalities. Moreover, a dynamic link node prediction mechanism is proposed to update the graph structure, enabling the network to adapt to changes in the data. Experiments on 28 MMOPs and the multiline distance minimization problem demonstrate that the proposed algorithm performs better than seven state-of-the-art representatives, including 22 MMOPs in CEC2020 and 6 MMMOPs.