Transformer-Based Intelligent Prediction Model for Multimodal Multi-Objective Optimization

Traditional multimodal multi-objective evolutionary algorithms (MMOEAs) usually adopt the reproduction strategy based on meta-heuristic and fail to make full use of changes of multi-generation population distribution, which can help the population to further evolve and improve the exploitation ability of algorithms. To address this issue, this paper proposes a deep learning-based evolutionary algorithm (DLEA), which converts historical population information into time series and uses deep neural networks to predict the population distribution. Specifically, a transformer-based prediction model is constructed to reproduce promising offspring by capturing changes of population distribution in adjacent generations. Moreover, many MMOEAs focus only on global Pareto optimal solution sets (PSs) and ignore local PSs. Although local PSs are inferior to global PSs in terms of objective values, the cost of obtaining global PSs in some practical applications is huge. Local PSs with similar objectives to global PSs are acceptable alternatives for decision makers. Therefore, a difference-based attention mechanism is designed for archive update, which saves solutions on the global PSs and local PSs by calculating the attention value. Experimental studies indicate that DLEA outperforms other six competitive MMOEAs.