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Dual-space co-evolution with temporal information learning for multi-modal multi-objective optimization
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DOI：10.1016/j.swevo.2026.102475.png)
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Abstract
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Traditional multi-modal multi-objective evolutionary algorithms (MMEAs) generally do not fully exploit the dynamic changes of population distributions across generations to enhance algorithmic exploitation ability. Therefore, this paper proposes dual-space co-evolution with temporal information learning for multi-modal multi-objective optimization evolutionary algorithm (Ds-TILEA). Ds-TILEA proposes a temporal information learning framework that transforms historical population information into time series and utilizes a deep neural network to forecast population distributions. Unlike conventional time-series-assisted evolutionary methods that mainly use historical information to predict external environments, scalar indicators, or auxiliary search states, Ds-TILEA treats generation-indexed population distributions as endogenous multivariate temporal data and directly uses the predicted decision-space positions for offspring generation. Specifically, the predictive model is developed to capture the evolutionary patterns of adjacent generations’ population distributions, thereby facilitating the generation of potentially high-quality offspring. Furthermore, achieving a balance between diversity and convergence of Pareto sets is a critical challenge in multi-modal multi-objective optimization problems (MMOPs). Accordingly, this study designs a dual-space updating strategy, where in the diversity archive incorporates dual crowding-distance calculations in both decision and objective spaces to improve solution diversity while maintaining convergence. To validate the performance of Ds-TILEA, experiments comparing it with six competing algorithms are conducted on two standard benchmark suites. Furthermore, seven algorithms were applied to a feature selection task aimed at minimizing dataset dimensionality and classification error rate. The experimental results demonstrate that Ds-TILEA exhibits superior performance in both convergence and diversity. Specifically, among the 12 IDMP test problems, Ds-TILEA achieved 6, 4, and 8 best optimal values in IGD, IGDX, and HV, respectively, with statistical significance confirmed by the Wilcoxon rank-sum test. Ds-TILEA demonstrates significant advantages in MMOPs, especially in efficiently balancing diversity and convergence by integration of temporal information to generate offspring.
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