Robust multiobjective evolutionary algorithms (RMOEAs) aim to obtain robust optimal solutions. However, traditional RMOEAs typically require evaluating a large number of sampling points, which is often impractical in real-world applications due to the high computational cost. In this article, we propose a robust multiobjective evolutionary algorithm based on surrogate-assisted (RMOEA-SA), which incorporates a radial basis function (RBF) surrogate model and a novel robust distance metric (RDM). The proposed algorithm employs the RBF surrogate model to approximate the fitness values of sampling points, thereby significantly reducing the number of function evaluations during the robust optimization process. Furthermore, an RDM assisted by the RBF surrogate model is introduced to measure the robustness of solutions. Besides, the RDM value of each solution is treated as an additional objective, expanding the original objective space, and selection is conducted in this augmented space to achieve a desirable trade-off between robustness and optimality. The experimental results on standard benchmark functions and two real-world application problems demonstrate the superior feasibility and effectiveness of the proposed method compared with several existing algorithms.

This study proposes a Neural-Assisted Combinatorial Optimizer with Adaptive Neighborhood Search (NANS) to address the challenges faced by unmanned delivery vehicles (UDV) in urban logistics, including dynamic demand fluctuations, road safety factors, and capacity constraints. Building on the traditional Capacitated Vehicle Routing Problem (CVRP) model, a mathematical model incorporating safety coefficients and constraints was developed, referred to as CVRP with Safety-Based Routing Preference (CVRP-SRP). To solve this complex constraint problem, NANS combines deep learning with heuristic algorithms. Specifically, a Light Encoder and Heavy Decoder (LEHD) deep learning model is integrated with an Adaptive Large Neighborhood Search (ALNS) algorithm. Using the Random Re-Construct (RRC) mechanism, the LEHD model generates multiple high-quality initial solutions. Building on these initial solutions, the ALNS algorithm applies various destroy-repair operators with an adaptive selection mechanism and incorporates a simulated annealing strategy to explore the solution space and perform local optimization. Experimental results demonstrate that NANS outperforms other algorithms in terms of both solution quality and computational efficiency. This study provides valuable insights into the efficient, safe, and flexible scheduling of UDV in urban logistics.

When solving multimodal multi-objective optimization problems (MMOPs), it is important to maintain the diversity in the decision space. Since traditional Pareto-dominance-based multimodal multi-objective evolutionary algorithms (MMEAs) prioritize the convergence of individuals through Pareto dominated sorting, several well-distributed individuals might be dominated by other well-converged individuals during the optimization process of MMOPs. In order to solve this problem, we propose a coevolutionary algorithm that extracts and utilizes the features of multiple populations to preserve diversity. The proposed algorithm simultaneously explores different regions of the decision space through multi-population coevolution and controls the cross-learning behavior among sub-populations. The cross-learning is conducted through a feature weight vector which maintain the characteristics of multiple populations and preserve the diversity of the decision space. Meanwhile, the assignment and merging methods are designed to adaptively adjust the scales of sub-populations to speed up the convergence. The experimental results show that the introduction of the feature weight vector is effective in maintaining the distribution of the decision space, and the proposed algorithm is competitive with other representative MMEAs.