Many real-world multi-objective optimization problems contain binary-encoding and large-scale decision variables but sparse Pareto solutions, posing stiff challenges to evolutionary algorithms. With the rapid developments and broad applications of deep neural networks (DNNs), DNN-based decision space reduction has attracted increasing attention in this area. Nevertheless, the computational overhead of DNNs is a lasting challenge, and existing methods struggle to learn sparse binary representations as their continuous activations and gradient-based updates may inherently mismatch. Differently, as the third generation of artificial neural networks, spiking neural networks (SNNs) offer a more natural and efficient framework for representing sparse binary data owing to their spike-triggered event-driven working mechanism. This paper presents a first attempt to introduce spike-driven sparse binary representation learning into sparse large-scale multi-objective optimization problems (SLMOPs). Specifically, a lightweight SNN with leaky integrate-and-fire neurons is developed for evolutionary online solution modeling in solving SLMOPs. In the training process, we integrate Hebbian learning to learn the patterns of non-zero variables as local plasticity, and Kullback-Leibler divergence loss to learn the distribution of obtained Pareto solutions as global plasticity. Moreover, an adaptive firing threshold mechanism is proposed to improve the versatility across problems with different sparsities and avoid parameter tuning. Experimental results demonstrate the advantage of our methods over algorithms tailored for SLMOPs on benchmark and 20 real-world problems from different areas in terms of both effectiveness and efficiency, especially on real-world problems with unknown characteristics and sparsities.
Automated algorithm configuration is an emerging area in evolutionary algorithms (EAs), where reinforcement learning (RL) has been increasingly adopted. However, most existing RL-assisted EAs still rely on simple handcrafted statistical information to construct states, which is often problem-dependent and may fail to capture complex search dynamics. To address this issue, this paper proposes a multi-agent self-supervised state representation framework with auxiliary guidance for providing agent-specific states to policy networks in RL-assisted EAs. Specifically, population observations collected online during the early stage of evolution are used to train a state encoder equipped with a multi-head readout. The encoder learns shared population tokens from these observations, while the multi-head readout derives agent-specific states, and both components are trained by integrating contrastive self-supervision with auxiliary guidance. Once trained, the encoder and readout are deployed to generate states from current population observations for downstream policy learning. The proposed framework is instantiated in four representative RL-assisted EA testbeds and evaluated across different optimization scenarios. Comparisons with three state representation methods show that MASSR generally provides more effective states for policy learning, while ablation and transfer studies further demonstrate the effectiveness and flexibility of the proposed framework.
The Dynamic Flexible Job Shop Scheduling Problem (DFJSSP) is challenging due to its combinatorial complexity and continuously changing production environments. In such settings, Reinforcement Learning (RL)-based methods for online scheduling have shown strong adaptability by training agent to dynamically select dispatching rules (DRs) from a predefined DR set. However, commonly used manually designed DRs limit their optimisation potential. Recent works have applied Genetic Programming Hyper-Heuristic (GPHH) to automatically generate DRs for RL-based methods to form the action set, but such hybrid frameworks often suffer from heterogeneous decision-making, where routing and sequencing decisions are handled by separately trained agents with weak coordination, and do not fully leverage the evolved DRs. To address these issues, this study presents a Dual Delayed routing enhanced Niching Genetic Programming assisted Deep Reinforcement Learning (D2NGPDRL) approach. By introducing dual routing delay strategies, D2NGPDRL first proposes a unified single-agent-based online scheduling framework that enables the joint execution of routing and sequencing decisions, thereby avoiding the coordination deficiencies inherent in conventional dual-agent architectures. Then, D2NGPDRL effectively exploits both evolved routing and sequencing rules as the DR set of the agent, thereby strengthening the synergy between evolutionary DR discovery and learning-based decision-making. Experimental results show that D2NGPDRL outperforms related existing dynamic scheduling methods across diverse dynamic scenarios and demonstrates greater behavioural diversity in the evolved DRs, indicating enhanced adaptability and robustness in dynamic environments.
Large-scale expensive optimization problems (LSEOPs) present a formidable challenge characterized by high-dimensional search spaces constrained by strictly limited evaluation budgets. Although surrogate-assisted evolutionary algorithms (SAEAs) have been widely adopted to mitigate evaluation costs, they often grapple with the prohibitive computational overhead of model training and the deterioration of surrogate accuracy as dimensionality increases. To address these limitations, this work proposes a Fractional-Order Block-Coordinate Evolution Strategy (FOBES) for LSEOPs, which departs from the conventional paradigm of fitness prediction. Instead of relying on complex surrogate models, the proposed method uses fractional-order gradient memory to extract and accumulate directional information from historical evaluations. This estimated ideal direction guides a novel directional consistency pre-screening mechanism, enabling efficient identification of promising candidate solutions within a block-coordinate descent framework. Furthermore, a dynamic random grouping strategy and an adaptive data-driven sampling technique are dynamically integrated to facilitate a smooth transition from exploration to exploitation. Experimental results on the CEC’2013 benchmark suite and the extended CEC’2010 suite with up to 5000 dimensions demonstrate that FOBES significantly outperforms state-of-the-art algorithms in terms of both solution quality and computational efficiency.
High-quality offline data with real evaluations is essential for training surrogate models in offline data-driven optimization. Most existing algorithms focus on enhancing training dataset quality by randomly selecting samples from the offline data and/or generating synthetic data. However, these approaches often fail to adequately account for the training data distribution, leading to suboptimal surrogate modeling for the optimization problem at hand. To address this issue, this paper proposes a data refinement method based on offline data distribution that combines subset selection with offline resampling, thereby ensuring consistency in promising regions between those revealed by the offline data and those of the surrogate model. Specifically, a subset selection process is employed to select high-quality data for alleviating the inconsistency, where a multi-layer perceptron is utilized to determine the selection proportion based on the distributional information of the offline data. Theoretical analysis demonstrates that the selected data promotes regional consistency by providing a tighter upper bound on the approximation error in promising regions. Furthermore, an offline resampling strategy is suggested to enhance such consistency by adding new data with real evaluations in promising regions, which are identified by each sample and its surrounding neighbors in the offline data. Experimental results on the benchmark problems and an airfoil shape optimization problem demonstrate the effectiveness and superiority of the proposed method.
