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.
In Evolutionary Reinforcement Learning (ERL), critic-based surrogate models have become a widely adopted solution for reducing population evaluation cost. However, existing methods commonly employ critics trained for single-policy value estimation to evaluate heterogeneous policy populations, overlooking the objective mismatch between single-policy value approximation and population-level evaluation. Meanwhile, existing evolutionary operators mainly focus on improving offspring quality, while explicit consideration of offspring behavioral diversity in ERL operator design remains limited. To address these challenges, we propose a Surrogate-Assisted Phenotypic Evolutionary Reinforcement Learning (SAP-ERL) algorithm. First, we propose a specialized critic-ensemble surrogate model tailored for population-level evaluation and provide a theoretical analysis showing its potential to improve policy ranking reliability. Second, we propose a dynamic H-step surrogate-based fitness evaluation strategy to improve the reliability and efficiency of population evaluation while reducing interaction cost. Finally, we propose a phenotype-guided crossover operator to explicitly promote offspring behavioral diversity during evolution. Extensive experiments on six MuJoCo tasks and three maze tasks demonstrate that SAP-ERL achieves superior overall performance compared with representative RL and ERL baselines.
In transfer optimization of expensive multi-objective optimization (ExMO), effectively reusing structural knowledge from Pareto-optimal solutions of source tasks is crucial for improving sample efficiency. This work proposes Expensive Transfer Evolutionary Multi-Objective Optimizer with Diffusion (ExTrEMO-D), a generative transfer framework that models the Pareto-set distribution p(x) in the decision space. Compared with forward transfer based on supervised surrogate modeling, ExTrEMO-D captures cross-task similarity in the Pareto-set geometric structure, which provides more informative guidance for optimization. Meanwhile, ExTrEMO-D mitigates the model collapse issue in inverse transfer, which can arise from one-to-many mappings introduced by non-Pareto-optimal samples, by avoiding explicit pairing between preference vectors and solutions. ExTrEMO-D realizes diffusion transfer via two-stage training and targetguided sampling. In terms of the two-stage training process, (i) the optimal transport aligns source non-dominated solutions to the target domain, and (ii) diffusion learns a geometry-consistent prior from the aligned samples. Then, target-guided sampling injects gradients from target multi-objective surrogates into the denoising dynamics, steering generation towards the target Pareto front. Extensive experiments on synthetic benchmarks and three real-world applications spanning materials science, robotics, and machine learning demonstrate that ExTrEMO-D consistently outperforms state-of-the-art baselines and achieves improved sample efficiency in ExMO.
A Feature Selection (FS) problem aims to identify an optimal subset of features such that the identified features can be used to expedite machine learning models’ training and enable the resulting models to achieve their optimal performance. Evolutionary computation methods have been proven to be effective in solving the problem due to their powerful search capability. Yet they face two thorny issues when handling high-dimensional data: 1) high-dimensional individual representation and 2) slow search efficiency. To address them, we propose a new learning-assisted FS method based on the Fireworks Algorithm, which is termed Evolutionary Feature Selection with Age-reinforced Reduction and Expansion (EFSARE). Regarding the first issue, we propose and utilize a novel individual encoding strategy where each individual in the population represents a feature, and the entire population represents all features. This strategy can effectively reduce the search space from multiple dimensions to a single one, thereby boosting EFSARE’s search efficiency. For the second issue, we propose a reduction-and-expansion strategy to adjust the number of individuals in the population, and use reinforcement learning to adaptively select reduction or expansion. We then propose an age-driven strategy to guide the reduction or expansion strategy to remove or add individuals according to their age. EFSARE speeds up its search efficiency by following a proper search direction and reducing the search range. Comprehensive experiments on 22 high-dimensional public datasets and 2 gene engineering ones are conducted for EFSARE and its 16 recently proposed peers. The results demonstrate that EFSARE achieves state-of-the-art performance in terms of average classification accuracy, number of selected features, and computational time.
Evolutionary multi-objective optimization (EMO) has demonstrated strong capability for balancing conflicting criteria such as accuracy, diversity and novelty in recommender systems (RSs). However, most existing EMO-based RSs adopt a two-stage learning–then–optimization paradigm, in which representation learning and EMO are executed sequentially and independently. In other words, the later optimization stage is constrained by the established prediction scores from the former learning stage, leading to a performance bottleneck in multi-objective recommendation. To address this limitation, we propose a learning–optimization interactive framework (LOIF) that enables a closed-loop feedback interaction between representation learning and EMO. At the core of LOIF, we design an adaptive Pareto-feedback interaction (APFI) strategy to determine when and how information is exchanged between learning and optimization. Learning-state signals, including loss stagnation and embedding stability, determine when prediction results are passed from learning to optimization. The resulting Pareto-optimal solutions determine how information from EMO is fed back into learning via probabilistic sampling. Building upon APFI, we further propose a semantic-enhanced initialization (SEI) strategy to improve representation quality during the learning stage. We also propose a fast search competitive optimization (FSCO) strategy to accelerate Pareto front convergence during the optimization stage, enabling efficient multi-objective search under frequent learning–optimization interactions. Extensive experiments on real-world datasets demonstrate that LOIF consistently outper-forms traditional two-stage frameworks in accuracy–diversity trade-offs and achieves faster Pareto convergence.
De novo therapeutic design is a complex multi-objective optimization problem over an enormous chemical space. Traditional virtual screening methods and deep generative models are constrained by predefined molecular libraries, unstable reinforcement learning fine-tuning, and weak controllability over multiple pharmacological objectives. Evolutionary algorithms (EAs) offer robust population-based search but often rely on heuristic, rule-based mutation operators that confine exploration to known scaffolds and lead to premature convergence. We introduce FragEvo, a novel language-model-guided evolutionary framework that deeply integrates a fragment-based molecular language model (FragMLM) with multi-objective optimization through NSGA-II. Its core innovation lies in embedding a pretrained FragMLM directly into the genetic variation process, where the model's contextual priors are used to parameterize the mutation and crossover distributions. This transforms genetic operators from static, rule-driven mechanisms into probabilistic, language-informed generators capable of producing chemically valid and semantically novel offspring. An adaptive feedback loop further aligns the semantic likelihood of generated molecules with evolving fitness signals, enabling a dynamic balance between exploration and exploitation. Across multiple molecular optimization benchmarks, FragEvo achieves stronger docking performance and Pareto-front quality while maintaining competitive scaffold diversity and favorable drug-likeness/syntheticaccessibility profiles, supporting a language-model-guided evolutionary computation paradigm for in silico molecular design.
Two-Stage Stochastic Programming (TSSP) has been widely used to model decision-making under uncertainty. However, when solved using evolutionary algorithms, its efficiency is often hindered by the heavy computational burden associated with Monte Carlo-based recourse cost estimation. This challenge is particularly prominent in Last-Mile Manufacturing with Mobile Microfactories (L4M), where varying first-stage microfactory locations induce a continuous family of structurally related recourse problems involving order allocation and sequencing. To address this challenge, we introduce a parametric multi-task optimization (PMTO) perspective and develop an L4M-oriented PMTO-TSSP framework. Specifically, the framework incorporates a parametric multitask genetic programming approach to learn an adaptive recourse solver that generalizes across the continuous task space induced by different first-stage configurations. In addition, we develop a parametric multitask surrogate that treats first-stage decisions as task parameters and rapidly approximates the expected recourse costs produced by the learned recourse solver, thereby substantially reducing the evaluation overhead during the first-stage search. We instantiate and evaluate the proposed framework for the emerging L4M paradigm in the Singapore–Johor region. Extensive experiments on 20 static and 20 dynamic test scenarios demonstrate that PMTO-TSSP provides a favorable trade-off between solution quality and computational efficiency in the static settings, while achieving strong overall performance in the dynamic settings.
Transfer-based adversarial attacks exploit surrogate models to generate perturbations that can fool unseen target models without any target queries. Existing methods formulate this attack as a constrained single-objective optimization problem. However, in the non-convex adversarial loss landscape, conventional single-objective optimizers are susceptible to local optima and gradient masking, making it difficult to balance visual imperceptibility and cross-model attack transferability. In this paper, we propose a multi-objective coevolutionary algorithm with multi-scale gradient smoothing (CoMGS). Specifically, the proposed CoMGS formulates transferable adversarial example generation as a bi-objective optimization problem and uses two coevolutionary sub-populations, namely the attack population and the shrinking population. Within this coevolutionary framework, the attack population integrates heterogeneous multi-scale gradient estimation operators with variable-radius neighborhood smoothing to alleviate gradient masking and reduce the risk of convergence to deceptive local optima. To complement this exploration-oriented search, the shrinking population adopts an analytical gradient descent operator to deterministically shrink perturbations, thereby improving population diversity. Experimental results demonstrate that CoMGS mitigates the dimensional bottleneck of conventional multi-objective evolutionary algorithms and achieves higher black-box attack success rate (ASR) than the baseline methods in most evaluated settings. On the Caltech-UCSD Birds dataset with ResNeXt50_32x4d as the surrogate model, CoMGS improves the overall average ASR by 9.1% over the strongest single-objective baseline.
In evolutionary robotics, applying uniform variation operators across all individuals can disrupt well-adapted morphologies while providing insufficient exploration for low-fitness solutions, especially acute in dynamic, biologically structured environments. Inspired by the biological phenomenon of fitness-dependent hypermutation, we propose a Hierarchical Operator Selection mechanism integrated with Age-Fitness Pareto Optimization (HOS-AFPO) for the co-evolution of nanorobot morphology and control within biological gradient field (BGF). HOS partitions the population into three fitness strata and assigns distinct variation strategies: an LLM-guided conservative mutation for elite individuals to preserve valuable adaptations; random exploration for the middle layer to maintain diversity; and a PPO-driven hypermutation engine for low-fitness individuals to aggressively escape local optima. The framework is evaluated under a COMSOL-derived tumor microenvironment model on locomotion and tumor-targeting tasks. Experimental results demonstrate that HOS-AFPO delivers superior best-fitness performance over representative operator-selection baselines, together with competitive hypervolume and compact, task-adaptive morphologies. Ablation studies support the synergistic contributions of hierarchical stratification, LLM-based elite protection, and PPO-based adaptive hypermutation, validating the framework’s effectiveness for embodied intelligence in complex dynamic environments.
Memetic Genetic Programming (MGP) has shown to be more effective than standard GP in addressing large search spaces by adding local search. However, existing local search procedures in MGP algorithms have three distinct limitations: imbalanced exploration and exploitation, inefficient neighbour generation, and insufficient redundancy handling. This article proposes a two-stage Semantic-Guided MGP (SMGP) to address these limitations and evolve effective scheduling rules. Specifically, three key novel elements are introduced to the existing local search processes of MGP. The first is a Semantic-Guided Neighbourhood Operator maintains behavioural diversity to balance exploration with exploitation. The second is a Knowledge-Guided Subtree Mutation that uses learned semantic structures from the initial stage to construct new neighbours, replacing inefficient random neighbour generation and focusing the search on promising regions. The third is an Iterative Semantic Equivalent Pruning procedure that simplifies the best-found solution into a smaller, equivalent rule to improve its interpretability and generality. Extensive experiments on a real-world online Yard Crane scheduling problem show that SMGP outperforms advanced MGP methods in both effectiveness and efficiency while maintaining rule simplicity. Moreover, the best SMGP-evolved rule significantly outperforms all manually crafted rules.
Dynamic Constrained Multi-Objective Optimization Problems (DCMOPs) are widely encountered in real-world engineering applications, where both objective functions and constraints change over time, significantly increasing the complexity of problem-solving. Existing approaches still face limitations in historical information utilization, prediction accuracy of feasible solutions, and maintenance of population diversity—particularly in environment involving rapid and drastic shifts in feasible regions. In response to these challenges, this paper proposes a Transformer-Based Spatiotemporal Perception Framework (TSPF). By exploiting the Transformer’s strength in long-sequence modeling, the framework learns temporal and spatial dependencies from historical population to forecast future feasible and high-value regions. Furthermore, a memory-restart mechanism based on environmental similarity and a clustering-guided selection strategy are introduced to enhance the stability and diversity of the population. Experimental results on 18 benchmark problems with varying severities and frequencies of change and a real-world case study indicate that the proposed method achieves superior performance compared to several state-of-the-art algorithms, demonstrating its effectiveness and robustness in solving complex dynamic optimization problems.
The dispatch optimization of Coal Mine Integrated Energy Systems (CMIES) is critical for energy efficiency and decarbonization in the mining industry, yet it poses challenges due to large-scale decision variables, strong multiple constraints, and a narrow feasible region. Existing constrained multi-objective evolutionary algorithms (CMOEAs) often fail to rapidly locate feasible solutions and suffer from slow convergence, making them impractical for real-time CMIES dispatch. To overcome these limitations, this paper proposes a Search Direction Learningbased Evolutionary Optimization (SDLEO) algorithm that prioritizes feasibility and convergence acceleration. A dual-direction learning mechanism via principal component analysis is proposed to guide the population toward high-quality Pareto regions, while tributary directions derived from constraint violation rankings steer the search directly into the union of feasible regions. An adaptive variable importance strategy selectively activates decision variables based on their sensitivity to objectives and constraints, further enhancing search efficiency. Three realistic dispatch optimization models for CMIES under typical scenarios are developed to faithfully characterize the complex constraints and trade-offs. Experimental results on benchmark problems and real-world CMIES cases demonstrate that SDLEO significantly outperforms 11 state-of-the-art CMOEAs, providing efficient solutions for large-scale constrained dispatch in CMIES.
The growing energy footprint of computational intelligence systems calls for approaches that are both efficient and scalable. Neuromorphic Computing (NC) addresses this challenge by allowing event-driven algorithms to operate with minimal power consumption through biologically inspired spiking dynamics. We present the NeurOptimiser, a fully spike-based optimisation framework that materialises the NC-based Metaheuristic (MH) paradigm via a decentralised system. This approach comprises a population of Neuromorphic Heuristic Units, each combining dynamic and spiking perturbation heuristics to asynchronously evolve candidate solutions. The NeurOptimiser’s coordination arises via spike-driven communication and best-so-far reduction over shared channels, which admits both centralised and distributed realisations on neuromorphic backends. We implement this framework on Intel’s Lava platform, targeting the Loihi 2 chip, and evaluate it on the noiseless BBOB suite up to 40D. We deploy several NeurOptimiser configurations, chiefly considering dynamic systems such as the Linear and Izhikevich models for neural dynamics, as well as fixed and Differential Evolution mutation operators for spike-triggered heuristics. These instantiations serve as concrete demonstrations of the framework rather than as exhaustive enhancements to optimisers. The primary contribution is the framework itself, together with the formal foundations, implementation, and empirical validation that establish its feasibility. Results show structured population dynamics and consistent best-so-far improvements, along with upper bounds on Loihi-class power derived from per-operation energy costs.
Networked cloud manufacturing requires coordinated scheduling of production and communication resources. However, operation assignment and network transmission are often modeled as weakly coupled decisions, making cyberphysical interactions difficult to capture. This paper investigates a networked dual-resource cloud manufacturing scheduling problem (N-DRCSP), where operation sequencing, processing node selection, machine and worker allocation, and transmission under network constraints are jointly optimized. A multiobjective mixed-integer linear programming model is formulated under a hierarchical hybrid control architecture to minimize total weighted tardiness and network load risk. To solve this large and strongly coupled problem, a bi-population heterogeneous graph attention network assisted non-dominated sorting genetic algorithm II, termed BP-HAN-NSGAII, is developed. Heterogeneous graph attention encodes operation-machine relations determined by worker availability, and the associated network states, while the bi-population mechanism balances exploitation and exploration. An online reverse teaching strategy further refines the learned search policy through Pareto guided policy distillation. Experiments on benchmark instances of different scales show that BP-HAN-NSGAII obtains better hypervolume and inverted generational distance values than the compared algorithms. Ablation studies, Pareto front comparisons, and statistical tests indicate that the heterogeneous representation, bipopulation cooperation, and reverse teaching mechanism improve convergence and diversity in complex networked dual-resource scheduling.
Evolutionary expensive optimization aims to solve optimization problems with expensive fitness evaluations, where data-driven evolutionary algorithms (DDEAs) learn fitness knowledge from evaluated data for constructing surrogates to approximate the fitness landscape and aid evolutionary search. However, different evolutionary stages may need different fitness knowledge for constructing a suitable surrogate, making it difficult for existing DDEAs to provide consistently accurate fitness approximation. Therefore, how to automatically learn the most suitable fitness knowledge for different search states remains a key challenge in DDEAs. To address this, this article proposes a mixture of experts (MoE) learning-based DDEA, termed MoE-DDEA. Different from existing DDEAs, the MoE-DDEA automatically learns the most suitable fitness knowledge across different search regions and evolutionary stages to guide optimization, along with three novel designs. First, a MoE-based learning framework is proposed, which builds expert models that learn different fitness knowledge and a gating model for expert activation. Second, an activation strategy is proposed to activate suitable expert models via the gating model for constructing surrogates, thereby leveraging the relevant fitness knowledge within the activated expert models across different evolutionary stages. Third, a knowledge-based initialization strategy is proposed to leverage prior knowledge from evaluated data to alleviate the cold-start problem and enhance search efficiency. The efficiency of the MoE-DDEA is validated not only on popular test suites but also on a practical application of the evaluation expert assignment problem for project evaluation. These suggest that MoE-DDEA is a promising and competitive learning approach for challenging expensive optimization.
In dynamic constrained multi-objective optimization problems (DCMOPs), both the constraints and objectives vary over time, potentially leading to changes in the constrained Pareto-optimal front. Feasibility prediction in the search region is crucial for responding to environmental changes, as it allows the algorithms to adopt the most appropriate response strategy based on shifts in feasibility. To this end, a dynamic constrained evolutionary algorithm with multi-tribe feasibility prediction based knowledge transfer (DCEA-MFPKT) is proposed to solve DCMOPs. In DCEA-MFPKT, a tribal region knee points-based classification strategy is first introduced. This strategy classifies the objective space into feasible and infeasible tribal regions based on the tribal region knee points. Then, a feasibility prediction strategy is proposed to capture the temporal behavior of the feasibility of tribal regions, where a long short term memory model is trained on sequences of historical data. Therefore, the feasibility of each tribal region can be predicted in the new environment. Based on the predicted feasibility status, a multi-tribe hybrid knowledge transfer strategy is proposed to select appropriate knowledge transfer operators adaptively for each tribal region to leverage historical solution archives. This helps construct a high-quality and environment-aware initial population in the new environment. Experimental results on a set of benchmarks and the operational optimization of the fluid catalytic cracking demonstrate the superiority of the proposed method over five state-of-the-art dynamic constrained multi-objective optimization methods.
With the development of unmanned surface vehicle (USV) and amphibious USV (AUSV) technologies, the corresponding coordination and scheduling problems are receiving increasing attention. However, the existing studies predominantly focus on the scheduling of USVs, with limited attention to the AUSV scheduling problems. This work considers the multi-objective AUSV scheduling problems with obstacle avoidance. The objectives are to minimize the maximum completion time and total energy consumption, simultaneously. First, two mathematical models are established to describe the concerned problems. Second, an improved A* algorithm is employed for avoiding obstacles. Third, four well-known meta-heuristics (artificial bee colony, genetic algorithm, particle swarm optimization, and Jaya algorithm) are employed and improved to solve the AUSV scheduling problems. Three K-means strategies are constructed to boost the quality of initial solutions. Seven problem-feature-based local search operators are designed to enhance the search efficiency of meta-heuristics. Then, a deep Q-network with problem-specific state representations and objective-based reward functions is designed to intelligently recommend suitable local search operators during iterations, thereby accelerating convergence. Finally, two mathematical models are solved by the Gurobi solver. The effectiveness of the improved strategies and the competitiveness of proposed algorithms are rigorously evaluated across 21 instances with different scales. Among all the compared algorithms, the enhanced Jaya algorithm with deep Q-network demonstrates the best overall performance.
The flexible job shop scheduling problem (FJSP) traditionally emphasizes machine flexibility, while worker heterogeneity is often simplified or neglected. In practical manufacturing systems, worker skill levels affect both processing efficiency and task feasibility, leading to the skilled-worker constrained flexible job shop scheduling problem (SWC-FJSP). This article investigates the SWC-FJSP with multi-level worker skills and skill-dependent processing efficiency, aiming to minimize the makespan. A mixed-integer linear programming model is first formulated to characterize the coupled operation–machine–worker assignment decisions. Then, a branching deep Q-network enhanced memetic algorithm, termed MABDQN, is developed as a learning-assisted evolutionary framework. MABDQN integrates an adaptive hybrid initialization strategy to generate high-quality and diverse populations, a BDQN-driven operator orchestration mechanism to select operator category and execution intensity according to the evolving search state, and a multi-stage adaptive restart strategy guided by a stage adaptive reward function to alleviate premature convergence. Extensive experiments on a newly constructed test set with different instance scales show that MABDQN outperforms several state-of-the-art algorithms in solution quality and robustness. Ablation studies further verify the contribution of the main components and demonstrate the effectiveness of state conditioned operator orchestration for complex SWC-FJSP instances.
Reconfigurable robots can dynamically adapt their footprint, enabling efficient traversal of narrow passages and more productive coverage in open spaces. Such adaptability is crucial for complete coverage path planning (CCPP), where both spatial constraints and energy efficiency must be addressed simultaneously. This paper presents an energy-aware CCPP framework for footprint-adaptive reconfigurable robots based on an extended n-state Glasius Bio-inspired Neural Network, denoted EGBNN(n). The proposed method combines biological neural dynamics with an energy-aware fitness-based decision mechanism to evaluate candidate motion and morphology transitions during online planning. An energy-aware cost function, embedded directly into the neural decision process, jointly models the robot’s transformation, translation, and rotational actions, allowing the robot to selectively compress in constrained regions and expand to maximize coverage efficiency. Extending from the classical population-based evolutionary algorithms, the proposed framework performs sequential online selection over candidate neighboring cell–morphology pairs using a fitness-like objective that balances spatial desirability and energy cost. Simulation studies and real-world experiments with a reconfigurable robot demonstrate that EGBNN(n) consistently reduces energy consumption compared to state-of-the-art methods, achieving up to a 31.1% reduction while maintaining complete coverage.
Current methods that use large language models to evolve heuristics for combinatorial optimization converge toward a single best algorithm or a small set of trade-off solutions. When the problem distribution shifts, these methods require expensive re-adaptation and their performance degrades. Here, we propose a quality-diversity evolutionary framework that maintains a structured archive of diverse heuristics, where each is specialized for a particular class of problem instances. A large language model serves as the variation operator within the evolutionary loop. Shapley additive explanations on abstract syntax tree features play a dual role in this framework: they guide the mutation prompts toward productive code modifications, and they extract the behavioral descriptors that organize the archive. An online selector then retrieves the best-matched heuristic for each new unseen instance. We evaluate the approach on vehicle routing, traveling salesman, and job shop scheduling problems under static, perturbed, stochastic, and dynamic conditions. The archive coverage provides inherent robustness to distributional shift, whereas single-heuristic baselines and neural solvers degrade considerably. The resulting heuristic library is interpretable, since each archive cell contains readable code at known feature coordinates.
