In this study, we propose an innovative dimension-based multi-strategy adaptive differential evolution algorithm, termed DMDE, by leveraging the dimensional information and search state of population to determine the offspring among various candidate solutions and dynamically adjust the population reduction module, respectively. First, to avoid the estimation bias caused by Euclidean distance in the process of selecting offspring in the composite search strategies, a new dimension-based pre-selection method is designed. Herein, the neighbor information of candidate solution based on each dimension is taken into account, and the median of their fitness values is leveraged to decide the offspring for target individual due to its strong tolerance for outliers. Meanwhile, a state-based adaptive population adjustment mechanism is further developed to dynamically regulate the algorithm’s search capability. In this mechanism, we record the fitness improvements of superior and inferior individuals to gauge the difficulty of optimization process, and we employ two distinct population reduction modules tailored to different optimization scenarios. Through these approaches, the proposed algorithm can more accurately identify suitable candidate solution as offspring and achieve a better trade-off between exploration and exploitation. Finally, the performance of DMDE is validated by benchmarking it against 21 renowned or up-to-date methods on CEC’2017 test suite within different dimensions and applying to two distinct practical application scenarios. Numerical outcomes reveal that the new algorithm exhibits significantly superior performance compared to its counterparts.
Surrogate-assisted constrained multi-objective evolutionary algorithms (SACMOEAs) have demonstrated favorable applications in real-world scenarios, whereas most existing SACMOEAs are confined to the combination or collaboration ways between the surrogate models and multi-objective evolutionary algorithms, neglecting the improvement on the internal architecture of surrogate models as well as the adaptive refinement of mutation parameters within the evolutionary framework. Therefore, this paper proposes an attention-enhanced RBF-assisted constrained multi-objective optimization algorithms, where the improvement value-driven adaptive global and local search framework (IVAGLS) is designed. Specifically, drawing inspiration from the construction mechanism of polar coordinate system, the attention information (reflected by angle value) between individuals and the Euclidean distance information are simultaneously used to construct the corresponding basis functions, thereby enhancing the adaptability of the RBF model to the complex landscapes. Moreover, the global and local search phases are sequentially conducted where the improvement values of the aggregate tchebycheff function in the two phases are employed to adaptively adjust the mutation parameters. Subsequently, for selecting best candidate, the constraint violation and TE values are alternately compared to determine the best individual. For obtaining the exact offspring, two different acquisition functions are designed in a periodical mechanism to determine excellent individuals with diverse potential. Therefore, the IVAGLS achieves the adaptive adjustment for parameters and selection mechanisms within the sequential global and local evolution framework, thus the adaptability to complex problems can be enhanced greatly. Systematical experimental results on two benchmark test suites demonstrate that the IVAGLS is competitive in solving expensive multi-objective constrained optimization problems.
In recent years, deep learning-based electric load forecasting models have been widely applied, but most existing approaches rely on single deep learning, where both neural architecture and hyper-parameters are typically designed through manual trial-and-error processes. Furthermore, these methods often focus exclusively on forecasting accuracy while neglecting model complexity considerations during the design process. To address these limitations, this paper proposes an innovative automated deep learning-based load forecasting method, i.e., multi-objective variable-length particle swarm optimization (MOVLPSO)-based convolutional neural network-bidirectional long short-term memory (CNN-BiLSTM), abbreviated as MOVLPSO-CNN-BiLSTM. The framework utilizes CNN-BiLSTM as its foundational predictor, effectively combining CNN’s feature extraction capabilities with BiLSTM’s temporal sequence processing strengths. Firstly, the automated design issue of the neural architecture and hyper-parameters for CNN-BiLSTM-based forecasting model is formulated as a multi-objective optimization problem by considering both minimizing the forecasting error, i.e., mean squared error, and the model complexity, i.e., the number of model parameters (NoMPs). Then, we develop a tailored hybrid variable-length encoding strategy to represent the neural architecture and hyper-parameters of CNN-BiLSTM and the adaptive particle updating mechanism to efficiently evolve the Pareto front in MOVLPSO framework. The experimental results on 12 real-world load datasets obtained from the Australian Energy Market Operator demonstrate that the proposed MOVLPSO-CNN-BiLSTM achieves superior forecasting performance and enhanced model lightweightness compared with one state-of-the-art handcrafted deep neural networks-based and four automated deep learning-based load forecasting approaches in terms of root mean square error, mean absolute error, mean absolute percentage error, and NoMPs.
Data-driven evolutionary algorithms (DDEAs) have gained increasing attention over the past decade for their effectiveness in solving expensive optimization problems. However, most research has focused on small-scale problems, while large-scale expensive optimization problems (LSEOPs) remain underexplored due to the challenges posed by the high-dimensional search space—commonly referred to as the “curse of dimensionality.” Although cooperative co-evolution (CC) offers a promising way to mitigate this issue, many of its advanced grouping strategies require frequent real fitness evaluations, rendering them unsuitable for DDEAs. To overcome this limitation, we propose a hierarchical teaching-cooperative data-driven evolutionary algorithm, termed HTC-DDEA. Firstly, a distribution-aware grouping strategy is designed to partition the decision space into multiple subspaces with different levels of population diversity. Then, a dual-stage search mechanism is developed to dynamically adjust the diversity and convergence of each subpopulation according to the grouping scheme, thereby maintaining a proper balance between exploration and exploitation throughout the optimization process, and a novel surrogate modeling framework is introduced to enable a smooth transition from local search to global search. Experiments on up to 1000-dimensional problems and the comparisons with state-of-the-art DDEAs validate the effectiveness of HTC-DDEA.
This paper examines the effectiveness and impact of different discretization methods used to transform continuous solution representations into integer values when addressing discrete optimization problems with originally continuous algorithms. Ten discretization methods from the literature are adapted and evaluated across five flow shop scheduling problems encompassing diverse objective functions, namely makespan, flowtime, idle and waiting times, total quadratic completion time, and completion time variance, thus covering just-in-time, non-regular, and trade-off performance criteria. Particle Swarm Optimization is employed as the common metaheuristic framework for implementing and comparing these discretization strategies. The computational results are assessed using analysis of variance (ANOVA), Tukey’s statistical test, and performance profiles. The findings indicate that while discretization methods such as Largest Order Value, Mapping Method, Random-Key, and Great Value Priority achieve superior performance depending on the objective function, the Backward Transformation method consistently underperforms. This study provides an updated comparative evaluation of discretization methods in flow shop scheduling contexts and offers practical insights for selecting effective discretization strategies when applying continuous metaheuristics to discrete optimization problems.
Assuming the Mobility as a Service (MaaS) paradigm, this paper addresses a sustainable multimodal user routing problem by jointly minimizing total travel time and CO2 emissions in large-scale public transport networks. We propose the enhanced Dijkstra-assisted Non-dominated Sorting Genetic Algorithm II (eD50N-II) method, an evolutionary multiobjective approach that uses the Dijkstra’s (DJ) shortest path algorithm to generate an informed seeding strategy with tailored crossover and mutation operators. The method operates on real-world multimodal multigraphs, supports flexible integer-based solution representations and considers realistic public transport schedules, transfer times, walking connections, and physical effort constraints. An extensive experimental evaluation is conducted on two large metropolitan case studies, Oporto and Lisbon, which are here made publicly available for the first time. Results show that eD50N-II consistently outperforms other evolutionary approaches, including the DJ Seeded NSGA-II (D2N-II, the baseline algorithm), eN-II (an improved NSGA-II variant) and Haq* (an adaptation of a state-of-the-art method), in terms of hypervolume, number of Pareto-optimal solutions, and feasibility with respect to walking distance constraints. As for simpler DJ configurations, such as the weighted D50 variant, they require less computation and may be suitable for time-critical applications where solution quality is less critical. Nevertheless, eD50N-II obtains a richer set of Pareto-optimal solutions under a reasonable computational effort, resulting in the most effective option when high-quality and practically meaningful (human effort-friendly) routes are required. The results also confirm the scalability and robustness of the proposed method across different urban contexts, reinforcing its suitability for real-world MaaS decision support systems.
When solving constrained multi-objective optimization problems (CMOPs), traditional methods often utilize a holistic constraint violation, which obscures the unique effect of individual constraints. Recently, methods based on constraint decomposition or prioritization have been proposed to consider constraints individually. However, those methods typically rely on pre-defined evaluation rules, which lack the ability to dynamically exploit the effect of an independent constraint for enhancing the exploration of the constrained Pareto front (CPF). To address this limitation, a Dynamically Competitive Constraint Handling algorithm (DCCHT) is proposed for Constrained Multi-objective Optimization. Specifically, DCCHT decomposes a CMOP with K constraints into K+1 distinct optimization pools, where one optimization pool considers all constraints and another K optimization pools respectively involve each constraint among the overall K constraints. The information exchange among distinct optimization pools is facilitated by a proposed bidirectional knowledge transfer strategy, which shares valuable landscape information and accelerates the overall convergence to the global feasible region. The ongoing progress of each optimization pool is dynamically controlled based on the competitiveness of the constraint. Computational resources are adaptively allocated to the optimization pool by a feedback-driven resource allocation method. More computational resources will be allocated to the optimization pool in which the considered constraint is more competitive with the exploration of the true CPF. Extensive experiments on three benchmark suites and various real-world engineering problems demonstrate the significantly better performance of DCCHT against some state-of-the-art algorithms.
Cloud computing has become a fundamental platform for data-intensive applications, but efficient task scheduling remains challenging because of workload variability, resource heterogeneity, and the need to balance multiple conflicting objectives. This study presents an Adaptive Enhanced Particle Swarm Optimization (AEPSO) model for a cloud task scheduling problem involving makespan, execution cost, load imbalance, and energy consumption. In the proposed framework, these objectives are handled through weighted, normalized scalarization, which reduces them to a single scalar fitness value. To improve convergence stability and scheduling quality, the model integrates stagnation-aware inertia control, time-varying schedules for the cognitive and social coefficients, velocity clamping, elitist preservation, and repair-based refinement. The method is evaluated in the CloudSim environment using Bitbrains-based workload traces for independent cloudlet scheduling and is compared with baseline algorithms, including PSO, PSO-Boost, MrLBA-ACO, and GA, over selected workload levels. The results indicate that AEPSO provides the most favorable overall trade-off among the methods compared, with clear gains in makespan and strong performance on load imbalance and energy consumption, while maintaining competitive execution-cost performance. Additional analysis through repeated-run statistics, significance testing, weight sensitivity analysis, and ablation study further supports the effectiveness of the proposed integrated scheduling framework under the considered simulation setting.
Cuckoo Search (CS) has demonstrated competitive performance in single- and multi-objective optimization. However, for many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs), the proliferation of dominance-resistant solutions severely weakens Pareto dominance-based selection pressure, hindering simultaneous convergence and diversity. To address this, a collaborative many-objective CS framework based on a new α-dominance mechanism, termed Nα-CMaOCS, is proposed. First, a collaborative co-evolution strategy is embedded into the CS search mechanism via a candidate-sharing pool covering the entire exploration–exploitation process. Specifically, the global update incorporates a Cauchy operator and a convergence-aware weighting factor to enhance exploration while guiding convergence. Conversely, the local update employs a convex-combination factor and a differential-vector strategy to improve exploitation precision on irregular PFs. Furthermore, a modified operator evolution mode adjusts the behavior of both global and local operators to improve robustness. Second, the proposed Nα-dominance mechanism adaptively expands or contracts the dominance region to reinforce selection pressure, and its theoretical validity is rigorously established via three lemmas and three theorems, which substantiate the strict monotonicity property, hierarchical implication theorems, and asymptotic convergence guarantee. A two-stage environmental selection strategy combining local–global principles is also developed, utilizing perpendicular Euclidean distance for subspace prioritization to mitigate overcrowding. Additionally, a fitness-based evaluation criterion preserves high-quality individuals. Extensive experiments on 15 irregular-PF benchmarks and four engineering problems, using eight state-of-the-art MaO algorithms, demonstrate that Nα-CMaOCS achieves superior convergence and robustness, indicating strong competitiveness for complex MaOPs.
In this paper, a novel particle swarm optimizer (PSO) is proposed based on a designed failure-aware searching (FAS) framework. Named FAS-PSO, the proposed algorithm seeks to learn potential valuable information from those non-improved evolutionary experiences rather than directly discarding them. Considering the topological status of population, each particle is equipped with a structural probe to assess local regions, which integrates information from different individuals and enhances the communication among population. Next, in case of a probing location with better fitness, the swarm will be updated accordingly. Otherwise, by measuring the deterioration extent of the probe as compared to the initial particle, an information reinvestigation mechanism is adopted to generate a positional modification for swarm update, including continuous forward search and escape in the opposite direction. Extensive experiments demonstrate the performance of FAS-PSO is superior to that of other state-of-the-art swarm intelligence-based algorithms. Moreover, the proposed FAS-PSO is further extended to a multi-objective version and is successfully applied to accomplish the reliable and robust parameter estimation of a Wendling neural mass model, showing considerable engineering practicality in solving the complicated biomedical model inversion task.
In evolutionary multitask optimization, search-direction-based knowledge transfer has attracted increasing attention because it can exploit directional information generated during evolution to promote cross-task collaboration. Although such methods can effectively use search information generated during evolution, existing designs still have limitations in transfer triggering, direction reliability, and coordinate alignment. Therefore, directional information from other tasks may be imposed on target individuals that are not yet suitable to receive it, and the received information may be ineffective for these individuals. To address the above problems, this paper proposes a topology-aware direction-adaptive multitask evolutionary algorithm (TADA-MTEA). First, an adaptive local aggregation assessment mechanism is developed to screen target individuals suitable for receiving cross-task information. It uses the shared-nearest-neighbor measure to quantify neighborhood compactness and dynamically adjusts the compactness criterion according to the cross-task transfer success rate, thereby determining whether each target individual is suitable for receiving cross-task information. Second, an evolutionary direction fusion and alignment mechanism is constructed to transform directional information from other tasks into reliable transfer directions adapted to the target individual. According to the reliability of the incoming directional information, it adaptively fuses the gradient-guided direction with the local best-guided differential vector, and then maps the fused direction to the target local coordinate system using the rotation estimated by orthogonal Procrustes analysis. Finally, experimental results on benchmark suites and real-world cases show that TADA-MTEA achieves competitive and robust performance across different multitask scenarios.
Beamforming design in simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided communications exhibits the characteristics of structured–topological mixed-variable optimization (STMVO), involving bounded, discrete, and periodic variables with structured coupling constraints. A theoretical analysis of these structural properties reveals that existing Euclidean-update-based evolutionary baselines may be insufficient when these structural and topological properties are not explicitly considered. From a system-level perspective, these challenges arise from mismatches between optimization dynamics and variable structure, rather than from specific algorithms. Motivated by these insights, we propose ST-EF, a unified evolutionary framework for STMVO. ST-EF introduces three major innovations: (i) a unified representation that embeds heterogeneous variables into a normalized space while preserving topology-specific adjacency; (ii) topology-aware repair operators that respect boundary and periodic conditions, ensuring unbiased geometric consistency; and (iii) topology-aligned deviation mapping with margin correction that maintains balanced sampling over discrete variables and structured coupling constraints, thereby preventing premature collapse. Extensive experiments on STAR-RIS beamforming tasks demonstrate that ST-EF achieves improved robustness and competitive runtime scalability over representative baselines, highlighting its potential as a principled paradigm for solving structured mixed-variable problems.
Many-objective optimization is hard because improving several competing objectives at once slows convergence and erodes the spread of the non-dominated set. This work introduces SNN-RET, a spiking-neural framework that couples membrane-state neural adaptation, reference-guided environmental selection, and a turbulence-based recovery mechanism. Unlike methods that adapt only at the operator level, its spiking layer directly drives candidate generation and is reinforced by Pareto survival and diversity contribution, steering the search toward promising regions while preserving a well-distributed Pareto front. SNN-RET is compared with six baselines, including the reference-vector method RVEA, over 31 runs on DTLZ, WFG, ZCAT, and the constrained MW suite, with all indicators computed on an equal-size output set. It gives the strongest overall profile at two and three objectives, leading on hypervolume and non-dominated count; on many-objective problems it is mid-pack at 5000 evaluations but reaches the best median hypervolume on several instances as the budget grows. Overall, SNN-RET raises the average hypervolume by 17.65% and the number of non-dominated solutions by 33.48%, while reducing GD, IGD, spacing, and additive epsilon, and a non-parametric analysis ranks it best on five of six indicators. These results show SNN-RET is a robust framework for multi- and many-objective optimization, combining spiking-neural adaptation, reference-based selection, and diversity recovery in one unified search process.
Cross-docking has become a widely adopted logistics strategy for improving distribution efficiency by reducing inventory requirements and accelerating freight transshipment across supply chains. However, efficient terminal operations require reliable coordination of inbound and outbound truck activities under tightly synchronized and time-sensitive operating conditions, making the development of efficient service schedules highly challenging in practice. This study investigates the truck scheduling problem at a mixed-mode cross-docking facility. A mixed-integer linear programming model aimed at reducing total operational costs is adopted. To effectively solve this computationally complex problem, a Hybridized Thompson Sampling Hyperheuristic (HTSH) algorithm is developed, which integrates a population-based evolutionary framework with a Thompson Sampling-based adaptive control mechanism that dynamically learns and selects search operators according to observed search performance. A mixed repair-penalization infeasibility handling strategy is incorporated to efficiently manage inbound-outbound coordination constraints. Moreover, a hybrid fitness evaluation mechanism combining fast approximate assessment with exact optimization evaluation is applied for efficient exploration together with accurate solution refinement. A set of extensive computational experiments demonstrates that HTSH consistently produces high-quality scheduling solutions comparable with exact optimization on small instances and substantially outperforms a set of classical and more recent metaheuristics across a wide range of problem instances. The HTSH algorithm is able to achieve improvement margins of up to approximately 24% while maintaining an average runtime of 186.71 s. The experimental results demonstrate that the proposed HTSH framework provides an effective and scalable solution approach for cross-docking truck scheduling, contributing to improved operational efficiency and service reliability in distribution terminal operations.
