Data-efficient image classification is critical in computer vision with applications across various domains. Although deep convolutional neural networks are successful for image classification, they often require large datasets and high computational resources, which are unsuitable for data-efficient classification tasks. Genetic programming (GP), on the other hand, offers an interpretable, flexible, and efficient alternative to learning features for image classification, particularly when dealing with insufficient training instances. Many multi-objective GP methods control model bloat by limiting tree size or reducing the number of features, but they rarely include objectives specifically aimed at improving generalization. As a result, the evolved models can still overfit the training data. To address these challenges, we propose an improved decomposition-based multi-objective genetic programming (IDMOGP) approach to feature learning in data-efficient image classification. IDMOGP maximizes the classification accuracy with a regularization term and simultaneously minimizes the number of learned features. To reduce overfitting in data-efficient image classification, a novel regularization method is proposed based on Rademacher complexity to improve generalization. In addition, an adaptive global replacement strategy is designed to balance convergence and diversity during evolution. IDMOGP provides a set of trade-off solutions to data-efficient image classification. Experimental results on five different datasets show that IDMOGP achieves superior hypervolume compared to traditional dominance-based multi-objective GP, and higher classification accuracy than non-GP methods. Further analysis demonstrates the effectiveness of the introduced strategies and shows the good interpretability of the IDMOGP approach.

New Zealand's aquaculture industry is experiencing significant growth, driven by its carbon efficiency and the lack of spatial constraints on land. Green-lipped mussels, a key farmed species, are grown on long lines supported by buoyant plastic floats. Managing tens of thousands of these floats is an operational challenge for mussel farmers. Accordingly, applying multi-object detection to farm imagery is a promising way to improve crop monitoring and productivity. This paper presents a Genetic Programming (GP)-based method for multi-object detection in mussel farms, designed to address site-specific challenges such as a high density of targets, high levels of partial occlusion, and substantial variation in apparent object size due to camera distance. The proposed method integrates image preprocessing techniques for object localisation and GP techniques for classification. In terms of detection performance, the proposed method surpasses YOLOv12 by achieving an F1 score of 95.2% compared with 88.6%. Although execution speed and bounding box precision could be further improved, the method demonstrates robustness, effectiveness, and practical applicability in mussel farms.

Skin cancer is one of the most prevalent malignant tumours worldwide, and its incidence has continued to climb in recent years. Traditional feature extraction methods often struggle with the high variability and complex patterns in skin cancer images, necessitating more adaptive and automated approaches. This study proposes a genetic programming (GP)-based method with flexible region detection operators (GPFRD) for automatically and flexibly learning discriminative features for various classification tasks of skin cancer images. The proposed GPFRD method integrates preprocessing, region detection, feature extraction, and feature concatenation into a cohesive framework, significantly enhancing flexibility. The newly designed operators precisely localize diagnostically critical regions based on lesion masks while suppressing irrelevant background interference. These operators enable the proposed method to evolve effective feature extraction solutions based on the characteristics of different image datasets. Experimental results on five datasets of varying difficulties demonstrate that the proposed method outperforms the benchmark GP-based method and four traditional feature extraction methods in the majority of cases.

The multi-objective Traveling Salesman Problem (TSP) extends the classical TSP by simultaneously optimizing multiple conflicting objectives, such as minimizing travel cost and maximizing route diversity. While existing multi-objective TSP algorithms focus on convergence and diversity in the objective space, they often overlook the multimodal nature of the problem-where structurally distinct tours may map to similar objective values. This gap leads to the loss of high-quality solutions that could offer decision-makers valuable alternatives. Therefore, it is essential to study traveling salesman problems with multimodal and multi-objective characteristics. To address this gap, this paper conducts an in-depth study of the Traveling Salesman Problem with multimodal and multi-objective characteristics (MMTSP) and proposes an algorithm called MMTSP_DS. This algorithm combines the Spearman distance with a diversity measurement criterion based on shared edges in the decision space, allowing for a more accurate assessment of the similarity between different tour solutions. Additionally, the algorithm incorporates the concept of a special crowding distance into the environmental selection process to ensure that the population maintains diversity in both the decision space and the objective space in a balanced manner. Finally, a series of experiments are conducted to systematically compare the proposed MMTSP_DS algorithm with state-of-the-art algorithms designed for multimodal multi-objective TSP. The experimental results verify that MMTSP_DS significantly improves population diversity and optimization performance, demonstrating its considerable advantages.

Molecular property prediction plays a critical role in drug discovery and materials science. However, existing graph neural network approaches often overlook the three-dimensional geometric information that fundamentally determines molecular behavior. To address this, this paper proposes a geometry-aware pretraining network for molecular representation learning. The model incorporates a geometry-aware attention mechanism to capture spatial relationships between atoms and employs multi-scale distance masking to model interactions across different spatial ranges. The architecture is augmented with a global node positioned at the molecular centroid that aggregates global information and facilitates graph-level predictions. The model is pretrained on approximately 250000 molecules from the ZINC dataset. Experiments on three molecular property prediction benchmarks demonstrate the effectiveness of the proposed method, with the full model achieving AUC-ROC scores of 0.7336 on BBBP, 0.8269 on BACE, and 0.6485 on SIDER. These results represent consistent improvements over baselines, including gains of up to 7.17% on the SIDER dataset, validating the benefits of incorporating geometric awareness into molecular representation learning.

Short-Term load forecasting (STLF) is essential for the secure operation and effective planning of power systems. Accurate load forecasting not only ensures system reliability but also supports economic dispatch, optimal resource allocation, and risk management. However, due to the highly nonlinear and volatile nature of load patterns, as well as the influence of various external factors such as weather conditions, holidays, and human activities, single-step forecasting is often insufficient to meet practical requirements, making multi-step STLF particularly important for operational decision-making and planning. To address this challenge, this paper proposes a multi-population genetic programming (MPGP) approach to multi-step STLF. This approach evolves prediction models through multiple independent populations, with each population specifically trained and optimized for a fixed forecasting time step, thereby generating accurate predictions corresponding to each time step. Experimental results on real-world datasets demonstrate that the proposed approach can effectively capture complex load variation patterns, adapt to nonlinear dynamics, and maintain high accuracy across multiple steps, confirming the feasibility, robustness, and reliability of MPGP for multi-step STLF in power systems.

In practical scenarios, there may be solutions in the decision space with close objective values but located far apart, a characteristic known as multimodal multiobjective problems (MMOPs). While most multimodal multiobjective evolutionary algorithms (MMEAs) focus on finding global Pareto optimal solution sets (PSs) and local PSs demonstrating satisfactory convergence performance, decision-makers in real-world scenarios are often also interested in local PSs that exhibit strong robustness. In this study, we propose several benchmark functions in which the global and local PSs have varying levels of robustness. Then, we introduce an innovative dual-population evolutionary algorithm, termed GLR-MMEA, designed to simultaneously find both global PSs and local PSs with strong robustness. In GLR-MMEA, the convergence population focuses on identifying global PSs, providing convergence information to the diversity population. Meanwhile, the diversity population manages the detection of both global PSs and local PSs with strong robustness. In the process of updating the diversity population, a robustness indicator is proposed to access the robustness of solutions. Furthermore, a selection mechanism founded on this robustness indicator is applied to identify local PSs with high robustness. The experimental results show that GLR-MMEA performs competitively against other leading MMEAs in working on the selected benchmark functions.

Multi-point dynamic aggregation (MPDA) is a prominent multi-robot task allocation problem with numerous real-world applications. Genetic programming (GP) has been employed to automatically evolve effective reactive coordination strategies (RCSs) for dynamic MPDA in order to make real-time decisions in the dynamic environment. However, existing methods have not fully explored the potential of GP in generating effective RCSs due to the use of simple search operators. In this paper, we propose a GP method with a new offspring selection method to enhance the diversity and convergence of the population, thereby improving the solution to the MPDA problem. Specifically, the number of offspring is increased by brood recombination, and then the offspring are divided into two subpopulations, where different selection strategies are developed. A niching selection strategy is proposed to reduce the complexity and to improve the diversity of the individuals. A K-nearest neighbor surrogate selection strategy is designed to improve the effectiveness. A self-adaptive scheme is designed to adjust the number of individuals selected from each subpopulation. The experimental results on various dynamic MPDA test sets show that the newly proposed algorithm significantly outperforms the traditional GP method and manually designed heuristics.

Medical image classification is challenging due to limited labeled instances, high inter-class similarity, and imbalanced class distributions. Although genetic programming (GP) has demonstrated strong potential in general image classification, its application to medical image classification remains underexplored. To address this research gap, this paper proposes a Multi-Objective Genetic Programming with Ensemble Construction (MOGPEC) algorithm for medical image classification. First, a new GP representation is designed to align with typical medical image processing workflows, enabling the evolved solutions to be more consistent with clinical reasoning. A multi-objective optimization framework is then introduced to encourage the generation of diverse solutions across different classes, creating a rich pool of candidate models for subsequent ensemble construction. Finally, an ensemble construction strategy is developed to select and combine complementary GP solutions, thereby enhancing the overall classification performance. Extensive evaluations on multiple medical image datasets demonstrate that MOGPEC outperforms traditional methods, representative GP methods, and deep-learning-based methods in most cases. Ablation experiments in the Supplementary Material further analyze the contributions of the proposed GP representation, multi-objective optimization, and ensemble construction strategy. Visualization of the evolved solutions provides valuable interpretability.

Engineering optimization problems are often nonlinear, high-dimensional, and constrained, making them challenging for conventional optimization techniques. Although L-SHADE, an adaptive differential evolution (DE) algorithm with success-history based parameter adaptation, has demonstrated competitive performance, it still suffer from limited population diversity and weak local exploitation, leading to an imbalance between exploration and exploitation in complex optimization. To address these limitations, this paper proposes LCO-LSHADE-GSRL, a novel DE variant that enhances both global exploration and local exploitation capabilities. The proposed algorithm integrates three key components: (1) a Logistic Chaos Orthogonal Initialization mechanism that improves initial population diversity and ensures uniform coverage of the search space. (2) a GAN-driven Specular Reflection Learning (SRL) mechanism that effectively escapes from local optima. (3) a design that adapts effectively to constrained optimization scenarios. Comprehensive experiments conducted on the CEC 2019 and 2022 benchmark suites demonstrate that LCO-LSHADE-GSRL exhibits superior convergence performance, solution accuracy, and robustness compared to L-SHADE, LSHADE-cnEpSin, and WOA, GJO, PO, PIMO, and CDO. Furthermore, in three real-world engineering problems-speed reducer, step-cone pulley, and hydrostatic thrust bearing, which reduces system weight and power loss while satisfying all design constraints. These results demonstrate its potential for solving complex engineering optimization tasks with high reliability and efficiency.

Accurate short-term load forecasting (STLF) is critical for optimizing energy scheduling and ensuring grid stability, particularly in increasingly complex and volatile operational conditions. Existing methods often face challenges in interpretability, feature engineering and generalization. Traditional models lack transparency and fail to uncover the underlying drivers of load variation, while complex nonlinear models rely on numerous parameters, increasing overfitting risk and limiting practical applicability. To address these challenges, this paper presents a hybrid framework, LR-GPSR, which integrates linear regression (LR) with genetic programming-based symbolic regression (GPSR). This method first employs LR to generate initial load predictions and compute residuals, then applies GP to model these residuals, effectively capturing nonlinear patterns. In this study, LR-GPSR extends the basic arithmetic operators (addition, subtraction, and multiplication) used in SGP-1 by incorporating a logarithmic function, addressing the limited expressive capacity of the original set and providing sufficient representation for modeling residuals. Experimental results on multiple real-world datasets show that the logarithmic function improves the quality of individuals generated during population initialization, enhancing the overall initial population. Comparative experiments further demonstrate that LR-GPSR outperforms traditional methods under high-load conditions with pronounced nonlinear characteristics, validating its effectiveness and robustness, and highlighting its potential to improve STLF reliability and support intelligent grid management.

Fine-grained image classification (FGIC) remains a challenging task due to subtle inter-class differences and significant intra-class variations, particularly under limited training data. While genetic programming (GP) offers promising adaptability, the performance of existing GP-based methods is limited due to the reliance on traditional image descriptors for feature extraction/learning. To address this limitation, this paper proposes CNNGP, i.e., a novel multi-tree GP approach that utilizes the rich representations of pre-trained convolutional neural networks (CNNs) for FGIC. In CNNGP’s multi-tree representation, two trees are used to explore multi-level feature maps from pre-trained CNNs to generate saliency masks that highlight informative regions, and one tree is used to integrate them to construct higher-level and more powerful features for classification. Experiments on four commonly used FGIC datasets demonstrate that CNNGP can achieve superior (or at least competitive) performance to popular deep neural network methods and the recent GP-based method. Further analysis verifies the benefit of using dual saliency trees and visualizes how CNNGP captures complementary visual patterns that enhance feature learning. It also examines convolutional layer selection to reveal dataset-specific feature usage, demonstrating CNNGP’s adaptive feature learning capability.

The graph neural networks (GNNs) have been successfully applied to non-Euclidean graph data mining tasks, attracting widespread attention. At present, to achieve promising performance, many researchers use neural architecture search (NAS) on GNNs to enhance applicability and accuracy without requiring significant manual intervention or rich domain knowledge. However, most existing graph NAS (GNAS) algorithms struggle with high-dimensional data and often overlook the characteristics and distribution of different solutions within the search space, which may result in local optima and underutilization of the search potential. This article proposes Ensemble-GNAS, a novel framework that integrates evolutionary GNAS with ensemble learning to address these limitations. Within this framework, we develop two key strategies: an evolutionary GNAS method based on a niche strategy to enhance local search capability and the diversify candidate networks and an ensemble fusion strategy based on a tree-structured Parzen estimator (TPE) to optimize the weights of candidate networks in an ensemble model. The proposed approach is evaluated on: 1) node classification datasets, including citation networks for paper classification and cancer-specific gene interaction networks for driver gene identification and 2) link prediction and graph classification datasets. The experimental results indicate that the proposed approach outperforms the state-of-the-art methods in both classification accuracy and performance stability. Moreover, the ablation study verifies the contribution of the integrated niche and TPE strategies within the overall framework. The source code of Ensemble-GNAS can be obtained from https://github.com/WilfongGuo/EnsembleGNAS

Given the limited function evaluations (FEs), accurately finding multiple Pareto solution sets (PSs) in expensive multimodal multiobjective optimization problems (EMMOPs) is a challenging task. To mitigate this issue, a surrogate-assisted multimodal multiobjective differential evolution algorithm based on zoning search (SMMODE_ZS) is introduced in this article. In the proposed SMMODE_ZS, both population diversity and surrogate generalization ability are taken into account to find as many multimodal solutions as possible. First, to improve population diversity and reduce the impact of multimodal characteristics on the surrogate model, the entire decision space is divided into multiple subspaces by the zoning search (ZS) strategy, and an independent surrogate model is constructed in each subspace. Second, a reliable infill criterion is developed, which adopts nondominated sorting and a special crowding distance (SCD) as selection metrics of convergence and diversity to accurately evaluate promising individuals. The comprehensive experimental results show that the proposed SMMODE_ZS outperforms other algorithms in solving EMMOPs, as evidenced by its performance on a commonly used test set and an antenna sparse array layout engineering problem.

Medical image classification is pivotal for computer-aided diagnosis, enabling automated and accurate disease detection or severity grading. However, high inter-class similarity, imbalanced data, and limited annotated images often limit performance on important classes, ultimately affecting the overall performance. In this paper, a novel genetic programming (GP) algorithm is proposed, where the selection method in crossover and the mutation operator are modified to allocate increased search pressure to more challenging classes. Specifically, the crossover operation with a new selection method is designed to increase the likelihood that better-performing individuals in the challenging class exchange their good genetic materials, while the new mutation operator mutates worse-performing individuals under the guidance from the better-performing ones, thereby steering the search toward more promising regions. Experimental results on six diverse medical image datasets demonstrate the superiority of the proposed algorithm over nine baseline methods. Further analysis highlights the potential of the new genetic operators to enhance the overall classification performance by targeting challenging classes. Moreover, the analysis of an evolved GP individual illustrates the potential interpretability of GP.

Effective scheduling of heterogeneous agricultural machinery (e.g., harvesters, tractors, and seeders) is critical for timely operations during busy farming seasons. However, most existing work focuses on homogeneous agricultural machinery scheduling, which is relatively simpler than heterogeneous agricultural machinery scheduling. To address this, the paper provides the first formal definition and mathematical model of the Heterogeneous Agricultural Machinery Scheduling Problem with Time Windows (HAMSP-TW). The model uniquely integrates multiple practical constraints previously treated in isolation, including heterogeneous machinery coordination, spatial transfer times between dispersed plots, multi-process job sequences, and plot-specific earliest start time windows. To solve HAMSP-TW, this paper proposes a Heuristic-Guided Genetic Algorithm (HGA) with problem-driven components, i.e., a two-part encoding scheme capturing machinery assignment and operation sequencing, a hybrid rule-based initialization strategy seeding high-quality, diverse solutions, and a heuristic-guided mutation operator leveraging domain knowledge for effective search. Experiments on 18 instances (60–400 plots) show the proposed HGA approach significantly outperforms benchmark algorithms, with advantages particularly pronounced in large-scale scenarios. Ablation studies confirm the substantial individual contribution of each proposed component. Gantt chart analysis reveals that optimized schedules are able to reduce idle time and improve machinery utilization, directly translating to shorter operation completion times.

An accurate model of the LLC resonant converter, serving as a critical energy conversion stage in new energy storage converters, plays a pivotal role in its optimized design. However, traditional modeling approaches often fail to achieve ideal performance in practical applications, particularly due to parasitic parameter effects that cause significant discrepancies between theoretical and actual voltage gain. To better capture the nonlinear characteristics of the circuit, this paper adopts a data-driven approach and introduces the Multi-Population Genetic Programming (MPGP) algorithm, which enhances model interpretability and clarity. MPGP employs a multi-population strategy to optimize the evolutionary process, improving search capability and ensuring the generation of more precise models even with limited training data. Experimental validation on four dataset groups of LLC resonant converter demonstrates that MPGP significantly outperforms first harmonic approximation (FHA), genetic programming (GP), and five state-of-the-art regression methods in terms of estimation accuracy, model visualization, and interpretability. Moreover, the algorithm strengthens support for power electronics converter design, contributing to improved optimization of power electronic systems.

In multiobjective feature selection, different feature subsets with the same number of selected features can achieve identical classification accuracy, meaning that it is a multimodal optimization problem. To effectively search for multimodal feature subsets within the vast search spaces of high-dimensional datasets, it is crucial to adopt reasonable encoding and search methods. Generally, applying a uniform evolutionary operator based on a single encoding method across the entire feature space is inefficient and prone to falling into local optima. To address the above issues, this article proposes a multimodal multiobjective feature selection method based on a joint encoding mechanism that combines discrete encoding and continuous encoding. It provides new perspectives to solve the high-dimensional feature selection problem from encoding methods to search operators. First, the search space is divided into a discrete encoding region and a continuous encoding region based on the knee points of feature importance ranking curve. A tailored initialization strategy is used to obtain the initial population for joint encoding. Second, an adaptive niche strategy based on three priorities is proposed, which ensures the similarity of individuals within a niche and the difference between niches. In addition, different search operators are cooperated with the two encoding strategies, respectively, to achieve effective and efficient search. The experimental results on 24 datasets show that the proposed algorithm achieves a better-classification performance than the state-of-the-art feature selection methods.

Remote sensing scene classification is a vital task in remote sensing image analysis with significant application potential. In recent years, convolutional neural network (CNN)-based methods have shown remarkable promise in classifying remote sensing scene images. However, these methods often require extensive trial and error and rely heavily on expert knowledge. To address these challenges, this article proposes a novel neural architecture search (NAS) approach that automatically designs CNNs for remote sensing scene classification. Specifically, an evolutionary algorithm (EA) is employed to search for well-structured basic modules, which are then combined to construct a new architecture. To further enhance the search process, a new population generation strategy is introduced to promote diversity and mitigate premature convergence. Additionally, a random forest-based selection mechanism is utilized to identify high-quality individuals based on estimated fitness values, effectively reducing computational complexity. The proposed approach is evaluated on three benchmark remote sensing scene datasets and compared with several widely used CNNs. The experimental results demonstrate that the proposed approach can discover CNN architectures that not only surpass state-of-the-art performance but also achieve this with fewer parameters and lower search cost.