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This document is a special issue of the journal Mathematics dedicated to recent advances in discrete optimization and scheduling. The issue includes 10 papers covering a range of topics such as batch loading and scheduling, optimization algorithms, scheduling surgeries, routing problems, and mathematical models for simplification. The papers present various approaches and algorithms for solving these problems, and they have been reviewed by experts in the field. The authors express their gratitude to the contributors, reviewers, and editorial staff, and hope that the readers will find stimulating ideas for further research in this area. [Extracted from the article]

Time-of-use pricing of electric energy, as an important part of the national policy of energy conservation and emission reduction, requires accurate electric energy data as support. However, due to various reasons, the electric energy data are often missing. To address this thorny problem, this paper constructs a CNN and GRU-based recovery model (RCNN-BiGRU) for electric energy data by taking the missing data as the output and the historical data of the neighboring moments as the input. Firstly, a convolutional network with a residual structure is used to capture the local dependence and periodic patterns of the input data, and then a bidirectional GRU network utilizes the extracted potential features to model the temporal relationships of the data. Aiming at the difficult selection of network structure parameters and training process parameters, an accelerated adaptive differential evolution (AADE) algorithm is proposed to optimize the electrical energy data recovery model. The algorithm designs an accelerated mutation operator and at the same time adopts an adaptive strategy to set the two key parameters. A large amount of real grid data are selected as samples to train the network, and the comparison results verify that the proposed combined model outperforms the related CNN and GRU networks. The comparison experimental results with other optimization algorithms also show that the AADE algorithm proposed in this paper has better data recovery performance on the training set and significantly better performance on the test set. [ABSTRACT FROM AUTHOR]

Predicting student performance in the future is a crucial behavior prediction problem in education. By predicting student performance, educational experts can provide individualized instruction, optimize the allocation of resources, and develop educational strategies. If the prediction results are unreliable, it is difficult to earn the trust of educational experts. Therefore, prediction methods need to satisfy the requirement of interpretability. For this reason, the prediction model is constructed in this paper using belief rule base (BRB). BRB not only combines expert knowledge, but also has good interpretability. There are two problems in applying BRB to student performance prediction: first, in the modeling process, the system is too complex due to the large number of indicators involved. Secondly, the interpretability of the model can be compromised during the optimization process. To overcome these challenges, this paper introduces a hierarchical belief rule base with interpretability (HBRB-I) for student performance prediction. First, it analyzes how the HBRB-I model achieves interpretability. Then, an attribute grouping method is proposed to construct a hierarchical structure by reasonably organizing the indicators, so as to effectively reduce the complexity of the model. Finally, an objective function considering interpretability is designed and the projected covariance matrix adaptive evolution strategy (P-CMA-ES) optimization algorithm is improved. The aim is to ensure that the model remains interpretable after optimization. By conducting experiments on the student performance dataset, it is demonstrated that the proposed model performs well in terms of both accuracy and interpretability. [ABSTRACT FROM AUTHOR]

Addressing the issues of the sand cat swarm optimization algorithm (SCSO), such as its weak global search ability and tendency to fall into local optima, this paper proposes an improved strategy called the multi-strategy integrated sand cat swarm optimization algorithm (MSCSO). The MSCSO algorithm improves upon the SCSO in several ways. Firstly, it employs the good point set strategy instead of a random strategy for population initialization, effectively enhancing the uniformity and diversity of the population distribution. Secondly, a nonlinear adjustment strategy is introduced to dynamically adjust the search range of the sand cats during the exploration and exploitation phases, significantly increasing the likelihood of finding more high-quality solutions. Lastly, the algorithm integrates the early warning mechanism of the sparrow search algorithm, enabling the sand cats to escape from their original positions and rapidly move towards the optimal solution, thus avoiding local optima. Using 29 benchmark functions of 30, 50, and 100 dimensions from CEC 2017 as experimental subjects, this paper further evaluates the MSCSO algorithm through Wilcoxon rank-sum tests and Friedman's test, verifying its global solid search ability and convergence performance. In practical engineering problems such as reducer and welded beam design, MSCSO also demonstrates superior performance compared to five other intelligent algorithms, showing a remarkable ability to approach the optimal solutions for these engineering problems. [ABSTRACT FROM AUTHOR]

When constructing an investment portfolio, it is important to maximize returns while minimizing risks. This portfolio optimization can be considered as a multi-objective optimization problem that is solved by means of multi-objective evolutionary algorithms. The use of multi-objective evolutionary algorithms (MOEAs) provides an effective approach for dealing with the complex data involved in multi-objective optimization problems. However, current MOEAs often rely on a single strategy to obtain optimal solutions, leading to premature convergence and an insufficient population diversity. In this paper, a new MOEA called the Synergistic MOEA with Diffusion Population Generation (DPG-SMOEA) is proposed to address these limitations by integrating MOEAs with diffusion models. To train the diffusion model, a mixed memory pool strategy is optimized, which collects improved solutions from the MOEA/D-AEE, an optimized MOEA, as training samples. The trained model is then used to generate offspring. Considering the cold-start mechanism of the diffusion model, particularly during the training phase where it is not suitable for generating initial offspring, this paper adjusts and optimizes the collaborative strategy to enhance the synergy between the diffusion model and MOEA/D-AEE. Experimental validation of the DPG-SMOEA demonstrates the advantages of using diffusion models in low-dimensional and relatively continuous data analysis. The results show that the DPG-SMOEA performs well on the low-dimensional Hang Seng Index test dataset, while achieving average performance on other high-dimensional datasets, consistent with theoretical predictions. Overall, the DPG-SMOEA achieves better results compared to MOEA/D-AEE and other multi-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

In this study, the portfolio optimization problem is explored, using a combination of classical and quantum computing techniques. The portfolio optimization problem with specific objectives or constraints is often a quadratic optimization problem, due to the quadratic nature of, for example, risk measures. Quantum computing is a promising solution for quadratic optimization problems, as it can leverage quantum annealing and quantum approximate optimization algorithms, which are expected to tackle these problems more efficiently. Quantum computing takes advantage of quantum phenomena like superposition and entanglement. In this paper, a specific problem is introduced, where a portfolio of loans need to be optimized for 2030, considering 'Return on Capital' and 'Concentration Risk' objectives, as well as a carbon footprint constraint. This paper introduces the formulation of the problem and how it can be optimized using quantum computing, using a reformulation of the problem as a quadratic unconstrained binary optimization (QUBO) problem. Two QUBO formulations are presented, each addressing different aspects of the problem. The QUBO formulation succeeded in finding solutions that met the emission constraint, although classical simulated annealing still outperformed quantum annealing in solving this QUBO, in terms of solutions close to the Pareto frontier. Overall, this paper provides insights into how quantum computing can address complex optimization problems in the financial sector. It also highlights the potential of quantum computing for providing more efficient and robust solutions for portfolio management. [ABSTRACT FROM AUTHOR]

During the load distribution of hydropower units, the frequent crossing of vibration zones as well as large output fluctuations affect the stability of the power station. A multi-objective double-layer intelligent nesting model that considers the constraint of the output fluctuation of units is proposed to address these problems. The nonlinear constraint unit commitment optimization model layer is built based on outer dynamic programming, and the load distribution optimization model layer is constructed based on the improved biogeography-based optimization algorithm. Simultaneously, the unit output fluctuation constraint is established based on whether the unit combination changes in order to limit the unit output fluctuation. The results of this model indicate that compared with traditional load allocation models, the application of the method proposed in this paper can reduce the fluctuation range of unit output by 85.01%. In addition, except for the inevitable vibration zone crossings during startup and shutdown processes, the unit does not cross the vibration zone during operation, which greatly improves the unit's vibration isolation and optimization capabilities. The multi-objective double-layer intelligent nested model proposed in this paper has significant advantages in the field of load allocation for hydropower units. It effectively improves the stability and reliability of unit operation, and this method can be applied to practical load allocation processes. It is of great significance for the research on load allocation optimization of hydropower units. [ABSTRACT FROM AUTHOR]

Deep learning technology has made significant progress in agricultural image recognition tasks, but the parameter adjustment of deep models usually requires a lot of manual intervention, which is time-consuming and inefficient. To solve this challenge, this paper proposes an adaptive parameter tuning strategy that combines sine–cosine algorithm with Tent chaotic mapping to enhance sea horse optimization, which improves the search ability and convergence stability of standard sea horse optimization algorithm (SHO). Through adaptive optimization, this paper determines the best parameter configuration in ResNet-50 neural network and optimizes the model performance. The improved ESHO algorithm shows superior optimization effects than other algorithms in various performance indicators. The improved model achieves 96.7% accuracy in the corn disease image recognition task, and 96.4% accuracy in the jade fungus image recognition task. These results show that ESHO can not only effectively improve the accuracy of agricultural image recognition, but also reduce the need for manual parameter adjustment. [ABSTRACT FROM AUTHOR]

Some problems exist in classical optimization algorithms to solve multi-modal optimization problems and other complex systems. A Dynamic Niches-based Improved Hybrid Breeding Optimization (DNIHBO) algorithm is proposed to address the multi-modal optimization problem in the paper. By dynamically adjusting the niche scale, it effectively addresses the issue of niche parameter sensitivity. The structure of the algorithm includes three distinct groups: maintainer, restorer, and sterile lines for updating operations. However, the maintainer individuals often stagnate, leading to the risk of the local optima. To overcome this, neighborhood search and elite mutation strategies are incorporated, enhancing the balance between exploration and exploitation. To further improve individual utilization within niches, a niche restart strategy is introduced, ensuring sustained population diversity. The efficacy of DNIHBO is validated through simulations on 16 multi-modal test functions, followed by comparative analyses with various multi-modal optimization algorithms. The results convincingly demonstrate that DNIHBO not only effectively locates multiple global optima but also consistently outperforms other algorithms on test functions. These findings underscore the superiority of DNIHBO as a high-performing solution for multi-modal optimization. [ABSTRACT FROM AUTHOR]

Extreme learning machines (ELMs), single hidden-layer feedforward neural networks, are renowned for their speed and efficiency in classification and regression tasks. However, their generalization ability is often undermined by the random generation of hidden layer weights and biases. To address this issue, this paper introduces a Hierarchical Learning-based Chaotic Crayfish Optimization Algorithm (HLCCOA) aimed at enhancing the generalization ability of ELMs. Initially, to resolve the problems of slow search speed and premature convergence typical of traditional crayfish optimization algorithms (COAs), the HLCCOA utilizes chaotic sequences for population position initialization. The ergodicity of chaos is leveraged to boost population diversity, laying the groundwork for effective global search efforts. Additionally, a hierarchical learning mechanism encourages under-performing individuals to engage in extensive cross-layer learning for enhanced global exploration, while top performers directly learn from elite individuals at the highest layer to improve their local exploitation abilities. Rigorous testing with CEC2019 and CEC2022 suites shows the HLCCOA's superiority over both the original COA and nine renowned heuristic algorithms. Ultimately, the HLCCOA-optimized extreme learning machine model, the HLCCOA-ELM, exhibits superior performance over reported benchmark models in terms of accuracy, sensitivity, and specificity for UCI breast cancer diagnosis, underscoring the HLCCOA's practicality and robustness, as well as the HLCCOA-ELM's commendable generalization performance. [ABSTRACT FROM AUTHOR]

Causal structure learning plays a crucial role in the current field of artificial intelligence, yet existing causal structure learning methods are susceptible to interference from data sample noise and often become trapped in local optima. To address these challenges, this paper introduces a continuous optimization algorithm based on the curriculum learning framework: CL-NOTEARS. The model utilizes the curriculum loss function during training as a priority evaluation metric for curriculum selection and formulates the sample learning sequence of the model through task-level curricula, thereby enhancing the model's learning performance. A curriculum-based sample prioritization strategy is employed that dynamically adjusts the training sequence based on variations in loss function values across different samples throughout the training process. The results demonstrate a significant reduction in the impact of sample noise in the data, leading to improved model training performance. [ABSTRACT FROM AUTHOR]

Multiobjective programming refers to a mathematical problem that requires the simultaneous optimization of multiple independent yet interrelated objective functions when solving a problem. It is widely used in various fields, such as engineering design, financial investment, environmental planning, and transportation planning. Research on the theory and application of convex functions and their generalized convexity in multiobjective programming helps us understand the essence of optimization problems, and promotes the development of optimization algorithms and theories. In this paper, we firstly introduces new classes of generalized (F , α , ρ , d) − I functions for semi-preinvariant convex multiobjective programming. Secondly, based on these generalized functions, we derive several sufficient optimality conditions for a feasible solution to be an efficient or weakly efficient solution. Finally, we prove weak duality theorems for mixed-type duality. [ABSTRACT FROM AUTHOR]

Addressing real-time optimization problems becomes increasingly challenging as their complexity continues to escalate over time. So bio-optimization algorithms (BoAs) come into the picture to solve such problems due to their global search capability, adaptability, versatility, parallelism, and robustness. This article aims to perform hyperparameter tuning of machine learning (ML) models by integrating them with BoAs. Aiming to maximize the accuracy of the hybrid bio-optimized defect prediction (HBoDP) model, this research paper develops four novel hybrid BoAs named the gravitational force Lévy flight grasshopper optimization algorithm (GFLFGOA), the gravitational force Lévy flight grasshopper optimization algorithm–sparrow search algorithm (GFLFGOA-SSA), the gravitational force grasshopper optimization algorithm–sparrow search algorithm (GFGOA-SSA), and the Lévy flight grasshopper optimization algorithm–sparrow search algorithm (LFGOA-SSA). These aforementioned algorithms are proposed by integrating the good exploration capacity of the SSA with the faster convergence of the LFGOA and GFGOA. The performances of the GFLFGOA, GFLFGOA-SSA, GFGOA-SSA, and LFGOA-SSA are verified by conducting two different experiments. Firstly, the experimentation was conducted on nine benchmark functions (BFs) to assess the mean, standard deviation (SD), and convergence rate. The second experiment focuses on boosting the accuracy of the HBoDP model through the fine-tuning of the hyperparameters in the artificial neural network (ANN) and XGBOOST (XGB) models. To justify the effectiveness and performance of these hybrid novel algorithms, we compared them with four base algorithms, namely the grasshopper optimization algorithm (GOA), the sparrow search algorithm (SSA), the gravitational force grasshopper optimization algorithm (GFGOA), and the Lévy flight grasshopper optimization algorithm (LFGOA). Our findings illuminate the effectiveness of this hybrid approach in enhancing the convergence rate and accuracy. The experimental results show a faster convergence rate for BFs and improvements in software defect prediction accuracy for the NASA defect datasets by comparing them with some baseline methods. [ABSTRACT FROM AUTHOR]

Due to the complexity and illegibility of medical images, it brings inconvenience and difficulty to the diagnosis of medical personnel. To address these issues, an optimization algorithm called GSL(Gradient sine linear) based on Adam algorithm improvement is proposed in this paper, which introduces gradient pruning strategy, periodic adjustment of learning rate, and linear interpolation strategy. The gradient trimming technique can scale the gradient to prevent gradient explosion, while the periodic adjustment of the learning rate and linear interpolation strategy adjusts the learning rate according to the characteristics of the sinusoidal function, accelerating the convergence while reducing the drastic parameter fluctuations, improving the efficiency and stability of training. The experimental results show that compared to the classic Adam algorithm, this algorithm can demonstrate better classification accuracy, the GSL algorithm achieves an accuracy of 78% and 75.2% on the MobileNetV2 network and ShuffleNetV2 network under the Gastroenterology dataset; and on the MobileNetV2 network and ShuffleNetV2 network under the Glaucoma dataset, an accuracy of 84.72% and 83.12%. The GSL optimizer achieved significant performance improvement on various neural network structures and datasets, proving its effectiveness and practicality in the field of deep learning, and also providing new ideas and methods for solving the difficulties in medical image recognition. [ABSTRACT FROM AUTHOR]

This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative optimization problem more challenging. A distributed online optimization algorithm is designed for the considered problem via the mirror descent algorithm and the distributed average tracking method. In particular, the dynamic environment and the gradient are estimated by the averaged tracking methods, and then an online optimization algorithm is designed via a dynamic mirror descent method. It is shown that the dynamic regret is bounded in the order of O (T) . Finally, the effectiveness of the designed algorithm is verified by some simulations of cooperative control of a multi-robot system. [ABSTRACT FROM AUTHOR]

In recent years, side-channel analysis based on deep learning has garnered significant attention from researchers. A pivotal reason for this lies in the fact that deep learning-based side-channel analysis requires minimal preprocessing of side-channel data. The automatic feature extraction property of deep learning methods drastically reduces the workload for researchers, enabling them to focus more on the core issues of side-channel analysis, namely, extracting sensitive information by attacking devices. However, in prior studies, most scholars have concentrated more on the model construction process, with little research focusing on the choice of optimizers.This paper explores a novel deep learning-based optimization algorithm—CPSGD (combined projection stochastic gradient descent). The algorithm comprises two variants, designed, respectively, for unprotected side-channel analysis (CPSGD1) and desynchronized side-channel analysis (CPSGD2), and their convergence has been theoretically proven. Experimental results demonstrate that, while maintaining the neural network structure unchanged, CPSGD1 exhibits the best performance on unprotected datasets compared to other publicly available optimizers, whereas CPSGD2 performs optimally on desynchronized datasets. [ABSTRACT FROM AUTHOR]

In Structural Health Monitoring (SHM) of bridges, accurately assessing damage is critical to maintaining the safety and integrity of a structure. One of the primary challenges in damage assessment is the precise localization and quantification of defects, which is essential for making timely maintenance decisions and reducing the risk of structural failures. This paper introduces a novel damage detection method for SHM of a truss bridge by coupling a Deep Neural Network (DNN) model with an evolved Artificial Rabbit Optimization (EVARO) algorithm. The integration of DNN with the stochastic search capability of the EVARO algorithm helps to avoid local minima, thereby ensuring more accurate and reliable results. Additionally, the optimization algorithm's effectiveness is further enhanced by incorporating evolving predator features and the Cauchy motion search mechanism. The proposed method is first validated using various data benchmark problems, demonstrating its effectiveness compared to other well-known algorithms. Secondly, a case study involving the Chuong Duong truss bridge under different simulated damage scenarios further confirms the superiority of the proposed method in both localizing and quantifying damages. [ABSTRACT FROM AUTHOR]

As a kind of space robot, the two-arm cascade combination system (TACCS) has been applied to perform auxiliary operations at different locations outside space cabins. The motion coupling relation of two arms and complex surrounding obstacles make the collision-free trajectory planning optimization of TACCS more difficult, which has become an urgent problem to be solved. For the above problem, this paper proposed collision-free and time–energy–minimum trajectory planning optimization algorithms, considering the motion coupling of two arms. In this method, the screw-based inverse kinematics (IK) model of TACCS is established to provide the basis for the motion planning in joint space by decoupling the whole IK problem into two IK sub-problems of two arms; the minimum distance calculation model is established based on the hybrid geometric enveloping way and basic distance functions, which can provide the efficient and accurate data basis for the obstacle-avoidance constraint condition of the trajectory optimization. Moreover, the single and bi-layer optimization algorithms are presented by taking motion time and energy consumption as objectives and considering obstacle-avoidance and kinematics constraints. Finally, through example cases, the results indicate that the bi-layer optimization has higher convergence efficiency under the premise of ensuring the optimization effect by separating variables and constraint terms. This work can provide theoretical and methodological support for the efficient and intelligent applications of TACCS in the space arena. [ABSTRACT FROM AUTHOR]

Predicting wind speed in advance at bridge sites is essential for ensuring bridge construction safety under high wind conditions. This study proposes a short-term speed prediction model based on outlier correction, Wavelet Denoising, the Osprey Optimization Algorithm (OOA), and the Transformer model. The outliers caused by data entry and measurement errors are processed by the interquartile range (IQR) method. By comparing the performance of four different wavelets, the best-performing wavelet (Bior2.2) was selected to filter out sharp noise from the data processed by the IQR method. The OOA-Transformer model was utilized to forecast short-term wind speeds based on the filtered time series data. With OOA-Transformer, the seven hyperparameters of the Transformer model were optimized by the Osprey Optimization Algorithm to achieve better performance. Given the outstanding performance of LSTM and its variants in wind speed prediction, the OOA-Transformer model was compared with six other models using the actual wind speed data from the Xuefeng Lake Bridge dataset to validate our proposed model. The experimental results show that the mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination ( R 2 ) of this paper's method on the test set were 4.16%, 0.0152, and 0.9955, respectively, which are superior to the other six models. The prediction accuracy was found to be high enough to meet the short-term wind speed prediction needs of practical projects. [ABSTRACT FROM AUTHOR]

In industries such as aircraft or train manufacturing, large-scale manufacturing companies often manage several complex projects. Each of these projects includes multiple tasks that share a set of limited resources. Typically, these tasks are also subject to time dependencies among them. One frequent goal in these scenarios is to minimize the makespan, or total time required to complete all the tasks within the entire project. Decisions revolve around scheduling these tasks, determining the sequence in which they are processed, and allocating shared resources to optimize efficiency while respecting the time dependencies among tasks. This problem is known in the scientific literature as the Resource-Constrained Project Scheduling Problem (RCPSP). Being an NP-hard problem with time dependencies and resource constraints, several optimization algorithms have already been proposed to tackle the RCPSP. In this paper, a novel discrete-event heuristic is introduced and later extended into an agile biased-randomized algorithm complemented with an adaptive capability to tune the parameters of the algorithm. The results underscore the effectiveness of the algorithm in finding competitive solutions for this problem within short computing times. [ABSTRACT FROM AUTHOR]

The vehicle routing problem with time windows (VRPTW) remains a formidable challenge, due to the intricate constraints of vehicle capacity and time windows. As a result, an algorithm tailored for this problem must demonstrate robust search capabilities and profound exploration abilities. Traditional methods often struggle to balance global search capabilities with computational efficiency, thus limiting their practical applicability. To address these limitations, this paper introduces a novel hybrid algorithm known as large neighborhood search with modified rat swarm optimization (LNS-MRSO). Modified rat swarm optimization (MRSO) is inspired by the foraging behavior of rat swarms and simulates the search process for optimization problems. Meanwhile, large neighborhood search (LNS) generates potential new solutions by removing and reinserting operators, incorporating a mechanism to embrace suboptimal solutions and strengthening the algorithm's prowess in global optimization. Initial solutions are greedily generated, and five operators are devised to mimic the position updates of the rat swarm, providing rich population feedback to LNS and further enhancing algorithm performance. To validate the effectiveness of LNS-MRSO, experiments were conducted using the Solomon VRPTW benchmark test set. The results unequivocally demonstrate that LNS-MRSO achieves optimal solutions for all 39 test instances, particularly excelling on the R2 and RC2 datasets with percentage deviations improved by 5.1% and 8.8%, respectively, when compared to the best-known solutions (BKSs). Furthermore, when compared to state-of-the-art algorithms, LNS-MRSO exhibits remarkable advantages in addressing VRPTW problems with high loading capacities and lenient time windows. Additionally, applying LNS-MRSO to an unmanned concrete-mixing station further validates its practical utility and scalability. [ABSTRACT FROM AUTHOR]

The identification of co-regulated genes and their Transcription-Factor Binding Sites (TFBSs) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for the detection of the co-expressed genes have been developed. Bi-clustering methods are used to discover subgroups of genes with similar expression patterns under to-be-identified subsets of experimental conditions when applied to gene expression data. By building two fuzzy partition matrices of the gene expression data with the Axiomatic Fuzzy Set (AFS) theory, this paper proposes a novel fuzzy bi-clustering algorithm for the identification of co-regulated genes. Specifically, the gene expression data are transformed into two fuzzy partition matrices via the sub-preference relations theory of AFS at first. One of the matrices considers the genes as the universe and the conditions as the concept, and the other one considers the genes as the concept and the conditions as the universe. The identification of the co-regulated genes (bi-clusters) is carried out on the two partition matrices at the same time. Then, a novel fuzzy-based similarity criterion is defined based on the partition matrices, and a cyclic optimization algorithm is designed to discover the significant bi-clusters at the expression level. The above procedures guarantee that the generated bi-clusters have more significant expression values than those extracted by the traditional bi-clustering methods. Finally, the performance of the proposed method is evaluated with the performance of the three well-known bi-clustering algorithms on publicly available real microarray datasets. The experimental results are in agreement with the theoretical analysis and show that the proposed algorithm can effectively detect the co-regulated genes without any prior knowledge of the gene expression data. [ABSTRACT FROM AUTHOR]

This paper presents a novel variant of the teaching–learning-based optimization algorithm, termed BLTLBO, which draws inspiration from the blended learning model, specifically designed to tackle high-dimensional multimodal complex optimization problems. Firstly, the perturbation conditions in the "teaching" and "learning" stages of the original TLBO algorithm are interpreted geometrically, based on which the search capability of the TLBO is enhanced by adjusting the range of values of random numbers. Second, a strategic restructuring has been ingeniously implemented, dividing the algorithm into three distinct phases: pre-course self-study, classroom blended learning, and post-course consolidation; this structural reorganization and the random crossover strategy in the self-learning phase effectively enhance the global optimization capability of TLBO. To evaluate its performance, the BLTLBO algorithm was tested alongside seven distinguished variants of the TLBO algorithm on thirteen multimodal functions from the CEC2014 suite. Furthermore, two excellent high-dimensional optimization algorithms were added to the comparison algorithm and tested in high-dimensional mode on five scalable multimodal functions from the CEC2008 suite. The empirical results illustrate the BLTLBO algorithm's superior efficacy in handling high-dimensional multimodal challenges. Finally, a high-dimensional portfolio optimization problem was successfully addressed using the BLTLBO algorithm, thereby validating the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces the election optimization algorithm (EOA), a meta-heuristic approach for engineering optimization problems. Inspired by the democratic electoral system, focusing on the presidential election, EOA emulates the complete election process to optimize solutions. By simulating the presidential election, EOA introduces a novel position-tracking strategy that expands the scope of effectively solvable problems, surpassing conventional human-based algorithms, specifically, the political optimizer. EOA incorporates explicit behaviors observed during elections, including the party nomination and presidential election. During the party nomination, the search space is broadened to avoid local optima by integrating diverse strategies and suggestions from within the party. In the presidential election, adequate population diversity is maintained in later stages through further campaigning between elite candidates elected within the party. To establish a benchmark for comparison, EOA is rigorously assessed against several renowned and widely recognized algorithms in the field of optimization. EOA demonstrates superior performance in terms of average values and standard deviations across the twenty-three standard test functions and CEC2019. Through rigorous statistical analysis using the Wilcoxon rank-sum test at a significance level of 0.05, experimental results indicate that EOA consistently delivers high-quality solutions compared to the other benchmark algorithms. Moreover, the practical applicability of EOA is assessed by solving six complex engineering design problems, demonstrating its effectiveness in real-world scenarios. [ABSTRACT FROM AUTHOR]

Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars' attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the final algorithm implementation effect is not ideal. In this paper, a multi-objective community detection method based on a pigeon-inspired optimization algorithm, MOPIO-Net, is proposed. Firstly, the PIO algorithm is discretized in terms of the solution space representation, position, and velocity-updating strategies to adapt to discrete community detection scenarios. Secondly, by minimizing the two objective functions of community score and community fitness at the same time, the community structure with a tight interior and sparse exterior is obtained. Finally, for the misclassification caused by boundary nodes, a mutation strategy is added to improve the accuracy of the final community recognition. Experiments on synthetic and real networks verify that the proposed algorithm is more accurate in community recognition compared to 11 benchmark algorithms, confirming the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The proliferation of Internet of Things (IoT) devices and their integration into critical infrastructure and business operations has rendered them susceptible to malware and cyber-attacks. Such malware presents a threat to the availability and reliability of IoT devices, and a failure to address it can have far-reaching impacts. Due to the limited resources of IoT devices, traditional rule-based detection systems are often ineffective against sophisticated attackers. This paper addressed these issues by designing a new framework that uses a machine learning (ML) algorithm for the detection of malware. Additionally, it also employed sequential detection architecture and evaluated eight malware datasets. The design framework is lightweight and effective in data processing and feature selection algorithms. Moreover, this work proposed a classification model that utilizes one support vector machine (SVM) algorithm and is individually tuned with three different optimization algorithms. The employed optimization algorithms are Nuclear Reactor Optimization (NRO), Artificial Rabbits Optimization (ARO), and Particle Swarm Optimization (PSO). These algorithms are used to explore a diverse search space and ensure robustness in optimizing the SVM for malware detection. After extensive simulations, our proposed framework achieved the desired accuracy among eleven existing ML algorithms and three proposed ensemblers (i.e., NRO_SVM, ARO_SVM, and PSO_SVM). Among all algorithms, NRO_SVM outperforms the others with an accuracy rate of 97.8%, an F1 score of 97%, and a recall of 99%, and has fewer false positives and false negatives. In addition, our model successfully identified and prevented malware-induced attacks with a high probability of recognizing new evolving threats. [ABSTRACT FROM AUTHOR]

As a classical combinatorial optimization problem, the traveling salesman problem (TSP) has been extensively investigated in the fields of Artificial Intelligence and Operations Research. Due to being NP-complete, it is still rather challenging to solve both effectively and efficiently. Because of its high theoretical significance and wide practical applications, great effort has been undertaken to solve it from the point of view of intelligent search. In this paper, we propose a two-stage probe-based search optimization algorithm for solving both symmetric and asymmetric TSPs through the stages of route development and a self-escape mechanism. Specifically, in the first stage, a reasonable proportion threshold filter of potential basis probes or partial routes is set up at each step during the complete route development process. In this way, the poor basis probes with longer routes are filtered out automatically. Moreover, four local augmentation operators are further employed to improve these potential basis probes at each step. In the second stage, a self-escape mechanism or operation is further implemented on the obtained complete routes to prevent the probe-based search from being trapped in a locally optimal solution. The experimental results on a collection of benchmark TSP datasets demonstrate that our proposed algorithm is more effective than other state-of-the-art optimization algorithms. In fact, it achieves the best-known TSP benchmark solutions in many datasets, while, in certain cases, it even generates solutions that are better than the best-known TSP benchmark solutions. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithms (MOEA) have attracted much attention because of their good global exploration ability; however, their local search ability near the optimal value is weak, and for large-scale decision-variable optimization problems the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient optimization algorithms can overcome these difficulties well, but gradient search methods are difficult to apply to multi-objective optimization problems (MOPs). To this end, this paper introduces a stochastic weighting function based on the weighted average gradient and proposes two multi-objective stochastic gradient operators. Further, two efficient evolutionary algorithms, MOGBA and HMOEA, are developed. Their local search capability has been greatly enhanced while retaining the good global exploration capability by using different offspring update strategies for different subpopulations. Numerical experiments show that HMOEA has excellent capture ability for various Pareto formations, and it can easily solve multi-objective optimization problems with many objectives, which improves the efficiency by a factor of 5–10 compared with typical multi-objective evolutionary algorithms. HMOEA is further applied to the multi-objective aerodynamic optimization design of the RAE2822 airfoil and the ideal Pareto front is obtained, which indicates that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on the spectral properties of mimetic finite-difference operators and their application in the robust fluid–structure interaction (FSI) analysis of aircraft wings under uncertain operating conditions. By delving into the eigenvalue behavior of mimetic Laplacian operators and extending the analysis to stochastic settings, we develop a novel stochastic mimetic framework tailored for addressing uncertainties inherent in the fluid dynamics and structural mechanics of aircraft wings. The framework integrates random matrix theory with mimetic discretization methods, enabling the incorporation of uncertainties in fluid properties, structural parameters, and coupling conditions at the fluid–structure interface. Through spectral and localization analysis of the coupled stochastic mimetic operator, we assess the system's stability, sensitivity to perturbations, and computational efficiency. Our results highlight the potential of the stochastic mimetic approach for enhancing reliability and robustness in the design of aircraft wings, paving the way for optimization algorithms that integrate uncertainties directly into the design process. Our findings reveal a significant impact of stochastic perturbations on the spectral radius and eigenfunction localization, indicating heightened system sensitivity. The introduction of randomized singular value decomposition (RSVD) within our framework not only enhances computational efficiency but also preserves accuracy in low-rank approximations, which is critical for handling large-scale systems. Moreover, Monte Carlo simulations validate the robustness of our stochastic mimetic framework, showcasing its efficacy in capturing the nuanced dynamics of FSI under uncertainty. This study contributes to the fields of numerical methods and aerospace engineering by offering a rigorous and scalable approach for conducting uncertainty-aware FSI analysis, which is crucial for the development of safer and more efficient aircraft. [ABSTRACT FROM AUTHOR]

This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array's element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to −33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is −42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to −187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as −98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as −63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is −22.8766 dB, which is 0.1998 dB lower than the lowest SLL of −22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is −20.1012 dB, and the null depth is −125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Supply Chain (SC) Optimization is a key activity in today's industry with the goal of increasing operational efficiency, reducing costs, and improving customer satisfaction. Traditional optimization methods often struggle to effectively use resources while handling complex and dynamic Supply chain networks. This paper introduces a novel biomimetic metaheuristic algorithm called the Wombat Optimization Algorithm (WOA) for supply chain optimization. This algorithm replicates the natural behaviors observed in wombats living in the wild, particularly focusing on their foraging tactics and evasive maneuvers towards predators. The theory of WOA is described and then mathematically modeled in two phases: (i) exploration based on the simulation of wombat movements during foraging and trying to find food and (ii) exploitation based on simulating wombat movements when diving towards nearby tunnels to defend against its predators. The effectiveness of WOA in addressing optimization challenges is assessed by handling the CEC 2017 test suite across various problem dimensions, including 10, 30, 50, and 100. The findings of the optimization indicate that WOA demonstrates a strong ability to effectively manage exploration and exploitation, and maintains a balance between them throughout the search phase to deliver optimal solutions for optimization problems. A total of twelve well-known metaheuristic algorithms are called upon to test their performance against WOA in the optimization process. The outcomes of the simulations reveal that WOA outperforms the other algorithms, achieving superior results across most benchmark functions and securing the top ranking as the most efficient optimizer. Using a Wilcoxon rank sum test statistical analysis, it has been proven that WOA outperforms other algorithms significantly. WOA is put to the test with twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems to showcase its ability to solve real-world optimization problems. The results of the simulations demonstrate that WOA excels in real-world applications by delivering superior solutions and outperforming its competitors. [ABSTRACT FROM AUTHOR]

The accurate and efficient inversion of permeability coefficients is significant for the scientific assessment of seepage safety in concrete face rockfill dams. In addressing the optimization challenge of permeability coefficients with few samples, multiple parameters, and strong nonlinearity, this paper proposes a novel intelligent inversion method based on the Sobol-IDBO-SVR fusion surrogate model. Firstly, the Sobol sequence sampling method is introduced to extract high-quality combined samples of permeability coefficients, and the equivalent continuum seepage model is utilized for the forward simulation to obtain the theoretical hydraulic heads at the seepage monitoring points. Subsequently, the support vector regression surrogate model is used to establish the complex mapping relationship between the permeability coefficients and hydraulic heads, and the convergence performance of the dung beetle optimization algorithm is effectively enhanced by fusing multiple strategies. On this basis, we successfully achieve the precise inversion of permeability coefficients driven by multi-intelligence technologies. The engineering application results show that the permeability coefficients determined based on the inversion of the Sobol-IDBO-SVR model can reasonably reflect the seepage characteristics of the concrete face rockfill dam. The maximum relative error between the measured and the inversion values of the hydraulic heads at each monitoring point is only 0.63%, indicating that the inversion accuracy meets the engineering requirements. The method proposed in this study may also provide a beneficial reference for similar parameter inversion problems in engineering projects such as bridges, embankments, and pumping stations. [ABSTRACT FROM AUTHOR]

China's policies about reducing carbon emissions mainly focus on saving energy and reducing pollutant emissions. However, the carbon emissions of the logistics industry remain high. Thus, logistics companies should not only reduce distribution costs, but also consider the impact of carbon emissions when planning distribution routes. This paper studies the supermarket delivery distribution route planning problem considering carbon emissions. Aiming at the lowest economic operating cost composed of fixed cost, driving cost, and carbon emission cost, we propose a grey wolf optimized genetic algorithm to generate delivery route plans, where the social rank and hunting behavior of the grey wolf optimization algorithm are integrated into the selection operation of the genetic algorithm. Finally, a real case of a large third-party logistics enterprise in Beijing is studied. The case study results verify the effectiveness and applicability of the model and algorithm. [ABSTRACT FROM AUTHOR]

Prompt optimization is a crucial task for improving the performance of large language models for downstream tasks. In this paper, a prompt is a sequence of n-grams selected from a vocabulary. Consequently, the aim is to select the optimal prompt concerning a certain performance metric. Prompt optimization can be considered as a combinatorial optimization problem, with the number of possible prompts (i.e., the combinatorial search space) given by the size of the vocabulary (i.e., all the possible n-grams) raised to the power of the length of the prompt. Exhaustive search is impractical; thus, an efficient search strategy is needed. We propose a Bayesian Optimization method performed over a continuous relaxation of the combinatorial search space. Bayesian Optimization is the dominant approach in black-box optimization for its sample efficiency, along with its modular structure and versatility. We use BoTorch, a library for Bayesian Optimization research built on top of PyTorch. Specifically, we focus on Hard Prompt Tuning, which directly searches for an optimal prompt to be added to the text input without requiring access to the Large Language Model, using it as a black-box (such as for GPT-4 which is available as a Model as a Service). Albeit preliminary and based on "vanilla" Bayesian Optimization algorithms, our experiments with RoBERTa as a large language model, on six benchmark datasets, show good performances when compared against other state-of-the-art black-box prompt optimization methods and enable an analysis of the trade-off between the size of the search space, accuracy, and wall-clock time. [ABSTRACT FROM AUTHOR]

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on both feasibility and ε feasibility of the solutions. Subsequently, a reinforcement learning model is employed to construct a mapping model between the population state and reproduction operators. Finally, based on the real-time population state, the mapping model is utilized to recommend the promising reproduction operator for the next generation. This approach demonstrates significant performance improvement for ε constrained mechanisms in constrained multi-objective optimization algorithms, and shows considerable advantages in comparison with state-of-the-art constrained multi-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

The Whale Optimization Algorithm (WOA) is a swarm intelligence algorithm based on natural heuristics, which has gained considerable attention from researchers and engineers. However, WOA still has some limitations, including limited global search efficiency and a slow convergence rate. To address these issues, this paper presents an improved whale optimization algorithm with multiple strategies, called Dynamic Gain-Sharing Whale Optimization Algorithm (DGSWOA). Specifically, a Sine–Tent–Cosine map is first adopted to more effectively initialize the population, ensuring a more uniform distribution of individuals across the search space. Then, a gaining–sharing knowledge based algorithm is used to enhance global search capability and avoid falling into a local optimum. Finally, to increase the diversity of solutions, Dynamic Opposition-Based Learning is incorporated for population updating. The effectiveness of our approach is evaluated through comparative experiments on blackbox optimization benchmarking and two engineering application problems. The experimental results suggest that the proposed method is competitive in terms of solution quality and convergence speed in most cases. [ABSTRACT FROM AUTHOR]

Predicting diseases in the early stages is extremely important. By taking advantage of advances in deep learning and fuzzy logic techniques, a new model is proposed in this paper for disease evaluation depending on the adaptive neuro-fuzzy inference system (ANFIS) with a genetic algorithm (GA) for classification, and the pre-trained DenseNet-201 model for feature extraction, in addition to the whale optimization algorithm (WOA) for feature selection. Two medical databases (chest X-ray and MRI brain tumor) for the diagnosis of two disease types were used as input in the suggested model. The optimization of ANFIS parameters was performed by GA to achieve the optimum prediction capability. DenseNet-201 for feature extraction was employed to obtain better classification accuracy. Having more features sometimes leads to lower accuracy, and this issue can be rectified using a feature selection strategy WOA which gave good results. The proposed model was evaluated utilizing statistical metrics root mean square error (RMSE), mean square error (MSE), standard deviation (STD), and coefficient of determination ( R 2 ), and it was compared with the conventional ANFIS model, with the proposed model (ANFIS-GA) showing a superior prediction capability over the ANFIS model. As a result, it can be concluded that the proposed ANFIS-GA model is efficient and has the potential for a robust diseases evaluation with good accuracy. Also, we conclude from this work that integrating optimization algorithms with ANFIS boosts its performance, resulting in a more accurate and reliable model. [ABSTRACT FROM AUTHOR]

Bayesian optimization algorithms are widely used for solving problems with a high computational complexity in terms of objective function evaluation. The efficiency of Bayesian optimization is strongly dependent on the quality of the surrogate models of an objective function, which are built and refined at each iteration. The quality of surrogate models, and hence the performance of an optimization algorithm, can be greatly improved by selecting the appropriate hyperparameter values of the approximation algorithm. The common approach to finding good hyperparameter values for each iteration of Bayesian optimization is to build surrogate models with different hyperparameter values and choose the best one based on some estimation of the approximation error, for example, a cross-validation score. Building multiple surrogate models for each iteration of Bayesian optimization is computationally demanding and significantly increases the time required to solve an optimization problem. This paper suggests a new approach, called exploratory landscape validation, to find good hyperparameter values with less computational effort. Exploratory landscape validation metrics can be used to predict the best hyperparameter values, which can improve both the quality of the solutions found by Bayesian optimization and the time needed to solve problems. [ABSTRACT FROM AUTHOR]

The Harris Hawks Optimization algorithm (HHO) is a sophisticated metaheuristic technique that draws inspiration from the hunting process of Harris hawks, which has gained attention in recent years. However, despite its promising features, the algorithm exhibits certain limitations, including the tendency to converge to local optima and a relatively slow convergence speed. In this paper, we propose the multi-strategy improved HHO algorithm (MSI-HHO) as an enhancement to the standard HHO algorithm, which adopts three strategies to improve its performance, namely, inverted S-shaped escape energy, a stochastic learning mechanism based on Gaussian mutation, and refracted opposition-based learning. At the same time, we conduct a comprehensive comparison between our proposed MSI-HHO algorithm with the standard HHO algorithm and five other well-known metaheuristic optimization algorithms. Extensive simulation experiments are conducted on both the 23 classical benchmark functions and the IEEE CEC 2020 benchmark functions. Then, the results of the non-parametric tests indicate that the MSI-HHO algorithm outperforms six other comparative algorithms at a significance level of 0.05 or greater. Additionally, the visualization analysis demonstrates the superior convergence speed and accuracy of the MSI-HHO algorithm, providing evidence of its robust performance. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel multi-target feature selection algorithm that incorporates adaptive graph learning and target correlations. Specifically, our proposed approach introduces the low-rank constraint on the regression matrix, allowing us to model both inter-target and input–output relationships within a unified framework. To preserve the similarity structure of the samples and mitigate the influence of noise and outliers, we learn a graph matrix that captures the induced sample similarity. Furthermore, we introduce a manifold regularizer to maintain the global target correlations, ensuring the preservation of the overall target relationship during subsequent learning processes. To solve the final objective function, we also propose an optimization algorithm. Through extensive experiments on eight real-world datasets, we demonstrate that our proposed method outperforms state-of-the-art multi-target feature selection techniques. [ABSTRACT FROM AUTHOR]

To address the drawbacks of the slow convergence speed and lack of individual information exchange in the cuckoo search (CS) algorithm, this study proposes an improved cuckoo search algorithm based on a sharing mechanism (ICSABOSM). The enhanced algorithm reinforces information sharing among individuals through the utilization of a sharing mechanism. Additionally, new search strategies are introduced in both the global and local searches of the CS. The results from numerical experiments on four standard test functions indicate that the improved algorithm outperforms the original CS in terms of search capability and performance. Building upon the improved algorithm, this paper introduces a numerical solution approach for differential equations involving the coupling of function approximation and intelligent algorithms. By constructing an approximate function using Fourier series to satisfy the conditions of the given differential equation and boundary conditions with minimal error, the proposed method minimizes errors while satisfying the differential equation and boundary conditions. The problem of solving the differential equation is then transformed into an optimization problem with the coefficients of the approximate function as variables. Furthermore, the improved cuckoo search algorithm is employed to solve this optimization problem. The specific steps of applying the improved algorithm to solve differential equations are illustrated through examples. The research outcomes broaden the application scope of the cuckoo optimization algorithm and provide a new perspective for solving differential equations. [ABSTRACT FROM AUTHOR]

The significance of precise gold price forecasting is accentuated by its financial attributes, mirroring global economic conditions, market uncertainties, and investor risk aversion. However, predicting the gold price is challenging due to its inherent volatility, influenced by multiple factors, such as COVID-19, financial crises, geopolitical issues, and fluctuations in other metals and energy prices. These complexities often lead to non-stationary time series, rendering traditional time series modeling methods inadequate. Our paper presents a multi-objective optimization algorithm that refines the interval prediction framework with quantile regression deep learning in response to this issue. This framework comprehensively responds to gold's financial market dynamics and uncertainties with a screening process of various factors, including pandemic-related indices, geopolitical indices, the US dollar index, and prices of various commodities. The quantile regression deep-learning models optimized by multi-objective optimization algorithms deliver robust, interpretable, and highly accurate predictions for handling non-linear relationships and complex data structures and enhance the overall predictive performance. The results demonstrate that the QRBiLSTM model, optimized using the MOALO algorithm, delivers excellent forecasting performance. The composite indicator AIS reaches −15.6240 and −11.5581 at 90% and 95% confidence levels, respectively. This underscores the model's high forecasting accuracy and its potential to provide valuable insights for assessing future trends in gold prices. The deterministic and probabilistic forecasting framework for gold prices captures the market dynamics with the new pandemic index and comprehensively sets a new benchmark for predictive modeling in volatile market commodities like gold. [ABSTRACT FROM AUTHOR]

A 2D topology optimization algorithm is proposed, which integrates the control of hole shape, hole number, and the minimum scale between holes through the utilization of an appearance target image. The distance between the structure and the appearance target image is defined as the hole appearance constraint. The appearance constraint is organized as inequality constraints to control the performance of the structure in an iterative optimization. Specifically, hole shapes are controlled by matching adaptable equivalent shape templates, the minimum scales between holes are controlled by a hole shrinkage strategy, and the hole number is controlled by a hole number calculation and filling method. Based on the SIMP interpolation topology optimization model, the effectiveness of the proposed method is verified through numerical examples. [ABSTRACT FROM AUTHOR]

The structural design of prestressed arched trusses presents a complex challenge due to the need to balance multiple conflicting objectives such as structural performance, weight, and constructability. This complexity is further compounded by the interdependent nature of the structural elements, which necessitates a comprehensive optimization approach. Addressing this challenge is crucial for advancing construction practices and improving the efficiency and safety of structural designs. The integration of advanced optimization algorithms and decision-making techniques offers a promising avenue for enhancing the design process of prestressed arched trusses. This study proposes the use of three advanced multi-objective optimization algorithms: NSGA-III, CTAEA, and SMS-EMOA, to optimize the structural design of prestressed arched trusses. The performance of these algorithms was evaluated using generational distance and inverted generational distance metrics. Additionally, the non-dominated optimal designs generated by these algorithms were assessed and ranked using multiple multi-criteria decision-making techniques, including SAW, FUCA, TOPSIS, PROMETHEE, and VIKOR. This approach allowed for a robust comparison of the algorithms and provided insights into their effectiveness in balancing the different design objectives. The results of the study indicated that NSGA-III exhibited superior performance with a GD value of 0.215, reflecting a closer proximity of its solutions to the Pareto front, and an IGD value of 0.329, indicating a well-distributed set of solutions across the Pareto front. In comparison, CTAEA and SMS-EMOA showed higher GD values of 0.326 and 0.436, respectively, suggesting less convergence to the Pareto front. However, SMS-EMOA demonstrated a balanced performance in terms of constructability and structural weight, with an IGD value of 0.434. The statistical significance of these differences was confirmed by the Kruskal–Wallis test, with p-values of 2.50 × 10 − 15 for GD and 5.15 × 10 − 06 for IGD. These findings underscore the advantages and limitations of each algorithm, providing valuable insights for future applications in structural optimization. [ABSTRACT FROM AUTHOR]

To overcome the limitations of single-type intelligent optimization algorithms prone to becoming stuck in local optima for complex problems, a hybrid intelligent optimization algorithm named SDIQ is proposed. This algorithm combines simulated annealing (SA), differential evolution (DE), quantum-behaved particle swarm optimization (QPSO), and improved particle swarm optimization (IPSO) into a unified framework. Initially, SA is used to explore the solution space and guide individuals toward preliminary optimization. The individuals are then ranked by fitness and divided into three subpopulations, each optimized by DE, QPSO, and IPSO, respectively. After each iteration, probabilistic learning based on fitness logarithms facilitates mutual learning among subpopulations, enabling global information sharing and improvement. The experimental results demonstrate that SDIQ exhibits strong global search capability and stability in solving both standard test functions and real-world engineering problems. Compared to traditional algorithms, SDIQ enhances global convergence and solution efficiency by integrating multiple optimization strategies and leveraging inter-individual learning, providing an effective solution for complex optimization problems. [ABSTRACT FROM AUTHOR]

Due to the dynamic complexities of the multi-unmanned vessel target assignment problem at sea, especially when addressing moving targets, traditional optimization algorithms often fail to quickly find an adequate solution. To overcome this, we have developed a multi-agent reinforcement learning algorithm. This approach involves defining a state space, employing preferential experience replay, and integrating self-attention mechanisms, which are applied to a novel offshore unmanned vessel model designed for dynamic target allocation. We have conducted a thorough analysis of strike positions and times, establishing robust mathematical models. Additionally, we designed several experiments to test the effectiveness of the algorithm. The proposed algorithm improves the quality of the solution by at least 30% in larger scale scenarios compared to the genetic algorithm (GA), and the average solution speed is less than 10% of the GA, demonstrating the feasibility of the algorithm in solving the problem. [ABSTRACT FROM AUTHOR]

The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace's production capacity and the steelmaking converter's consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is a crucial phase in data mining (DM) and machine learning (ML) tasks, aimed at removing uncorrelated and redundant attributes to enhance classification accuracy. This study introduces an improved binary crayfish optimization algorithm (IBCOA) designed to tackle the FS problem. The IBCOA integrates a local search strategy and a periodic mode boundary handling technique, significantly improving its ability to search and exploit the feature space. By doing so, the IBCOA effectively reduces dimensionality, while improving classification accuracy. The algorithm's performance was evaluated using support vector machine (SVM) and k-nearest neighbor (k-NN) classifiers on eighteen multi-scale benchmark datasets. The findings showed that the IBCOA performed better than nine recent binary optimizers, attaining 100% accuracy and decreasing the feature set size by as much as 0.8. Statistical evidence supports that the proposed IBCOA is highly competitive according to the Wilcoxon rank sum test (alpha = 0.05). This study underscores the IBCOA's potential for enhancing FS processes, providing a robust solution for high-dimensional data challenges. [ABSTRACT FROM AUTHOR]

An isogeometric topology optimization (ITO) model for multi-material structures under thermal-mechanical loadings using neural networks is proposed. In the proposed model, a non-uniform rational B-spline (NURBS) function is employed for geometric description and analytical calculation, which realizes the unification of the geometry and computational models. Neural networks replace the optimization algorithms of traditional topology optimization to update the relative densities of multi-material structures. The weights and biases of neural networks are taken as design variables and updated by automatic differentiation without derivation of the sensitivity formula. In addition, the grid elements can be refined directly by increasing the number of refinement nodes, resulting in high-resolution optimal topology without extra computational costs. To obtain comprehensive performance from ITO for multi-material structures, a weighting coefficient is introduced to regulate the proportion between thermal compliance and compliance in the loss function. Some numerical examples are given and the validity is verified by performance analysis. The optimal topological structures obtained based on the proposed model exhibit both excellent heat dissipation and stiffness performance under thermal-mechanical loadings. [ABSTRACT FROM AUTHOR]

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve these problems, we established a mathematical model and proposed a dynamic constrained multiobjective optimization evolution algorithm for the fluid catalytic cracking process. In this algorithm, we design an offspring generation strategy based on minimax solutions, which can explore more feasible regions and converge quickly. Additionally, a dynamic response strategy based on population feasibility is proposed to improve the feasible and infeasible solutions by different perturbations, respectively. To verify the effectiveness of the algorithm, we test the algorithm on ten instances based on the hypervolume metric. Experimental results show that the proposed algorithm is highly competitive with several state-of-the-art competitors. [ABSTRACT FROM AUTHOR]