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A quadratic programming problem with positive definite Hessian subject to box constraints is solved, using an active-set approach. Convex quadratic programming (QP) problems with box constraints appear quite frequently in various real-world applications. The proposed method employs an active-set strategy with Lagrange multipliers, demonstrating rapid convergence. The algorithm, at each iteration, modifies both the minimization parameters in the primal space and the Lagrange multipliers in the dual space. The algorithm is particularly well suited for machine learning, scientific computing, and engineering applications that require solving box constraint QP subproblems efficiently. Key use cases include Support Vector Machines (SVMs), reinforcement learning, portfolio optimization, and trust-region methods in non-linear programming. Extensive numerical experiments demonstrate the method’s superior performance in handling large-scale problems, making it an ideal choice for contemporary optimization tasks. To encourage and facilitate its adoption, the implementation is available in multiple programming languages, ensuring easy integration into existing optimization frameworks. Full article

In the research and practice of integrated scheduling problems, the tree structure of complex products usually presents an asymmetric and complex form. This asymmetry is mainly reflected in the hierarchical relationship between the various components of the product, the degree of dependence, and the sequence of production processes. Existing studies often neglect that leaf nodes with the lowest layer priority can be scheduled at any moment, leading to underutilization of parallelism potential under symmetric structures and exacerbation of critical path delays under asymmetric structures. Aiming at solving this kind of problem, an integrated scheduling algorithm based on the improved Floyd algorithm (ISA-IFA) is proposed. According to the improved Floyd algorithm, the algorithm proposed a path-weighted strategy, which constructs the vertical path value according to the processing time of the process itself. Combined with the proposed process scheduling advantage strategy, the leaf node process is especially emphasized as the priority scheduling object, which makes the connection between the processes more closely, and then significantly reduces the idle time of the equipment. The empirical results show that the ISA-IFA algorithm shortens the completion time of complex products and simultaneously improves the equipment utilization rate to 55.9%, verifying its effectiveness in dynamic scheduling and resource co-optimization. Full article

This paper introduces a two-phase decision support system based on information theory and financial practices to assist investors in solving cardinality-constrained portfolio optimization problems. Firstly, the approach employs a stock-picking procedure based on an interactive multi-criteria decision-making method (the so-called TODIM method). More precisely, the best-performing assets from the investable universe are identified using three financial criteria. The first criterion is based on mutual information, and it is employed to capture the microstructure of the stock market. The second one is the momentum, and the third is the upside-to-downside beta ratio. To calculate the preference weights used in the chosen multi-criteria decision-making procedure, two methods are compared, namely equal and entropy weighting. In the second stage, this work considers a portfolio optimization model where the objective function is a modified version of the Sharpe ratio, consistent with the choices of a rational agent even when faced with negative risk premiums. Additionally, the portfolio design incorporates a set of bound, budget, and cardinality constraints, together with a set of risk budgeting restrictions. To solve the resulting non-smooth programming problem with non-convex constraints, this paper proposes a variant of the distance-based parameter adaptation for success-history-based differential evolution with double crossover (DISH-XX) algorithm equipped with a hybrid constraint-handling approach. Numerical experiments on the US and European stock markets over the past ten years are conducted, and the results show that the flexibility of the proposed portfolio model allows the better control of losses, particularly during market downturns, thereby providing superior or at least comparable ex post performance with respect to several benchmark investment strategies. Full article

This study examines the effects of implementing a movement-integrated instruction (MII) program in third-grade mathematics classes with a focus on students’ mathematical learning outcomes and physical literacy development. The program was designed using the Analysis, Design, Development, Implementation and Evaluation (ADDIE) instructional model and was implemented in a public elementary school in South Korea. While the primary instructional emphasis was placed on improving mathematical concept comprehension and problem solving, the study also evaluated outcomes in three core areas of physical literacy: physical competence, motivation and confidence, and knowledge and understanding of physical activity. A descriptive qualitative approach was adopted and supplemented with quantitative data. The data sources included classroom observations, learning artifacts, teacher reflections, semi-structured interviews, and structured student surveys. The results showed that 82.6% of students reported improved bodily control and coordination, while 75.4% indicated that they used skills acquired through physical education (PE) to solve math problems. Student work demonstrated an increasing use of multi-step reasoning, diagrammatic representations, and contextual explanations, suggesting that embodied learning reinforces both cognitive engagement and physical development. Although challenges related to time, space, and varying motor abilities were encountered, they were addressed through interdisciplinary integration and differentiated instructional strategies. This study provides empirical support for MII as a pedagogical model that effectively bridges academic learning and physical development, and offers practical recommendations for broader applications in elementary education. Full article

The Diminishing-Return (DR)-submodular function maximization problem has garnered significant attention across various domains in recent years. Classic methods often employ continuous greedy or Frank–Wolfe approaches to tackle this problem; however, high iteration and subproblem solver complexity are typically required to control the approximation ratio effectively. In this paper, we introduce a strategy that employs a binary search to find the dynamic stepsize, integrating it into traditional algorithm frameworks to address problems with different constraint types. We demonstrate that algorithms using this dynamic stepsize strategy can achieve comparable approximation ratios to those using a fixed stepsize strategy. In the monotone case, the iteration complexity is $O\left({\parallel \nabla F\left(\mathbf{0}\right)\parallel }_1{ϵ}^{-1}\right)$, while in the non-monotone scenario, it is $O\left(n+{\parallel \nabla F\left(\mathbf{0}\right)\parallel }_1{ϵ}^{-1}\right)$, where F denotes the objective function. We then apply this strategy to solving stochastic DR-submodular function maximization problems, obtaining corresponding iteration complexity results in a high-probability form. Furthermore, theoretical examples as well as numerical experiments validate that this stepsize selection strategy outperforms the fixed stepsize strategy. Full article

In this paper, the dispatch for the industrial micro-grid with an integrated photovoltaic-gas-manufacturing facility system considering carbon emissions and operation costs is investigated. Two kinds of energy, electricity and natural gas, are contained in the integer energy system, in which the electricity mainly comes from the PV panels and the utility electricity network, and the natural gas mainly comes from the utility gas network. In addition, electricity and natural gas can be converted into each other. Four kinds of loads, electricity load, gas load, heating load and cooling load, need to be satisfied, in which the electricity load can be divided into fixed load and flexible load. The flexible load comes from the scheduling for manufacturing facilities, and the scheduling of manufacturing facilities is modeled as a kind of deferable load to be integrated into the energy system. Moreover, daily operation costs and carbon emissions are considered in the decision, and the deviation preference strategy is used to solve this multi-objective optimization problem. Finally, a case study with a lithium-ion battery assembly system is proposed. According to the results, it can be found that the proposed model can help managers realize effective scheduling of the industrial micro-grid. Full article

The steady-state energy flow calculation (EFC) of multi-energy systems (MESs) is a fundamental foundation for MES planning and operation. However, most of the existing MES models are designed case-specifically, making them incapable of modelling diverse scenarios. Moreover, since it involves initial value setting, the convergence of the Newton–Raphson (NR) method to solve the EFC problem of MESs is often unsatisfactory. To tackle these problems, a matrix-based EFC method of MESs is proposed in this paper. The universal matrix formulations of heat and gas subnetworks are first constructed, where the injection of alternative gas sources and the effect of gas compressibility factor on the MES state are both considered. Due to the uncertainty of gas flow direction during the NR iteration process, the gas composition tracking equations are modified to avoid ill conditions. The Jacobian matrices for the constructed subnetwork models are then derived and expressed in matrix form. On this basis, the unified NR strategy is adopted to solve the constructed models. Finally, the performance of the proposed method is verified through case studies. The results demonstrate that the proposed models can accurately capture the MES operating state and achieve significant improvements in convergence and computational efficiency compared to traditional models. Full article

As the second largest power source in the world, hydropower plays a crucial role in the operation of power systems. This paper focuses on the key issues of regulating hydropower stations participating in the spot market. It aims at the core challenges, such as the conflict of cascade hydro plants’ joint clearing, the lack of adaptability for different types of power supply bidding on the same platform, and the contradiction between long-term operation and the spot market. Through the construction of a water spillage management strategy and settlement compensation mechanism, the competitive abandoned water problem caused by mismatched quotations of cascade hydro plants can be solved. In order to achieve reasonable recovery of the power cost, a separate bidding mechanism and capacity cost recovery model are designed. Subsequently, the sufficient electricity supply constraint of the remaining period is integrated into the spot-clearing model, which can coordinate short-term hydropower dispatch with long-term energy storage demand. The operation of the Yunnan electricity spot market is being simulated to verify the effectiveness of the proposed method. Full article

The physical health of college students is an important basis for societal development, which directly impacts the competitiveness of future talents and the overall vitality of the nation. To accurately and timely identify the physical health status of college students, a hybrid model of DE-XGBoost is proposed in this study: a discrete coding strategy is designed to solve the XGBoost hyperparameter optimization problem, and differential evolution (DE) is used to achieve global parameter optimization. Based on 20,452 physical test records of a university in 2022, the empirical comparison shows that the accuracy rate, recall rate, and F1 value of the model are improved by 3.5–7.9% compared with support vector machine (SVM), gradient boosting machine (GBM), and multi-layer perceptron (MLP), showing significant performance advantages. This research provides a novel and efficient framework for physical fitness classification, with potential applications in educational curriculum design. Full article

This paper presents an adaptive strategy to solve the formation control problem for a set of second-order agents with parametric uncertainty and nonlinearity. The strategy regards a group of agents where the nonlinearities and uncertainties are represented by a linearly parametrized term, which allows us to consider non-identical agents. In order to ensure the collision-free motion of agents, we propose the use of a repulsive vector field component that is applied only when a pair of agents becomes nearer than a predefined minimum bound. Numerical simulations were carried out to show the effectiveness of the proposed scheme. First, a simplified example was used to verify the key features of the control law, followed by a general case to illustrate the performance of the algorithm in a more complex scenario. Full article

Collagenase has a wide range of applications in the medicine, cosmetic, and food industries. Inefficient expression of collagenase impedes its industrial production and commercial applications. In this study, a secretory expression system for collagenase ColH from Clostridium histolyticum was constructed in Bacillus subtilis. Signal peptide optimization effectively solved the secretion problem of large collagenase with a molecular weight of about 116 kDa, doubling the extracellular enzyme activity. Then, promoter optimization further improved the enzyme activity to 264 U/mL. By the co-optimization of the nitrogen sources and carbon sources, and employing a fed-batch fermentation strategy, the enzyme activity could reach 669 U/mL, which is, currently, the highest level reported in the industry. The recombinant collagenase ColH was purified through a purification process suitable for industrial production with a specific activity of 565.25 U/mg. Based on the purified collagenase, cells were successfully prepared from adipose tissue, indicating its potential use in cell therapy. This study provides a promising candidate for the industrial production of collagenase and highlights its potential application to extract cells from tissues. Full article

Within the 21st century, in the Maritime Silk Road, wave energy, a clean renewable source, is drawing more interest, especially in areas with power shortages. This paper investigates wave energy in ships, particularly in a hybrid electric bulk carrier, by designing a system that supplements the existing power setup with oscillating buoy wave energy converters. The system includes diesel generators (DGs), a wave energy generation system, heterogeneous energy storage (consisting of battery storage (BS) and thermal storage (TS)), a combined cooling heat and power (CCHP) unit, and a power-to-thermal conversion (PtC) unit. To ensure safe and reliable navigation despite uncertainties in wave energy output, onboard power loads, and outdoor temperature, a robust coordination method is adopted. This method employs a two-stage robust optimization (RO) strategy to coordinate the various onboard units across different time scales, minimizing operational costs while satisfying all operational constraints, even in the worst-case scenarios. By applying constraint linearization, the robust coordination model is formulated as a mixed-integer linear programming (MILP) problem and solved using an efficient solver. Finally, the effectiveness of the proposed method is validated through case studies and comparisons with existing ship operation benchmarks, demonstrating significant reductions in operational costs and robust performance under various uncertain conditions. Notably, the simulation results for the Singapore–Trincomalee route show an 18.4% reduction in carbon emissions compared to conventional systems. Full article

The design of differential evolution (DE) operators has long been a key topic in the research of metaheuristic algorithms. This paper systematically reviews the functional differences between mechanism improvements and operator improvements in terms of exploration and exploitation capabilities, based on the general patterns of algorithm enhancements. It proposes a theoretical hypothesis: operator improvement is more directly associated with the enhancement of an algorithm’s exploitation capability. Accordingly, this paper designs a new differential operator, DE/current-to-pbest/order, based on the classic DE/current-to-pbest/1 operator. This new operator introduces a directional judgment mechanism and a replacement strategy based on individual fitness, ensuring that the differential vector consistently points toward better individuals. This enhancement improves the effectiveness of the search direction and significantly strengthens the algorithm’s ability to delve into high-quality solution regions. To verify the effectiveness and generality of the proposed operator, it is embedded into two mainstream evolutionary algorithm frameworks, JADE and LSHADE, to construct OJADE and OLSHADE. A systematic evaluation is conducted using two authoritative benchmark sets: CEC2017 and CEC2011. The CEC2017 set focuses on assessing the optimization capability of theoretical complex functions, covering problems of various dimensions and types; the CEC2011 set, on the other hand, targets multimodal and hybrid optimization challenges in real engineering contexts, featuring higher structural complexity and generalization requirements. On both benchmark sets, OLSHADE demonstrates outstanding solution quality, convergence efficiency, and result stability, showing particular advantages in high-dimensional complex problems, thus fully validating the effectiveness of the proposed operator in enhancing exploitation capability. In addition, the operator has a lightweight structure and is easy to integrate, with good portability and scalability. It can be embedded as a general-purpose module into more DE variants and EAs in the future, providing flexible support for further performance optimization in solving complex problems. Full article

In this paper, we develop an analytical approximate solution for the nonlinear time-fractional Fisher’s equation using a right starting space function and a unique analytic-numeric technique referred to as the Laplace residual power series approach. The generalized Taylor’s formula and the Laplace transform operator are coupled in the aforementioned method, where the coefficients, obtained through fractional expansion in the Laplace space, are determined by applying the limit concept. In order to validate and illustrate the theoretical methodology of the LRPS technique, as well as to show its effectiveness, adaptability, and superiority in solving various types of nonlinear time and space fractional differential equations, numerical experiments are generated. The obtained analytical solutions are compatible with the precise solutions and concur with those proposed by the other approaches. The outcomes show that the Laplace residual power series strategy is incredibly successful, straightforward to implement, and well suited for handling the complexity of nonlinear problems. Full article

In response to the limitations observed in existing single intelligent optimization algorithms, particularly their shortcomings in their global search capability and population diversity, we propose the Adaptive Differential Evolution Integral (ADEI) algorithm. Drawing inspiration from the collective behaviors observed in social organisms, this algorithm introduces four roles—“leaders”, “followers”, “contemplators”, and “rationalists”—employing a dynamic following strategy to effectively integrate these diverse particles and populations. Specifically, individuals in the Differential Evolution algorithm serve as the leader population, with tailored trial vector generation strategies implemented to enhance the global search capability. Concurrently, improvements are made to the particle swarm optimization algorithm to facilitate its role as the evolution strategy for other populations. By adopting this approach, the algorithm’s population diversity is enhanced, striking a balance between the global and local search performance, thereby augmenting its search efficiency and convergence accuracy. Extensive tests using benchmark functions and engineering problems show that the proposed algorithm excels in over half of the 28 test functions. It demonstrates strong convergence and adaptability for unimodal, multimodal, and composite problems. Experiments on solving inverse heat conduction problems validate its effectiveness in real-world scenarios and highlight its potential for engineering applications. Full article