Real-world Problems Research Articles

Critical Thinking Skills of Slow Learners in Mathematical Problem-Solving: A Systematic Literature Review

Although much research has highlighted slow learners' difficulties in learning mathematics, most studies have focused only on the final learning outcomes without delving into the thinking processes during problem-solving. The lack of research on the cognitive steps slow learners take to develop critical thinking skills creates a gap in the literature that needs to be filled. The article examines the connection between the "critical thinking ability of slow learner students" and "solving mathematical problems." We recommend using the PRISMA flowchart article selection steps for systematic literature reviews. This systematic literature review investigates the critical thinking skills of slow learners in mathematical problem-solving. We screened 756 studies using the PRISMA framework, which yielded 8 relevant articles. Findings identify four main categories of errors (conceptual, principled, algorithmic, and computational) commonly encountered by slow learners, emphasising the necessity of tailored teaching methods and technological interventions. Clinical teaching is crucial for guiding slow learners through their educational journey. Recommendations include employing open-ended tasks and integrating real-world problems to develop critical thinking skills effectively. The study offers valuable insights for educators and curriculum developers aiming to enhance inclusive mathematics education.

A segmented differential evolution with enhanced diversity and semi-adaptive parameter control

Differential evolution (DE) is widely recognized as one of the most potent optimization algorithms, capable of effectively addressing a broad spectrum of optimization challenges. Nevertheless, even the most advanced variants of DE share some common challenges. This paper introduces a novel multi-stage semi-adaptive DE algorithm with enhanced diversity (MSA-DE), offering several key contributions: first, the algorithm is structured into three distinct stages, each employing a unique new mutation strategy and designed a new evolutionary scheme based on this segmentation, to better balance exploration and development at all stages of the process. Secondly, building on the idea of parameter restriction in the evolutionary stage of delineation, a semi-adaptive parameter control method based on the fitness of the irrelevant function is proposed which effectively solves the instability problem of excessive fluctuations in the convergence of adaptive parameters. Thirdly, new diversity maintenance mechanisms are proposed, including population initialization, shrinkage, and updating, which better ameliorated the conflicting issues of search range and search rate that existed at all stages of the DE variant. Finally, comprehensive experiments were conducted on the CEC2013, CEC2014, and CEC2017 benchmark test suites to rigorously assess the accuracy, convergence rate, and overall effectiveness of each module. The results show that MSA-DE exhibits strong competitiveness in single-objective optimisation problems. In addition, the experimental results demonstrate the superiority of the algorithm for real-world engineering problems.

Quantum annealing applications, challenges and limitations for optimisation problems compared to classical solvers

Quantum computing is rapidly advancing, harnessing the power of qubits’ superposition and entanglement for computational advantages over classical systems. However, scalability poses a primary challenge for these machines. By implementing a hybrid workflow between classical and quantum computing instances, D-Wave has succeeded in pushing this boundary to the realm of industrial use. Furthermore, they have recently opened up to mixed integer linear programming (MILP) problems, expanding their applicability to many relevant problems in the field of optimisation. However, the extent of their suitability for diverse problem categories and their computational advantages remains unclear. This study conducts a comprehensive examination by applying a selection of diverse case studies to benchmark the performance of D-Wave’s hybrid solver against that of industry-leading solvers such as CPLEX, Gurobi, and IPOPT. The findings indicate that D-Wave’s hybrid solver is currently most advantageous for integer quadratic objective functions and shows potential for quadratic constraints. To illustrate this, we applied it to a real-world energy problem, specifically the MILP unit commitment problem. While D-Wave can solve such problems, its performance has not yet matched that of its classical counterparts.

Adaptive predator prey algorithm for many objective optimization

Balancing diversity and convergence among solutions in many-objective optimization is challenging, particularly in high-dimensional spaces with conflicting objectives. This paper presents the Many-Objective Marine Predator Algorithm (MaOMPA), an adaptation of the Marine Predators Algorithm (MPA) specifically enhanced for many-objective optimization tasks. MaOMPA integrates an elitist, non-dominated sorting and crowding distance mechanism to maintain a well-distributed set of solutions on the Pareto front. MaOMPA improves upon traditional metaheuristic methods by achieving a robust balance between exploration and exploitation using the predator–prey interaction model. The algorithm underwent evaluation on various benchmarks together with complex real-world engineering problems where it showed superior outcomes when compared against state-of-the-art generational distance and hypervolume and coverage metrics. Engineers and researchers can use MaOMPA as an effective reliable tool to address complex optimization scenarios in engineering design. The MaOMPA source code is available at https://github.com/kanak02/MaOMPA.

Project Based Learning and Technology Integration on Vocational Students’ Learning Experience

ABSTRACT Project-based learning (PBL) is a student-centered and experiential approach that encourages active learning by involving students in the examination of real-world problems within a collaborative environment. This study aims to develop a PBL environment based on information and communication technologies (ICTs) and assess students’ learning experiences. The participants of the study were students taking the Digital Technologies in Tourism course in the Tourism Management Undergraduate Program. Study data were collected through focus group interviews and research diary. By using ICTs as cognitive tools in the learning process, the levels of satisfaction, interest, motivation, and participation of the students were increased and the process was made more active, instructive, and collaborative. The training program in the study made significant contributions to the development of students’ higher order thinking skills, such as collective work, research, analysis and synthesis, communication, design and creativity, critical thinking, problem solving, and decision making.

Leakage Prediction in Real-World Water Distribution Networks using Multi-Objective Multi-Gene Genetic Programming

Understanding leakage is an important challenge within the water sector to minimise waste, energy use and carbon emissions in water distribution networks. Leakage is usually approximated as minimum night flow for each District Metered Area (DMA). However, not all DMAs have instruments to monitor leakage directly, or the main dynamic factors that contribute to it. Therefore, here the leakage is estimated by using the recorded features of its pipes, making use of readily available asset data collected routinely by water companies. The problem is interpreted as a feature construction task for multiple-instance regression and uses a multi-objective multi-gene strongly-typed genetic programming approach to create a set of features that are used by a linear regression model to estimate the average leakage in DMAs. The methodology is applied to a dataset of a large supply area for a water company with 790 DMAs and the results are compared to a previous work which used human-constructed features. A non-dominated analysis is conducted on the appearance of particular features across multiple runs and Shapley values are used to understand the impact and importance of each feature. The results show better performance with significantly fewer, and less complex features. In addition, novel features are found that were not part of the human-constructed features. This article contributes to the wide body of application-focused literature that continues to demonstrate the effectiveness and creativity of digital evolution for real-world problems.

Colored linear inverse model: A data-driven method for studying dynamical systems with temporally correlated stochasticity

In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The linear inverse model (LIM) is a class of data-driven methods that extract dynamic and stochastic information from finite time-series data of complex systems. In this study, we introduce a new variant of LIM, called colored LIM, which models stochasticity using Ornstein-Uhlenbeck colored noise. Despite the nontrivial correlation between observable and colored noise, we show that colored LIM unveils the desired information merely from the correlation function of the observable. Therefore, this approach not only accounts for the memory effects of environmental noise, traditionally represented by time-uncorrelated white noise in the classical-LIM framework, but does so using the same observational dataset without requiring additional data. Furthermore, we show that colored LIM does not reduce to classical LIM in the white noise limit, underscoring the importance of temporal dependencies in stochastic systems. In this paper, we rigorously develop the colored LIM, explore its connections with the classical LIM, dynamic mode decomposition, and vector autoregressive moving average models, and validate its effectiveness on both ideal linear and nonlinear systems. In addition, we illustrate the potential applications and implications of colored LIM for real-world problems, including the El Niño–southern oscillation and the electricity network of Tohoku University. Published by the American Physical Society 2025

DiverSAT: A Novel and Effective Local Search Algorithm for Diverse SAT Problem

For many real-world problems, users are often interested not only in finding a single solution but in obtaining a sufficiently diverse collection of solutions. In this work, we consider the Diverse SAT problem, aiming to find a set of diverse satisfying assignments for a given propositional formula. We propose a novel and effective local search algorithm, DiverSAT, to solve the problem. To cope with diversity, we introduce three heuristics and a perturbation strategy based on some relevant information. We conduct extensive experiments on a large number of public benchmarks, collected from semiformal hardware verification, logistics planning, and other domains. The results show that DiverSAT outperforms the existing algorithms on most of these benchmarks.

Increasing load factor in logistics and evaluating shipment performance with machine learning methods: A case from the automotive industry

The insufficient loading of vehicles, which leads to a low logistics load factor is a common problem in the logistics industry. This study addresses this issue by utilizing actual shipment data from an automotive company. An effective method has been proposed to improve the company’s logistics efficiency through a scenario-based approach. Two real- world scenarios were developed to enhance vehicle loading performance. Machine learning algorithms were employed to evaluate the shipment performance of these scenarios. For the study, a dataset was generated from the company’s ERP system and real-world shipment data. Since this is a real-world problem, the dataset consisted of unlabeled data. To solve this problem, both supervised and unsupervised learning algorithms were applied. First, unsupervised clustering algorithms were used to group the shipment performance based on similarities. Then, supervised learning algorithms were utilized to classify the data within each group. The average cost was used to evaluate the clusters obtained through the unsupervised methods, while classification performance was measured using supervised machine learning techniques. The scenario-based approach has significantly improved the performance of the shipments as it shows the changes in load factor more clearly. In the actual case, only %25.7 of shipments were high performing, while this percentage gradually increased to %98.4 in the scenarios. The results show that optimizing the load factor makes the transports more efficient and balanced.

User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization

Incorporating user preferences into multi-objective Bayesian optimization (MOBO) allows for personalization of the op- timization procedure. Preferences are often abstracted in the form of an unknown utility function, estimated through pair- wise comparisons of potential outcomes. However, utility-driven MOBO methods can yield solutions that are dominated by nearby solutions, as non-dominance is not enforced. Additionally, classical MOBO commonly relies on estimating the entire Pareto front to identify the Pareto-optimal solutions, which can be expensive and ignore user preferences. Here, we present a new method, termed preference-utility-balanced MOBO (PUB-MOBO), that allows users to disambiguate between near-Pareto candidate solutions. PUB-MOBO combines utility-based MOBO with local multi-gradient descent to refine user-preferred solutions to be near-Pareto-optimal. To this end, we propose a novel preference-dominated utility function that concurrently preserves user-preferences and dominance amongst candidate solutions. A key advantage of PUB-MOBO is that the local search is restricted to a (small) region of the Pareto front directed by user preferences, alleviating the need to estimate the entire Pareto-front. PUB-MOBO is tested on three synthetic benchmark problems: DTLZ1, DTLZ2 and DH1, as well as on three real-world problems: Vehicle Safety, Conceptual Marine Design, and Car Side Impact. PUB-MOBO consistently outperforms state-of-the-art competitors in terms of proximity to the Pareto-front and utility regret across all the problems.

Destroy and Repair Using Hyper-Graphs for Routing

Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in this domain has explored two primary categories of methods: iterative and non-iterative. While non-iterative methods struggle to generate near-optimal solutions directly, iterative methods simplify the task by learning local search steps. However, existing iterative methods are often limited by restricted neighborhood searches, leading to suboptimal results. To address this limitation, we propose a novel approach that extends the search to larger neighborhoods by learning a destroy-and-repair strategy. Specifically, we introduce a Destroy-and-Repair framework based on Hyper-Graphs (DRHG). This framework reduces consecutive intact edges to hyper-edges, allowing the model to pay more attention to the destroyed part and decrease the complexity of encoding all nodes. Experiments demonstrate that DRHG achieves state-of-the-art performance on TSP with up to 10,000 nodes and shows strong generalization to real-world TSPLib and CVRPLib problems.

Fast and Interpretable Mixed-Integer Linear Program Solving by Learning Model Reduction

By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers mainly focus on end-to-end solution learning, which suffers from the scalability issue due to the high dimensionality of the solution space. Instead of directly learning the optimal solution, this paper aims to learn a reduced and equivalent model of the original MILP as an intermediate step. The reduced model often corresponds to interpretable operations and is much simpler, enabling us to solve large-scale MILP problems much faster than existing commercial solvers. However, current approaches rely only on the optimal reduced model, overlooking the significant preference information of all reduced models. To address this issue, this paper proposes a preference-based model reduction learning method, which considers the relative performance (i.e., objective cost and constraint feasibility) of all reduced models on each MILP instance as preferences. We also introduce an attention mechanism to capture and represent preference information, which helps improve the performance of model reduction learning tasks. Moreover, we propose a SetCover based pruning method to control the number of reduced models (i.e., labels), thereby simplifying the learning process. Evaluation on real-world MILP problems shows that 1) compared to the state-of-the-art model reduction ML methods, our method obtains nearly 20% improvement on solution accuracy, and 2) compared to the commercial solver Gurobi, two to four orders of magnitude speedups are achieved.

A novel reindeer cyclone optimization algorithm (RCOA)

This paper introduces the Reindeer Cyclone Optimization Algorithm (RCOA), a novel metaheuristic optimization technique inspired by the survival behavior of reindeer during predator attacks in formation cyclonic storms. RCOA imitates the defense-centric cooperative behavior of reindeer, where individuals cluster together to withstand external threats. This behavior is analogous to the optimization process where exploration (global search for exploring new areas) and exploitation (local refinement to copy or learn from neighbor in cyclonic form) are carefully balanced. The algorithm has been extensively evaluated against 14 unimodal and multimodal benchmark functions and 4 real-world complex optimization problems. RCOA demonstrates a moderate improvement of around 5–12% over other algorithms such as PSO, DE, COA and GSA on unimodal functions. On multimodal functions, RCOA shows more competitive performance, especially in terms of stability, with an improvement of around 10–15% in accuracy and consistency compared to WDO and PSO. The algorithm is evaluated using the CEC’17 benchmark suite with 50 dimensions and compared against different well-established optimization algorithms, including WOA, PSO, GSA, and DE. Experimental results demonstrate that RCOA outperforms existing methods on multiple test functions by achieving superior convergence speed and solution accuracy. The Wilcoxon Signed-Rank test confirms the statistical significance of RCOA’s performance, indicating its robustness and reliability in handling diverse optimization landscapes. The findings suggest that RCOA is a competitive optimization method suitable for a wide range of real-world applications.

BOIDS: High-Dimensional Bayesian Optimization via Incumbent-Guided Direction Lines and Subspace Embeddings

When it comes to expensive black-box optimization problems, Bayesian Optimization (BO) is a well-known and powerful solution. Many real-world applications involve a large number of dimensions, hence scaling BO to high dimension is of much interest. However, state-of-the-art high-dimensional BO methods still suffer from the curse of dimensionality, highlighting the need for further improvements. In this work, we introduce BOIDS, a novel high-dimensional BO algorithm that guides optimization by a sequence of one-dimensional direction lines using a novel tailored line-based optimization procedure. To improve the efficiency, we also propose an adaptive selection technique to identify most optimal lines for each round of line-based optimization. Additionally, we incorporate a subspace embedding technique for better scaling to high-dimensional spaces. We further provide theoretical analysis of our proposed method to analyze its convergence property. Our extensive experimental results show that BOIDS outperforms state-of-the-art baselines on various synthetic and real-world benchmark problems.

On Shallow Planning Under Partial Observability

Formulating a real-world problem under the Reinforcement Learning framework involves non-trivial design choices, such as selecting a discount factor for the learning objective (dis- counted cumulative rewards), which articulates the planning horizon of the agent. This work investigates the impact of the discount factor on the bias-variance trade-off given structural parameters of the underlying Markov Decision Process. Our results support the idea that a shorter planning horizon might be beneficial, especially under partial observability.

Expensive Multi-Objective Bayesian Optimization Based on Diffusion Models

Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is difficult with limited function evaluations. Existing Pareto set learning algorithms may exhibit considerable instability in such expensive scenarios, leading to significant deviations between the obtained solution set and the Pareto set (PS). In this paper, we propose a novel Composite Diffusion Model based Pareto Set Learning algorithm (CDM-PSL) for expensive MOBO. CDM-PSL includes both unconditional and conditional diffusion model for generating high-quality samples efficiently. Besides, we introduce a weighting method based on information entropy to balance different objectives. This method is integrated with a guiding strategy to appropriately balancing different objectives during the optimization process. Experimental results on both synthetic and real-world problems demonstrates that CDM-PSL attains superior performance compared with state-of-the-art MOBO algorithms.

From Crayons to Code: AI-Driven Insights into a Child’s Mental Health Through Drawings

Children's mental health is crucial for their development, but it's often overlooked, leading to psychological issues. Many children struggle to express their thoughts and feelings effectively. To address this issue, we have proposed a novel approach to analyze children's drawings for psychological screening using artificial intelligence. Specifically, we're focusing on the `draw a person' (DAP) test, where a child's drawing is used to identify potential indicators of their mental and emotional state. Thus, we are introducing an AI-powered technique to automate the psychological screening process for children using the DAP test, which a human professional would traditionally conduct. The screening tool would suggest whether the child needs or doesn’t need further psychological referral. We have collected a dataset consisting of children's drawings and labeled them by experts as either `need' or `no need', indicating whether the child needs or does not need a referral. We have proposed two alternative approaches for the screening process. The first approach consists of extracting features from the drawings following expert guidelines and training a classification model using the features to classify the drawing as either `need' or `no need'. We also propose an out-of-the-box technique applying prompt engineering on state-of-the-art LLMs to automatically extract features from the images. The second approach involves training an image classification model using the drawings. Both approaches are challenged by the issue of class imbalance, as most of the drawings correspond to the `no-need' class. To address this challenge, we introduce Siamese++, a novel Siamese network for image classification, which uses feature embedding and an adaptive distance threshold for classification, instead of the nearest neighbor classification employed by traditional Siamese. Our proposed method achieves a high F1 score (up to 88%) even with a large class imbalance and without the need for any image augmentation. Thus, we have proposed an innovative interdisciplinary integration of AI with psychology and developed novel techniques to solve the real-world problem of psychological screening.

A Novel Beagle Inspired Optimization Algorithm: Compre-hensive Evaluation on Benchmarking Functions

This paper presents an evaluation of the novel Beagle-Inspired Optimization Algorithm (BIOA), inspired by the scent detection and rabbit hunting strategies of beagle dogs, such as scent detection, tracking, trail following, pattern recognition, continuous adaptation, persistent and exhaustive search, and escape and retrieval. BIOA is compared with well-established algorithms, including Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), and Cuckoo Search (CS), across a set of benchmark functions, including Sphere, Rosenbrock, Rastrigin, Griewank, Ackley, Levy, and Schwefel functions. The results demonstrate BIOA's superior performance, achieving the lowest mean fitness values and best solutions across most test cases. Its balanced exploration and exploitation phases enable effective optimization. While BIOA excels in many instances, it requires further improvements in computational efficiency, particularly for high-dimensional problems. Future research should focus on enhancing BIOA's performance through advanced models, hybrid optimization techniques, and real-world problem applications, thus broadening its practical impact in solving complex optimization tasks.

Dimension Reduction with Locally Adjusted Graphs

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often involves converting the original high-dimensional data into a graph. In this graph, each edge represents the similarity or dissimilarity between pairs of data points. However, this graph is frequently suboptimal due to unreliable high-dimensional distances and the limited information extracted from the high-dimensional data. This problem is exacerbated as the dataset size increases. If we reduce the size of the dataset by selecting points for a specific sections of the embeddings, the clusters observed through DR are more separable since the extracted subgraphs are more reliable. In this paper, we introduce LocalMAP, a new dimensionality reduction algorithm that dynamically and locally adjusts the graph to address this challenge. By dynamically extracting subgraphs and updating the graph on-the-fly, LocalMAP is capable of identifying and separating real clusters within the data that other DR methods may overlook or combine. We demonstrate the benefits of LocalMAP through a case study on biological datasets, highlighting its utility in helping users more accurately identify clusters for real-world problems.

Optimising work-sharing in disassembly line balancing problems: a multi-cycle strategy

To improve workload balance and reduce cycle time in disassembly line balancing problems, a multi-cycle work-sharing strategy that allows tasks to be reassigned across sub-cycles is proposed for the first time. While this strategy enhances disassembly efficiency, it also increases total resource demands, as different tasks may require distinct resources for effective execution. Therefore, to effectively address this challenge, a bi-objective integer linear programming model is established with the goal of minimising both overall cycle time and total resource count. The epsilon constraint method is then employed to obtain solutions for small-scale problems. For large-scale problems, a Double Deep Q-Network-based Hyper-Heuristic (DDQN-HH) algorithm is developed. This approach incorporates specialised encoding and decoding strategies, two state functions, and eight heuristic action rules to enhance its effectiveness. And comparative experiments using multi-objective evaluation metrics demonstrate the DDQN-HH algorithm's superiority over three other leading algorithms: the Deep Q-Network-based Hyper Heuristic (DQN-HH) algorithm, the Random, Greedy-based Hyper Heuristic (RG-HH) algorithm, and the Multi-objective Equilibrium Optimiser (MOEO) algorithm. Furthermore, the DDQN-HH's practical significance in addressing real-world engineering problems is validated through managerial applications.