Solution Space Research Articles

GOHBA: Improved Honey Badger Algorithm for Global Optimization

Aiming at the problem that the honey badger algorithm easily falls into local convergence, insufficient global search ability, and low convergence speed, this paper proposes a global optimization honey badger algorithm (Global Optimization HBA) (GOHBA), which improves the search ability of the population, with better ability to jump out of the local optimum, faster convergence speed, and better stability. The introduction of Tent chaotic mapping initialization enhances the population diversity and initializes the population quality of the HBA. Replacing the density factor enhances the search range of the algorithm in the entire solution space and avoids premature convergence to a local optimum. The addition of the golden sine strategy enhances the global search capability of the HBA and accelerates the convergence speed. Compared with seven algorithms, the GOHBA achieves the optimal mean value on 14 of the 23 tested functions. On two real-world engineering design problems, the GOHBA was optimal. On three path planning problems, the GOHBA had higher accuracy and faster convergence. The above experimental results show that the performance of the GOHBA is indeed excellent.

Three-dimensional inversion algorithm of magnetotelluric data based on solution space dimensionality reduction technique

The magnetotelluric (MT) method is highly advantageous in geothermal resource exploration because of its deep probing capability, low cost, and sensitivity to key geothermal system elements such as heat sources, reservoirs, and caprocks. To address the challenge of balancing the MT inversion resolution and computational efficiency, we propose a Gauss–Newton optimization inversion algorithm based on the solution space dimensionality reduction technique. This algorithm uses solution space dimensionality reduction to establish algebraic mapping relationships between the edges of grid cells, effectively reducing the degrees of freedom in the linear equation system required for forward and pseudo-forward modeling, thereby saving computational costs. In addition, during the inversion process, a multiple right-hand direct–iterative hybrid solver is employed to solve the dimensionally reduced linear equation s, further enhancing the computational efficiency of the inversion. We then validate and analyze the accuracy and efficiency of the forward and inversion algorithms using various synthetic models. Finally, we apply this inversion strategy to field MT data from the Dabie Mountain geothermal area in eastern China. On the basis of the inversion results, we then analyze the thermal genesis model of the region, providing technical support for the exploration and development of deep geothermal resources.

A Social Group Optimization Algorithm Using the Laplace Operator for the Economic Dispatch Problem

The economic dispatch (ED) problem focuses on the optimal scheduling of thermal generating units in a power system to minimize fuel costs while satisfying operational constraints. This article proposes a modified version of the social group optimization (SGO) algorithm to address the ED problem with various practical characteristics (such as valve-point effects, transmission losses, prohibited operating zones, and multi-fuel sources). SGO is a population-based metaheuristic algorithm with strong exploration capabilities, but for certain types of problems, it may stagnate in a local optimum due to a potential imbalance between exploration and exploitation. The new version, named SGO-L, retains the structure of the SGO but incorporates a Laplace operator derived from the Laplace distribution into all the iterative solution update equations. This adjustment generates more effective search steps in the solution space, improving the exploration–exploitation balance and overall performance in terms of solution stability and quality. SGO-L is validated on four power systems of small (six-unit), medium (10-unit), and large (40-unit and 110-unit) sizes with diverse characteristics. The efficiency of SGO-L is compared with SGO and other metaheuristic algorithms. The experimental results demonstrate that the proposed SGO-L algorithm is more robust than well-known algorithms (such as particle swarm optimization, genetic algorithms, differential evolution, and cuckoo search algorithms) and other competitor algorithms mentioned in the study. Moreover, the non-parametric Wilcoxon statistical test indicates that the new SGO-L version is more promising than the original SGO in terms of solution stability and quality. For example, the standard deviation obtained by SGO-L shows significantly lower values (6.02 × 10−9 USD/h for the six-unit system, 7.56 × 10−5 USD/h for the 10-unit system, 75.89 USD/h for the 40-unit system, and 4.80 × 10−3 USD/h for the 110-unit system) compared to SGO (0.44 USD/h for the six-unit system, 50.80 USD/h for the 10-unit system, 274.91 USD/h for the 40-unit system, and 1.04 USD/h for the 110-unit system).

Impact of bivariate Gaussian potentials on quantum walks for spatial search

Abstract Quantum search algorithms are crucial for exploring large solution spaces, but their robustness to environmental perturbations, such as noise or disorder, remains a critical challenge. We examine the impact of biased disorder potentials modeled by a bivariate Gaussian distribution function on the dynamics of quantum walks in spatial search problems. Building on the Ambainis-Kempe-Rivosh (AKR) model for searching on a two-dimensional grid, we incorporate potential fields to investigate how changes in standard deviation and normalization of the bivariate Gaussian function impact the performance of the search algorithm. Our results show that the quantum walk closely mirrors the AKR algorithm when the standard deviation is small but exhibits a rapid decay in success probability as the standard deviation increases.
This behavior demonstrates how the bivariate Gaussian can effectively model a noisy oracle within the AKR algorithm. Additionally, we compare the AKR-based model with an alternative quantum walk model using a Hadamard coin and standard shift. These findings contribute to understanding the robustness of quantum walk search algorithms, and provide insights into how quantum walks can be applied to optimization algorithms.

The high-pressure, vacancy-stabilized component in clinopyroxenes

Abstract Motivated by the recent discovery of albitic clinopyroxene, we assess the molar volume systematics of vacancy-stabilized, high-pressure clinopyroxenes. Previous assessments used the Ca-Eskola component (Ca0.5□0.5)M2AlM1Si2TO6 (where the empty rectangle symbol denotes a vacancy) as an end-member and were limited to compositions with ≤ 50% vacancies in the M2 site. The discovery of albitic jadeite calls for extension of the solid solution space towards an end member with entirely vacant M2 sites, □M2SiM1Si2TO6, i.e. silica in the C2/c pyroxene structure. Based on our new and compiled data, we fit a model for volumes of clinopyroxenes in an 11-component subsystem. We tested two different scenarios: ideal mixing and symmetric excess volumes. Ideal mixing is easily rejected, as the correlation between vacancy concentration and volume at standard conditions is clearly nonlinear. The symmetric excess volume model, however, yields an adequate fit to the data when using 3 excess terms (Hd-En, Hd-Di, and Hd-Jd). The estimated molar volume of the clinopyroxene-structured silica end member, which has one octahedrally-coordinated silicon atom per formula unit, is 60.77 ± 0.75 cm3/mol on a six-oxygen formula basis, slightly smaller than that of coesite (61.73 cm3/mol) but much larger than that of stishovite (41.44 cm3/mol). We also obtained a molar volume of 62.16 ± 0.75 cm3/mol for the Ca-Eskola component, modestly larger than earlier estimates extrapolated with an ideal mixing assumption from natural samples (60.52 ± 0.73 cm3/mol) or experiments (60.87 ± 0.63 cm3/mol). The proposed volume model provides a partial basis for assessing the formation conditions of vacancy-stabilized pyroxenes.

Dynamic behavior of solitons in nonlinear Schrödinger equations

The primary objective of this study is to derive analytical solutions for a significant system that models the evolution of complex wave fields in nonlinear media. This system extends the framework of nonlinear Schrödinger equations and is pivotal in various physical applications, including optical fibers and Bose-Einstein condensates. By employing advanced analytical techniques such as the Khater II, III (Khat II, Khat III) and Unified (UF) methods, we successfully obtain exact analytical solutions that enhance our understanding of the system’s dynamic behavior. The findings reveal a variety of soliton-like solutions, demonstrating the robustness and effectiveness of the methodologies employed. This research underscores the importance of the system in modeling intricate physical phenomena and offers a novel perspective on its solution space. The originality of this study lies in the innovative application of Khat II, Khat III, and UF methods to this system, providing valuable insights and methodologies for future research endeavors. This work represents a significant contribution to applied mathematics and nonlinear dynamics, emphasizing the physical relevance of the system in representing nonlinear wave interactions. The analytical solutions obtained can facilitate precise control and prediction of wave behaviors in practical applications, thereby advancing our capability to manipulate and harness nonlinear wave phenomena in diverse scientific and engineering contexts.

A fast local search for the identical parallel machine scheduling problem with the position‐based deteriorating effect and maintenance

AbstractIn this paper, we develop a fast local search for the identical parallel machine scheduling problem with maintenance activities and the position‐based deteriorating under the maximum lateness minimization. Our approach allows us to calculate criterion values in a constant time per solution in a neighbourhood. The application is given on the basis of the Nawaz–Ensore–Ham method, iterative local search, tabu search, and a family of memetic search algorithms, where their efficiency equipped with our method is compared with their classical versions. The computational experiments confirm the theoretical analysis that our approach essentially overwhelms the typical implementation and speeds up the related algorithms over 200 times for reasonable problem sizes. Thereby it allows us to search for significantly larger solution space at the same time and, therefore, radically improve the criterion values of the obtained solutions.

Research on large-scaled wire-bonding machine scheduling in SAT: EAHA with knowledge learning and progressive fusion decomposition

ABSTRACT Wire-bonding machine scheduling in Semiconductor Assembly and Testing (SAT) involves thousands of lots and hundreds of machines, challenging high-quality solutions in a reasonable time. This paper proposes a framework named the Enhanced Artificial Hummingbird Algorithm with Knowledge Learning and Progressive Fusion Decomposition (EAHA-KLPFD), integrating knowledge learning and progressive fusion decomposition. It is employed for rational decomposition, preserves solution space integrity, accelerates solving, and enhances search efficiency. Otherwise, the enhanced artificial hummingbird algorithm proposed improves subproblem precision. Experiments demonstrate that the framework excels in accuracy and speed and provides an effective solution for wire-bonding machine scheduling in SAT system.

Joint optimization of storage assignment and order batching in robotic mobile fulfillment system with dynamic storage depth and surplus items

This paper studies the joint optimization of storage location assignment and order batching in robotic mobile fulfillment systems (RMFS), considering dynamic storage depth and surplus items. Firstly, a joint optimization model of storage location assignment and order batching is established. The model is divided into two stages. The first stage is the item location assignment optimization model, which is used to describe the types and quantities of items placed in each slot on each pod. The second stage is the joint optimization model of pod location assignment and order batching, which is used to describe the coordinates of each pod, the number of order batches, and the order combinations contained in each batch. Considering the vast solution space and the numerous constraints of the constructed model, a two-stage greedy variable neighborhood simulated annealing algorithm (TGVNSA) is introduced to address these challenges. Finally, numerical experiments prove that the algorithm can effectively solve the established model. TGVNSA is evaluated against two conventional methods: variable neighborhood search and adaptive genetic algorithms, focusing on metrics such as pod retrieval times, comprehensive picking costs, CPU time, and CQ value (comprehensive quality in the item location assignment). The findings demonstrate that TGVNSA boasts superior comprehensive performance. Compared with other commonly used strategies in the field such as random, classification, and optimal relevance, the method proposed in this paper demonstrates superior optimization performance, particularly when considering dynamic storage depth and surplus items. Moreover, this paper also proves that, under the same combination of strategies, the joint optimization method proposed in this paper reduces the comprehensive picking costs by 11.46% compared to the separate optimization approach.

Deconvolution Density Estimation with Penalized MLE

Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all infinite-dimensional deconvolution methods in the literature use Fourier transformations. These methods are mathematically neat, but unstable, and produce bad estimates when signal-noise ratio or sample size are low. A popular alternative is to maximize penalized likelihood for a finite-dimensional basis expansion of the unknown density. We develop a new method to optimize penalized likelihood over the infinite-dimensional space of all functions. This gives the stability of regularized likelihood methods without restricting the space of solutions. Our method compares favorably with state-of-the-art methods on simulated and real data, particularly for small sample size or low signal-noise ratio. We also provide the first results on the consistency and rate of convergence of penalized maximum likelihood estimates for density deconvolution. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Projected Wave Function Extrapolation Scheme to Accelerate Plane-Wave Hybrid Functional-Based Born-Oppenheimer Molecular Dynamics Simulations.

Born-Oppenheimer molecular dynamics (BOMD) simulations are of great interest for the dynamic properties of molecular and solid systems. However, BOMD simulations necessitate not only an extensive period of dynamical evolution but also costly self-consistent-field (SCF) electronic structure calculations, especially for hybrid functional-based BOMD (H-BOMD) simulations within plane-wave basis sets. Here, we propose an improved always stable predictor-corrector (ASPC) method for the wave function extrapolation to accelerate the plane-wave H-BOMD simulations, named projected ASPC (PASPC), yielding a wave function closer to the actual solution space and efficiently reducing the number of SCF iterations at each MD step. We investigated the convergence properties of different extrapolation schemes for molecular and solid systems. Numerical results demonstrate that plane-wave H-BOMD simulations can be significantly faster than conventional cases by combining the accelerated algorithms with the PASPC method. The energy drift is also evaluated, showing that PASPC produces energy drift with smaller oscillations and can simulate a larger time step for systems containing heavy atoms, demonstrating the accuracy of the extrapolation schemes. Furthermore, H-BOMD simulations showcase more accurate power and infrared spectra of silicon dioxide and liquid water that are comparable to those of experimental measurements.

A low-carbon scheduling method based on improved ant colony algorithm for underground electric transportation vehicles

Improved scheduling of underground transportation vehicles in coal mines can significantly enhance work efficiency and contribute to safer production. However, the specific working conditions and limitations of electric vehicles pose significant challenges to effective vehicle scheduling. To address this issue, a constrained single-objective optimization model is developed to minimize transportation costs for low-carbon scheduling of underground electric transportation vehicles (ETVs). The model incorporates constraints related to load capacity, cruising range, and safety regulations. A specific energy consumption model for ETVs is formulated, considering factors such as road conditions, load, and driving state. To solve this problem, an improved ant colony optimization algorithm integrated with Q-learning (ACO-QL) is proposed. Specifically, ant colony optimization explores the global solution space and identifies promising regions, while the split strategy effectively distributes demand across multiple vehicles. Q-learning enhances local search by selecting the most appropriate operator, preventing premature convergence to local optima. Experimental results on four real-world instances demonstrate the superior performance of ACO-QL compared to state-of-the-art algorithms.

The Global Solutions to a Cartan’s Realization Problem

We introduce a systematic method to solve a type of Cartan’s realization problem. Our method builds upon a new theory of Lie algebroids and Lie groupoids with structure group and connection. This approach allows to find local as well as complete solutions, their symmetries, and to determine the moduli spaces of local and complete solutions. We illustrate our method with the problem of classification of extremal Kähler metrics on surfaces.

Enhancing constrained MOEA/D with direct mating using hybrid mating strategies and diverse crossover methods

Abstract The direct mating strategy, which is a constraint-handling method in multi-objective evolutionary algorithms, selects a second parent on the basis of the optimal direction in the objective space, disregarding feasibility. This approach, although effective in early generations, encounters difficulties as solutions better than the current Pareto solutions become scarce, reducing diversity and hindering exploration. Herein, we introduce a hybrid approach that combines direct mating with newly proposed local mating strategies, aiming to generate offspring around the Pareto optimal solutions to improve the solution search performance via a direct mating strategy. Our method addresses the limitations of conventional direct mating, thereby improving its applicability to real-world design problems. Our hybrid strategy employs local mating to select an additional parent close to the initially chosen parent, preserving solution diversity and effectively exploring the solution space. This enhances the effectiveness of direct mating across all generations. In addition, we introduce two types of crossover methods, i.e., simulated binary crossover and differential evolution, for parents selected by direct and local mating, respectively. The synergy among these techniques facilitates a robust search process that can efficiently yield superior solutions. We evaluated the proposed approach using three mathematical problems with distinct Pareto fronts and two practical applications, including an aerospace design problem. The performances of these methods were assessed on the basis of the averages and standard deviations of the hypervolume and inverted generational distance metrics across multiple solution attempts to determine the average performances and the dependencies on initial population variance. The obtained results demonstrate that the hybrid method significantly outperforms the existing methods in the case of constrained multi-objective optimization. Specifically, the hybrid method yielded higher average hypervolumes and lower dependency on initial population variance than the existing methods. The hybrid method also yielded a lower average and less dependency on initial population variance in the inverted generational distance compared to existing methods. This result suggests that the proposed method can obtain high-quality non-dominated solutions, regardless of the initial population.

Extrapolation of cavitation and hydrodynamic pressure in lubricated contacts: a physics-informed neural network approach

A comprehensive understanding of the dynamics of tribological interactions is essential for enhancing efficiency and durability in a multitude of technical domains. Conventional experimental techniques in tribology are frequently costly and time-consuming. In contrast, elastohydrodynamic lubrication (EHL) simulation models present a viable alternative for calculating frictional forces in sealing contacts. These calculations are based on the hydrodynamics within the sealing contact, as defined by the Reynolds equation, the deformation of the seal, and the contact mechanics. However, a significant drawback of these simulations is the time-consuming calculation process. To overcome these experimental and computational limitations, machine learning algorithms offer a promising solution. Physics-informed machine learning (PIML) improves on traditional data-driven models by incorporating physical principles. In particular, physics-informed neural networks (PINNs) are as effective hybrid solvers that combine data-driven and physics-based methods to solve the partial differential equations that drive EHL simulations. By integrating physical laws into the parameter optimization of the neural network (NN), PINNs provide accurate and fast solutions. Thus, unlike traditional NNs, PINNs have the potential to make accurate predictions beyond the limited training domain. The objective of this study is to demonstrate the feasibility of spatial and temporal extrapolation of the PINN and to analyze its reliability, both with and without consideration of cavitation. Two test cases are employed to examine the pressure and cavitation distribution within a sealing contact that extends beyond the spatial and temporal training range. The findings indicate that PINNs can surmount the typical constraints associated with NNs in the extrapolation of solution spaces, which represents a notable advancement in terms of computational efficiency and model flexibility.

A framework for nurturing champions of digital innovation

Abstract Information Systems (IS) champions enthusiastically promote a digital innovation project throughout its development by obtaining the necessary resources. These individuals shape the innovativeness of an organization, as they initiate digital innovation projects and lead them toward successful completion. We still know little about how these champions can be identified and nurtured in organizations. We follow the Design Science Research approach in developing a framework for nurturing IS champions that can guide human resource practitioners. Our framework offers a strategic view of the champion journey and prescribes recommendations for action. The design decisions were derived from literature on digital innovation and innovation champions, and the framework was subsequently refined and evaluated meticulously. The design underwent two stages based on expert interviews from the IT industry (formative evaluation) and was subsequently evaluated by experts in digital innovation project management and human resource development in the IT industry (summative evaluation). The results demonstrate the feasibility of the framework and offer further insights into the problem and solution space of nurturing IS champions.

Geometric stability and optimization in reaction–diffusion models for tissue engineering: A case study with hydrogel scaffolds

This paper presents a thorough qualitative analysis of coupled reaction–diffusion equations, with an emphasis on the careful selection of boundary conditions that govern the interactions between stem cell and nanozyme concentrations within hydrogel scaffolds. These scaffolds, widely applied in cartilage tissue repair, possess unique attributes such as tunable mechanical strength and high water content, which are captured within the model through carefully chosen parametric constraints. The precision in defining boundary conditions is particularly crucial, as stem cell proliferation within these scaffolds is highly sensitive to external parameters, directly influencing their behavior. Our approach employs a geometric framework to analyze the stability of the coupled system, with a focus on discerning the delicate balance between stem cell populations and nanozyme concentrations. The goal is to ensure that the scaffold sustains optimal mechanical integrity, achieves uniform cell distribution, and maintains controlled degradation rates. Through a rigorous stability and bifurcation analysis of the reaction–diffusion equations, we explore the system’s equilibrium points and establish conditions under which these equilibria are stable or unstable. This analysis serves as a theoretical foundation for optimizing the design of hydrogel scaffolds, particularly in the context of ensuring consistent mechanical properties and efficient cellular integration. In addition to the qualitative geometric methods, we integrate Optuna, an advanced optimization algorithm, to fine-tune the model parameters. This computational tool enhances the accuracy of the parameter selection process by efficiently navigating the solution space, thereby refining the predictions of scaffold performance. The combination of geometric stability analysis with the state-of-the-art optimization provides a novel framework for addressing challenges in tissue engineering, offering new insights into the dynamics of scaffold design and the development of experimental protocols. These findings not only elucidate the stability conditions of the system but also contribute in establishing rigorous guidelines for the control of stem cell populations and nanozyme delivery rates in practical applications.

Physiology-informed regularisation enables training of universal differential equation systems for biological applications.

Systems biology tackles the challenge of understanding the high complexity in the internal regulation of homeostasis in the human body through mathematical modelling. These models can aid in the discovery of disease mechanisms and potential drug targets. However, on one hand the development and validation of knowledge-based mechanistic models is time-consuming and does not scale well with increasing features in medical data. On the other hand, data-driven approaches such as machine learning models require large volumes of data to produce generalisable models. The integration of neural networks and mechanistic models, forming universal differential equation (UDE) models, enables the automated learning of unknown model terms with less data than neural networks alone. Nevertheless, estimating parameters for these hybrid models remains difficult with sparse data and limited sampling durations that are common in biological applications. In this work, we propose the use of physiology-informed regularisation, penalising biologically implausible model behavior to guide the UDE towards more physiologically plausible regions of the solution space. In a simulation study we show that physiology-informed regularisation not only results in a more accurate forecasting of model behaviour, but also supports training with less data. We also applied this technique to learn a representation of the rate of glucose appearance in the glucose minimal model using meal response data measured in healthy people. In that case, the inclusion of regularisation reduces variability between UDE-embedded neural networks that were trained from different initial parameter guesses.

A multitasking ant system for multi-depot pick-up and delivery location routing problem with time window

Instant delivery service has brought great convenience to our modern life. In order to improve its efficiency, multi-depot pick-up-and-delivery location routing problem with time windows (MDPDLRPTW) is proposed in this paper. Existing works related to MDPDLRPTW focus on obtaining a depot location scheme by clustering and perform route planning on it through single-task optimization. They are powerless to simultaneously explore the solution spaces of multiple routing tasks under different location schemes. Furthermore, ignoring the potential general knowledge among different schemes leads to redundant optimization. In this work, MDPDLRPTW is modeled as a multi-transformation optimization (MTFO) problem and a novel two-stage algorithm based on multitasking ant system (MTAS) is designed to solve it. In the first stage, a clustering algorithm based on spatio-temporal feature is used to group similar customer pairs, and the clustering centers are set as warehouses. Afterward, multiple localization schemes are selected through non-dominated sorting based on spatio-temporal density. In the second stage, MTAS concurrently optimizes multiple routing tasks based on these location schemes, each task is assigned to an ant system solver. Furthermore, MTAS achieves knowledge sharing among all routing tasks through adaptive similarity measurement and cross-task pheromone fusion strategy. The former can dynamically capture the relationship between tasks to adjust the transfer strength of task pairs, and the latter realizes adaptive knowledge transfer by pheromone-matrix mixing. Experimental results show that MTAS can efficiently utilize the common knowledge to achieve competitive performance.

CPI-Pred: A deep learning framework for predicting functional parameters of compound-protein interactions.

Recent advancements in deep learning have enabled functional annotation of genome sequences, facilitating the discovery of new enzymes and metabolites. However, accurately predicting compound-protein interactions (CPI) from sequences remains challenging due to the complexity of these interactions and the sparsity and heterogeneity of available data, which constrain the generalization of patterns across their solution space. In this work, we introduce CPI-Pred, a versatile deep learning model designed to predict compound-protein interaction function. CPI-Pred integrates compound representations derived from a novel message-passing neural network and enzyme representations generated by state-of-the-art protein language models, leveraging innovative sequence pooling and cross-attention mechanisms. To train and evaluate CPI-Pred, we compiled the largest dataset of enzyme kinetic parameters to date, encompassing four key metrics: the Michaelis-Menten constant ( K M ), enzyme turnover number ( k cat ), catalytic efficiency ( k cat /K M ), and inhibition constant ( K I ).These kinetic parameters are critical for elucidating enzyme function in metabolic contexts and understanding their regulation by compounds within biological networks. We demonstrate that CPI-Pred can predict diverse types of CPI using only the amino acid sequence of enzymes and structural representations of compounds, outperforming state-of-the-art models on unseen compounds and structurally dissimilar enzymes. Over workflow provides a valuable tool for tackling a range of metabolic engineering challenges, including the designing of novel enzyme sequences and compounds, such as enzyme inhibitors. Additionally, the datasets curated in this study offer a valuable resource for the scientific community, serving as a benchmark for machine learning models focused on enzyme activity and promiscuity prediction.