Combinatorial Explosion Research Articles

Discovering a Novel Cyan‐Light‐Emitting Thiosilicate Phosphor, Li2BaSiS4:Eu2+, via Experimental Active Learning

AbstractThere are likely numerous known and yet‐to‐be‐discovered alkaline earth (AE)‐alkali metal (A) thiosilicates, thioaluminates, and thiophosphates that can serve as suitable hosts for the Eu2+ 5d‐4f emission. These structures offer an infinite number of possible compositions, with the potential for multi‐elemental occupancy at the AE and A sites. Screening such an extensive exploratory space through conventional experimentation poses a significant challenge due to the so‐called combinatorial explosion issue. To address this challenge, an artificial intelligence, more specifically a particle swarm optimization (PSO) algorithm within an experimental active learning framework, that enables to explore the effectively infinite search space and ultimately identify a novel, promising host structure candidate for Eu2⁺ 5d‐4f emission is employed. Starting with completely random compositions and no preset structures in the vast exploratory space, the PSO‐driven experimental active learning process converges on a single‐phase Li2BaSiS4:Eu2+ phosphor, featuring a tetragonal structure with I‐42 m symmetry (a = 6.5825 Å, c = 8.0015 Å). The Li2BaSiS4:Eu2+ phosphor exhibits cyan‐blue light emission with a peak at 480 nm, a full width at half maximum of 35 nm (1423 cm−1), and a broad excitation range from 325 to 425 nm, indicating its potential for application in light‐emitting diodes (LEDs).

Tensor Train Optimization for Conformational Sampling of Organic Molecules.

Exploring the conformational space of molecules remains a challenge of fundamental importance to quantum chemistry: identification of relevant conformers at ambient conditions enables predictive simulations of almost arbitrary properties. Here, we propose a novel approach, called TTConf, to enable conformational sampling of large organic molecules where the combinatorial explosion of possible conformers prevents the use of a brute-force systematic conformer search. We employ tensor trains as a highly efficient dimensionality reduction algorithm, effectively reducing the scaling from exponential to polynomial. In our approach, the conformational search is expressed as global energy minimization task in a high-dimensional grid of dihedral angles. Dimensionality reduction is achieved through a tensor train representation of the high-dimensional torsion space. The performance of the approach is assessed on a variety of drug-like molecules in direct comparison to the state-of-the-art metadynamics based conformer search as implemented in CREST. The comparison shows significant acceleration of up to an order of magnitude, while maintaining comparable accuracy. More importantly, the presented approach allows treatment of larger molecules than typically accessible with metadynamics.

MEDOC: A Fast, Scalable, and Mathematically Exact Algorithm for the Site-Specific Prediction of the Protonation Degree in Large Disordered Proteins.

Intrinsically disordered regions are found in most eukaryotic proteins and are enriched with positively and negatively charged residues. While it is often convenient to assume that these residues follow their model-compound pKa values, recent work has shown that local charge effects (charge regulation) can upshift or downshift side chain pKa values with major consequences for molecular function. Despite this, charge regulation is rarely considered when investigating disordered regions. The number of potential charge microstates that can be populated through acid/base regulation of a given number of ionizable residues in a sequence, N, scales as ∼2N. This exponential scaling makes the assessment of the full charge landscape of most proteins computationally intractable. To address this problem, we developed "multisite extent of deprotonation originating from context" (MEDOC) to determine the degree of protonation of a protein based on the local sequence context of each ionizable residue. We show that we can drastically reduce the number of parameters necessary to determine the full, analytical Boltzmann partition function of the charge landscape at both global and site-specific levels. Our algorithm applies the structure of the q-canonical ensemble, combined with novel strategies to rapidly obtain the minimal set of parameters, thereby circumventing the combinatorial explosion of the number of charge microstates even for proteins containing a large number of ionizable amino acids. We apply MEDOC to several sequences, including a global analysis of the distribution of pKa values across the entire DisProt database. Our results show differences in the distribution of predicted pKa values for different amino acids and good agreement with NMR-measured pKa values in proteins.

Mechanical property prediction of random copolymers using uncertainty-based active learning

The copolymer, a widely used material in our daily lives, presents a significant challenge in targeted sequence design. While recent advancements in computational simulation and data science offer a promising avenue for addressing this complex issue, challenges persist in labeled data scarcity. In this study, we introduce an uncertainty-based active learning framework for predicting the properties of random copolymers. We found that the active learning strategy allowed for labeling only 40 data points within the design space of 1550 data points, drastically reducing the labeling efforts by 97%. Most data selected by active learning were positioned on the design space’s periphery, transforming the learning task into an interpolation problem. Through integrating active learning and molecular dynamics, we successfully overcame the combinatorial explosion problem in copolymer sequence design, streamlining the data labeling process and culminating in a highly accurate model. This research demonstrates data science’s potential in polymer design, especially when facing data scarcity.

An incremental attribute reduction algorithm based on the matrix dimension reduction method

In view of the dynamic change of decision system data in practical problems, the concept of attribute importance function is proposed, which eff ectively avoids the defi ciency of considering only each attribute based on importance reduction algorithm. In the calculation process of matrix reduction algorithm, the sample combination explosion between big data causes huge time consumption. The matrix dimension reduction processing method is proposed, which greatly improves the effi ciency and accuracy of calculation. Finally, an incremental reduction algorithm based on matrix dimensionality reduction is presented, and the correctness of the algorithm is tested. Meanwhile, the results of the four algorithms are compared to verify the eff ectiveness of the algorithm.

Accelerated enumeration of extreme rays through a positive-definite elementarity test.

Analysis of metabolic networks through extreme rays such as Extreme Pathways and Elementary Flux Modes has been shown to be effective for many applications. However, due to the combinatorial explosion of candidate vectors, their enumeration is currently limited to small- and medium-scale networks (typically less than 200 reactions). Partial enumeration of the extreme rays is shown to be possible, but either relies on generating them one-by-one or by implementing a sampling step in the enumeration algorithms. Sampling-based enumeration can be achieved through the Canonical Basis Approach (CBA) or the Nullspace approach (NSA). Both algorithms are very efficient in medium-scale networks, but struggle with elementarity testing in sampling-based enumeration of larger networks. In this paper, a novel elementarity test is defined and exploited, resulting in significant speedup of the enumeration. Even though NSA is currently considered more effective, the novel elementarity test allows CBA to significantly outpace NSA. This is shown through two case studies, ranging from a medium-scale network to a genome-scale metabolic network with over 600 reactions. Extreme Pathways are chosen as the extreme rays in this study, but the novel elementarity test and CBA are equally applicable to the other types. With the increasing complexity of metabolic networks in recent years, CBA with the novel elementarity test shows even more promise as its advantages grows with increased network complexity. Given this scaling aspect, CBA is now the faster method for enumerating extreme rays in genome-scale metabolic networks. All case studies are implemented in Python. The codebase used to generate Extreme Pathways using the different approaches is available at https://gitlab.kuleuven.be/biotec-plus/pos-def-ep. Supplementary data are available at Bioinformatics online.

Concurrent multi-scale design optimization of fiber-reinforced composite material based on an adaptive normal distribution fiber optimization scheme for minimum structural compliance and additive manufacturing

Structural lightweight is a core technical requirement for the structural design of aerospace and new energy power equipment structures. For multi-scale variable stiffness design optimization of discrete fiber-reinforced composite laminates, one of the challenges is how to avoid the explosion of design variable combinations caused by the increase in the number of candidate discrete fiber laying angles. The Normal Distribution Fiber Optimization (NDFO) interpolation scheme has the numerical advantage that the number of design variables does not increase with an increase in the number of candidate discrete fiber laying angles. However, the traditional NDFO interpolation scheme uses uniform penalty parameters across all elements, which means that normalizing the penalty parameters for all the elements ignores the convergence differences of discrete fiber laying angles in different elements within the macro-scale structure topology. This leads to time-consuming and unstable optimization iteration of the macro-scale structural topology and micro-scale discrete fiber laying angle selection. Especially, it easily causes the micro-scale discrete fiber laying angle selection to fall into the local optimum prematurely. Therefore, considering the difficulties and challenges of the traditional NDFO interpolation scheme in the multi-scale variable stiffness design optimization of fiber-reinforced composites. This paper proposes an Adaptive Normal Distribution Fiber Optimization (ANDFO) interpolation scheme, and the feedback mechanism of the convergence rate of the element design variable and the objective function is introduced to achieve the adaptive reduction of the penalty parameters. Based on the proposed ANDFO interpolation scheme, a multi-scale design optimization model of fiber-reinforced composite laminates is established, considering the macro-scale structure topology and micro-scale discrete fiber laying angel selection. The explicit sensitivity of the objective function of minimizing structural compliance to the macro-scale topological design variables and the micro-scale fiber laying angle design variables is derived. Considering the manufacturability of additive manufacturing based on the optimized design results, a multi-scale nonlinear continuous filtering strategy for discrete fiber laying angle is adopted to improve the continuity of the local fiber laying path. Numerical examples systematically present the coupling effects of macro-scale structural topology and micro-scale fiber laying path, multi-scale nonlinear discrete fiber continuous filtering laying path structure, and continuous fiber additive manufacturing multi-scale optimized structure. The proposed ANDFO scheme provides a new theoretical and methodological approach for the lightweight and integrated multi-scale design and manufacturing of fiber-reinforced composite laminates through additive manufacturing technology.

Discovering Multi-Compositional Li-Argyrodite Solid-State Electrolytes via Experimental Active Learning.

Significant research has focused on doping third-party elements into representative Li-Argyrodites, which typically consist of a metal cation, a sulfide anion, and a halide. These efforts have generally been limited to doping or substituting a single element at each atomic site in the Argyrodite structure, resulting in, at most, binary combinations at each site. Multi-elemental doping or substitution poses a challenge due to the so-called combinatorial explosion issue. Here, the study reports quaternary and ternary combinations at either the cation or anion sites, optimizing the composition for ambient-temperature ionic conductivity. Managing such a complex multi-compositional system requires artificial intelligence that surpasses human intuition. A particle swarm optimization (PSO) algorithm is employed within an active learning framework to tackle this multi-dimensional optimization problem. Unlike typical active learning approaches that rely on theoretical computational data, the process is driven by experimental data from the synthesis and characterization of a few hundred multi-compositional Argyrodite samples This experimental active learning approach ultimately enables identifying a novel multi-compositional Li-Argyrodite, exhibiting ambient-temperature ionic conductivity of 13.02 mS cm⁻¹ and enhanced cell performance, with the composition Li6.425Ge0.25Si0.375Sb0.375S4.8I1.2.

Advanced Ab Initio Simulations of Layered Oxide Cathodes: Screening Atomistic Arrangements and Accurate Electronic Structures

Layered oxide cathode materials have already been successfully utilized in state-of-the-art commercial lithium-ion batteries and are among the most promising materials for the next generation of non-lithium-based batteries, e.g., sodium-ion batteries. However, there is still a lack of understanding structure-property relations in these materials to such a level that allows for a rational design approach. Ab initio simulations are an important tool to characterize novel materials and to obtain additional insights such as redox mechanisms at the electronic structure level that are not (easily) available by experimental studies. Modelling layered oxide materials faces several challenges such as model selection, geometry calculation, and electronic structure calculations. The main challenge in the model selection is the combinatorial explosion that arises from partial occupations in doped cathode materials which allow for numerous atomistic arrangements. Finding the most reasonable initial atomistic arrangement to perform a full geometry optimization and to obtain a realistic model is of great importance for a reliable prediction of material properties. Once a reasonable geometric model is obtained, the electronic structure calculation by ab initio methods such as density functional theory (DFT) is also challenging due to the delocalized d-orbitals of the transition metals and complex redox processes involving (partial) oxidations of oxygen anions. As accurate electronic structures are crucial to unveil the redox processes in cathode materials, advanced DFT approaches such as (optimized) hybrid functionals or even more accurate GW calculations are required. In this presentation we will show our recent advances for the modelling of layered oxide cathode materials in terms of model selection (atomistic arrangement) and electronic structure calculations.Finding the lowest energy atomistic arrangement is a combinatorial problem that scales dramatically with supercell size and the concentration of elements. Supercells of novel and practical ternary or quaternary cathode materials can easily have up to 1030 atomistic arrangements. Determining the global energy minimum in these systems becomes a rather complex global optimization problem. Screening for all arrangements by performing DFT calculations is computationally too demanding, and therefore smart heuristic-based optimizers relying on Coulomb- or cluster-expansion-based approaches are required. Here, we will present a novel, self-written software tool to select likely atomistic structures for systems with numerous possible permutations. Our software is able to obtain the global minimum of combinatorial atomistic arrangement problems with 1030 permutations within few minutes on a desktop computer and to obtain low energy structures for problems with 10 to the power of more than 100 on a cluster within a few hours. We will show that, to the best of our knowledge, our software is faster and can tackle larger combinatorial problems than existing solvers (cf. Figure 1) which is particularly useful for modern layered oxide cathode battery materials comprising of a variety of different elements and concentrations. It will be shown how our software can be efficiently used to obtain reasonable atomistic structures for a given composition with a very low computational demand.Once atomistic arrangements are obtained, the redox process can be predicted by calculating the electronic structure. Hence highly accurate electronic structures are required which can be obtained by hybrid functionals or even more accurate, yet computationally demanding, GW calculations. Therefore, we will continue by discussing methods for accurate electronic structure calculations for layered oxide materials including different hybrid functionals and highly accurate GW calculations. Recent results of our GW studies indicate that smaller Hartree-Fock mixing parameters than the default value are required to describe the electronic structure of layered oxide materials [Phys. Rev. B; 10.1103/PhysRevB.109.155134]. Furthermore, we will show by systematic studies that varying the Hartree-Fock mixing has a significant influence on the electronic structure and thereby on the redox processes assigned from DFT calculations as visualized in Figure 1. Tuning ab initio electronic structure methods becomes especially important for complex materials with oxygen redox that are particularly interesting for practical novel cathodes.Finally, it will be discussed how our advanced ab initio methods can be utilized together with experimental results to obtain in-depth understanding of layered oxides as cathode materials for sodium-ion batteries (e.g., Adv. Energy Mater.; 10.1002/aenm.202302017) that might enable a more rational design for the next generation of cathode materials. Figure 1

Computational Design of a Kit of Parts for Bending Active Structures

Bending-active structures are composed of elastic elements that deform to achieve a desired target shape. To support effective design, inverse algorithms have been proposed that optimize the geometry of each element specifically for each design. This makes it difficult to reuse elements across designs or gain efficiency in fabrication through mass production. We address this issue and propose a computational framework to rationalize bending-active structures into a sparse kit of parts. Our method solves for the optimal part geometry such that multiple input designs can be faithfully realized with the same kit of parts. Assigning parts to different assemblies leads to a combinatorial explosion that makes exhaustive search intractable. Instead, we propose a relaxed continuous optimization incorporating a physics-based simulation in its inner loop to model the elastic deformation of the bending-active structure accurately. Our algorithm allows analyzing different design trade-offs of a kit of parts to tune the balance between fabrication complexity and fidelity to the original designs. We demonstrate our method on three different classes of bending-active structures, showcasing the effectiveness of our approach for part reuse and sustainable practices in fabrication-driven design.

K-Clique counting on large scale-graphs: a survey.

Clique counting is a crucial task in graph mining, as the count of cliques provides different insights across various domains, social and biological network analysis, community detection, recommendation systems, and fraud detection. Counting cliques is algorithmically challenging due to combinatorial explosion, especially for large datasets and larger clique sizes. There are comprehensive surveys and reviews on algorithms for counting subgraphs and triangles (three-clique), but there is a notable lack of reviews addressing k-clique counting algorithms for k > 3. This paper addresses this gap by reviewing clique counting algorithms designed to overcome this challenge. Also, a systematic analysis and comparison of exact and approximation techniques are provided by highlighting their advantages, disadvantages, and suitability for different contexts. It also presents a taxonomy of clique counting methodologies, covering approximate and exact methods and parallelization strategies. The paper aims to enhance understanding of this specific domain and guide future research of k-clique counting in large-scale graphs.

Accurate and Efficient Structure Elucidation from Routine One-Dimensional NMR Spectra Using Multitask Machine Learning.

Rapid determination of molecular structures can greatly accelerate workflows across many chemical disciplines. However, elucidating structure using only one-dimensional (1D) NMR spectra, the most readily accessible data, remains an extremely challenging problem because of the combinatorial explosion of the number of possible molecules as the number of constituent atoms is increased. Here, we introduce a multitask machine learning framework that predicts the molecular structure (formula and connectivity) of an unknown compound solely based on its 1D 1H and/or 13C NMR spectra. First, we show how a transformer architecture can be constructed to efficiently solve the task, traditionally performed by chemists, of assembling large numbers of molecular fragments into molecular structures. Integrating this capability with a convolutional neural network, we build an end-to-end model for predicting structure from spectra that is fast and accurate. We demonstrate the effectiveness of this framework on molecules with up to 19 heavy (non-hydrogen) atoms, a size for which there are trillions of possible structures. Without relying on any prior chemical knowledge such as the molecular formula, we show that our approach predicts the exact molecule 69.6% of the time within the first 15 predictions, reducing the search space by up to 11 orders of magnitude.

Efficient Search Algorithms for Identifying Synergistic Associations in High-Dimensional Datasets.

In recent years, there has been a notably increased interest in the study of multivariate interactions and emergent higher-order dependencies. This is particularly evident in the context of identifying synergistic sets, which are defined as combinations of elements whose joint interactions result in the emergence of information that is not present in any individual subset of those elements. The scalability of frameworks such as partial information decomposition (PID) and those based on multivariate extensions of mutual information, such as O-information, is limited by combinational explosion in the number of sets that must be assessed. In order to address these challenges, we propose a novel approach that utilises stochastic search strategies in order to identify synergistic triplets within datasets. Furthermore, the methodology is extensible to larger sets and various synergy measures. By employing stochastic search, our approach circumvents the constraints of exhaustive enumeration, offering a scalable and efficient means to uncover intricate dependencies. The flexibility of our method is illustrated through its application to two epidemiological datasets: The Young Finns Study and the UK Biobank Nuclear Magnetic Resonance (NMR) data. Additionally, we present a heuristic for reducing the number of synergistic sets to analyse in large datasets by excluding sets with overlapping information. We also illustrate the risks of performing a feature selection before assessing synergistic information in the system.

Research on combined damage characteristics of underwater armor-piercing and explosion based on supercavitating projectile

Recent studies of supercavitating projectiles primarily focus on the formation and evolution of the cavity, as well as its underwater ballistic characteristics, while neglecting the terminal damage effects. Little attention has been given to exploring the combined damage effects of armor-piercing-explosion supercavitating projectiles (APESP). Therefore, this study comparatively analyzes the response processes and failure modes of an underwater aluminum alloy cylindrical shell target under the action of three different types of loads: armor piercing, explosion, and combined armor-piercing and explosion. This study investigates the underwater combined damage mechanisms of the APESP, clarifies each damage phase under the combined effect, discusses the advantages of damage resulting from the combined armor-piercing and explosion effect based on the target responses and damage modes, and explores the reasons for dissipation of explosion energy. The results show that: the APESP combines localized point damage characteristics of armor piercing with overall surface damage features of underwater explosion. Depending on load stages and target responses, the target response process under the action of the APESP can be divided into the hydrodynamic ram phase, penetration phase, shock wave phase, stable vibration phase, and bubble pulsation phase. The entire physical system can be abstracted as a low-frequency series spring system (equivalent to bubble pulsation frequency) with high-frequency external energy input, based on the energy relationship of the medium and the structure. The concept of the 'blower effect' is proposed based on target behavior during the stable vibration phase. Following the application of different loads, the plastic deformation of the target in a stable state is ranked as: underwater explosion > combined armor-piercing and explosion > underwater armor piercing. Supercavity, shell casing and penetration hole will cause the dissipation of explosion energy.

Belief-Rule-Based System with Self-organizing and Multi-temporal Modeling for Sensor-based Human Activity Recognition.

Smart environment is an efficient and cost- effective way to afford intelligent supports for the elderly people. Human activity recognition (HAR) is a crucial aspect of the research field of smart environments, and it has attracted widespread attention lately. The goal of this study is to develop an effective sensor-based HAR model based on the belief-rule-based system (BRBS), which is one of representative rule-based expert systems. Specially, a new belief rule base (BRB) modeling approach is proposed by taking into account the self- organizing rule generation method and the multi-temporal rule representation scheme, in order to address the problem of combination explosion that existed in the traditional BRB modelling procedure and the time correlation found in continuous sensor data in chronological order. The new BRB modeling approach is so called self-organizing and multi-temporal BRB (SOMT-BRB) modeling procedure. A case study is further deducted to validate the effectiveness of the SOMT-BRB modeling procedure. By comparing with some conventional BRBSs and classical activity recognition models, the results show a significant improvement of the BRBS in terms of the number of belief rules, modelling efficiency, and activity recognition accuracy.

MEDOC: A fast, scalable and mathematically exact algorithm for the site-specific prediction of the protonation degree in large disordered proteins.

Intrinsically disordered regions are found in most eukaryotic proteins and are enriched in positively and negatively charged residues. While it is often convenient to assume these residues follow their model-compound pK a values, recent work has shown that local charge effects (charge regulation) can upshift or downshift sidechain pK a values with major consequences for molecular function. Despite this, charge regulation is rarely considered when investigating disordered regions. The number of potential charge microstates that can be populated through acid/base regulation of a given number of ionizable residues in a sequence, N , scales as ∼2 N . This exponential scaling makes the assessment of the full charge landscape of most proteins computationally intractable. To address this problem, we developed MEDOC (Multisite Extent of Deprotonation Originating from Context) to determine the degree of protonation of a protein based on the local sequence context of each ionizable residue. We show that we can drastically reduce the number of parameters necessary to determine the full, analytic, Boltzmann partition function of the charge landscape at both global and site-specific levels. Our algorithm applies the structure of the q -canonical ensemble, combined with novel strategies to rapidly obtain the minimal set of parameters, thereby circumventing the combinatorial explosion of the number of charge microstates even for proteins containing a large number of ionizable amino acids. We apply MEDOC to several sequences, including a global analysis of the distribution of pK a values across the entire DisProt database. Our results show differences in the distribution of predicted pK a values for different amino acids, in agreement with NMR-measured distributions in proteins.

CHA: Conditional Hyper-Adapter method for detecting human–object interaction

Human–object interactions (HOI) detection aims at capturing human–object pairs in images and predicting their actions. It is an essential step for many visual reasoning tasks, such as VQA, image retrieval and surveillance event detection. The challenge of this task is to tackle the compositional learning problem, especially in a few-shot setting. A straightforward approach is designing a group of dedicated models for each specific pair. However, the maintenance of these independent models is unrealistic due to combinatorial explosion. To address the above problems, we propose a new Conditional Hyper-Adapter (CHA) method based on meta-learning. Different from previous works, our approach regards each <verb, object> as an independent sub-task. Meanwhile, we design two kinds of Hyper-Adapter structures to guide the model to learn “how to address the HOI detection”. By combining the different conditions and hypernetwork, the CHA can adaptively generate partial parameters and improve the representation and generalization ability of the model. Finally, our proposed method can be viewed as a plug-and-play module to boost existing HOI detection models on the widely used HOI benchmarks.

Quantum Probabilistic Model Checking for Time-Bounded Properties

Probabilistic model checking (PMC) is a verification technique for analyzing the properties of probabilistic systems. However, existing techniques face challenges in verifying large systems with high accuracy. PMC struggles with state explosion, where the number of states grows exponentially with the size of the system, making large system verification infeasible. While statistical model checking (SMC) avoids PMC’s state explosion problem by using a simulation approach, it suffers from runtime explosion, requiring numerous samples for high accuracy. To address these limitations in verifying large systems with high accuracy, we present quantum probabilistic model checking (QPMC), the first method leveraging quantum computing for PMC with respect to time-bounded properties. QPMC addresses state explosion by encoding PMC problems into quantum circuits that superpose states within qubits. Additionally, QPMC resolves runtime explosion through Quantum Amplitude Estimation, efficiently estimating the probabilities of specified properties. We prove that QPMC correctly solves PMC problems and achieves a quadratic speedup in time complexity compared to SMC.

Optimal Location for Tower Crane and Dynamic Trailer Parking in High-Rise Modular Building Construction Project

Optimization of tower crane positioning is essential in precast building construction to ensure that a crane is in the right position to offer the best value for placing precast elements. The first goal is the optimization of transportation distances made by tower cranes, which will address the issues of efficiency and cost. This is done in a way that provides for minimization of the distances that lie between the trailer parking where elements are parked, the tower crane, and the construction installation point. However, current research fails to address the dynamic movement efficiency of trailers, especially when handling multiple trailers and several models of tower cranes, making this scenario an optimization problem that is classified as NP-hard due to the likelihood of causing a combinatorial explosion. This work endeavors to present a new mathematical model that has been applied to the Genetic Algorithm (GA). The ideal demand-generated model is designed to solve the optimal model and position of tower cranes and the prospective positioning of trailers for parking. The feasibility and applicability of the method exploited in the study are also established through a project case study. When adopting the proposed planning model compared to the earlier planning scale, comparisons highlight a small yet significant saving of 6% in time and cost when lifting elements instead of providing them from the trailers by setting up a new on-site stockyard. In addition, a great deal of enhancement is also observed in the final solution aspects, where the developed GA has even reduced the operational time and cost by half a percent each. The results of this research offer best-practice approaches to the position analysis of tower cranes in precast building construction to bring scalability and cost optimization to bear on the construction business.

Interpretable large-scale belief rule base for complex industrial systems modeling with expert knowledge and limited data

Complex system modeling technology is a hot topic. Nowadays, many complex industrial systems present three characteristics: multiple input indicators, limited data and interpretability requirements. With good interpretability, belief rule base (BRB) serves as an efficient tool for modeling complex systems. However, as the number of input indicators of industrial systems increases, BRB suffers from the combinatorial explosion problem, which makes it hard to generate large-scale BRB and optimize it while maintaining its interpretability. For this purpose, an interpretable large-scale BRB is proposed for complex systems with limited data, where expert knowledge can be utilized effectively. First, a framework for generating an initial large-scale BRB using expert knowledge and limited data is developed, including the determination of attribute weight, basic belief degree and rule weight. Afterwards, a new parameter optimization model is designed to reduce the burden of parameter optimization and maintain the interpretability of BRB, where the Adaptive Moment Estimation (Adam) algorithm is adopted to further improve the efficiency of large-scale parameter optimization. Finally, a health assessment case of an inertial navigation system (INS) verifies the proposed method.