Optimal Tree Research Articles

A data-driven approach for linking models of large-scale bridges and monitoring data

Predictive maintenance of large-scale structures such as bridges requires precise numerical models to describe their current condition. Typically, solving an inverse problem is necessary to determine model parameters from Structural Health Monitoring (SHM) data. However, conventional methods such as Finite Element Updating through optimization algorithms demand substantial computational resources, as numerous parameter combinations need to be assessed to identify the optimal model state in each calibration step. Consequently, these methods are only partially suitable for creating digital twins of bridges.This paper introduces an alternative approach by treating the inverse problem as a model parameter classification problem. This involves establishing a model database that covers a wide range of damage states. Notably, this method eliminates the need for multiple simulations during the application phase, as simulations are performed only once in an offline context. Subsequently, a classification algorithm is trained based on this database, enabling real-time selection of the best-fit model for practical applications using SHM data, without the necessity for additional simulations.Transparency in algorithm decisions is crucial for infrastructure maintenance, therefore, optimal classification trees from the field of interpretable machine learning are employed. Decision trees offer a balance between high accuracy and interpretability while providing additional advantages, such as sensor placement evaluation. In summary, this approach demonstrates the potential for linking numerical models with SHM data through the application of interpretable machine learning techniques, facilitating real-time decision-making for the preservation and management of critical infrastructure.

Estimation method of earthwork excavation using shield tunneling data -- a case study of Chengdu Metro

The occurrence of over-excavation or under-excavation in tunnel construction poses significant safety risks. Moreover, there is currently no automatic estimation method available for real-time estimation of earthwork excavation, particularly in the case of shield tunnels. In this study, we tracked the excavation process of Chengdu Metro Line 19, acquired tunneling parameters and earthwork excavation data using various sensors, and subsequently proposed an automatic estimation method that combines Bayesian optimization (BO) and gradient boosting regression tree (GBRT) algorithm. The results of our case study indicate that the BO-GBRT model improves the performance of earthwork excavation estimation, reducing the residual after each calculation with a root mean square error (RMSE) of 1.712 and mean absolute error (MAE) of 1.331. Furthermore, compared to other machine learning methods, the proposed BO-GBRT model demonstrates superior estimation performance. Additionally, the importance distribution of input parameters reveals that propulsion pressure, foam pressure, and rotation speed are the most critical factors affecting earthwork excavation. Overall, the proposed automatic estimation method shows great promise as a tool for efficiently estimating earthwork excavation in shield tunnel construction.

New optimization models for optimal classification trees

The most efficient state-of-the-art methods to build classification trees are greedy heuristics (e.g. CART) that may fail to find underlying characteristics in datasets. Recently, exact linear formulations that have shown better accuracy were introduced. However they do not scale up to datasets with more than a few thousands data points. In this paper, we introduce four new formulations for building optimal trees. The first one is a quadratic model based on the well-known formulation of Bertsimas et al. We then propose two different linearizations of this new quadratic model. The last model is an extension to real-valued datasets of a flow-formulation limited to binary datasets (Aghaei et al.). Each model is introduced for both axis-aligned and oblique splits. We further prove that our new formulations have stronger continuous relaxations than existing models. Finally, we present computational results on 22 standard datasets with up to thousands of data points. Our exact models have reduced solution times with learning performances as strong or significantly better than state of the art exact approaches.

Complete Mitochondrial Genome of the Backswimmer: Notonecta triguttata Motschulsky, 1861 (Hemiptera: Notonectidae): Sequence, Structure, and Phylogenetic Analysis

Notonecta triguttata Motschulsky, 1861 (Hemiptera, Notonectidae) is distributed in China, Japan, and South Korea. It is the dominant hexapod predator in aquatic ecosystems and can control harmful insects, such as mosquitoes and parasites. This study presents the first determination of the complete mitochondrial genome of N. triguttata. The mitogenome was 15,156 base pairs in length and was made up of 13 protein-coding genes (PCGs), 2 ribosomal RNAs, 22 transfer RNAs, and one non-coding control region. All genes were arranged in the same order as most other known heteropteran mitogenomes. All PCGs started with the ATN codon except COX1 (TTG) and NAD2 (GTG) and ended with TAA, TAG, or the partial stop codon T. The tRNAs had a typical cloverleaf secondary structure, except tRNA-Ser (GCT). The A + T content (75.96%) was relatively high across the entire mitogenome. The optimal phylogenetic trees were inferred through the Bayesian inference and maximum likelihood methods. The trees suggested a topology of (Corixoidea + ((Nepoidea + Ochteroidea) + (Naucoroidea + (Pleoidea + Notonectoidea)))) and identified that N. triguttata belongs to Notonectoidea. The complete mitogenome of N. triguttata provides a potentially useful resource for further exploration of the taxonomic status and phylogenetic history of the Notonecta species.

A Distributed Multicast QoS Routing Construction Approach in Information-Centric Networking

Many applications suitable for multicast transmission, such as video conferencing and live e-commerce, demand high Quality of Service (QoS) and require data delivery to be completed within specified delay constraints. Some methods have been proposed for constructing delay-constrained multicast routing based on network state. However, obtaining precise network latency can be challenging, resulting in inaccuracies in delay-constrained routing calculations and, ultimately, the inability to meet application requirements. Additionally, many methods engage in an indiscriminate exploration of potential paths in the network, causing significant message processing overhead. This paper proposes an Information-Centric Networking (ICN)-based approach for delay-constrained multicast routing. Our method dynamically constructs multicast paths from tree nodes to receivers based on real-time path status detection during the join message propagation phase. Additionally, we present a method for acquiring neighborhood state information to facilitate real-time routing decisions. To curtail indiscriminate path exploration, our approach uses the ICN Name Resolution System (NRS) to obtain and select potential optimal tree nodes. For this purpose, we design a multicast service registration and resolution mechanism using the ICN Name Resolution System (NRS). Simulation results indicate that our approach exhibits a higher success ratio and concurrently incurs lower message processing overhead than some other methods, particularly in situations with stringent delay constraints.

TREE-GPT: MODULAR LARGE LANGUAGE MODEL EXPERT SYSTEM FOR FOREST REMOTE SENSING IMAGE UNDERSTANDING AND INTERACTIVE ANALYSIS

Abstract. This paper introduces a novel framework, Tree-GPT, which incorporates Large Language Models (LLMs) into the forestry remote sensing data workflow, thereby enhancing the efficiency of data analysis. Currently, LLMs are unable to extract or comprehend information from images and may generate inaccurate text due to a lack of domain knowledge, limiting their use in forestry data analysis. To address this issue, we propose a modular LLM expert system, Tree-GPT, that integrates image understanding modules, domain knowledge bases, and toolchains. This empowers LLMs with the ability to comprehend images, acquire accurate knowledge, generate code, and perform data analysis in a local environment. Specifically, the image understanding module extracts structured information from forest remote sensing images by utilizing automatic or interactive generation of prompts to guide the Segment Anything Model (SAM) in generating and selecting optimal tree segmentation results. The system then calculates tree structural parameters based on these results and stores them in a database. Upon receiving a specific natural language instruction, the LLM generates code based on a thought chain to accomplish the analysis task. The code is then executed by an LLM agent in a local environment and . For ecological parameter calculations, the system retrieves the corresponding knowledge from the knowledge base and inputs it into the LLM to guide the generation of accurate code. We tested this system on several tasks, including Search, Visualization, and Machine Learning Analysis. The prototype system performed well, demonstrating the potential for dynamic usage of LLMs in forestry research and environmental sciences.

Innovative method to solve the minimum spanning tree problem: The Dhouib-Matrix-MSTP (DM-MSTP)

The Minimum Spanning Tree problem aims to create a subset of a graph where all the vertices are connected with the minimum edge weights and with no cycle. In this field, an innovative method entitled Dhouib-Matrix-MSTP (DM-MSTP) is designed in this research work with a time complexity independently of the number of edges O(n*log(n)) where n is the number of vertices. DM-MSTP is a constructive algorithm based on a matrix navigation with two new lists (Min-Columns and MST-Path) in order to organize the steering flow. DM-MSTP is composed of four simple steps where the first and the fourth steps are repeated only once, whereas the second and third are reiterated (n-1). For more clarification, a step-by-step application of the proposed method is presented in details. Besides, the performance of DM-MSTP is proved through different examples from the literature including a graph with negative weighted edges and complete graphs from TSP-LIB. Moreover, with a simple modification (Min by Max) the DM-MSTP is tested on the Maximum (Largest) Spanning Tree Problem. Also, DM-MSTP is applied on eight case studies and compared to six methods developed in the literature. All these experimental results in the above different environments show that DM-MSTP can rapidly plan the shortest spanning tree with a stable performance and convivial representation of the optimal tree. Hence, DM-MSTP is developed under Python programming language using Matplotlib and Numpy standard libraries.

Congenital Heart Surgery Machine Learning-Derived In-Depth Benchmarking Tool

BackgroundWe previously showed that machine learning-based methodologies of optimal classification trees (OCTs) can accurately predict risk after congenital heart surgery and assess case-mix–adjusted performance after benchmark procedures. We extend this methodology to provide interpretable, easily accessible, and actionable hospital performance analysis across all procedures. MethodsThe European Congenital Heart Surgeons Association Congenital Cardiac Database data subset of 172,888 congenital cardiac surgical procedures performed in European centers between 1989 and 2022 was analyzed. OCT models (decision trees) were built predicting hospital mortality (area under the curve [AUC], 0.866), prolonged postoperative mechanical ventilatory support time (AUC, 0.851), or hospital length of stay (AUC, 0.818), thereby establishing case-adjusted benchmarking standards reflecting the overall performance of all participating hospitals, designated as the “virtual hospital.” OCT analysis of virtual hospital aggregate data yielded predicted expected outcomes (both aggregate and for risk-matched patient cohorts) for the individual hospital’s own specific case-mix, readily available on-line. ResultsRaw average rates were hospital mortality, 4.9%; mechanical ventilatory support time, 14.5%; and length of stay, 15.0%. Of 146 participating centers, compared with each hospital’s overall case-adjusted predicted hospital mortality benchmark, 20.5% statistically (<90% CI) overperformed and 20.5% underperformed. An interactive tool based on the OCT analysis automatically reveals 14 hospital-specific patient cohorts, simultaneously assessing overperformance or underperformance, and enabling further analysis of cohort strata in any chosen time frame. ConclusionsMachine learning-based OCT benchmarking analysis provides automatic assessment of hospital-specific case-adjusted performance after congenital heart surgery, not only overall but importantly, also by similar risk patient cohorts. This is a tool for hospital self-assessment, particularly facilitated by the user-accessible online-platform.

Optimal multivariate decision trees

Optimal multivariate decision trees

Tree Recovery by Dynamic Programming.

Tree-like structures are common, naturally occurring objects that are of interest to many fields of study, such as plant science and biomedicine. Analysis of these structures is typically based on skeletons extracted from captured data, which often contain spurious cycles that need to be removed. We propose a dynamic programming algorithm for solving the NP-hard tree recovery problem formulated by Estrada et al. [1], which seeks a least-cost partitioning of the graph nodes that yields a directed tree. Our algorithm finds the optimal solution by iteratively contracting the graph via node-merging until the problem can be trivially solved. By carefully designing the merging sequence, our algorithm can efficiently recover optimal trees for many real-world data where [1] only produces sub-optimal solutions. We also propose an approximate variant of dynamic programming using beam search, which can process graphs containing thousands of cycles with significantly improved optimality and efficiency compared with [1].

An efficient 3-approximation algorithm for the Steiner tree problem with the minimum number of Steiner points and bounded edge length.

We present improved algorithms for the Steiner tree problem with the minimum number of Steiner points and bounded edge length. Given n terminal points in a 2D Euclidean plane and an edge length bound, the problem asks to construct a spanning tree of n terminal points with minimal Steiner points such that every edge length of the spanning tree is within the given bound. This problem is known to be NP-hard and has practical applications such as relay node placements in wireless networks, wavelength-division multiplexing(WDM) optimal network design, and VLSI design. The best-known deterministic approximation algorithm has O(n3) running time with an approximation ratio of 3. This paper proposes an efficient approximation algorithm using the Voronoi diagram that guarantees an approximation ratio of 3 in O(n log n) time. We also present the first exact algorithm to find an optimal Steiner tree for given three terminal points in constant time. Using this exact algorithm, we improve the 3-approximation algorithm with better performance regarding the number of required Steiner points in O(n log n) time.

Correction: K-means tree: an optimal clustering tree for unsupervised learning

Correction: K-means tree: an optimal clustering tree for unsupervised learning

Supervised feature compression based on counterfactual analysis

Counterfactual Explanations are becoming a de-facto standard in post-hoc interpretable machine learning. For a given classifier and an instance classified in an undesired class, its counterfactual explanation corresponds to small perturbations of that instance that allows changing the classification outcome. This work aims to leverage Counterfactual Explanations to detect the important decision boundaries of a pre-trained black-box model. This information is used to build a supervised discretization of the features in the dataset with a tunable granularity. Using the discretized dataset, an optimal Decision Tree can be trained that resembles the black-box model, but that is more interpretable and compact. Numerical results on real-world datasets show the effectiveness of the approach in terms of accuracy and sparsity.

Prescriptive price optimization using optimal regression trees

This paper is concerned with prescriptive price optimization, which integrates machine learning models into price optimization to maximize future revenues or profits of multiple items. The prescriptive price optimization requires accurate demand forecasting models because the prediction accuracy of these models has a direct impact on price optimization aimed at increasing revenues and profits. The goal of this paper is to establish a novel framework of prescriptive price optimization using optimal regression trees, which can achieve high prediction accuracy without losing interpretability by means of mixed-integer optimization (MIO) techniques. We use the optimal regression trees for demand forecasting and then formulate the associated price optimization problem as a mixed-integer linear optimization (MILO) problem. We also develop a scalable heuristic algorithm based on the randomized coordinate ascent for efficient price optimization. Simulation results demonstrate the effectiveness of our method for price optimization and the computational efficiency of the heuristic algorithm.

PREDICTION OF BODY WEIGHT OF NIGERIAN NON-DESCRIPT GOATS FROM MORPHOMETRIC TRAITS USING CLASSIFICATION AND REGRESSION TREE MODEL

This study was conducted to evaluate the relationship between body weight and eleven (11) morphometric traits (body weight, body length, height at withers, rump height, chest girth, hind leg, fore leg, head length, ear length, neck length, and tail length) of non-descript goats using classification and regression tree technique. The data were generated from 120 non-descript goats randomly selected from different herds in three LGA areas of Kaduna State, North West Nigeria. Pearson’s moment correlation (r) between body weight and morphometric traits ranged from low to high values (r = 0.21-0.97; P≤0.05, P≤0.01). Based on the importance of the independent variables in predicting the body weight of goats, six body measurements namely; chest girth, body length, rump height, height at withers, head length and neck length were found to be more efficient. Thus, they were the variables entered to obtain the optimal regression tree. Among these six variables, chest circumference was found to be the primary splitting variable; and together with neck length accounted for about 84.20% of the variation in body weight. The regression tree analysis indicated that animals with chest circumference &gt; 60.00cm and neck length &gt;15cm could be expected to have higher body weights. This information could be exploited by livestock producers and researchers for determining the feed amount, drug dose, and market price of an animal, management, selection and genetic improvement of Nigerian non-descript goats.

Contrasting growth responses to drought in three tree species widely distributed in northern China

Tree species-specific responses to drought are urgently needed for assessing the impacts of current climate change on forest ecosystems. Here, we characterized the resistance, recovery, resilience, and growth recovery periods in response to different drought events based on tree-ring width index data (>30 years) for three tree species widely distributed in northern China, among which larch (Larix principis-rupprechtii Mayr) and Mongolian pine (Pinus sylvestris L. var. mongolica Litv.) are two major species used for afforestation, and birch (Betula platyphylla Suk.) is one of the most common natural tree species. Despite no significant effects of mild drought on tree growth, severe drought events significantly reduced the growth of all species, with contrasting species-specific responses. Larch trees had the lowest resistance and resilience among the three species, and Mongolian pine trees were more resistant but had a longer recovery period than birch trees. The drought responses varied with tree size. Large Mongolian pine and birch trees were more resistant but large larch trees were much more vulnerable than small trees during severe droughts. Smaller birch trees had higher resilience to severe droughts. Our study shows species-specific differences in drought responses and suggests that drought responses are tree-size dependent and drought-intensity associated, which further provides a guidance for selecting optimal cultivated tree species and designing forest managements in this region.

A study on the influence of teacher certification concept on the construction of art majors in universities based on big data analysis

Abstract The development of the data era has put higher requirements for college art courses, but the imperfect evaluation system of practical teaching of college art courses has become a stumbling block to the flourishing development of college art. Based on the decision tree model, this paper proposes constructing the optimal decision tree using pruning techniques. The optimized decision tree is adopted to explore the differences in the construction of art majors in universities under the condition of normal major certification and feedback on the influence of normal major certification on art majors through the evaluation results. From the analysis of the three index examples, the mean values of cognitive evaluation, pedagogical evaluation, and effectiveness evaluation of art courses were 2.527, 4.756, and 3.267, respectively, indicating the best evaluation in the pedagogical evaluation of art courses, but the cognitive evaluation was slightly lower. Normal major certification significantly influences the construction of art majors in colleges and universities. The decision tree model can also guide the innovation direction of college art courses more intuitively through data so that the evaluation system of college art courses can enjoy the development dividend of the new technology era.

Improving node connectivity by optimized dual tree-based effective node consolidation

As an effective way to defend against network failure, nodes or links in a network can be protected to ensure connectivity. The consolidation of critical nodes is a necessary strategy, especially when nodes are important infrastructure elements, such as in wireless environments. However, since the problem is NP-hard, even the optimal algorithm is of high computational complexity on small-scale graphs, which makes it difficult to handle large-scale networks in feasible time. Fortunately, we have found an effective pairwise node cut set (NCS)-tree search method to locate small NCSes. The critical nodes in these NCSes are then selected to construct the optimal dual tree, and to determine the near optimal set of consolidation nodes. Comparison results show that the serial version of the proposed algorithm achieves a remarkable acceleration ratio of more than 105 compared to the optimal algorithm, with only a minimal additional cost. In addition, the consolidation solution provides protection for over 99.9% of vulnerable node pairs in large-scale networks and can significantly outperform common heuristics. Moreover, the ready-to-parallelization algorithm has the potential to be further accelerated hundreds of times in full parallelization.

Optimal classification tree for frequency security assessment of power systems with inverter‐based resources reinforcement

AbstractFrequency security is the premise of realizing the net‐zero transition. A novel assessment scheme is proposed to quantify the frequency security levels of transmission systems under different inverter‐based resources (IBRs) and their control parameter combinations. A novel system frequency dynamic model is proposed as a parametric optimization method, where the saturation of generators, energy storage systems, and renewable energy sources is incorporated as differential algebra equations. This problem is further reformulated as a mixed‐integer linear programming problem to generate a sufficient amount of data under different IBR integration and control parameters. The frequency security assessment problem is formulated as a data‐driven multivariate classification problem, which is solved by the optimal classification tree (OCT) algorithm with better interptretionability. Simulations are conducted on a transmission system. Numerical results indicate that the proposed system frequency dynamic model can capture the frequency dynamic under different IBR reinforcement plans and the OCT can realize accurate classification of the synthetic data regarding frequency security.

Errata to “Optimal Tree Topology for a Submarine Cable Network With Constrained Internodal Latency” [May 21 2673-2683

Errata to “Optimal Tree Topology for a Submarine Cable Network With Constrained Internodal Latency” [May 21 2673-2683