Programming Optimization Research Articles

INCREASING THE EFFICIENCY OF THE TRAINING PROCESS OF ATHLETES USING FITNESS TECHNOLOGIES

Annotation. The article examines the use of fitness technologies to improve the effectiveness of the training process of athletes-runners. The aim of the work is to analyze the impact of modern fitness technologies on the optimization of training programs and the improvement of the physical performance of athletes. The article is based on data collected using various fi tness technologies, in particular: fitness trackers for monitoring physiological indicators (heart rate, energy expenditure, steps, activity level); heart rate monitors for determining the intensity of the load and recovery; GPS navigators for assessing distance training and speed of movement; mobile applications for tracking training results and planning progress; video analytics and motion sensors for analyzing the technique of performing exercises. These technologies were used to collect information about athletes, in particular about their physiological indicators during training, as well as to assess the effectiveness of recovery between training sessions. The study took into account the feedback of coaches and athletes on the impact of technologies on their training processes and results. The impact of fitness technologies on individualization of training, monitoring of physiological indicators, correction of exercise technique, as well as recovery processes was analyzed. The results show that the integration of fitness technologies allows for the creation of personalized training plans that contribute to better control over loads and faster recovery. Thanks to the use of devices for monitoring physiological indicators, athletes were able to achieve high results, reducing the risk of injuries. In addition, the developed technologies contributed to the improvement of the psychological state of athletes through monitoring progress and motivation. It was determined that the use of fitness technologies is an effective tool for increasing training efficiency, optimizing recovery and preventing injuries, which opens up new opportunities for the development of sports training at all levels. Further research should be aimed at improving these technologies and adapting them to different sports.

Surface water quality evaluation of Mahanadi and its Tributary Katha Jodi River, Cuttack District, Odisha, using WQI, PLSR, SRI, and geospatial techniques

Surface water depletion in Odisha tract poses significant challenges for sustainable water management. An important part of the effort to satisfy the growing demand for water is surface water quality control. For that purpose, this study’s primary goal is to assess the surface water quality for drinking and irrigation at nine different locations, via the use of the innovative techniques. In this regard, Drinking Water Quality Index (DWQI), Partial Least Square Regression (PLSR) and Spatial reflectance (SR) Indices (I), were considered to determine water suitability for different people’s activities. The samples were collected in the study area during the pre-monsoon season of period 2023–2024. The parameters analyzed: pH, DO, Alkalinity, Conductivity, Nitrate, Phosphate and Hardness. The results were subsequently contrasted with the water quality requirements, as instructed by World Health Organizations (WHO). The major anionic trend is expressed in the subsequent order: NO3− > PO43−. Finally, the analytical results were collected in order to produce the parameters’ numerical geographic distribution using the geographical information system (GIS) environment. According to the results of pH, the obtained average value is recorded as 8.0. This implies that the water is slight alkaline in nature. The results of the DWQI showed that 44.44% shared investigated locations, were classified as excellent to good, and 11% as poor, 22.22% as very poor and, 22.22% is indicated as unsuitable for drinking purpose classes. In addition, the new SRIs that were taken out of the VIS and NIR regions demonstrated a substantial correlation with DWQI, according to the results. The new SRIs and DWQI had R2 correlations with values ranging from 0.65 to 0.82. The results from DWQI and SRI depicts that Nitrate and Phosphate concentration were higher and exceeds the WHO standards. At five sites, which confers as poor water quality, these parameters were recorded very high. Additionally, the main factors causing variations in water quality were fertilizer, organic waste, and soil leaching. Based on the values of R2, the PLSR model generated an evaluation of DWQI that was more accurate. Furthermore, the PLSR model generated accurate predictions for DWQI, with an R2 of 0.82 and 0.85, in the validation and calibration dataset. Hence, PLSR is efficient and provides us with a clear image for evaluating surface water’s fitness for drinking and its regulating elements. This study provides a quantitative framework for assessing surface water suitable potential zones in the chosen region. By identifying the hidden variables influencing water quality, the three approaches work together to maintain their advantages while also offering crucial information for water management. The results allow for the monitoring of restoration measures to be prioritized, the identification of the anthropogenic impact on the five locations (S-(1), (2), (3), (4), and (5)) and the type of anthropogenic pressure associated with each location, as well as the optimization of monitoring programs to reflect significant anthropogenic pressures. The resulting maps and data offer valuable insights for policy makers and water resource managers to develop targeted surface water management strategies. These findings have significant implications for sustainable water resource management in the region, particularly in addressing challenges related to drinking and agricultural water demand and climate change adaptation. A more thorough assessment of the surface water quality would result from the addition of more water quality indicators, such as hydrological, biological, and particular pollutants, to the straightforward and trustworthy assessment scheme that has been suggested.

Optimization of international talent training program in biological and biomechanical field of Shaanxi universities by integrating Transformer-GRU model under the “Belt and Road” initiative

In the field of biology of Shaanxi universities, there are problems such as insufficient internationalization of course content, limited internationalization level of teachers, and difficulty in meeting the personalized needs of students’ foreign language ability. To this end, under the Belt and Road Initiative, this paper proposes an intelligent solution based on Transformer and GRU (Gated Recurrent Unit) models, aiming to improve the quality of international education in the field of biology of universities by optimizing course content and teaching methods. This study first uses the Transformer model to integrate and analyze a large number of international education resources, identify global cutting-edge knowledge and cross-cultural education elements in biology courses, including biomechanical principles that underpin biological functions and interactions. This provides scientific support for the optimization of course content. At the same time, the GRU model is used to dynamically analyze the progress of teachers’ international teaching and students’ learning feedback. Just as organisms can adjust their metabolic rate according to the changes in the environment, the model automatically adjusts the pace and difficulty of the subsequent teaching content according to the students’ speed of mastery and difficulties in understanding biomechanics knowledge, ensuring that each student can keep up with the pace of teaching. Additionally, the integration of biomechanical concepts into the curriculum helps students understand the mechanical properties and behaviors of biological systems, fostering interdisciplinary thinking and enhancing their global vision. Experimental results show that the students in Class A who adopt this research program are significantly better than the control Class B in terms of knowledge mastery, interdisciplinary thinking, and global vision (P < 0.05); after the experiment, the average foreign language ability score of the students in Class A is 7.04 points higher than that of Class B; the overall satisfaction of the students in Class A with the new teaching program is as high as 82.5%. This paper, based on the combination of Transformer and GRU models, can effectively promote the international talent training process of biology majors in Shaanxi universities, particularly by incorporating biomechanical insights, thereby enhancing the competitiveness of this major in global academic and scientific research cooperation.

Hybrid Optimization-Based Sequential Placement of DES in Unbalanced Active Distribution Networks Considering Multi-Scenario Operation

The increasing penetration of distributed generation (DG) brings about great economic and environmental benefits, while also negatively affecting the operation of distribution networks due to its high intermittency. Although distributed energy storage (DES) can effectively deal with the problems caused by massive DG penetrations by decoupling the generation and consumption of electricity, the placement of DES significantly determines the effectiveness of its capabilities. Unfortunately, existing DES placement studies are commonly based on a balanced network model, whereas practical distribution networks are unbalanced. In addition, existing DES placement studies are mostly based on an extreme scenario and rarely consider the operational complexity resulting from the uncertainties of DGs and loads. To address the aforementioned challenges, this paper proposes a hierarchical and sequential DES placement strategy in distribution networks by considering multi-scenario operations. Specifically, the proposed hierarchical framework for DES placement includes three sequential layers: outer, inter, and inner. In the outer layer, a multi-scenario comprehensive loss sensitivity index (MSCLSI) is first introduced to search for the most effective DES placement location. Subsequently, the sizing and scheduling of DES for the selected location are conducted through coordinated optimization across the inter and inner layers, which can be solved using a hybrid method combining particle swarm optimization and second-order cone programming (PSO-SOCP). Finally, a series of detailed simulations are carried out over the IEEE-33 test system and the experimental results demonstrate that the proposed scheme can provide significant effectiveness and superiority compared to the state-of-the-art schemes.

Topology Unveiled: A New Horizon for Economic and Financial Modeling

Sinceits introduction in the 19th century to address geometric problems, topology as a methodology has undergone a series of evolutions, encompassing branches of geometric topology, point-set topology (analytic topology), algebraic topology, and differential topology, gradually permeating into various interdisciplinary applied fields. Starting from disciplines with typical geometric characteristics such as geography, physics, biology, and computer science, topology has found its way to economic fields in the 20th century. Given that the introduction of topology to economics is relatively new and presents features of being fragmented and non-systematic, this review aimed to provide scholars with a systematic evolution map to refine the characteristics of topology as a methodology applied in economics and finance, thereby aiding future potential interdisciplinary developments in these fields. By collecting abundant literature indexed in SCOPUS/WoS and other famous databases, with a qualitative analysis to classify and summarize it, we found that topological methods were introduced to modern economics when dealing with dynamic optimization, functional analysis, and convex programming problems, including famous applications such as uncovering equilibrium with fixed-point theorems in Walrasian economics. Topology can help uncover and refine the topological properties of these function space transformations, thus finding unchangeable features. Meanwhile, in contemporary economics, topology is being used for high-dimension reduction, complex network construction, and structural data mining, combined with techniques of machine learning, and applied to high-dimensional time series and structure analysis in financial markets. The most famous practical applications include the use of topological data analysis (TDA) and topological machine learning (TML) for different applied problems.

Evaluating Whether Nonimmersion Virtual Reality Simulation Training Improves Nursing Competency in Isolation Wards: Randomized Controlled Trial.

During infectious disease outbreaks such as the COVID-19 pandemic, nurses are crucial in patient care and public health safety; however, they face challenges such as inadequate training and high stress in isolation wards. Virtual reality (VR) technology offers innovative training solutions to enhance nurses' clinical skills and preparedness. However, extensive studies on its effectiveness in isolation ward environments are still limited. This study aims to develop a nonimmersive VR (NIVR) simulation training program for isolation wards and further validate its feasibility and training effectiveness in aiding nurses in adapting to isolation ward settings. This study was a prospective, parallel, open-label, randomized controlled trial. A total of 90 nurses from 3 hospitals in China were randomly assigned to either the control or intervention group, with 45 (50%) individuals in each group. Both groups received training on isolation ward layout and nursing procedures. The control group underwent a 4-hour conventional training session consisting of 2 hours of face-to-face lectures and 2 hours of ward visits. The intervention group received a 4-hour NIVR simulation training session. Subsequently, both groups completed approximately 4 hours of emergency drills and assessments. After the intervention, there were no significant differences in theoretical test or performance assessment scores between the 2 groups (t88=-0.30, P=.75; Cohen d=-0.06; z score=0.00, P>.99), using a 2-tailed t test. However, the intervention group completed 6 tasks faster than the control group (t88=5.10, P<.001; Cohen d=1.08), with an average reduction of about 3 minutes (control group: mean 43.91, SD 2.99 min; intervention group: mean 40.77, SD 2.85 min). Notably, they completed task 3 (patient reception inward) and task 6 (exiting the isolation area) significantly quicker (t88=3.22, P=.002; Cohen d=0.68; t88=3.03, P=.003; Cohen d=0.64, respectively), with no significant differences for the other tasks. This study highlights the potential of NIVR simulation training for nurses working in isolation wards. Although NIVR simulation training does not significantly surpass traditional methods in imparting theoretical knowledge, it does reduce task completion time for specific activities. Its capacity for safe, repetitive practice and realistic scenario simulation makes NIVR a valuable tool in medical education. Further research and optimization of VR simulation training programs are recommended to enhance nurses' practical skills and pandemic preparedness. Chinese Clinical Trial Registry ChiCTR240083155; https://www.chictr.org.cn/hvshowproject.html?id=250356&v=1.0.

Linear Programming Optimization of Local Food-Based Recommendations for Undernourished Urban Poor Malaysian Children Aged 2 to 5 Years.

Poor diet quality may contribute to undernutrition, particularly affecting young children from low-income households. Therefore, affordable and healthy local food-based recommendations (FBRs) are needed. This study aimed to (1) identify problem nutrient(s), (2) identify locally available nutrient-dense food sources that can provide adequate nutrients to meet the recommended dietary intakes of undernourished urban poor children aged 2-5 years, and (3) use linear programming to recommend a daily diet based on the current food patterns that achieves dietary adequacy and meets average food costs for these children. A cross-sectional study was conducted in Seremban, Malaysia. Three-day 24hour dietary recalls were collected from the mothers (n = 168). Food costs were estimated using market surveys. The FBRs were formulated by linear programming analysis using Optifood software. Folate was an "absolute problem nutrient" (such a nutrient does not achieve the 100% recommended nutrient intake even upon diet optimization). Full-cream milk, chocolate malted milk, fortified cornflakes, and chicken egg were the common locally available nutrient-dense foods that would provide adequate nutrients to meet the recommended dietary intakes of undernourished urban poor children. The final FBR set would ensure dietary adequacy for eight to nine of 11 nutrients at a cost of ringgit Malaysia (RM) 4.80/day (US $1.05/day) and RM6.20/day (US $1.34/day), depending on the age group. Interventions are required to ensure dietary adequacy for undernourished urban poor children under 5 years old. Dietary adequacy could be improved via realistic changes in habitual food consumption practices.

Профессионально важные качества сотрудников уголовно-исполнительной системы в условиях цифровой трансформации

In the new socio-economic conditions, the requirements for professionally important qualities of specialists and the formation of their competencies are not just changing, but are being transformed and rebuilt, and this is primarily due to the restructuring of social processes and the introduction of digital technologies in various fields of professional activity. Professionally important qualities are understood as the individual properties of the subject of labor, a certain set of psychological characteristics that are necessary and generally sufficient for the implementation of effective and reliable professional activities, thus ensuring the success of its implementation. Understanding the formation of the necessary professionally important qualities among employees of the penitentiary system, ensuring the success of their official activities, is significant in terms of making timely, highly likely, objective managerial decisions on issues of professional and career growth of employees, assessing the prospects for appointment to certain positions, the possibility of forming a personnel reserve on a regular basis, conducting professional selection procedures, professional certification, professional training. The main professionally important qualities and competencies of employees of the penitentiary system in the context of digital transformation are considered. A promising scientific direction of research on professionally important qualities of employees of the penal correction system using the method of structural analysis of the organization of psychological indicators is highlighted. The issue of professional mentoring in the penal system of the Russian Federation has been updated. Additionally, such professionally important qualities as mastery of digital culture, digital competence, mastery of information hygiene skills when working with software and information systems, compliance with information security and information protection issues were noted. The study of the issues of professionally important qualities of employees of the penitentiary system is of promising scientific practice-oriented interest in such areas of psychological support of professional activity as professional selection optimization of programs to support professional adaptation of employees at various stages of professional development, development of an up-to-date professional description of professional activity, identification of factors of psychological success

Local Government Policy on Handling Stunting in Mandailing Natal Regency

Stunting is an issue that requires serious attention from the Central Government to the Regional Governments, particularly the Regional Government of Mandailing Natal Regency. This is because Mandailing Natal Regency is one of the regions in North Sumatra with a high stunting rate, reaching 47.7% in 2021, placing Mandailing Natal at the top rank in North Sumatra for stunting cases, according to the Indonesian Nutrition Status Study (SSGI). In 2022, Mandailing Natal dropped to third place with a stunting rate of 34.2%. However, this figure is still far from the national target set for Mandailing Natal, which is 14% by 2024. This study aims to analyze the policies of the Mandailing Natal Regional Government to reduce the stunting rate to 14% by 2024 and examine the various challenges faced. The method used in this research is qualitative descriptive analysis. Data collection techniques include interviews, observation, and documentation. The informants for this study included officials from the Mandailing Natal Health Office, Family Planning Office, village heads, and village assistants. The study found that the Mandailing Natal Government has implemented cross-sectoral policies, specific interventions, and the "Foster Father" program to reduce stunting. Success depends on policy continuity, program optimization, and increasing public awareness. The main challenges are limited funding, poor sanitation, and cultural barriers.

Supervisory controller for minimizing fuel consumption and NOx emissions of plug-in hybrid electric vehicles operating in zero-emission zones

This paper introduces a supervisory controller designed for Plug-in Hybrid Electric Vehicles (PHEVs) to minimize total energy consumption and tailpipe NOx emissions while adhering to Zero Emission Zone (ZEZ) constraints. The case study exploits historical driving cycle data from an urban bus route in Zurich to analyze trip correlations, where a ZEZ restriction was added to assess the vehicle performance under such conditions. A PHEV bus model was built, integrating the powertrain and After-Treatment System (ATS), where an electric heater is included to mitigate NOx emissions. The supervisory controller is tasked with determining the optimal power split and the electric heater power to ensure adherence to feasible operating conditions along the route. Historical driving cycle data analysis demonstrates that the speed profiles along the selected route exhibit similarities. This observation is leveraged by a Dynamic Programming (DP) optimization, where an arbitrary bus trip is employed to generate a cost-to-go matrix. Then, the resulting cos-to-go matrix was indexed by the position in the route and is used on the real-time controller by applying the one-step look-ahead roll-out algorithm. Simulation results demonstrate the controller effectiveness in addressing ZEZ restrictions, presenting a trade-off between energy consumption and tailpipe NOx emissions. A benchmark was carried out, comparing the results obtained with the DP solution as the baseline, assuming perfect knowledge of driving cycle disturbances, revealing a 7% increase in tailpipe NOx emissions and a 1.3% increase in fuel consumption compared to the theoretical minimum and fulfilling the ZEZ restrictions in all the cases.

Dis/Equality Graphs

E-graphs are a data structure to compactly represent a program space and reason about equality of program terms. E-graphs have been successfully applied to a number of domains, including program optimization and automated theorem proving. In many applications, however, it is necessary to reason about disequality of terms as well as equality. While disequality reasoning can be encoded, direct support for disequalities increases performance and simplifies the metatheory. In this paper, we develop a framework independent of a specific implementation to formally reason about e-graphs. For the first time, we prove the equivalence of e-graphs to the reflexive, symmetric, transitive, and congruent closure of the equivalence relation they are expected to encode. We use these results to present the first formalization of an extension of e-graphs that directly supports disequalities and prove an analytical result about their superior efficiency compared to embedding techniques that are commonly used in SMT solvers and automated verifiers. We further profile an SMT solver and find that it spends a measurable amount of time handling disequalities. We implement our approach in an extension to egg, a popular e-graph Rust library. We evaluate our solution in an SMT solver and an automated theorem prover using standard benchmarks. The results indicate that direct support for disequalities outperforms other encodings based on equality embedding, confirming the results obtained analytically.

Linear and Non-linear Relational Analyses for Quantum Program Optimization

The phase folding optimization is a circuit optimization used in many quantum compilers as a fast and effective way of reducing the number of high-cost gates in a quantum circuit. However, existing formulations of the optimization rely on an exact, linear algebraic representation of the circuit, restricting the optimization to being performed on straightline quantum circuits or basic blocks in a larger quantum program. We show that the phase folding optimization can be re-cast as an affine relation analysis , which allows the direct application of classical techniques for affine relations to extend phase folding to quantum programs with arbitrarily complicated classical control flow including nested loops and procedure calls. Through the lens of relational analysis, we show that the optimization can be powered-up by substituting other classical relational domains, particularly ones for non-linear relations which are useful in analyzing circuits involving classical arithmetic. To increase the precision of our analysis and infer non-linear relations from gate sets involving only linear operations — such as Clifford+t — we show that the sum-over-paths technique can be used to extract precise symbolic transition relations for straightline circuits. Our experiments show that our methods are able to generate and use non-trivial loop invariants for quantum program optimization, as well as achieve some optimizations of common circuits which were previously attainable only by hand.

Optimization of a comprehensive rehabilitation program for patients with motor dysfunction following a stroke

This study aims to optimize rehabilitation strategies for stroke patients with motor dysfunction by integrating traditional therapies with emerging technologies. A mixed-methods approach will be used to evaluate the effectiveness of a personalized rehabilitation program that combines physical therapy, occupational therapy, robotic-assisted therapy, virtual reality (VR), and neurostimulation. Participants will include stroke patients with motor impairments, and outcomes will be measured in terms of motor recovery, functional independence, and quality of life. Data will be analyzed through both quantitative (e.g., Fugl-Meyer Assessment, Stroke Impact Scale) and qualitative methods (e.g., interviews, thematic analysis). The study emphasizes the importance of patient-centered care and evidence-based practices, with the goal of providing more effective and individualized rehabilitation for stroke survivors.

Synergistic Hierarchical Bi-Level Optimization of Demand Response Programs and Smart Inverter Volt/Var Control for Maximizing Hosting Capacity of Power Systems With Renewable-Based Distributed Generators

Synergistic Hierarchical Bi-Level Optimization of Demand Response Programs and Smart Inverter Volt/Var Control for Maximizing Hosting Capacity of Power Systems With Renewable-Based Distributed Generators

Electrode functional microorganisms in bioelectrochemical systems and its regulation: A review.

Bioelectrochemical systems (BES) as environmental remediation biotechnologies have boomed in the last two decades. Although BESs combined technologies with electro-chemistry, -biology, and -physics, microorganisms and biofilms remain at their core. In this review, various functional microorganisms in BESs for CO2 reduction, dehalogenation, nitrate, phosphate, and sulfate reduction, metal removal, and volatile organic compound oxidation are summarized and compared in detail. Moreover, interrelationship regulation approaches for functional microorganisms and methods for electroactive biofilm development, such as targeted electrode surface modification, chemical treatment, physical revealing, biological optimization, and genetic programming are pointed out. This review provides promising guidance and suggestions for the selection of microbial inoculants and provides an analysis of the role of individual microorganisms in mixed microbial communities and its metabolisms.

Joint beamforming and reflection design for IRS‐aided co‐existing radar and communication

AbstractOptimum performance of co‐existing radar and communication (CRC) system is a challenging task when target and user exist within a crowded area where path‐loss is dominant. Inspired by the application of intelligent reflecting surface (IRS) in reconstructing the wireless transmission environment, this paper investigates deploying IRS to the CRC system to pursue performance improvement. Particularly, we consider an IRS‐assisted CRC system where the IRS not only provides an indirect communication path but inevitably introduces additional interfering paths. Our goal is to maximize the radar signal‐to‐interference‐plus noise ratio (SINR) by jointly optimizing the transmit beamform and the phase of IRS while satisfying the user SINR, the total transmit power at the radar and base station, the restriction of IRS phaseshift. An efficient alternative optimization algorithm combining the second‐order cone programming and semidefinite programming optimization methods is exploited to solve the complicated non‐convex unit‐norm problem. Simulation results reveal the advantages of deploying IRS in the CRC system and the effectiveness of our proposed algorithm.

Leveraging Multicriteria Integer Programming Optimization for Effective Team Formation

Leveraging Multicriteria Integer Programming Optimization for Effective Team Formation

Optimization of enterprise production programs taken into account of uncertainty

Optimization of enterprise production programs taken into account of uncertainty

A Deep Q-Learning Based UAV Detouring Algorithm in a Constrained Wireless Sensor Network Environment

Unmanned aerial vehicles (UAVs) play a crucial role in various applications, including environmental monitoring, disaster management, and surveillance, where timely data collection is vital. However, their effectiveness is often hindered by the limitations of wireless sensor networks (WSNs), which can restrict communications due to bandwidth constraints and limited energy resources. Thus, the operational context of the UAV is intertwined with the constraints on WSNs, influencing how they are deployed and the strategies used to optimize their performance in these environments. Considering the issues, this paper addresses the challenge of efficient UAV navigation in constrained environments while reliably collecting data from WSN nodes, recharging the sensor nodes’ power supplies, and ensuring the UAV detours around obstacles in the flight path. First, an integer linear programming (ILP) optimization problem named deadline and obstacle-constrained energy minimization (DOCEM) is defined and formulated to minimize the total energy consumption of the UAV. Then, a deep reinforcement learning-based algorithm, named the DQN-based UAV detouring algorithm, is proposed to enable the UAV to make intelligent detour decisions in the constrained environment. The UAV must finish its tour (data collection and recharging sensors) without exceeding its battery capacity, ensuring each sensor has the minimum residual energy and consuming energy for transmitting and generating data, after being recharged by the UAV at the end of the tour. Finally, simulation results demonstrate the effectiveness of the proposed DQN-based UAV detouring algorithm in data collection and recharging the sensors while minimizing the total energy consumption of the UAV. Compared to other baseline algorithm variants, the proposed algorithm outperforms all of them.

FDFK2D: Efficient Two-Dimensional Teleseismic Wavefield Modeling for Receiver Function Analysis Using a Hybrid Method

Abstract We develop a Fortran package with high programming optimization and parallel computing for simulating high-frequency (&amp;gt;1 Hz) teleseismic wavefields using a hybrid numerical method that couples the finite-difference (FD) and frequency–wavenumber (FK) methods. This method can simulate the interactions of incoming teleseismic wavefields with local heterogeneities but reduce computational region to a much smaller localized domain, which can significantly reduce the computing cost of the high-frequency teleseismic wavefields. The local heterogeneities are allowed to vary arbitrarily in a localized heterogeneous domain. In this package, the geographical locations of earthquakes are permitted, which can consider the real azimuthal effect of the source. Numerical benchmark tests first demonstrate the effectiveness of the developed method for P- and S-wave receiver functions (RFs). The consistent travel times of synthetic and theoretical RFs phases demonstrate its high accuracy. Application on a dense array generally obtains consistent RFs profiles with observed ones and successfully reproduces the observed common-converted-point (CCP) stacking image, which further verifies the effectiveness of the presented method. In addition, statistics of the time-consuming of typical models illustrate the high efficiency of this package, which needs very little computing resources even to be feasible on a laptop.