Linear Optimization Method Research Articles

Improvements to Quantum Interior Point Method for Linear Optimization

Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major bottleneck is the inexactness of quantum Tomography to extract classical solutions from quantum states. In addition, QLSAs are sensitive to the condition number, and this sensitivity is exacerbated when the Newton systems arising in IPMs converge to a singular matrix. Recently, an Inexact Feasible Quantum IPM (IF-QIPM) has been developed that addresses the inexactness of QLSAs. However, this method requires a large number of gates and qubits to be implemented. Here, we propose a new IF-QIPM using the normal equation system, which requires less number of gates and qubits. To mitigate the sensitivity to the condition number and other input data-related parameters, we use preconditioning coupled with iterative refinement to obtain better complexity. Finally, we demonstrate the effectiveness of our approach on IBM Qiskit simulators.

A Signed Subgraph Encoding Approach via Linear Optimization for Link Sign Prediction.

In this article, we consider the problem of inferring the sign of a link based on known sign data in signed networks. Regarding this link sign prediction problem, signed directed graph neural networks (SDGNNs) provides the best prediction performance currently to the best of our knowledge. In this article, we propose a different link sign prediction architecture called subgraph encoding via linear optimization (SELO), which obtains overall leading prediction performances compared to the state-of-the-art algorithm SDGNN. The proposed model utilizes a subgraph encoding approach to learn edge embeddings for signed directed networks. In particular, a signed subgraph encoding approach is introduced to embed each subgraph into a likelihood matrix instead of the adjacency matrix through a linear optimization (LO) method. Comprehensive experiments are conducted on five real-world signed networks with area under curve (AUC), F1, micro-F1, and macro-F1 as the evaluation metrics. The experiment results show that the proposed SELO model outperforms existing baseline feature-based methods and embedding-based methods on all the five real-world networks and in all the four evaluation metrics.

Optimization design of unmanned mining truck path tracking controller based on road adhesion coefficient estimation

Abstract In response to the issues of inaccurate tracking precision caused by continuous turning and variable road adhesion coefficients on complex roads in mining areas for unmanned mining trucks, this paper adopts unscented Kalman filter (UKF) to estimate the road adhesion coefficient. Based on this, an adaptive preview feedforward linear quadratic regulator (LQR) control algorithm is designed using genetic algorithm, feedforward control, and linear quadratic optimal path tracking control methods. Firstly, a nine degree of freedom vehicle dynamics model and a two degree of freedom vehicle lateral dynamics model are established, and the Dugoff model to calculate tire forces is introduced; secondly, utilizing UKF to estimate the road adhesion coefficient, and leveraging active disturbance rejection control for rapid tracking of road curvature, an optimized design of the LQR controller is carried out. Then, the effectiveness of the designed controller was verified through Trucksim/Simulink joint simulation testing. Finally, the hardware in the loop test results showed that the designed controller had good tracking accuracy and strong adaptability in complex road and special working conditions in mining areas.

Optimization by linear kinetic equations and mean-field Langevin dynamics

One of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al. in the middle of last century. In this paper, we show how the tools of linear kinetic theory allow the description of this gradient-free algorithm from the perspective of statistical physics and how convergence to the global minimum can be related to classical entropy inequalities. This analysis highlights the strong link between linear Boltzmann equations and stochastic optimization methods governed by Markov processes. Thanks to this formalism, we can establish the connections between the simulated annealing process and the corresponding mean-field Langevin dynamics characterized by a stochastic gradient descent approach. Generalizations to other selection strategies in simulated annealing that avoid the acceptance–rejection dynamic are also provided.

Water–Energy–Food Nexus in the Yellow River Basin of China under the Influence of Multiple Policies

The water–energy–food (WEF) nexus constitutes a pivotal aspect of regional ecological protection and high-quality development. The exertion of multiple WEF-related policies would engender both synergies and trade-offs within the WEF nexus. However, a quantified framework that integrates the impact of multiple WEF-related policies with conventional WEF nexus assessments and simulations is currently lacking. This study quantified the WEF nexus in the Yellow River basin (YRB) of China under the influence of multiple policies, calculated the current and future WEF scores under different policy combination scenarios using the improved entropy weight method, the auto-regressive integrated moving average (ARIMA) model, and the linear optimization method. The results revealed the following: (1) From 2000 to 2020, WEF overall scores and subsystem scores were substantially increased with spatial heterogeneity. (2) Scenario analysis indicated that policy implementation would generally accelerate WEF score improvements in each city, yet embracing all policies simultaneously was not optimal for each city. (3) The spatial heterogeneity in policy impacts was also found in the YRB, with higher trade-offs in the upper reaches of cities, and higher synergies in the middle and lower reaches of cities. To attain high-quality development within the YRB, the related policies’ implementation should consider the regional disparities and enhance the optimization of resource allocation across the regions.

Stochastic Optimization of Distribution Networks: Application of Probabilistic Graphical Models in Electrical Grid Management

In electricity grid management, optimizing distribution networks is a must for making sure that the grid is reliable, efficient, and resilient. Stochastic optimization methods have become very useful for dealing with the unknowns that come up in grid operations because of things like adding green energy, changing demand, and broken equipment. We present a new way to improve distribution networks when there is doubt in this study. It uses probabilistic graphical models (PGMs). Using PGMs lets us describe the complicated connections between loads, producers, and grid infrastructure, as well as the relationships between these parts of the distribution network. By recording these relationships, we can accurately show how unclear the grid is and make smart choices to make it work better. In particular, we use Bayesian networks (BNs) and Markov random fields (MRFs) to describe how the different factors in the network are likely to be related to each other. We show how well our method works by using it on a real-life delivery network problem. We look at a case study of a distribution network that has a lot of green energy sources and changing load levels. We use PGMs to build a statistical model of the distribution network by combining past data, weather forecasts, and real-time measures. Then, we create a stochastic optimization problem to find the best way to reduce the predicted operational cost while still meeting different operational restrictions, like voltage limits, power balance, and equipment limitations. We use advanced optimization algorithms, like stochastic gradient descent and genetic algorithms, to quickly solve the optimization problem that was given. We show that our method works and can be scaled up for handling distribution networks when there is doubt by doing a lot of computer tests and risk analyses. The suggested method can make delivery networks much more reliable, cost-effective, and resilient than traditional linear optimization methods, as shown by our results. Overall, this study shows that probabilistic graphical models can be a very useful tool for managing the electricity grid and finding the best ways to use distribution networks in the face of randomness. Including unknowns in the modeling process helps we make stronger and more dependable choices that will help current distribution systems work well.

Age-Stage, Two-Sex Life Table of Atractomorpha lata (Orthoptera: Pyrgomorphidae) at Different Temperatures.

Atractomorpha lata Motschoulsky (Orthoptera: Pyrgomorphidae) has recently emerged as an important agricultural pest in China. Understanding the impact of temperature on its developmental period is crucial for predicting its population dynamics. This study systematically observed the biological characteristics of A. lata at five temperatures (16, 20, 24, 28, and 32 °C) using the age-stage, two-sex life table method. The effects of temperature on the developmental period, survival rate, and fecundity of A. lata were studied using fresh bean leaves as host. The results demonstrated that as temperature increased from 16 °C to 32 °C, the developmental period, preadult time, adult longevity, adult preoviposition period (APOP), and total preoviposition period (TPOP) significantly decreased. The developmental threshold temperatures for various stages were calculated, ranging from 10.47 °C to 13.01 °C, using the linear optimal method. As temperature increased, both the intrinsic rate of increase (r) and the finite rate of increase (λ) also increased, while the mean generation time (T) decreased. The optimal values of the net reproductive rate (R0 = 54.26 offspring), gross reproductive rate (GRR = 185.53 ± 16.94 offspring), and fecundity (169.56 ± 9.93 eggs) were observed at 24 °C. Similarly, the population trend index (I) for A. lata peaked at 24 °C (61.64). Our findings indicate that A. lata exhibits its highest population growth rate at 24 °C, providing a scientific basis for predicting its population dynamics in the field.

A Linear Optimization for Slope Leveling of Ground-Mounted Centralized Photovoltaic Sites

Slope leveling is essential for the successful implementation of ground-mounted centralized photovoltaic (PV) plants, but currently, there is a lack of optimization methods available. To address this issue, a linear programming approach has been proposed to optimize PV slope leveling. This method involves dividing the field into blocks and grids and using hyperbolic paraboloids to simulate the design surface. By programming in MATLAB, the globally optimal solution for PV slope leveling can be calculated. Engineering case studies have demonstrated that this optimization method can achieve significant cut-and-fill volume savings ranging from 58% to 78%, when compared to the traditional segmented plane method. Additionally, the effectiveness of the optimization method improves with larger site areas and more complex terrains. A parameter analysis considering slope ratio, grid size, and block size reveals that grid size has a minimal impact on cut-and-fill volume, while slope ratio and block size have a significant influence. For typical PV projects, the recommended ranges of slope ratio, grid size, and block size are 3–7%, 5–20 m, and 30–50 m, respectively, for slope leveling design. In summary, the proposed linear optimization method provides an optimal slope leveling scheme for ground-mounted centralized PV plants, with convenient operation and fast computation.

A High-Precision Hand-Eye Coordination Localization Method under Convex Relaxation Optimization.

Traditional switching operations require on-site work, and the high voltage generated by arc discharges can pose a risk of injury to the operator. Therefore, a combination of visual servo and robot control is used to localize the switching operation and construct hand-eye calibration equations. The solution to the hand-eye calibration equations is coupled with the rotation matrix and translation vectors, and it depends on the initial value determination. This article presents a convex relaxation global optimization hand-eye calibration algorithm based on dual quaternions. Firstly, the problem model is simplified using the mathematical tools of dual quaternions, and then the linear matrix inequality convex optimization method is used to obtain a rotation matrix with higher accuracy. Afterwards, the calibration equations of the translation vectors are rewritten, and a new objective function is established to solve the coupling influence between them, maintaining positioning precision at approximately 2.9 mm. Considering the impact of noise on the calibration process, Gaussian noise is added to the solutions of the rotation matrix and translation vector to make the data more closely resemble the real scene in order to evaluate the performance of different hand-eye calibration algorithms. Eventually, an experiment comparing different hand-eye calibration methods proves that the proposed algorithm is better than other hand-eye calibration algorithms in terms of calibration accuracy, robustness to noise, and stability, satisfying the accuracy requirements of switching operations.

An Enhanced Alternating Direction Method of Multipliers-Based Interior Point Method for Linear and Conic Optimization

An Enhanced Alternating Direction Method of Multipliers-Based Interior Point Method for Linear and Conic Optimization

Adaptive finite‐time recoil control of deepwater drilling riser systems with nonlinear forces and saturation input using switched event‐triggered scheme

AbstractThis article investigates the finite‐time recoil control problem of deepwater drilling riser systems with nonlinear friction force, tension force and saturation input. For the friction force, a new approximation model based on radial basis function neural networks is presented, which not only can ensure a better approximation effect than the sine‐function type and exponential‐polynomial‐function type computational models, but also can be easily used for control design. Different from the existing linear optimal control methods, a neural‐network‐based adaptive backstepping control method is proposed to deal with the nonlinear friction and tension forces, which can achieve better recoil control responses. An auxiliary system combining with the change of coordinates is employed to compensate the saturation input effect. To prolong the average release interval of control input while preserving satisfied control performance, a new switched event‐triggered control (ETC) scheme is developed, in which the triggering conditions are switched between the fixed and relative thresholds based on the strength of control signal. With the event‐triggered controller, the practical finite‐time stability condition of recoil control system is derived and the Zeno behavior is avoided. Numerical results are given to show the advantages of the proposed methods in handling the model nonlinearities, finite‐time stability and ETC performance of riser‐tension systems.

Research on Detection System of Intelligent Computer Optimization Algorithm for Concrete Mix Ratio Based on Big Data

PLC is used to complete the control function of the concrete proportioning system. The MCGS (Configuration Software Monitor and Control System) is used to realize the real-time monitoring, data management and fault warning of the whole monitoring system. The material feed and PLC control process in the feed system are emphatically introduced. A concrete proportioning design method based on multiple parameters is proposed. The nonlinear multi-objective optimization model of concrete mix ratio was established by stepwise regression analysis and complex optimization method. The problems of narrow range of variables and single form of objective and constraint in traditional linear optimization methods are solved, which makes the selection of optimal index simpler and more flexible. Through the calculation of examples, it is clear that this method can obtain the mixture that meets the use conditions, and can greatly save the experimental work and construction cost.

Optimization of Pengga Reservoir in The Mandalika Special Economic Zone for Irrigation and Water Supply

Mandalika Special Economic Zone is tourism area that is expected to improve the economy in West Nusa Tenggara Province. To support these activities, an allocation of domestic water needs of 200 liters second -1 is needed. The potential availability of water in the Pengga Reservoir is planned to be a source of domestic water needs in the Mandalika Special Economic Zone. Pengga Reservoir has an effective storage volume of 17.26 MCM. Potential water resources in Pengga Reservoir are obtained from reservoir outflow upstream and lateral inflow from several tributaries. The study was carried out to determine the reservoir storage capacity to meet domestic water needs and irrigation water needs covering an area 3189 ha. The cropping pattern used in the Pengga irrigation area is Paddy – Paddy/Secondary Crops – Paddy/Secondary Crops. To optimize the potential of water resources in the Pengga Reservoir, a linear programming optimization method is used. Indicators of the success of optimization calculations are indicated by the value of cropping intensity, k factor and reliability that have met the minimum limit value. The k factor value for irrigation water needs is 0.70 and domestic water needs is 0.85. Based on the optimization results, it is known the largest annual cropping intensity value occurs in the November I planting season. This conclusion can be seen from the comparison of annual cropping intensity values for the November I and November II planting schedules for the dry year inflow discharge scenario of 99.98% and 97.22% respectively. The cropping intensity value in the November I planting season is greater than November II, namely 100% and 97.25%, for the normal year discharge inflow scenario. This study provides an information for policy makers can use the November I planting schedule to obtain values for maximum cropping intensity and domestic water requirements.

Optimization of Biped Robot Walking Based on the Improved Particle Swarm Algorithm

The central pattern generator (CPG) is widely applied in biped gait generation, and the particle swarm optimization (PSO) algorithm is commonly used to solve optimization problems for CPG network controllers. However, the canonical PSO algorithms fail to balance exploration and exploitation, resulting in reduced optimization accuracy and stability, decreasing the control effectiveness of CPG controllers. In order to address this issue, a balanced PSO (BPSO) algorithm is proposed, which achieves better performance by balancing the algorithm’s exploration and exploitation capabilities. The BPSO algorithm’s solving process consists of two phases: the free exploration phase (FEP), which emphasizes exploration, and the attention exploration phase (AEP), which emphasizes exploitation. The proportion of each phase during optimization is controlled by an adjustable parameter. The BPSO algorithm is subjected to qualitative, numerical, convergence, and statistical analyses based on 13 benchmark functions. The experimental results from the benchmark functions demonstrate that the BPSO algorithm outperforms other comparison algorithms. Finally, a linear walking optimization method for humanoid robots based on the BPSO algorithm is established and tested in the Webots simulator. Comparative results with two other optimization methods show that the BPSO‐based optimization method enables the robot to achieve greater walking distance and smaller lateral deviation within a fixed number of iterations. Compared to the other two methods, walking distance increases by at least 60.98% and lateral deviation decreases by at least 1.96%. This research contributes to enhancing the locomotion capabilities of CPG‐controlled humanoid robots, enriching biped gait optimization theory and promoting the application of CPG gait control methods in humanoid robots.

A multi-scenario evaluation of the energy transition mechanism in the Philippines towards decarbonization

The Philippines relies heavily on fossil fuels for energy, posing environmental issues. To counter this, the study suggests increasing the use of renewable energy sources like wind and solar power. By optimizing the electricity supply mix, the study shows that coal usage can be reduced by 37.23%, with solar power accounting for 20.07% and wind power accounting for 8.83% without using Battery Energy Storage System (BESS). By incorporating Battery Energy Storage Systems (BESS) and scaling up the utilization of solar and wind power, which is aligned with the country's 2030 target, coal consumption can be reduced by 30.44%. However, transmission expansion may have limited effects due to the country's archipelagic nature. Therefore, a decentralized approach is necessary to minimize coal usage and encourage renewable energy sources. The study uses linear programming optimization methods to explore scenarios that can mitigate climate change by increasing solar and wind power use, reducing coal usage, and investigating the benefits of transmission line expansion and energy storage integration for enhancing grid flexibility.

Linear Constrained Optimization Method (LiCOM): A Novel Paradigm to Handle Engineering Optimization Problems

Linear Constrained Optimization Method (LiCOM): A Novel Paradigm to Handle Engineering Optimization Problems

Application of Coal Tar Products and Evaluation of the Stability of Residual Marine Fuels

Although the quality of coal tar does not meet the demands for blended marine fuel, the properties of its components after processing are improved, and they can be considered as inexpensive blending components. Three types of coal tar products including light coal tar I, light coal tar II, and hydrogenated coal tar have been obtained and used in production of residual marine fuels. To minimize costs, a linear optimization method has been used, and all properties of the resulting products have met the required criteria. In addition, a novel analytical method was used to characterize the fuel stability. The analysis of a hydrocarbon composition and a mechanism of interaction between the resin and asphaltene have shown the main coal tar components affecting fuel oil stability are polycyclic aromatic hydrocarbons (PAHs) and resin. A condensation of PAHs and resin into asphaltene and an increasing complexity of asphaltene structure causes deposition of oil products under heating. Hydrogenation is able to effectively reduce the PAH content and the volume of formation of massive asphaltenes thus preventing fuel flocculation and deposition during aging in fuel tanks.

A loading contribution degree analysis-based strategy for time-variant reliability analysis of structures under multiple loading stochastic processes

This paper proposes a new single-loop method based on the loading contribution degree analysis (LCDA) and decoupling strategy for analyzing the time-variant reliability of structures considering multiple loading stochastic processes and degradation processes. In this method, the loading stochastic processes are first discretized using the expansion optimal linear estimation method. Then, the LCDA is carried out to obtain a total weighted loading stochastic process used to accurately reflects the structural response, thus constructing a single loading stochastic process analysis problem. Subsequently, a decoupling strategy is applied to decouple the degradation processes and the total weighted loading stochastic process to obtain the equivalent extreme-value limit state function (EEV-LSF) of the structure. Finally, an efficient probability distribution reconstruction tool is applied to derive the probability density function of EEV-LSF. Notably, the proposed LCDA can avoid the calculation of the response time series of a structure under the input loading stochastic processes, providing a novel perspective to simplify the calculation of structural extreme-value response. Additionally, the proposed method requires only one round of deterministic analysis to obtain the structural time-variant failure probability at the specified time, constructing an efficient single-loop analysis method. Three numerical examples are used to validate the proposed method.

A joint machine learning and optimization approach for incremental expansion of electric vehicle charging infrastructure

As Electric vehicle (EV) adoption increases worldwide, public charging infrastructure must be expanded to meet the growing charging demand. Furthermore, insufficient and improperly deployed public charging infrastructure poses a real risk of slowing EV adoption. The infrastructure thus needs to be expanded intelligently and flexibly while accounting for uncertain dynamics in future charging demand. Nevertheless, current methods for demand-based expansion often rely on rigid and error-prone tools, such as travel surveys and simple rules of thumb. The former is more appropriate for long-term, equilibrium scenarios, where we consider the charging network as a whole rather than incrementally expanding it. At the same time, the latter relies on business experience in a rapidly changing field. We propose a predictive optimization approach for intelligent incremental expansion of charging infrastructure. At each time step, we estimate the future charging demand through a Gaussian Process, which is subsequently used in a linear chance-constrained optimization method to expand the charging infrastructure incrementally. To develop and validate this framework, we account for environmental feedback by simulating user behavior changes based on historical charging records and considering an optimized charging network at every iteration. We apply this approach to a case study of EV charging in Dundee, Scotland. We compare different strategies and reasons for their pros and cons for monthly incremental expansion of the charging network. In particular, combining machine learning and optimization results in the cheapest expansion and one that serves the most demand.

Assessment of the competitiveness of tourism services in the region: modern realities

The purpose of the article is to develop theoretical provisions and methodological support for assessing the competitiveness of tourist services as the basis of a tourist destination. And the methods of factor analysis, the method of multi-criteria assessment, the correlation-regression method, the methods of indicative planning and economic and mathematical modeling were used. Some problems have been solved using comparison and linear optimization methods. The article explores theoretical and methodological approaches to the evaluation of tourist services in a constantly changing competitive environment and the actualization of new technologies. The methods of assessing and transforming the quality and increasing the competitiveness of tourist services within the regional recreation and tourism market were studied using the example of the Republic of Tatarstan, which predetermined the relevance of the stated topic, the purpose of the study and the tasks set. The practical value is confirmed by the possibility of using the results obtained in the development strategy of tourist organizations by regional government bodies, as well as in the activities of federal and regional tour operators.