Local Optimal Solution Research Articles

BP neural network-based prediction and optimal control of thermoelectric output of distributed solar PV/T systems

Abstract This study employs An evolutionary algorithm to set up a multilayer BP neural network. The goal is to solve the issue that BP neural systems converge slowly and readily fall into local optimal solutions. The genetic algorithm reaches an initial set of evolutionary generations and outputs a BP neural network’s most appropriate starting weights and thresholds. In the GA-BP model, the fitness value is calculated as the sum of the total errors between the network’s output and the desired output. A communication protocol device was used to gather performance information for the global solar PV/T system, and the GA-BP neural network model parameters were adjusted. The GA-BP model had a mean absolute error of 0.7% lower than the BP model’s for the forecast of electrical efficiency. The GA-BP model has an average relative error of 0.21 in forecasting heating power.

An Adaptive Ant Colony Optimization for Solving Large-Scale Traveling Salesman Problem

The ant colony algorithm faces dimensional catastrophe problems when solving the large-scale traveling salesman problem, which leads to unsatisfactory solution quality and convergence speed. To solve this problem, an adaptive ant colony optimization for large-scale traveling salesman problem (AACO-LST) is proposed. First, AACO-LST improves the state transfer rule to make it adaptively adjust with the population evolution, thus accelerating its convergence speed; then, the 2-opt operator is used to locally optimize the part of better ant paths to further optimize the solution quality of the proposed algorithm. Finally, the constructed adaptive pheromone update rules can significantly improve the search efficiency and prevent the algorithm from falling into local optimal solutions or premature stagnation. The simulation based on 45 traveling salesman problem instances shows that AACO-LST improves the solution quality by 79% compared to the ant colony system (ACS), and in comparison with other algorithms, the PE of AACO-LST is not more than 1% and the Err is not more than 2%, which indicates that AACO-LST can find high-quality solutions with high stability. Finally, the convergence speed of the proposed algorithm was tested. The data shows that the average convergence speed of AACO-LST is more than twice that of the comparison algorithm. The relevant code can be found on our project homepage.

Evolved opposition-based Mountain Gazelle Optimizer to solve optimization problems

A recently established swarm-based algorithm, namely, Mountain Gazelle Optimizer (MGO) which draws inspiration from social structure and hierarchy of wild mountain gazelles is competitive for solving optimization problems. However, the MGO has some drawbacks: when dealing with higher dimensions, early iterations could become stuck in suboptimal search area. It would be difficult for the MGO to abandon the local optimal solution if the early best solutions neglect the relevant search space. Therefore, to overcome these limitations, this paper offers an Evolved Opposition-based Learning (EOBL) mechanism which helps the algorithm to jump out of the local optima while accelerating the convergence speed. This novel mechanism is incorporating with MGO to propose Evolved Opposition-based Mountain Gazelle Optimizer (EOBMGO). The experiments are conducted with CEC2005 and CEC2019 benchmark functions, along with seven engineering challenges to examine the performance of the proposed EOBMGO. Furthermore, the statistical tests, like the t-test and Wilcoxon rank-sum test, are verified and demonstrate that the proposed EOBMGO outperforms the existing top-performing algorithms. The outcomes indicated that the proposed technique may be seen as an efficient and successful approach for complex optimization challenges.

Receding Horizon Optimization for Cooperation of Connected Vehicles at Signal-Free Intersections under Mixed-Automated Traffic

This paper proposes a distributed coordination scheme for connected vehicles, including automated vehicles (AVs) and manual vehicles (MVs), at signal-free intersections. The cooperation issue of vehicles at an intersection is formulated into a multi-objective optimization problem that aims to eliminate conflicts and improve traffic mobility and fuel economy. For this purpose, the future trajectories of AVs and MVs are predicted by the respective car-following models, and are shared with neighboring vehicles in conflict relationships. The proposed scheme optimizes the sum of the performance of AVs within the cooperative zone in a prediction horizon. A distributed optimization algorithm in the receding horizon is presented to obtain the local optimal solutions, and is tested in simulations with different demand levels and penetration rates of AVs. The results show that the proposed scheme reduces travel time by 29.7–45.5% and 34.5–49.2%, and decreases fuel consumption by 27.6–35.3% and 21.6–29.9% under 70–100% penetration rates of AVs, compared to the no-control operation and fixed-time signal control strategy. In addition, a comparison simulation with the strategy of jointly optimizing the vehicle trajectory and signal timing is conducted to evaluate the relative merits of the proposed scheme.

Control Problem Related to a 2D Parabolic–Elliptic Chemo-Repulsion System with Nonlinear Production

In this work, we analyze a bilinear optimal control problem related to a 2D parabolic–elliptic chemo-repulsion system with a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a generic result on the existence of Lagrange multipliers in Banach spaces, we obtain first-order necessary optimality conditions and derive an optimality system for a local optimal solution.

A novel robust design optimization method combining improved flower pollination algorithm and dual Kriging

PurposeThis study aims to propose a more precise method for robust design optimization of mechanical structures with black-box problems, while also considering the efficiency of uncertainty analysis.Design/methodology/approachThe method first introduces a dual adaptive chaotic flower pollination algorithm (DACFPA) to overcome the shortcomings of the original flower pollination algorithm (FPA), such as its susceptibility to poor accuracy and convergence efficiency when dealing with complex optimization problems. Furthermore, a DACFPA-Kriging model is developed by optimizing the relevant parameter of Kriging model via DACFPA. Finally, the dual Kriging model is constructed to improve the efficiency of uncertainty analysis, and a robust design optimization method based on DACFPA-Dual-Kriging is proposed.FindingsThe DACFPA outperforms the FPA, particle swarm optimization and gray wolf optimization algorithms in terms of solution accuracy, convergence speed and capacity to avoid local optimal solutions. Additionally, the DACFPA-Kriging model exhibits superior prediction accuracy and robustness contrasted with the original Kriging and FPA-Kriging. The proposed method for robust design optimization based on DACFPA-Dual-Kriging is applied to the motor hanger of the electric multiple units as an engineering case study, and the results confirm a significant reduction in the fluctuation of the maximum equivalent stress.Originality/valueThis study represents the initial attempt to enhance the prediction accuracy of the Kriging model using the improved FPA and to combine the dual Kriging model for uncertainty analysis, providing an idea for the robust optimization design of mechanical structure with black-box problem.

Two-timescale projection neural networks in collaborative neurodynamic approaches to global optimization and distributed optimization

In this paper, we propose a two-timescale projection neural network (PNN) for solving optimization problems with nonconvex functions. We prove the convergence of the PNN with sufficiently different timescales to a local optimal solution. We develop a collaborative neurodynamic approach with multiple such PNNs to search for global optimal solutions. In addition, we develop a collaborative neurodynamic approach with multiple PNNs connected via a directed graph for distributed global optimization. We elaborate on four numerical examples to illustrate the characteristics of the approaches.

Prediction of agricultural carbon emissions in China based on a GA-ELM model

Introduction: Strengthening the early warning of greenhouse gas emissions from agriculture is an important way to achieve Goal 13 of the Sustainable Development Goals. Agricultural carbon emissions are an important part of greenhouse gases, and accelerating the development of green and low-carbon agriculture is of great significance for China to achieve high-quality economic development and the goal of “carbon neutrality in peak carbon dioxide emissions”.Methods: By measuring the total agricultural carbon emissions in China and seven administrative regions from 2000 to 2021, the paper analyzes the influencing factors of agricultural carbon emissions in China by using STIRPAT environmental pressure model, and on this basis, predicts the peak trend of agricultural carbon emissions in China under different development scenarios by using the extreme learning machine model optimized by genetic algorithm.Results: The results showed that the extreme learning machine model improved by the genetic algorithm can overcome the shortcoming that the extreme learning machine model is easy to fall into the local optimal solution, thus obtaining higher prediction accuracy. At the same time, from 2000 to 2021, the total agricultural carbon emissions in China showed a continuous fluctuation trend, and due to the constraints of the agricultural economic level, agricultural industrial structure, and agricultural human capital, the agricultural carbon emissions showed spatial differentiation. It is worth noting that, in the context of green development, the agricultural carbon emissions of the seven regions in China all have the potential to achieve the “peak carbon dioxide emissions” goal in 2030, with only a slight difference at the peak.Discussion: The research results of this paper provide evidence for the government to formulate flexible, accurate, reasonable and appropriate agricultural carbon reduction policies, which is helpful to strengthen the exchanges and cooperation of regional agricultural and rural carbon reduction and fixation, and actively and steadily promote China's agriculture to achieve the goal of “peak carbon dioxide emissions carbon neutrality”.

Reliability Optimization of Hybrid Systems Driven by Constraint Importance Measure Considering Different Cost Functions

The requirements of high reliability for hybrid systems are urgent for engineers to maximize the system reliability under the limited cost budget. The cost constraint importance measure (CIM) is an important tool to achieve the local optimal solution by considering the relationship between constraint conditions and objective functions in the optimization problem. To better consider the contribution of the CIM, this paper considers three different cost function forms, including power type, trigonometric type, and exponential type. Combining the global search ability of the arithmetic optimization algorithm (AOA) with the local search ability of the CIM, a CIM-based arithmetic optimization algorithm (CIAOA) is developed to analyze the contribution of the CIM. Through the numerical experiments, the optimal system reliability and convergence generation of the CIAOA and AOA under different cost function forms are regarded as the indexes to analyze algorithm performance. The experimental results show that the average system reliability improvement percentages under power type, trigonometric type, and exponential cost constraint are 8.07%, 0.14%, and 0.53%, respectively, while the average convergence improvement percentages under three cost forms are 37.30%, 0.08%, and 1.66%, respectively. Therefore, the CIAOA performs the best under power cost constraints. Finally, a numerical example of a hybrid power vehicle system is introduced to analyze the contribution of the CIM under different cost functions by considering the reliability improvement rate in the optimal solution and the ranking of the CIM. The higher prioritization components in the two rankings are similar, which shows that the component with higher a CIM is selected to improve its reliability.

Autonomous Control System with Passive Positioning for Unmanned-Aerial-Vehicle-Assisted Edge Communication in 6G

UAVs can be deployed in many scenarios to provide various types of services via 6G edge communication. In these scenarios, it is necessary to obtain the position of the UAVs in a timely and accurate manner to avoid UAV collisions. In this paper, we consider improved passive localization algorithms aimed at reducing convergence time and adapting to extreme conditions. For the sake of reducing the complexity of signals and ensuring the reliability of receiving processes, we reconsidered the angle between arrival signals as the feature in positioning. Then, according to the characteristics of the positioning process, we draw on the cyclical process of the iterative greedy algorithm to construct the coding, destruction, and reorganization process to guide the movement of the UAV. Moreover, an improved Metropolis criterion is added to prevent falling into the local optimal solution. Finally, the proposed algorithm is verified in the simulation results. The results show that the algorithm can achieve precise positioning and excellent track planning within a small number of iterations, and it reduces the amount of information carried by the signal and convergence time compared with the traditional method.

Combination optimization method of grid sections based on deep reinforcement learning with accelerated convergence speed

A modern power system integrates more and more new energy and uses a large number of power electronic equipment, which makes it face more challenges in online optimization and real-time control. Deep reinforcement learning (DRL) has the ability of processing big data and high-dimensional features, as well as the ability of independently learning and optimizing decision-making in complex environments. This paper explores a DRL-based online combination optimization method of grid sections for a large complex power system. In order to improve the convergence speed of the model, it proposes to discretize the output action of the unit and simplify the action space. It also designs a reinforcement learning loss function with strong constraints to further improve the convergence speed of the model and facilitate the algorithm to obtain a stable solution. Moreover, to avoid the local optimal solution problem caused by the discretization of the output action, this paper proposes to use the annealing optimization algorithm to make the granularity of the unit output finer. The proposed method in this paper has been verified on an IEEE 118-bus system. The experimental results show that it has fast convergence speed and better performance and can obtain stable solutions.

A multilayer stacking method base on RFE-SHAP feature selection strategy for recognition of driver’s mental load and emotional state

The driver state monitoring is becoming one of the research hotspots in the field of traffic and vehicle safety, which can ensure driving safety by monitoring the driver’s state. Therefore, this work makes an attempt to recognize driver's mental load and emotional states. However, the reliability and accuracy of driver status detection largely depend on the extracted features and the detection algorithm. The existing methods mainly improve accuracy by increasing the number of features, but for the problem with limited training samples, the increase in features may lead to an increase in model variance, and resulting in overfitting. In addition, single-model based methods may fall into local optimal solutions when performing local search. To alleviate these, we firstly propose an RFE-SHAP algorithm that improves the recursive feature elimination algorithm by using the Shapley Additive exPlanning value, and paired it with the eXtreme Gradient Boosting (XGBoost) algorithm to screen out the subset of features that best represent the driver's mental load and emotional state. Secondly, we proposed a multilayer stacking ensemble learning method based on different optimal feature subsets to further improve the accuracy of the driver’s mental load and emotional state recognition. For each base models used for integration learning, the corresponding optimal feature subsets are selected using the RFE-SHAP algorithm, and then the different optimal feature subsets are combined with multilayer stacking ensemble learning. The validation via experimental data demonstrates that the XGBoost-RFE-SHAP algorithm achieves superior model performance with fewer feature combinations than the classic algorithm. The proposed driver state detection model based on multiple optimum feature subsets and multilayer stacking integration methods would more accurately identify the driver's mental load and emotional state than the single model, commonly used machine learning and integrated learning algorithms.

MO-CBACORP: A new energy-efficient secure routing protocol for underwater monitoring wireless sensor network

With the rapid progress of sensor technology, underwater monitoring wireless sensor network (UMWSN) equipped with water resource monitoring capabilities have surfaced. UMWSN is currently emerging as a popular research and application area, with a wide range of applications in various fields, including but not limited to disaster warning, pollutant monitoring and hydrological data monitoring. However, due to the limited size and computing power of wireless sensors, UMWSN are exceedingly susceptible to network security attacks by contaminating entities. In order to tackle the problems of inadequate security, elevated network energy consumption, and high system latency in existing QoS routing research, this paper puts forward an innovative multi-objective routing protocol named multi-objective chaotic Boltzmann ant colony optimization routing protocol (MO-CBACORP). MO-CBACORP can minimize the energy consumption of sensor nodes in UMWSN routing, thereby effectively diminishing system latency and significantly enhancing routing security. During the routing optimization process, MO-CBACORP proposed an innovative design of the chaos operator and Boltzmann selection strategy, which effectively avoids the issue of being stuck in local optimal solutions and greatly enhances the convergence speed of the algorithm. Additionally, a novel experiment for underwater monitoring environments is presented that precisely replicates underwater monitoring conditions and attack scenarios. According to the experimental results, MO-CBACORP exhibits superior performance compared to the latest state-of-the-art research including THOA-MHR, ACO-MCMC, and MAP-ACO, with a minimum improvement of 7.25%, 9.31%, and 7.68% in terms of route security, network energy consumption, and delay, respectively. All in all, MO-CBACORP exhibits superior performance compared to the three latest research algorithms.

Hybrid Variable Neighborhood Search for Solving School Bus-Driver Problem with Resource Constraints

The School Bus-Driver Problem with Resource Constraints (SBDP-RC) is an optimization problem with many practical applications. In the problem, the number of vehicles is prepared to pick a number of pupils, in which the total resource of all vehicles is less than a predefined value. The aim is to find a tour minimizing the sum of pupils’ waiting times. The problem is NP-hard in the general case. In many cases, reaching a feasible solution becomes an NP-hard problem. To solve the large-sized problem, a metaheuristic approach is a suitable approach. The first phase creates an initial solution by the construction heuristic based on Insertion Heuristic. After that, the post phase improves the solution by the General Variable Neighborhood Search (GVNS) with Random Neighborhood Search combined with Shaking Technique. The hybridization ensures the balance between exploitation and exploration. Therefore, the proposed algorithm can escape from local optimal solutions. The proposed metaheuristic algorithm is tested on a benchmark to show the efficiency of the algorithm. The results show that the algorithm receives good feasible solutions fast. Additionally, in many cases, better solutions can be found in comparison with the previous metaheuristic algorithms.

An improved inversion method for shale elastic parameters measurement based on ultrasonic resonance spectroscopy

The accurate measurement of elastic parameters of shale cores has important guidance for the exploration and development of shale oil and gas. The traditional shale acoustic experiment requires multiple samples from different angles and its preparation process is complex. Resonant Ultrasound Spectroscopy has the advantages of repeatable measurement, high accuracy, and the ability to obtain all elastic parameters from a single small sample. However, the influence of clamping force and measuring angle needs comprehensive analysis to ensure that formant can be measured as many and accurately as possible. This research first conducts sensitivity analysis on the elastic parameters of different shale to guide the experiment. In addition, due to the more complex inversion objective function of the anisotropic shale compared to isotropic samples, the traditional Levenberg–Marquardt method has a strong dependence on the initial value and is prone to falling into local optimal solution. The L-BFGS (limited memory BFGS) method is introduced into the inversion of anisotropic elastic parameters of shale, which can significantly improve the inversion efficiency. Finally, the robustness and reliability of the inversion method are validated through theoretical and experimental measurement results. [Work supported by the National Natural Science Foundation of China (42004117 and 42127807).]

Interferometric Calibration Based on a Constrained Evolutionary Algorithm without Ground Control Points for a Tiangong-2 Interferometric Imaging Radar Altimeter

The interferometric imaging radar altimeter (InIRA), mounted on the Tiangong-2 space laboratory, utilizes a small incidence and a short interferometric baseline to achieve altimetry for wide swathes of ocean surface topography and inland water surface elevation. To obtain a high-precision digital elevation model (DEM), calibration of the interferometric system parameters is necessary. Because InIRA utilizes the small-incidence interference system design, serious coupling occurs between the interferometric parameters. Commonly used interferometric calibration methods tend to fall into the local optimal solution for InIRA. Because evolutionary algorithms have a stronger robustness and global search ability, they are better suited to handling the solution space structure under the coupling of complex interferometric parameters. This article establishes an interferometric calibration optimization model for InIRA by utilizing the relative flatness of the lake surface as an inequality constraint. Furthermore, an adaptive penalty coefficient constraint evolutionary algorithm is designed to solve the model. The proposed method was tested on actual InIRA data, and the results indicate that it efficiently adjusts interferometric parameters, enhancing the precision of measurements for Qinghai Lake elevation.

Crude oil price forecasting: An ensemble‐driven long short‐term memory model based on CEEMDAN decomposition and ALS‐PSO optimization

AbstractAs the lifeline of various industries, crude oil is frequently considered a pillar of economic development. The accurate and reliable prediction of crude oil price can provide investors and decision makers with valuable guidance for formulating their strategies. However, the complexity of the crude oil market and the volatility of oil prices pose significant challenges to forecasting crude oil price. To achieve higher prediction accuracy, this paper proposes a new model in which a new modal component reconstruction rule based on sample entropy (SE) is innovatively proposed and includes an improved particle swarm optimization model to avoid getting trapped in a local optimal solution. Two real crude oil price series are selected for experimentation, and the results demonstrate that the proposed model exhibits superior performance in predicting crude oil price. The developed model outperforms the compared models in terms of mean absolute error, root‐mean‐square error, mean absolute percentage error, and coefficient of determination. This result indicates that Complete Ensemble Empirical Mode Decomposition with Adaptive Noise exhibits better decomposition performance. SE can effectively reduce error accumulation, and particle swarm optimization with an adaptive learning strategy (ALS‐PSO) achieves better optimization results for a long short‐term memory network compared with PSO only. Therefore, the proposed model is an effective crude oil price prediction tool that can be applied in practice for investment and policy‐making.

Automatic DNN architecture design using CPSOTJUTT for power system inspection

To quickly and accurately automatically design more high-precision deep neural network models (DNNs), this paper proposes an automatic DNN architecture design ensemble model based on consensus particle swarm optimization-assisted trajectory unified and TRUST-TECH (CPSOTJUTT), called CPSOTJUTT-EM. The proposed model is a three-layer model, and its core is a three-stage method for addressing the sensitivity of the local solver to the initial point and enabling fast and robust training DNN, effectively avoiding missing high-quality DNN models in the process of automatic DNN architecture design. CPSOTJUTT has the following advantages: (1) high-quality local optimal solutions (LOSs) and (2) robust convergence against random initialization. CPSOTJUTT-EM consists of the bottom layer: stable and fast design high-quality DNN architectures, the middle layer: exploration for a diverse set of optimal DNN classification engines, and the top layer: ensemble model for higher performance. This paper tests the performance of CPSOTJUTT-EM on public datasets and three self-made power system inspection datasets. Experimental results show that the CPSOTJUTT-EM has excellent performance in automatic DNN architecture design, DNN model optimization. And the CPSOTJUTT-EM can automatically design high-quality DNN ensemble models, laying a solid foundation for the application of DNN in other fields.

A fast and differentiable optimization model for finding the minimum dominating set in large-scale graphs

The minimum dominating set is an important NP-hard problem in graph theory, widely used in various fields such as computer network layout and social networks. Although linear programming algorithms can obtain a global optimal solution on small graphs, they are not suitable for large graphs. To find a local optimal solution, many heuristic algorithms have been proposed. These algorithms require strong techniques and programming, and most of them still need improvement in performance on large graphs. This paper presents a cooperative–competitive model that transforms the discrete problem into a continuously differentiable problem. By using the gradient descent method, this approach can handle all vertices simultaneously, and its time complexity is linear. Compared to existing search algorithms, this method is based on a straightforward principle and is fast. For small graphs, it can achieve performance almost comparable to linear programming methods. For large graphs, this method can explore more diverse local optimal solutions in the same amount of time, making it easier to obtain better performance. In this paper, a comparison and analysis of this gradient-based algorithm and graph theory-based search algorithms are conducted on the minimum dominating set, allowing researchers to have a clearer understanding of the advantages and disadvantages of search algorithms and gradient methods in complex problems. The referenced search algorithms may potentially improve the gradient descent algorithm, leading to better solutions in other fields. At the same time, gradient-based methods can be used to solve many similar NP-hard problems in graph theory.

Improved artificial potential field route planning method based on stochastic perturbation

As a typical route planning algorithm, the APF method has been widely used in robotics, autopilot and other fields. However, it also has weakness in local optimal point. In computer science and mathematics, stochastic perturbation is an accepted approach that can assist optimization algorithms leave the local optimal solution and achieve the global optimal solution as well as improve robustness and adaptability in specific application situations. therefore, the problem can be successfully solved by using stochastic perturbation. In this article, the traditional APF improved through stochastic perturbation. When the robot is running in an APF, the distance between the robot and the target point is calculated at all times. If the distance between the robot and the target point remains unchanged for a period of time or if the stop point oscillates, it is determined whether the robot has reached the target point at this time. If not, it is determined that the robot has fallen into a local optimal point at this time. After completing the judgment, stochastic perturbation is applied to the robot, causing it to jump out of the local optimal point and continue to navigate to the target point. The results of the comparison between the paths generated by the traditional method and the improved method validate the effectiveness of this method.