Global Optimal Solution Research Articles

An edge‐based event‐triggered delayed distributed algorithm for economic dispatch in smart grids

AbstractThis paper presents an edge‐based event‐triggered delay distributed algorithm for solving the economic dispatch problem (EDP) in smart grids. The objective of the EDP is to minimize the total generation cost by allocating power to individual generators, each with its local generation constraint. To save the overhead of communication resources between agents, an edge‐based event‐triggered mechanism is suggested. By setting distinct triggering thresholds for each communication edge, the agent may efficiently regulate the communication frequency among all neighbors. However, in practice, owing to the instability of the network, the agent may receive information regarding its neighbors, leading to communication lags for every communication link. The virtual agent technique and double‐stochastic matrix augmentation technique provide an equivalent delay‐free EDP. It is demonstrated that the proposed algorithm can asymptotically converge to the global optimal solution as long as the communication delay is arbitrary, time‐varying, and random, but bounded. Objective and clear evidence is provided through a case study in smart grids to verify the algorithm's feasibility.

A coevolutionary algorithm using Self-organizing map approach for multimodal multi-objective optimization

Multimodal Multi-Objective Problems (MMOPs) are frequently encountered in the real world. Traditional Multimodal Multi-Objective Evolutionary Algorithms (MMEAs) often find multiple Pareto optimal solutions with the same objective values. However, in real-world problems, there often exist multiple global optimal solutions and local optimal solutions at the same time. Ensuring that these solution sets are obtained simultaneously is the concern of most current researchers. To address this issue, this paper proposes a novel multimodal multi-objective evolutionary algorithm named CoSOMEA. In the CoSOMEA, a Self-organizing map (SOM) neural network is used to extract the information of decision space to ensure better exploration of the global optima and exploitation of the local optima. Meanwhile, coevolutionary mechanism are used to ensure a balance between the exploration and exploitation in order to avoid the algorithm falling into local areas. The three test suites named IDMP, IDMP_ee and MMF are adopted to verify the effectiveness of proposed algorithm. Experimental results demonstrate that the CoSOMEA exhibits competitive performance in solving MMOPs compared to other state-of-the-art MMEAs.

AN EFFICIENT STUDY OF PV/WIND/BATTERY/ELECTROLYZER/H2-TANK/FC FOR A REMOTE AREA ELECTRIFICATION

With the rapid development of the use of renewable energy systems, it is becoming more and more important to combine different sources into hybrid renewable energy systems. Many parameters in hybrid renewable energy systems must be optimized to effectively size hybrid system components to achieve economic, technical, and design goals practically. This paper focuses on the optimal configuration of off-grid hybrid renewable energy systems (HRES). The system consists of a photovoltaic (PV), wind turbine (WT) and battery bank (BB), fuel cell (FC) with hydrogen tank (H2-tank), and electrolyzer (Elect). The optimal size of the proposed HRES component is achieved using a novel meta-heuristic technique called the whale optimization algorithm (WOA). WOA improves the optimal configuration of HRES to produce the best minimum value of the fitness function, which converges to the global optimal solution after several iterations. The proposed WOA is used to solve the multi-objective optimization problem of the cost of energy (COE) in $/kWh and the total net present cost (TNPC) in $. Two recent algorithms, particle swarm optimization (PSO) and gray wolf optimizer (GWO), have also been implemented in this work to demonstrate the effectiveness of the proposed algorithm.

Application of QPSO-BPSO in fault self-healing of distributed power distribution networks

With the widespread application of distributed power sources in distribution networks, fault self-healing technology has become the key to ensuring the reliability of power systems. The micro-grid ensures system stability with a three-layer structure, where the designed method handles optimization problems, achieving faster global search and optimal solutions. Agents develop targeted recovery strategies by understanding network load, which are then executed by higher-level agents to ensure that the optimal recovery command is implemented by the system. According to the research results, during peak load, the system successfully outputted 7 kilowatts and met the load demand through battery discharge, demonstrating its self-healing ability. The output analysis of photovoltaic and wind turbines showed that the system reasonably scheduled within 24 h according to the changes in solar energy and wind power. Based on the quantum behavior particle swarm optimization algorithm, the system has achieved lower active power loss and greater power supply capacity. Although the number of switch operations has increased, the system performance has significantly improved, meeting the requirements for improving system economy and safety. It has promoting effects on the sustainable development of future power systems.

Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

Ultrasonic-Assisted Tungsten Inert Gas Welding of Inconel 625 Joints to Reduce Hot Cracking and Improve Microhardness: Optimization and Prediction Methods

Abstract This research article investigated the optimized process parameters for decreasing the hot cracking phenomenon and improving the microhardness of ultrasonic vibratory-assisted tungsten inert gas (U-TIG) welding of Inconel 625 alloy. The study employed two approaches: response surface methodology (RSM) and RSM coupled with a genetic algorithm (RSM-GA). The objective was to analyze the impact of welding process parameters, including welding current, gas flow rate, presence or absence of ultrasonic vibration, and filler material, on the crack length and microhardness of the welded joints. Experimental tests were conducted using RSM with a full factorial central composite design matrix, enabling comprehensive parameter space exploration. Parametric mathematical models were developed based on the obtained experimental data. These models were then utilized as fitness functions within the GA to determine the global optimal solution, aiming to minimize crack length and maximize microhardness. Additionally, artificial neural network (ANN) models were developed to predict the responses and optimize the welding process. The comparison between the experimental and predicted data demonstrated the reliability of the ANN model in accurately estimating the crack length and microhardness of U-TIG welded Inconel 625 alloy joints. The developed models achieved a prediction accuracy of less than 5 % error.

CMRLCCOA: Multi-Strategy Enhanced Coati Optimization Algorithm for Engineering Designs and Hypersonic Vehicle Path Planning.

The recently introduced coati optimization algorithm suffers from drawbacks such as slow search velocity and weak optimization precision. An enhanced coati optimization algorithm called CMRLCCOA is proposed. Firstly, the Sine chaotic mapping function is used to initialize the CMRLCCOA as a way to obtain better-quality coati populations and increase the diversity of the population. Secondly, the generated candidate solutions are updated again using the convex lens imaging reverse learning strategy to expand the search range. Thirdly, the Lévy flight strategy increases the search step size, expands the search range, and avoids the phenomenon of convergence too early. Finally, utilizing the crossover strategy can effectively reduce the search blind spots, making the search particles constantly close to the global optimum solution. The four strategies work together to enhance the efficiency of COA and to boost the precision and steadiness. The performance of CMRLCCOA is evaluated on CEC2017 and CEC2019. The superiority of CMRLCCOA is comprehensively demonstrated by comparing the output of CMRLCCOA with the previously submitted algorithms. Besides the results of iterative convergence curves, boxplots and a nonparametric statistical analysis illustrate that the CMRLCCOA is competitive, significantly improves the convergence accuracy, and well avoids local optimal solutions. Finally, the performance and usefulness of CMRLCCOA are proven through three engineering application problems. A mathematical model of the hypersonic vehicle cruise trajectory optimization problem is developed. The result of CMRLCCOA is less than other comparative algorithms and the shortest path length for this problem is obtained.

Optimal allocation of renewable energy systems in a weak distribution network

In the context of a real electrical distribution network in Puerto Carreño, Colombia, this paper addresses the challenge of enhancing power supply reliability through the strategic integration of Renewable Energy Sources with Hydrogen Energy Systems. The planning problem is reformulated as a Mixed-Integer Quadratically Constrained Programming problem, enabling the use of efficient solvers with global optimal solution. Considering the extensive curtailment options and numerous allocation components, the optimization problem naturally scales up. To address this computational intensity, representative scenarios are derived from the original high-dimensional probability distribution employing the Gaussian Mixture Model. These scenarios are used in conjunction with the proposed optimization framework to achieve cost-effective power grids while reducing fossil fuel dependency.

Gas identification using electronic nose via gramian-angular-field-based image conversion and convolutional neural networks architecture search

Recent years have witnessed the splendid performance of deep learning methods used in gas recognition for electronic noses (E-nose). In addition to effective feature extraction, the architecture of the deep neural network plays a vital role. Currently, most applied network structures are hand-crafted by human experts, which is time-consuming and problem-dependent, making it necessary to design the structures of neural networks according to specific demands. In this work, a genetic algorithm with particle swarm optimization (GA-PSO), which possesses promising optimization capabilities, is applied to search for effective deep convolutional neural networks (CNNs) for gas classification based on E-nose technology. A novel image transformation strategy using Gramian angular field and a hybrid cost-saving method is employed in the search process, enabling adaptive and efficient CNN search on gas datasets. With the proposed methods, we can achieve an average classification accuracy of over 90 % on two public gas datasets, while also significantly reducing the model size compared to state-of-the-art CNNs. By using these novel strategies, our approach surpasses random search and basic PSO algorithm in achieving the global optimal solution, higher and more stable accuracy, and faster convergence in pattern recognition using E-nose. Our work suggests that the proposed method can quickly identify excellent CNN structures for E-nose applications.

A sequence decomposition genetic algorithm for petrophysical inversion with spatial correlation

Predicting petrophysical properties based on seismic attributes is essential for accurate subsurface characterization. Typically, a forward model is first established to relate the petrophysical properties to geophysical measurements, and then the petrophysical properties are inverted from the actual measurements. Imposing prior constraints of the spatial relationship is also desirable to regularize the ill-posed inverse problem. However, petrophysical inversion involving spatial correlation presents a high-dimensional optimization problem with multiple local extrema. This problem can be challenging to solve, particularly when discrete variables (such as lithofacies) and continuous variables (such as porosity and fluid saturation) are considered together. Therefore, we develop a global optimization algorithm that uses the Markov chain decomposition and a genetic algorithm for a joint discrete-continuous petrophysical inversion with spatial correlation. The innovation of this algorithm is to spatially decouple the sequence optimization problem into multiple low-dimensional subproblems and overcome the initial value dependence to converge to the global optimal solution. Furthermore, an approximation operation is introduced to expedite the optimization algorithm. Numerical experiments show that after algorithmic acceleration, the spatially correlated inversion requires the same computational time as a simple spatially uncorrelated inversion and achieves significantly better accuracy than the latter. Finally, we apply the method to a case study in East China, wherein the lithofacies, clay content, porosity, and water saturation are inferred from the data of the wave velocities and density. The inversion results around the wells generally match the well-logging data, verifying the feasibility of the new method.

Moboa: a proposal for multiple objective bean optimization algorithm

The primary objective of multi-objective evolutionary algorithms (MOEAs) is to find a set of evenly distributed nondominated solutions that approximate the Pareto front (PF) of a multi-objective optimization problem (MOP) or a many-objective optimization problem (MaOP). This implies that the approximated solution set obtained by MOEAs should be as close to PF as possible while remaining diverse, adhering to criteria of convergence and diversity. However, existing MOEAs exhibit an imbalance between achieving convergence and maintaining diversity in the objective space. As far as the diversity criterion is concerned, it is still a challenge to achieve an evenly distributed approximation set with different sizes for a problem with a complicated PF shape. Furthermore, Pareto dominance has its own weaknesses as the selection criterion in evolutionary multiobjective optimization. Algorithms based on Pareto criterion (PC) can suffer from problems such as slow convergence to the optimal front and inferior performance on problems with many objectives. To effectively address these challenges, we propose a multi-objective bean optimization algorithm (MOBOA). Given that the selection of parent species, representing global optimal solutions, directly influences the convergence and diversity of the algorithm, MOBOA incorporates a preference order equilibrium parent species selection strategy (POEPSS). By extending the Pareto criterion with the preference order optimization criterion, the algorithm effectively enhances parent species selection pressure across multiple objectives. To balance convergence and diversity, MOBOA proposes a multi-population global search strategy explicitly maintaining an external archive during the search process. Leveraging the inherent multi-population advantages of bean optimization algorithm (BOA), the algorithm facilitates information sharing among the main population, auxiliary populations, and historical archive solution sets. Additionally, a diversity enhancement strategy is employed in the environmental selection stage, introducing the environmental selection strategy of the SPEA2 algorithm to generate a set of evenly distributed nondominated solutions. Experimental results on a series of widely used MOPs and MaOPs demonstrate that the proposed algorithm exhibits higher effectiveness and competitiveness compared to state-of-the-art algorithms.

SSA-ELM: A Hybrid Learning Model for Short-Term Traffic Flow Forecasting

Nowadays, accurate and efficient short-term traffic flow forecasting plays a critical role in intelligent transportation systems (ITS). However, due to the fact that traffic flow is susceptible to factors such as weather and road conditions, traffic flow data tend to exhibit dynamic uncertainty and nonlinearity, making the construction of a robust and reliable forecasting model still a challenging task. Aiming at this nonlinear and complex traffic flow forecasting problem, this paper constructs a short-term traffic flow forecasting hybrid optimization model, SSA-ELM, based on extreme learning machine by embedding the sparrow search algorithm in order to solve the above problem. Extreme learning machine has been widely used in short-term traffic flow forecasting due to its characteristics such as low computational complexity and fast learning speed. By using the sparrow search algorithm to optimize the input weight values and hidden layer deviations in the extreme learning machine, the sparrow search algorithm is utilized to search for the global optimal solution while taking into account the original characteristics of the extreme learning machine, so that the model improves stability while increasing prediction accuracy. Experimental results on the Amsterdam A10 road traffic flow dataset show that the traffic flow forecasting model proposed in this paper has higher forecasting accuracy and stability, revealing the potential of hybrid optimization models in the field of short-term traffic flow forecasting.

Reduced Outer Space Algorithm for Globally Computing Affine Sum-of-Ratios Problems

This paper investigates the affine sum-of-ratios problem (SRP) which has numerous applications in many fields of economy and engineering. For globally computing the affine SRP, based on equivalent transformation and new affine relaxation problem, a reduced outer space branch-and-bound algorithm is designed. The designed algorithm has been proven to converge to a global optimal solution of the problem (SRP) eventually. Meanwhile, the maximum iteration time for the algorithm in the worst case is estimated by analyzing its computational complexity. Finally, numerical experimental results indicate that the presented algorithm is robust and effective.

Modeling a Multimodal Routing Problem with Flexible Time Window in a Multi-Uncertainty Environment

In this study, we extend the research on the multimodal routing problem by considering flexible time window and multi-uncertainty environment. A multi-uncertainty environment includes uncertainty regarding the demand for goods, the travel speed of the transportation mode, and the transfer time between different transportation modes. This environment further results in uncertainty regarding the delivery time of goods at their destination and the earliness and lateness caused by time window violations. This study adopts triangular fuzzy numbers to model the uncertain parameters and the resulting uncertain variables. Then, a fuzzy mixed integer nonlinear programming model is established to formulate the specific problem, including both fuzzy parameters and fuzzy variables. To make the problem easily solvable, this study employs chance-constrained programming and linearization to process the proposed model to obtain an equivalent credibilistic chance-constrained linear programming reformulation with an attainable global optimum solution. A numerical case study based on a commonly used multimodal network structure is presented to demonstrate the feasibility of the proposed method. Compared to hard and soft time windows, the numerical case analysis reveals the advantages of the flexible time window in reducing the total costs, avoiding low reliability regarding timeliness, and providing confidence level-sensitive route schemes to achieve flexible routing decision-making under uncertainty. Furthermore, the numerical case analysis verifies that it is necessary to model the multi-uncertainty environment to satisfy the improved customer requirements for timeliness and enhance the flexibility of the routing, and multimodal transportation is better than unimodal transportation when routing goods in an uncertain environment. The sensitivity analysis in the numerical case study shows the conflicting relationship between the economic objective and the reliability regarding the timeliness of the routing, and the result provides a reference for the customer to find a balance between them.

Location-Routing Optimization for Two-Echelon Cold Chain Logistics of Front Warehouses Based on a Hybrid Ant Colony Algorithm

Diverse demands have promoted the rapid development of the cold chain logistics industry. In the paper, a novel approach for calculating the comprehensive carbon emission cost was proposed and the front warehouse mode was analyzed under the background of energy conservation and emission reduction. To solve the two-echelon low-carbon location-routing problem (2E-LCLRP), a mathematical model considering operating cost, total transportation cost, fixed cost, refrigeration cost, cargo damage cost, and comprehensive carbon emission cost was proposed to determine the minimum total cost. A hybrid ant colony optimization (HACO) algorithm based on an elbow rule and an improved ant colony optimization (IACO) algorithm was proposed to solve the 2E-LCLRP. According to the elbow rule, the optimal number of front warehouses was determined and an IACO algorithm was then designed to optimize vehicle routes. An adaptive hybrid selection strategy and an optimized pheromone update mechanism were integrated into the HACO algorithm to accelerate convergence and obtain global optimal solutions. The proposed model and algorithm were verified through the case study of the 2E-LCLRP in Nanjing, China. The HACO algorithm outperformed the original ant colony optimization (ACO) algorithm in terms of convergence rate and solution quality. This study provides significant insights for enhancing heuristic algorithms as well as valuable research methods. Furthermore, the results can help cold chain logistics companies in balancing economic costs and environmental benefits and address cold chain distribution of agricultural products.

Shape optimization of autonomous underwater helicopters based on different parameter curves and various optimization algorithms

This study aimed to compare the non-uniform rational B-spline (NURBS) and Bezier curves to design the shape of an autonomous underwater helicopter (AUH). Currently, there is no established method for AUH shape design. The optimal solutions obtained from both curves were compared to evaluate their performance. A parametric model was constructed to determine the design variables of the two curves. Computational fluid dynamics was used to solve the resistance values of different shapes. Sample points were generated using the design of the experimental approach, and an approximate model was established using the radial basis function neural network method. Based on the combinatorial optimization strategy, three intelligent optimization algorithms were used for the global search. Then, the resulting solution was used as the starting point for a local search to obtain the global optimal solution. The resistance optimal solutions achieved by employing the NURBS and Bezier curves were 25.2% and 24.1% smaller than the initial values, respectively. These findings indicate that, within the design parameters of this study, the shape design approach using the NURBS curve yields superior performance for the AUH.

HCSMBO: A hybrid cat swarm and monarch butterfly optimization algorithm for energy consumption optimization in industrial internet of things

Energy consumption optimization is crucial for improving the quality of application services in the industrial Internet of Things (IIoT) environment. Traditional optimization methods often adopt blind search strategies, which leads to a significant waste of computing resources and low efficiency. This paper proposes a Hybrid Cat Swarm Optimization and Monarch Butterfly Optimization (HCSMBO), which combines the advantages of Cat Swarm Optimization (CSO) and Monarch Butterfly Optimization (MBO) to solve this problem. By utilizing the characteristics of swarm intelligence, including strong spatial search ability, high stability, and fast convergence, HCSMBO focuses on detailed optimization of the coverage, efficiency, and energy balance coefficient of Support Vector Machine (SVM) networks. By adjusting the weight factors of the fitness function, this algorithm can effectively find the global optimal solution. The experimental results confirm that HCSMBO significantly improves the intelligence, accuracy, and stability of task scheduling in resource management configuration, while achieving lower energy consumption. The research results of this paper are of great significance for improving the service quality of IIoT applications, meeting personalized business needs, and improving resource utilization and execution efficiency. In addition, they also provide new ideas and methods for energy consumption optimization research in the future IIoT.

SHM data compression and reconstruction based on IGWO-OMP algorithm

The long-term operating structural health monitoring (SHM) system generates massive monitoring data, whose transmission and storage are challenging tasks. To address this issue, this study proposed an improved grey wolf optimizer-orthogonal matching pursuit (IGWO-OMP) algorithm for SHM data compression and reconstruction. The effectiveness of the proposed algorithm was validated using four SHM datasets including ultrasonic guided wave (UGW), acceleration, and audio signals. Firstly, the optimization results of IGWO were compared with those of other classical algorithms to verify its superiority in reconstruction accuracy. Secondly, the reconstruction accuracy under various compression factors was investigated and the optimal compression factor was determined. Finally, the relationship between reconstruction accuracy and signal sparsity as well as the performance of IGWO-OMP in dealing with noise-containing signals were discussed. The results demonstrate the generalizability and excellent noise robustness of IGWO-OMP in SHM data compression and reconstruction. Compared with other optimization algorithms, IGWO exhibits the best global optimal solution searching ability and obtains the reconstructed signal closest to the original one. Comprehensively considering the compressed signal length, reconstruction accuracy and computational efficiency, the optimal compression factor is suggested to be 0.2. In IGWO-OMP, the signal reconstruction accuracy is related to its sparsity, the variation of the CCD index for the reconstructed signal with relative sparsity follows an exponential growth relationship.

An efficient image space branch-reduction-bound algorithm to globally solve generalized fractional programming problems for large-scale real applications

This study focuses on finding a global optimal solution to a generalized fractional programming problem (GFP) in the perspective of large-scale applications. However, few algorithms exist to solve the GFP due to its nonconvexity and NP-hard. Therefore, it is significant to propose an efficient algorithm for the GFP. For this purpose, first of all, using logarithmic and exponential properties, we transform the GFP into an equivalent problem (EP) by introducing some image space variables. Next, the relaxation problem (RP) is constructed using a two-phase relaxation method and bilinear relaxation technique based on the structure of the EP. Furthermore, through the comprehensive utilization of the unique structures of EP and RP, along with the attributes of branch and bound algorithms, some novel region-reduction techniques have been introduced to eliminate regions devoid of the global optimal solution. Subsequently, the integration of the two-phase relaxation method and region-reduction techniques within the branch-and-bound framework has led to the design of the image space branch-reduction-bound algorithm (ISBRBA). Moreover, the convergence and computational complexity of the ISBRBA are analyzed by considering the infinite approximation property between the objective functions of the EP and RP. Finally, the effectiveness and robustness of the ISBRBA are demonstrated through numerous numerical experiments.

An improved white shark optimizer algorithm used to optimize the structural parameters of the oil pad in the hydrostatic bearing

Abstract An improved white shark optimizer (MWSO) algorithm has been proposed. The algorithm adopts an improved tent chaotic mapping strategy to enhance the diversity of the initial population of white sharks, introduces the balance pool strategy of the EO algorithm to improve the convergence speed and accuracy of the algorithm, applies adaptive t-distribution dynamic selection probability perturbation to the global optimal solution, and adjusts the exploration and development ability of the algorithm at different iteration periods. MWSO, WSO, and seven excellent metaheuristic algorithms are tested and compared on 23 classic test functions and the CEC2017 test suite, and two non-parametric tests, a Wilcoxon rank sum test with a significance level of 0.05 and Friedman test, are conducted. The statistical results indicate that the proposed MWSO is significantly superior to other algorithms. In addition, nine algorithms are applied for the first time to optimize the structural parameters of the oil sealing edge of oil pads in response to the issue of the bearing capacity of hydrostatic bearings. This not only further verified the superiority of MWSO, but also provided new ideas for the optimization of hydrostatic bearings.