Optimization Model Research Articles

Contact analysis of output mechanism of cycloidal pinwheel reducer

In order to study the effect of design parameters on the contact performance of cycloid reducer, a new contact collision force model applicable to various restitution coefficients is proposed. Firstly, based on the L-N nonlinear contact theory and improved Winkler model, a contact force model with contact depth index and damping was proposed. Secondly, Hertzian contact theory was used to clarify the contact area, precise position and relative contact speed between the output pin and the cycloidal wheel in the presence of a clearance. By using the improved contact force model and simulation analysis, the effects of structural design parameters and working condition parameters on contact force were discussed. Finally, with the goal of reducing the contact force and volume of the reducer, the NSGA-II multi-objective genetic algorithm was used to construct an optimization model for the structural parameters of the reducer. The results show that the optimized structural parameters can effectively reduce the contact force of the output mechanism.

Two-stage optimization model for scheduling multiproduct pipeline network with multi-source and multi-terminal

The multiproduct pipeline network with multi-source and multi-terminal encompasses multi-point injection and multi-point distribution. Upon reorganization of batches at transfer depots, the intricacies of precise batch tracking become increasingly complex, thereby rendering the optimization of multiproduct pipeline network scheduling particularly arduous. In this paper, we introduce a dynamic index batch numbering method. By delineating the boundaries of intermediate injection points, the issue is bifurcated into two sub-problems: the optimization of batch planning for multiproduct pipeline with single-source and multi-terminal and the optimization of resource allocation at intermediate oil depots. The proposed algorithm is validated on two genuine multiproduct pipeline networks in China, demonstrating its capability to generate feasible solutions within a computational constraint of 18,000 CPU seconds. The findings reveal that this methodology holistically considers the entire pipeline network system, encompassing upstream oil intake, downstream oil supply, and the tank capacities of transfer depots, thereby establishing a coherent link between pipeline scheduling and depot planning. This paper may serve as a reference for the automated formulation of multiproduct pipeline network scheduling strategies.

Optimal Operation of Virtual Power Plants Based on Stackelberg Game Theory

As the scale of units within virtual power plants (VPPs) continues to expand, establishing an effective operational game model for these internal units has become a pressing issue for enhancing management and operations. This paper integrates photovoltaic generation, wind power, energy storage, and constant-temperature responsive loads, and it also considers micro gas turbines as auxiliary units, collectively forming a typical VPP case study. An operational optimization model was developed for the VPP control center and the micro gas turbines, and the game relationship between them was analyzed. A Stackelberg game model between the VPP control center and the micro gas turbines was proposed. Lastly, an improved D3QN (Dueling Double Deep Q-network) algorithm was employed to compute the VPP’s optimal operational strategy based on Stackelberg game theory. The results demonstrate that the proposed model can balance the energy complementarity between the VPP control center and the micro gas turbines, thereby enhancing the overall economic efficiency of operations.

Optimization of Charging Station Capacity Based on Energy Storage Scheduling and Bi-Level Planning Model

With the government’s strong promotion of the transformation of new and old driving forces, the electrification of buses has developed rapidly. In order to improve resource utilization, many cities have decided to open bus charging stations (CSs) to private vehicles, thus leading to the problems of high electricity costs, long waiting times, and increased grid load during peak hours. To address these issues, a dual-layer optimization model was constructed and solved using the Golden Sine Algorithm, balancing the construction cost of CSs and user costs. In addition, the problem was alleviated by combining energy storage scheduling and the M/M/c queue model to reduce grid pressure and shorten waiting times. The study shows that energy storage scheduling effectively reduces grid load, and the electricity cost is reduced by 6.0007%. The average waiting time is reduced to 2.1 min through the queue model, reducing the electric vehicles user’s time cost. The bi-level programming model and energy storage scheduling strategy have positive implications for the operation and development of bus CSs.

Towards optimal customized electricity pricing via iterative two-layer optimization for consumers and prosumers

Designing an electricity price mechanism that efficiently enables users to manage their self-production and consumption behavior to accommodate renewable energy and regulate peak load is a hard task with the emergence of prosumer with photovoltaic and energy storage. To address this issue, we propose an iterative two-layer optimization to investigate customized price of electricity for different types of users in the presence of photovoltaic uncertainty. By taking into account power flow restrictions, the model is used to explore the optimal time-of-use, demand, and on-grid prices for both electricity consumers and prosumers. The consumer and prosumer peak-flat-valley periods are initially divided in the upper layer. Then, a model for distribution system operator profit maximization is proposed to minimize operation cost, power loss, and peak–valley difference. A stochastic optimization model is presented in the lower layer for consumer and prosumer to hedge against the risk of uncertain photovoltaic with the aim of minimizing electricity tariff, demand tariff, and life cycle cost of energy storage. Numerical experiments conducted on modified 15-bus and 69-bus distribution systems with different types of users show the effectiveness of the iterative two-layer optimization for customized price of electricity in peak-shaving and valley-filling while ensuring the interests of distribution system operator and users. Results show that the total profit increases by more than 4% and the net load fluctuation variance reduces higher than 20% compared with the traditional pricing method.

Multi‐objective interval planning for 5G base station virtual power plants considering the consumption of photovoltaic and communication flexibility

AbstractLarge‐scale deployment of 5G base stations has brought severe challenges to the economic operation of the distribution network, furthermore, as a new type of adjustable load, its operational flexibility has provided a potential way to promote the consumption and utilization of photovoltaic. In this paper, a multi‐objective interval collaborative planning method for virtual power plants and distribution networks is proposed. First, on the basis of in‐depth analysis of the operating characteristics and communication load transmission characteristics of the base station, a 5G base station of virtual power plants participating in the cellular respiratory demand response model is constructed. In view of the inherent contradiction between system economy and environmental performance, a multi‐objective interval optimization model for collaborative planning of virtual power plants and distribution networks is established with the lowest system investment and operating costs and the lowest carbon emissions as the optimization goals. The established model is transformed into a deterministic optimization problem, which is solved by NSGA‐II algorithm. The modified IEEE‐33 node system is used in the case analysis to analyse the impact of different planning schemes and response characteristics on the system economy. The calculation results verify the effectiveness of the proposed method.

Density-Based Isogeometric Topology Optimization of Shell Structures

Shell structures with high stiffness-to-weight ratios are desirable in various engineering applications. Topology optimization serves as a popular and effective tool for generating optimal shell structures. The solid isotropic material with penalization (SIMP) method is often chosen because of its simplicity and convenience. However, SIMP method is typically integrated with conventional Finite Element Analysis (FEA) which has limitations in computational accuracy. Achieving high accuracy with FEA necessitates a substantial number of elements, leading to computational burdens. In addition, the discrete representation of the material distribution function may result in rough boundaries. Owing to these limitations, this paper proposes an Isogeometric Analysis (IGA) based SIMP method for optimizing the topology of shell structures based on Reissner–Mindlin theory. This method uses Non-Uniform Rational B-Splines (NURBS) to represent both the shell structure and the material distribution function with the same basis functions, allowing for higher accuracy and smoother boundaries. The optimization model takes compliance as the objective function with a volume fraction constraint and the coefficients of the density function as design variables, resulting in an optimized shell structure defined by the material distribution function. To obtain fairing boundaries of the holes in the optimized shell structure, further process is conducted by fitting the boundaries with fair B-spline curves automatically. Furthermore, the proposed IGA-SIMP framework is applied to generate porous shell structures by imposing different local volume fraction constraints. Numerical examples are provided to demonstrate the feasibility and efficiency of the IGA-SIMP method, showing that it outperforms the FEA-SIMP method and produces smoother boundaries.

Wear state identification of ball screw meta action unit based on parameter optimization VMD and improved Bilstm

In this paper, a novel neural network based on parameter optimization Variational Mode Decomposition (VMD) and improved bidirectional long short-term memory (BiLSTM) is proposed. Wear state recognition method of ball screw element action unit component based on Bilstm. Firstly, Tent chaotic map and adaptive sine cosine Algorithm were used to improve the improved Northern Goshawk Optimisation Algorithm (INGO) to verify the superiority of INGO algorithm and determine the optimal parameter combination of VMD. Secondly, INGO-VMD was used to decompose the collected vibration signals and calculate the correlation of IMF components, and the multi-feature information matrix that could characterize the wear state change of the lead screw was constructed after retaining the IMF components with large correlation. Finally, the divided feature information matrix and labels were input into the Bilstm network model of Bayesian optimization (BO) for training, and the Softmax classifier was used to classify and identify the wear state category.

Solving the resource constrained project scheduling problem with quantum annealing

Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations research.

Modelling and optimization method for energy saving of computer numerical control machine tools under operating condition

The widespread application of machine tools in industry results in very high energy consumption. In order to save energy, it is an effective means to reduce the processing power while improving the processing efficiency of machine tools. Since milling parameters directly affect machine performance, the selection of suitable milling parameters is particularly important. In this regard, this study proposes an integrated modelling and optimization method for energy saving of computer numerical control (CNC) machine tools under operating condition. Firstly, the operating condition of the CNC machine are analyzed and the processing power and efficiency mathematical models are established based on the four milling parameters (n, fz, ae, ap). Subsequently, the Pareto optimal solution is introduced to establish an optimization model integrating the processing power and time. To solve the optimization problem, an adaptive chaotic multi-objective chimp algorithm with fast convergence and satisfactory optimization is proposed considering three aspects: search space, convergence factor, and chaotic mapping. Afterwards, further degrees of freedom and sensitivity analyses were carried out on the constructed model using the Sobol method. Finally, comparative analysis and validation are conducted through simulation cases and actual processing experiments, respectively. The results show that both validation scenarios have the same conclusion. Compared with three existing algorithms, the proposed method reduces the processing power by 5.63 %, 4.65 % and 4.51 % and improves the processing efficiency by 27.88 %, 15.11 % and 15.31 %, respectively. Based on the above enhancements, the energy consumption is reduced by 58.21 %, 45.54 % and 41.45 % respectively.

Equilibrium Interaction Strategies for Integrated Energy System Incorporating Demand-Side Management Based on Stackelberg Game Approach

This paper analyzes the balanced interaction strategy of an integrated energy system (IES) operator and an industrial user in the operation process of the IES under the demand-side management (DSM) based on game theory. Firstly, we establish an electric–thermal IES, which includes a power grid, a heat grid and a natural gas grid. Secondly, a two-stage Stackelberg dynamic game model is proposed to describe the game behavior of IES operators and industrial users in the process of participating in DSM. The interactions between the IES operator (leader) and the user (follower) are formulated into a one-leader–one-follower Stackelberg game, where optimization problems are formed for each player to help select the optimal strategy. A pricing function is adopted for regulating time-of-use (TOU), which acts as a coordinator, inducing users to join the game. Then, for the complex two-stage dynamic game model established, the lower user-side constraint optimization problem is replaced by its KKT condition, so that the two-stage hierarchical optimization problem is transformed into a single-stage mixed-integer nonlinear optimization model, and the branch-and-bound method is introduced to solve it. Finally, the equilibrium strategies and income values of both sides of the game are obtained through a case simulation, and the dynamic equilibrium strategy curves under different capacity configurations are obtained through the sensitivity analysis of key parameters. The equilibrium income of the IES is USD 93.859, while the equilibrium income of industrial users in the park is USD 92.720. The simulation results show that the proposed method and model are effective.

Multi-objective optimization analysis of construction management site layout based on improved genetic algorithm

In construction management, the rationality of on-site layout is crucial for project progress, cost, and safety. In order to improve the rationality of on-site layout, a multi-objective optimization model combining ant colony algorithm and Pareto optimal solution was constructed based on genetic algorithm, and this model was applied to practical engineering cases. The results show that in terms of computational time, the genetic algorithm takes an average of 1702.0 s, while the improved algorithm takes an average of 421.0 s, which is 1281s less and 85.9% more than before the improvement. The performance of the improved algorithm is the best, and the optimal solution can be obtained through multiple iterations. The improved algorithm has improved the efficiency of on-site layout optimization, and possesses practical application value for the layout of construction management sites. It offers a certain reference for the reasonable setting of construction management sites.

Improving capacity configuration and load scheduling for an integrated multi-sourced cogeneration system

The integration of renewable energy sources and fossil fuel e.g. coal in a heat and power cogeneration system has been proven to be an effective way to reduce CO2 emissions. An integrated multi-sourced cogeneration (IMC) system consisting of wind, solar photovoltaic (PV), and coal-fired combined heat and power (CHP) plant on the energy supply side, is studied in this paper. A bi-level collaborative optimization model for capacity configuration and load scheduling of the wind-PV-coal IMC system is developed. In the upper level, the capacity of wind farm and PV farm are optimized with the enumeration method, while the load scheduling under typical annual conditions is optimized with adaptive particle swarm optimization algorithm in the lower level. The results show that the optimal capacities of wind and PV are 120 MW and 280 MW for the IMC system, respectively. The annual and typical day load scheduling with optimal wind and PV capacities are analyzed. The result of the load scheduling shows that heating and power load distribution unevenly between the two CHP units contributes to reducing total standard coal consumption, which saves 34.96 t in a typical day during the heating season. This study can provide a reference for the capacity configuration and operation scheduling of the IMC system.

Two-Stage Optimal Scheduling for Urban Snow-Shaped Distribution Network Based on Coordination of Source-Network-Load-Storage

With the widespread integration of distributed resources, optimizing the operation of urban distribution networks faces challenges including uneven source-load-storage distribution, fluctuating feeder power flows, load imbalances, and network congestion. The urban snow-shaped distribution network (SDN), characterized by numerous intra-station and inter-station tie switches, serves as a robust framework to intelligently address these issues. This study focuses on enhancing the safe and efficient operation of SDNs through a two-phase optimal scheduling model that coordinates source-network-load-storage. In the day-ahead scheduling phase, an optimization model is formulated to minimize operational costs and mitigate load imbalances. This model integrates network reconfiguration, energy storage systems (ESSs), and flexible load (FL). During intra-day scheduling, a rolling optimization model based on model predictive control adjusts operations using the day-ahead plan to minimize the costs and penalties associated with power adjustments. It provides precise control over ESS and FL outputs, promptly correcting deviations caused by prediction errors. Finally, the proposed model is verified by an actual example of a snow-shaped distribution network in Tianjin. The results indicate significant improvements in leveraging coordinated interactions among source-network-load-storage, effectively reducing spatial-temporal load imbalances within feeder clusters and minimizing the impact of prediction inaccuracies.

RIRNet: A Direction-Guided Post-Processing Network for Road Information Reasoning

Road extraction from high-resolution remote sensing images (HRSIs) is one of the tasks in image analysis. Deep convolutional neural networks have become the primary method for road extraction due to their powerful feature representation capability. However, roads are often obscured by vegetation, buildings, and shadows in HRSIs, resulting in incomplete and discontinuous road extraction results. To address this issue, we propose a lightweight post-processing network called RIRNet in this study, which include an information inference module and a road direction inference task branch. The information inference module can infer spatial information relationships between different rows or columns of feature images from different directions, effectively inferring and repairing road fractures. The road direction inference task branch performs the road direction prediction task, which can constrain and promote the road extraction task, thereby indirectly enhancing the inference ability of the post-processing model and realizing the optimization of the initial road extraction results. Experimental results demonstrate that the RIRNet model can achieve an excellent post-processing effect, which is manifested in the effective repair of broken road segments, as well as the handling of errors such as omission, misclassification, and noise, proving the effectiveness and generalization of the model in post-processing optimization.

Low‐carbon economic operation of multi‐energy microgrid based on multi‐level robust optimisation

AbstractThe economic and low‐carbon operation strategy of multi‐energy microgrids (MEM) has become an important research topic in smart grids. The operation of MEM is affected by uncertain factors from renewable energy and internal load. To handle uncertainties from both source and load sides, the authors propose a novel worst‐case‐and‐probability uncertainty sets and a novel worst‐expectation min‐max‐max‐min two‐stage four‐level robust optimisation (RO) model considering stepped carbon trading for MEM. This four‐level RO model is a more generalised model compared with the traditional two‐stage RO and distributionally robust optimisation based models. First, the unsolvable original four‐level model is decoupled into a master problem and a sub‐problem (SP). Second, Karush–Kuhn–Tucker condition is applied to convert SP into a solvable problem. Third, column and constraint generation (C&CG) algorithm is employed to solve the reformulated four‐level RO. Finally, the effectiveness of the proposed model and solution method is verified by case studies. The results indicate that the convergence behaviour of this solution method is excellent. The MEM operator can select appropriate robustness factors and comprehensive norms to control its conservatism level. Besides, MEM could reduce carbon emissions by participating in carbon trading and installing carbon capture devices.

Optimizing Maintenance Resource Scheduling and Site Selection for Urban Metro Systems: A Multi-Objective Approach to Enhance System Resilience

This study developed an optimization model for the strategic location of maintenance resource supply sites and the scheduling of multiple resources following failures in urban metro systems, with the objective of enhancing system resilience. The model employs a multi-objective optimization framework, focusing primarily on minimizing resource scheduling time and reducing costs. It incorporates critical factors such as spatial location, network topology, station size, and passenger flow. A hybrid method, combining the non-dominated sorting genetic algorithm III and the technique for order of preference by similarity to ideal solution, is used to solve the model, with its effectiveness confirmed through a case study of the Nanjing Metro system. The simulation results yielded an optimal number of 21 maintenance resource supply stations and provided their placement. In the event of large-scale failures, the optimal resource scheduling strategy ensures demand satisfaction rates exceed 90% at critical stations, maintaining an overall rate of 87.09%, therefore significantly improving resource scheduling efficiency and the system’s emergency response capabilities and enhancing the physical resilience and recovery capabilities of the urban metro system. Moreover, the model accounts for economic factors, striving to balance emergency response capabilities with production continuity and cost efficiency through effective maintenance strategies and resource utilization. This approach provides a systematic framework for urban metro systems to manage sudden failures, ensuring rapid recovery to normal operations and minimizing operational disruptions in scenarios of limited resources.

A methodology to determine target gas supply reliability of natural gas pipeline system based on cost-benefit analysis

In this study, a methodology to determine the target gas supply reliability of the natural gas pipeline system based on cost-benefit analysis is proposed. In the methodology, an optimization model is developed firstly, and the objective function is constructed to maximize the difference between the benefits and investment when improving system reliability. Secondly, the investment and the benefits of reduced unreliability cost due to the implementation of the reliability improvement measures are considered in the optimization model. Thirdly, the virtual age model is employed to quantify the impact of reliability improvement measures on the unit's reliability, and the gas supply reliability evaluation method of the natural gas pipeline system is developed. Finally, the optimization model used to determine the target gas supply reliability is solved by a heuristic genetic algorithm. Furthermore, a real natural gas pipeline system located in China is applied to confirm the feasibility of the methodology, and the target gas supply reliability is determined, with a value of 0.998608. At last, the effect of system operational age on the target gas supply reliability is investigated through sensitivity analysis. The results show that the target gas supply reliability decreases with the increase of the operational age, which is consistent with the engineering practice.

Seismic retrofitting optimization model using fiber-reinforced polymer jacketing and NSGA-III

Fiber-reinforced polymer (FRP) is widely used for retrofitting structural elements due to its easy application. However, establishing a retrofit strategy is challenging due to conflicting objectives, such as cost and performance level, requiring optimization for effective decision-making. This study proposes a many-objective optimization model for seismic retrofitting using FRP and the Non-dominated Sorting Genetic Algorithm (NSGA)-III. The model's efficacy was demonstrated through two numerical examples: a reinforced concrete building retrofitted with FRP jackets and a masonry-infilled reinforced concrete building retrofitted with FRP bracings. Each example included three objective functions and multiple constraints. Nonlinear static pushover analysis provided optimal strategies to enhance base shear and energy dissipation while minimizing costs and retrofitting locations. Among the Pareto-optimal solutions, the optimal solution with the minimum Euclidean distance was selected. NSGA-III offered a wider distribution and more Pareto-optimal solutions compared to NSGA-II, demonstrating its potential in addressing many-objective problems related to retrofit decision-making.

Techno-economic optimization of agricultural biomass to electricity supply chain network: A case study of Tunisia

The manure biogas plant is a promising technology for the future. It represents a closed-loop system that reinforces the circular economy. However, effective and viable implementation requires optimization of the entire supply chain. In this paper, a cost optimization model for manure to electricity supply chain has been developed. The model aims to determine the best configuration for the biogas plant network (Decentralized/Centralized Biogas plant), identify the optimal locations and capacities, and give a distribution plan of materials flow within the supply chain while minimizing the overall costs. The novelty of this work consists in adopting a holistic approach that addresses a multi-region, multi-period and multi-product problem which considers seasonal variation in manure availability, different manure mixtures, the physico-chemical properties of manure and the technical aspects related to the biogas plant by adapting the open source tool OSEMOSYS. The model is applied to the Tunisian case study to provide the optimal pathway to achieve the Tunisian solar plan’s target of 100MW from biogas by 2030. As a result of the optimization, the optimal network of biogas plants across 6 regions in Tunisia is identified. Our results have shown that the LCOE of generating electricity across all regions ranges between 14.2 US$ cent/kWh and 19 US$ cent/kWh. Additionally, a sensitivity analysis on two key parameters distance and capital cost is performed.