Optimization Model Research Articles

Stochastic modeling of integrated order fulfillment processes with delivery time promise: Order picking, batching, and last-mile delivery

To guarantee high customer service and short and accurate lead times, many e-commerce retailers have started to home deliver their customer orders within a few hours or even minutes, also known as quick-commerce order fulfillment. Quick-commerce order fulfillment consists of three main processes: order picking in the warehouse, order batching for delivery, and last-mile delivery. The ultimate delivery performance depends on managing all three processes, which are highly stochastic, and interdependent. We capture this stochasticity and interdependency in an integrated analytical framework and derive approximate analytical expressions for the mean and variance of the total order fulfillment time. We validate the analytical expressions with both in-house detailed process simulations and external-party output measures. We then analyze the delivery cost-service quality trade-offs using an optimization model that minimizes the expected order fulfillment cost with a delivery probability (DP) constraint, focusing on meeting delivery time deadlines. The optimization model determines the number of pickers, the optimal delivery batch size, and the number of vehicles required to deliver the customer orders. Achieving a high delivery reliability comes at a cost. In comparison to the model with DP constraints, we observe that the expected order fulfillment cost averaged over all data parameter settings obtained from the model without DP constraints is 8.9% lower; however, the mean and standard deviation of order fulfillment time increase by 44.1% and 18.6%, respectively, which results in low delivery reliability. We further demonstrate that an integrated analysis of the order fulfillment process is essential to set reliable fulfillment due times.

An Improved Voltage Sag Monitor Placement Method by using Simple Probability Reach Area Matrix

Aim: A novel optimization model is introduced in this paper to achieve monitor placements of voltage sag. Background: Considering the uncertainty of system parameters, calculation errors and measurement errors, the method of MRA is not suitable. Objective: The contradiction between the number of monitors and observation areas can be coordinated to achieve voltage sag observation with fewer monitor quantities. Method: A new generalized approach defined as a simple probability reach area matrix (SPMRA) is proposed. Result: SPMRA method is simulated by the IEEE-39 bus system, which reveals that monitor placement quantities can be reduced effectively under probabilistic observability. Conclusion: SPMRA method is a general method for monitor placements of voltage sag. This method not only performs the functions of conventional MRA methods, but also addresses the challenges of errors and conflicts between observation requirements and installation costs.

Arterial Signal Coordination Optimization Model Based on All-Direction Pairs at Intersections

Arterial Signal Coordination Optimization Model Based on All-Direction Pairs at Intersections

Two-stage optimization model for day-ahead scheduling of electricity- heat microgrids with solid electric thermal storage considering heat flexibility

Traditional electricity-heat microgrid (EHM) is limited in flexibility due to real-time balancing between the supply and demand of electric and heat system. The heat flexibility (HF) can be released by thermal inertia and heat storage characteristics of district heating systems (DHS) and heat storage units, and it can be used to increase the electric power flexibility (EF) of EHM. In this paper, the quantitative relationship between HF and EF is investigated, and a two-stage optimization model for day-ahead scheduling of EHM with solid electric thermal storage (SETS) is established. Firstly, the electric-heat flexibility conversion coefficient (EHFC) is developed to decide the allocation of HF among different electricity-heat coupling units, such as CHP and SETS, and EF supply model of EHM based on HF is built. Secondly, a two-stage optimization model is proposed for day-ahead scheduling of EHM to improve EF and economy of EHM by optimizing the heating power and HF's allocation. Thirdly, the equivalent energy storage of the DHS is quantitatively analyzed, providing a reference for planning and operating of EHM's flexibility resource. Finally, the case study shows that by considering HF and deploying SETS, the total cost can be reduced by 18.8 % and 22.6 %, respectively.

A sample robust optimal bidding model for a virtual power plant

In many energy markets, the trade amount of electricity must be committed to before the actual supply. This study explores one consecutive operational challenge for a virtual power plant—the optimal bidding for highly uncertain distributed energy resources in a day-ahead electricity market. The optimal bidding problem is formulated as a scenario-based multi-stage stochastic optimization model. However, the scenario-tree approach raises two consequent issues—scenario overfitting and massive computation cost. This study addresses the issues by deploying a sample robust optimization approach with linear decision rules. A tractable robust counterpart is derived from the model where the uncertainty appears in a nonlinear objective and constraints. By applying the decision rules to the balancing policy, the original model can be reduced to a two-stage stochastic mixed-integer programming model and then efficiently solved by adopting a dual decomposition method combined with heuristics. Based on real-world business data, a numerical experiment is conducted with several benchmark models. The results verify the superior performance of our proposed approach based on increased out-of-sample profits and decreased overestimation of in-sample profits.

Automated optimization for steel mold of precast components based on multi-objective evolutionary algorithm

Designing an economical and reliable steel mold for precast concrete (PC) components can accelerate the promotion of prefabricated buildings. This paper presents an automated design framework for a steel mold of PC components to generate manufacturing information, including dimensions and location of each plate. The profile and dimensions of PC components are extracted from the shop drawings, and a finite element model of the steel mold is established and initialized. A multi-objective optimization model considering material usage and manufacturing convenience is developed to determine the geometry and quantity of plates in steel molds. The non-dominated sorting genetic algorithm II (NSGA-II) is applied to obtain a Pareto solution set for steel mold design. The production information in DXF format can be automatically generated by parsing Industry Foundation Classes (IFC) model. The cost-effectivity and practicality of the proposed framework were verified via the design case for a real PC stair mold.

An optimization model for determining cost-efficient maintenance policies for multi-component systems with economic and structural dependencies

In most multi-component systems, the cost-efficiency of maintenance policies depends on technical structural dependencies. Motivated by the recognition that these dependencies must be accounted for in the development of optimal maintenance policies, we develop an optimization model to determine cost-efficient maintenance schedules for multi-component systems. Our main contribution is twofold. First, we introduce directed graphs as an expressive tool to represent the economic and structural dependencies of the system, including situations in which the maintenance of a given component may require other components to be disassembled or maintained. Second, we formulate a Markov Decision Process model, which is solved through the modified policy-iteration algorithm to determine the most cost-efficient policy. This policy indicates which maintenance actions consisting of disassembly and component replacement decisions are optimal when mandatory replacements must be made whenever the system fails, or the reliability of the system falls below a predefined reliability threshold. To our knowledge, this is the first model that provides optimal maintenance policies that comply with reliability requirements in the presence of constraints arising from technical structural dependencies. We illustrate the model with a realistic case study on the development of cost-efficient maintenance policies and show that its results compare favorably with heuristic maintenance policies.

A new financial risk prediction model based on deep learning and quasi-oppositional coot algorithm

Incorporating ground-breaking technologies such as deep learning (DL) has revolutionized predictive modelling in the rapidly evolving landscape of the finance sector. DL approaches, capable of extracting complex patterns from vast data collections, become an efficient approach for predicting financial trends. By integrating the complex neural network architecture with comprehensive datasets, including investor sentiment, market indicators, and economic variables, finance experts have introduced prediction models well known for their ability to capture the nuanced dynamics of financial markets with remarkable performance. Incorporating DL approaches within the finance sector provided the basis for more informed decision-making, enabling institutions, investors, and analysts to capitalize on emerging opportunities with greater confidence and precision and navigate market volatility. This study develops a novel quasi-oppositional coot algorithm with a deep learning-based predictive method on the financial sector (QOCODL-PMFC) technique. The QOCODL-PMFC technique aims to perform a prediction process on the financial sector. The QOCODL-PMFC method applies min-max normalization to measure the input dataset into a meaningful format to achieve this. Next, the QOCODL-PMFC method designs the QOCO technique for selecting an optimal set of features. The QOCODL-PMFC technique applies the attention bidirectional gated recurrent unit (ABiGRU) model for the prediction process. The Harris Hawks Optimization (HHO) model is utilized to boost the performance of the ABiGRU network. The simulation evaluation of the QOCODL-PMFC technique is tested under a benchmark finance dataset. The experimental values of the QOCODL-PMFC technique exhibit a minimal MSE of 0.7452 over other models.

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.

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.

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.

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.

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.

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.

Considering the Optimization Design of Urban Bus Network Scheduling

At present, the optimization of public transportation networks and vehicle scheduling are carried out independently in stages. However, through analysis, it has been found that scheduling information such as route schedules is an important factor related to passenger route selection. Therefore, in order to further improve the optimization effect, this article proposes an innovative idea of simultaneously optimizing the line network and scheduling. Based on the construction of a real–virtual public transportation network, this article constructs a synchronous optimization model for the line network and scheduling by considering both passenger waiting and on-board time. To achieve the consideration of passengers for different route choices, a shortest path traversal algorithm based on Yen was proposed to analyze the number and weight of the shortest paths between the same OD, and a genetic algorithm was used to solve the model. Finally, the effectiveness of the model was verified through numerical examples, and the results showed that synchronous optimization was superior to phased optimization: the passenger time cost was reduced by 21.5%, the bus operation cost was reduced by 13.7%, and the total bus system cost was reduced by 18.0%.

LSMOF-AD: Three-Stage Optimization Approach with Adaptive Differential for Large-Scale Container Scheduling

Container technology has gained a widespread application in cloud computing environments due to its low resource overhead and high flexibility. However, as the number of containers grows, it becomes increasingly challenging to achieve the rapid and coordinated optimization of multiple objectives for container scheduling, while maintaining system stability and security. This paper aims to overcome these challenges and provides the optimal allocation for a large number of containers. First, a large-scale multi-objective container scheduling optimization model is constructed, which involves the task completion time, resource cost, and load balancing. Second, a novel optimization algorithm called LSMOF-AD (large-scale multi-objective optimization framework with muti-stage and adaptive differential strategies) is proposed to effectively handle large-scale container scheduling problems. The experimental results show that the proposed algorithm has a better performance in multiple benchmark problems compared to other advanced algorithms and can effectively reduce the task processing delay, while achieving a high resource utilization and load balancing compared to other scheduling strategies.

Mechanical performance simulation and optimal design of carbon fiber composite B-pillar

This study primarily concentrates on the layer optimization and structural refinement of carbon fiber composite B-pillars. In the initial phase, an initial layer configuration for the carbon fiber composite material B-pillar was devised, followed by comprehensive finite element numerical simulations. The weight of the B-pillar was effectively diminished by 44.9% compared to its metal counterpart, while maintaining consistent performance across diverse operational conditions. Subsequently, an advanced layer thickness optimization model was formulated, incorporating the innovative ‘super layer’ concept. Integration of simulation software, such as ISIGHT and ABAQUS, facilitated the determination of optimal layer thickness and ratio for the composite material. The layer order was systematically optimized through the application of a discrete particle swarm optimization algorithm based on exchange order, adeptly addressing issues related to discontinuous design variables and potential combinations. The incorporation of a ply drop-off structure laying scheme was derived, resulting in an impressive weight reduction of 57.5%. In the final phase, adherence to NCAP side collision testing standards enabled a comprehensive evaluation, where in various indicators including deformation mode, intrusion amount, and intrusion speed were employed. The results substantiate that the composite B-pillar exhibits equivalent side impact resistance to the original metal B-pillar, ensuring robust passenger protection.