Optimization Model Research Articles

Numerical Calculation and Application for Crushing Rate and Fracture Conductivity of Combined Proppants

Proppant is one of the key materials for hydraulic fracturing. For special situations, such as middle-deep reservoirs and closure pressures ranging from 40 MPa to 60 MPa, using a single proppant cannot solve the contradiction between performance, which means crushing rate and fracture conductivity, and cost. However, using combined proppants is an economically effective method for hydraulic fracturing of such special reservoirs. Firstly, for different types, particle sizes, and proportions of combined proppants, various contact relationships between proppant particles are considered. The random phenomenon of proppant particle arrangement is described using the Monte Carlo method, and the deterministic phenomenon of proppant particles is processed using an optimization model, achieving computer simulation of the microscopic arrangement of proppant particles. Secondly, a mathematical model for the force analysis of combined proppant particles is established, and an improved singular value decomposition method is used for numerical solution. A computational model for the crushing rate and fracture conductivity of combined proppants is proposed. Thirdly, the numerical calculation results are compared and discussed with the test values, verifying the accuracy of the computational model. Finally, the application of combined proppants is discussed, and a model for optimizing the proportion of combined proppants is proposed. The onsite construction technology is introduced, and the cost and economic benefits of combined proppants are compared with those of all ceramic particles and excessive all-quartz sand. It is proved that combined proppants can balance performance and price, and are an economically effective method for hydraulic fracturing of special reservoirs. The research results can select the optimal proppant material and optimize the combination of different proppant types, which can help achieve cost reduction and efficiency increase in oil and gas development.

A Terminal Residual Vibration Suppression Method of a Robot Based on Joint Trajectory Optimization

Vibration problems have become one of the most important factors affecting robot performance. To this end, a terminal residual vibration suppression method based on joint trajectory optimization is proposed to improve the accuracy and stability of robot motion. Firstly, based on the characteristics of the friction nonlinearity due to joint coupling and physical feasibility of dynamic parameters, a semidefinite programming method is used to identify dynamic parameters with actual physical meaning, thereby obtaining an accurate dynamic model. Then, based on the result of the residual vibration time domain analysis, a joint trajectory optimization model with the goal of minimizing joint tracking error is established. The Chebyshev collocation method is used to discretize the optimization model. The dynamic model is used as the optimization constraint, and barycentric interpolation is used to obtain the optimized joint motion trajectory. Finally, industrial robot experiments prove that the vibration suppression method proposed in this article can reduce the maximum acceleration amplitude of residual vibration by 62% and the vibration duration by 71%. Compared with the input shaping method, the method proposed in this paper can reduce the terminal residual vibration more effectively and ensure the consistency of running time and trajectory.

Multi-Laser Scan Assignment and Scheduling Optimization for Large Scale Metal Additive Manufacturing

Metal additive manufacturing (AM) has attracted significant attention in various industry sectors for large-scale fabrication. However, the limited fabrication efficiency has hindered its practical implementation. In comparison to traditional methods of tuning process parameters, concurrent AM equipped with multiple independently driven lasers is a more promising technique recently developed for the efficient fabrication of large metal parts. To maximize fabrication efficiency while ensuring quality for multi-laser AM processes, an optimization problem is proposed in this work for multi-laser scanning plan, including scan vector assignment and scheduling. The goal is to minimize the makespan while considering factors that may affect the quality of metal AM parts as constraints. Specifically, the constraints associated with heat-affected zones (HAZs) and the user-specified single-laser scanning area are considered. The optimization model is solved by deep reinforcement learning (DRL), offering the flexibility to include or exclude considerations for different quality/process requirements. Two case studies demonstrate the application of DRL models considering different sets of constraints and compare their performance with two baseline scheduling methods in terms of fabrication efficiency and violation of quality constraints. In addition, the impact of the laser number on operational improvement and the computational cost of the DRL model is also studied.

Repurposing coal plants into thermal energy storage—a techno-economic assessment in the Indian context

Abstract Substantial coal phase out initiatives have been growing as the world mobilizes to meet the Paris climate goals. However, the stranded asset risk associated with this critical transition could fall disproportionately on Asian economies with younger coal fleets, like India. Here, we undertake plant-level techno-economic analysis to explore the value of installing commercially available, molten-salt thermal energy storage (TES) systems for repurposing existing coal power plants in the Indian context. We combine process simulation and an economic optimization model to evaluate design and operations of TES systems for a variety of technology assumptions, coal plant archetypes, and electricity price scenarios. Key drivers of economic viability identified include longer remaining plant lifetime, increasing peak TES temperature, lower TES energy capacity cost, co-production of waste heat for end-uses, and increasing temporal variability of electricity prices. The plant-level analysis was then extended to screen for the potential of TES retrofits within the coal power fleet in Uttar Pradesh, the most populous Indian state with a significant share of India’s coal capacity. Analysis for a single electricity price scenario indicates that over 82% of the coal units in the state can be retrofitted and recover the installed costs of TES retrofits, provided that fixed operating and maintenance costs are excluded. These results reinforce the opportunity for decision-makers to consider TES retrofits of coal plants into cost-effective grid decarbonization strategies.

Stochastic Techno-Economic Optimization of Hybrid Energy System with Photovoltaic, Wind, and Hydrokinetic Resources Integrated with Electric and Thermal Storage Using Improved Fire Hawk Optimization

In this paper, a stochastic techno-economic optimization framework is proposed for three different hybrid energy systems that encompass photovoltaic (PV), wind turbine (WT), and hydrokinetic (HKT) energy sources, battery storage, combined heat and power generation, and thermal energy storage (Case I: PV–BA–CHP–TES, Case II: WT–BA–CHP–TES, and Case III: HKT–BA–CHP–TES), with the inclusion of electric and thermal storage using the 2m + 1 point estimate method (2m + 1 PEM) utilizing real data obtained from the city of Espoo, Finland. The objective function is defined as planning cost minimization. A new meta-heuristic optimization algorithm named improved fire hawk optimization (IFHO) based on the golden sine strategy is applied to find the optimal decision variables. The framework aims to determine the best configuration of the hybrid system, focusing on achieving the optimal size for resources and storage units to ensure efficient electricity and heat supply simultaneously with the lowest planning cost in different cases. Also, the impacts of the stochastic model incorporating the generation and load uncertainties using the 2m + 1 PEM are evaluated for different case results compared with the deterministic model without uncertainty. The results demonstrated that Case III obtained the best system configuration with the lowest planning cost in deterministic and stochastic models and. This case is capable of simply meeting the electrical and thermal load with the contribution of the energy resources, as well as the CHP and TESs. Also, the IFHO superiority is proved compared with the conventional FHO, and particle swarm optimization (PSO) achieves the lowest planning cost in all cases. Moreover, incorporating the stochastic optimization model, the planning costs of cases I–III are increased by 4.28%, 3.75%, and 3.57%, respectively, compared with the deterministic model. Therefore, the stochastic model is a reliable model due to its incorporating the existence of uncertainties in comparison with the deterministic model, which is based on uncertain data.

An adaptive suspended-dome structure: Static control methods based on minimum strain energy

The suspended-dome structure is a rigid-flexible and pre-stressed space structure composed of grid shells, cable and struts. It is widely used in large-span space structures for its efficient mechanical properties. The emergence of adaptive structure enables the structure to change its shape and stiffness according to the change of external environment, realizing light weight, high efficiency and intelligence of the structure. The concept of adaptivity is introduced into the traditional suspended-dome structure, presenting an Adaptive Suspended-Dome Structure (ASDS) where actuators replace the struts. A static control method utilizing a multi-population gradient genetic algorithm based on a strain energy optimization control model is proposed and developed in terms of control model research, control algorithm theory, and control effects. Specifically, an ASDS control optimization model is established with the adjustment values of the actuators as control variables and the strain energy of the upper grid shell as the objective function. The multi-population gradient genetic algorithm is improved to overcome the premature convergence problem of traditional genetic algorithms, further enhancing the search speed. A numerical simulation of a suspended-dome structure model with a span of 12 m, an aspect ratio of 10, and equipped with 16 actuator struts is featured. The overall strain energy of the controlled structure is reduced by about 40 % at maximum and the sum of squared displacements is reduced by nearly 41 % at maximum, which verifies the adaptability of ASDS to loads and the effectiveness of the control method. The suspended-dome structure of Jinan Olympic Sports Center Gymnasium is selected for data simulation to verify the effectiveness and application value of ASDS in engineering. The research methodology and conclusions provide valuable references for the design and control of adaptive structures.

Multi-Objective Constrained Optimization Model and Molten Iron Allocation Application Based on Hybrid Archimedes Optimization Algorithm

The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace’s production capacity and the steelmaking converter’s consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods.

Hierarchical Optimization Framework for Layout Design of Star–Tree Gas-Gathering Pipeline Network in Discrete Spaces

The gas-gathering pipeline network is a critical infrastructure for collecting and conveying natural gas from the extraction site to the processing facility. This paper introduces a design optimization model for a star–tree gas-gathering pipeline network within a discrete space, aimed at determining the optimal configuration of this infrastructure. The objective is to reduce the investment required to build the network. Key decision variables include the locations of stations, the plant location, the connections between wells and stations, and the interconnections between stations. Several equality and inequality constraints are formulated, primarily addressing the affiliation between wells and stations, the transmission radius, and the capacity of the stations. The design of a star–tree pipeline network represents a complex, non-deterministic polynomial (NP) hard combinatorial optimization problem. To tackle this challenge, a hierarchical optimization framework coupled with an improved genetic algorithm (IGA) is proposed. The efficacy of the genetic algorithm is validated through testing and comparison with other traditional algorithms. Subsequently, the optimization model and solution methodology are applied to the layout design of a pipeline network. The findings reveal that the optimized network configuration reduces investment costs by 16% compared to the original design. Furthermore, when comparing the optimal layout under a star–star topology, it is observed that the investment needed for the star–star topology is 4% higher than that needed for the star–tree topology.

A Transformer Maintenance Interval Optimization Method Considering Imperfect Maintenance and Dynamic Maintenance Costs

As one of the most critical components of the power grid system, transformer maintenance strategy planning significantly influences the safe, economical, and sustainable operation of the power system. Periodic imperfect maintenance strategies have become a research focus in preventive maintenance strategies for large power equipment due to their ease of implementation and better alignment with engineering realities. However, power transformers are characterized by long lifespans, high reliability, and limited defect samples. Existing maintenance methods have not accounted for the dynamic changes in maintenance costs over a transformer’s operational lifetime. Therefore, we propose a maintenance interval optimization method that considers imperfect maintenance and dynamic maintenance costs. Utilizing defect and maintenance cost data from 400 220 KV oil-immersed transformers in northern China, we employed Bayesian estimation for the first time to address the distribution fitting of defect data under small sample conditions. Subsequently, we introduced imperfect maintenance improvement factors to influence the number of defects occurring in each maintenance cycle, resulting in more realistic maintenance cost estimations. Finally, we established an optimization model for transformer maintenance cycles, aiming to minimize maintenance costs throughout the transformer’s entire lifespan while maintaining reliability constraints. Taking a transformer’s strong oil circulation cooling system as an example, our method demonstrates that while meeting the reliability threshold recognized by the power grid company, the system’s maintenance cost can be reduced by 41.443% over the transformer’s entire life cycle. Through parameter analysis of the optimization model, we conclude that as the maintenance cycle increases, the factors dominating maintenance costs shift from corrective maintenance to preventive maintenance.

Optimization of Green Multimodal Transport Schemes Considering Order Consolidation under Uncertainty Conditions

As society becomes increasingly concerned with sustainable development, the demand for high-efficiency, low-cost, and green technology makes air–land multimodal transportation one of the effective means of fast freight transportation. In the actual transportation business, some orders will have overlapping transportation routes, and transporting each order separately will result in resource waste, high costs, and carbon emissions. This paper proposes a multimodal transportation scheme optimization model considering order consolidation to improve transport efficiency and reduce costs and carbon emissions. An improved genetic algorithm incorporating the ride-sharing scheduling method is designed to solve the model. The results show that order consolidation will reduce multimodal transport costs and carbon emissions but increase transportation time slightly, and the advantages in cost and carbon emission reduction will vary with origin–destination scenarios, which are ranked in order of single-origin single-destination, single-origin multi-destinations, multi-origin single-destination, and multi-origin multi-destination. For the fourth scenario, the cost and carbon emissions decrease by 16.6% and 26.69%, respectively, and the time increases by 5.56% compared with no consolidation. For the sensibility of customer demands, it is found that order consolidation has the advantage for price-sensitive, time- and price-sensitive, and time- and carbon emission-sensitive customers; however, it is specifically beneficial for time-sensitive customers only in single-origin single-destination scenarios.

Diagnosing infeasible optimization problems using large language models

Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields, such as economics, engineering, transportation, and health care. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat’s reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility.

A Multi-Objective Optimization Design for Enhancing Space Utilization and Minimizing Cutting Time in Nuclear Facility Component Decommissioning

According to the International Atomic Energy Agency’s requirements for the minimization of radioactive waste, nuclear facility components need to be cut into smaller blocks and packaged in waste containers during decommissioning. Therefore, it is important to increase the space utilization (SU) of the cut blocks in the containers while reducing the cutting time (CT). In engineering practice, increasing SU often leads to longer CTs, which poses a great challenge to improve the efficiency of the nuclear decommissioning process. To overcome this challenge and to determine the optimal operational parameters, this paper introduces a multi-objective optimization design method for cutting and packaging nuclear facility components. The goal is to increase SU while concurrently reducing CTs, ultimately minimizing the waste and reducing the decommissioning cost. First, we project the intricate three-dimensional (3D) irregular parts packing problem onto a two-dimensional plane to simplify the complexity inherent in 3D parts packing and to formulate a packing optimization model. Second, we employ the Morris method to perform global sensitivity analysis on critical parameters, including cutting angle, height, component radius, and plate thickness parameters, throughout the cutting process of nuclear facility components. This analysis produces global sensitivity indicators for each parameter, facilitating a precise assessment of the sensitivity values associated with different operational parameters. Finally, we formulate a multi-objective design optimization model for cutting and packing nuclear facility components that yields a series of alternative operating parameter solutions upon solving it. This methodology offers a resolution for the selection of optimal operational parameters in the decommissioning process of nuclear facility components, thereby attaining optimal outcomes in waste disposal and furnishing guidance for subsequent decommissioning activities.

A classifier based on mixed radial basis function network and combinatorial optimization model for medical diseases diagnosis

A classifier based on mixed radial basis function network and combinatorial optimization model for medical diseases diagnosis

Seismic retrofit optimization of water distribution systems based on the reduction of uncertain damage scenarios

Pre-event interventions, such as retrofit of critical components, are effective strategies to improve the seismic performance and resilience of infrastructure systems. This paper proposes a damage scenario reduction method aims to reduce the computation burden within the seismic retrofit optimization for water distribution systems (WDSs) considering the uncertain damages of pipelines. The optimization framework consists of a multi-objective optimization model for WDS pipeline retrofit and a sequential optimization model for the reduction of uncertain damage scenarios. The multi-objective optimization model is established to minimize the retrofit cost and maximize the seismic performance of WDS. The sequential optimization model, namely weighted optimization-based probabilistic scenarios (OPS + W), was designed to mitigate the computational burden of the multi-objective optimization model, which arises from considering pipeline damage uncertainties through quasi-Monte Carlo (QMC) sampling that generates numerous damage scenarios. The OPS + W selects a few representative damage scenarios from numerous QMC scenarios, aiming to minimize the error of pipeline damage probabilities counted by the representative scenarios, where the error is weighted by the importance of pipeline. The effectiveness of OPS + W is verified through its application in seismic retrofit optimization of two WDS cases and compared with other scenario reduction methods. Application results reveal that the retrofit strategies derived from OPS + W have the highest similarity to those obtained from QMC scenarios while requiring only 3 %–10 % of the computation time compared to using QMC scenarios.

A Hierarchical Optimization Model for Enhancing Reliability of Fire Alarm Systems

Fire alarm systems are crucial for mitigating the risks and damages associated with fires in process industries. These systems heavily depend on the performance of fire detection sensors to provide early detection and warnings, facilitating prompt evacuation and intervention measures. In order to improve the reliability of sensor systems typically requires the use of redundancy allocation techniques, such as a k-out-of-n configuration. In k-out-of-n configuration, the signals from all sensors are directed to a voter, which compares them and transmits a final signal once at least k signals are matched. However, challenges arise due to diverse failure modes with distinct impacts on the system. Integrating sensors through a single-layer k-out-of-n configuration, when there is only one voter, fails to fully highlight the potential advantages of redundancy in sensor systems. This paper addresses the limitations of the conventional configurations by introducing a hierarchical k-out-of-n system in which sensors can be integrated across multiple layers. In the k-out-of-n hierarchical system, sensors are organized into distinct groups, each employing its own k-out-of-n sub-system. Subsequently, the outputs of these sensor groups can be integrated with other groups through their respective voters in higher layers of the hierarchy. Ultimately, at the top layer, all the voters from the preceding layers must be connected to a top voter to transmit a final signal. Furthermore, an optimization model is developed to minimize the system cost while maximizing reliability, considering the best selection of sensors and the system configuration. The proposed optimization model takes into account a multi-sensor system with two competing failure modes and incorporates the probability of sensors' failure modes in the system. The hierarchical k-out-of-n system provides an opportunity to validate sensors by comparing them within their designated groups, allowing for the identification of the location of a failure and the planning of appropriate actions accordingly. The proposed optimization model is applied to a case of a fire detection system in storage warehouse to demonstrate its advantages over the conventional model.

Strengthening energy system resilience planning under uncertainty using optimization models and regret

This study applies the concept of regret in decision-making under uncertainty to an energy system optimization model to identify optimal robust and stochastic solutions amongst several design options. The approach is demonstrated on the case study of Accra, Ghana, considering uncertainties pertinent to the city, particularly under climate change. The evaluated uncertainty scenarios consider volatile fossil fuel supply, reduced hydropower generation, rising demand due to climate change-driven rural-urban migration and global warming, unplanned power outages due to increasing natural disasters, and currency depreciation. The evaluated systems include Pareto-optimal system solutions typically under consideration by planners, which balance costs and CO2 emissions. The regret performance is evaluated for each system subject to each uncertainty scenario. A near-CO2-minimized system is the optimal robust and stochastic least-regret solution. Two factors drive this result: 1) a diverse technology set, which provides generation and cross-sectoral flexibility for adaptation under uncertainty, and 2) effectively balancing rising investment and operation costs with decreasing unmet demand costs. The demonstrated method provides energy planners and policymakers with a pragmatic, effective and fast approach, which offers new insights into long-term energy system planning to improve resilience under uncertainty, supporting the aims of the United Nations Sustainable Development Goals 7 and 11.

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.

Water quality constrained adjustment planning for regional breeding management with nonlinear programming model under uncertainty in Wenchang City, China

Basin water pollution caused by livestock, poultry and fish breeding is still a serious problem for remote villages, however, reliable regional breeding management programming have the potentials to improve pollution status. This paper focuses on the optimal model design and water quality analysis of the livestock, poultry and fish breeding system for Wenchang City, China. Methods of multi-objective programming (MOP), interval parameter programming (IPP), fuzzy-stochastic parameter programming (FSPP), and chance constrained programming (CCP) were incorporated into the developed model to tackle multi uncertainties described by interval values, probability distributions, fuzzy membership function. Based on the estimation of local breeding potential and current situation of surface water section, a multi-objective mixed fuzzy-stochastic nonlinear programming optimization model is presented with one-dimensional water quality model. In order to evaluate the environmental carrying capacity of livestock, poultry and fishery manure, predict its development trend and investigate the implementation effect of different emission reduction policies, this paper designs quantization system of the urban water environmental carrying capacity for the model. The results indicated that the water environment pollutant absorption capacity and carrying capacity of Wenchang city have approached the limit especially the towns in the northeast of City which limited the overall development space of the City. The modeling results are valuable for supporting the adjustment of the existing livestock, poultry and fish breeding schemes within a complicated system benefit and surface water quality situation under uncertainty.

Prediction and compensation of stretch-bending springback for L-section profile

This study aimed to achieve one-time stretch-bending forming in an L-shaped profile. Consequently, it focused on two main aspects: springback compensation and process parameter optimization. The process first combined simulation and experimental data, through a Co-Kriging model, facilitating the construction of an approximate model of a profile’s stretch-bending forming. A multi-objective optimization model was then formulated, to minimize springback displacement, deformation, and residual stress. The study employed the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to explore the solution space for optimal combinations in stretch-bending processes. It created a single-objective optimization model to minimize the average positional error across each profile node. Subsequently, a simulated annealing algorithm was used to solve this model, enabling the determination of an optimal die profile, which met the required specifications of the one-time stretch-bending forming process. Moreover, a novel variable compensation factor method was proposed, which accurately determined the optimal compensation factors for each node, thereby enhancing node compensation precision.

Coordinated operation optimization strategy for multiple microgrids considering uncertainties in renewable energy output

Abstract In the process of constructing a new power system with a focus on new energy sources, microgrids will be vigorously developed as an effective means of accommodating renewable resources. The synergistic operation of multiple microgrids, merging into a multi-stakeholder framework, is a method to strengthen the overall effectiveness of the system. However, existing Nash bargaining models consider relatively fewer influencing factors. To enhance the reliability and economic viability of microgrids, this paper effectively proposes a model that combines Nash bargaining with two-stage robust optimization. Specifically, the optimization model is divided into two stages. In the first stage, equipment configuration is optimized with the objective of system economy. In the second stage, uncertainties arising from renewable energy sources are considered. Subsequently, the two-stage robust model utilizes C&CG to obtain energy exchange values between microgrids. The Nash bargaining model is then addressed using the ADMM algorithm. Finally, through case simulations, the improvement in the benefits of different microgrids is verified to be in the range of 13% to 24%.