Two-stage Optimization Method Research Articles

A Two-Stage LLVM Option Sequence Optimization Method to Minimize Energy Consumption

Existing methods for optimizing the LLVM compiler face challenge in quickly obtaining high-quality solutions due to the large and discrete optimization space of option sequences, time-consuming energy consumption evaluation, and complex interactions among options. To address these challenges, we present a Two-Stage LLVM Option Sequence Optimization Method to Minimize Energy Consumption (TSOMFEC). In the first stage, we propose an Option Selection algorithm based on Pattern Mining (OSPM). OSPM integrates a pattern mining algorithm and CRC algorithm to precisely preselect options, with the goal of reducing the search space of option sequences while guaranteeing optimization quality. In the second stage, we present an Option Sequence Evolutionary Algorithm (OSOA). OSOA encodes options and their positions in the sequence as individual items and then constructs an item interaction graph to capture complex interactions among different items. The item interaction graph is utilized in a genetic algorithm to reduce actual energy consumption evaluations and rapidly obtain high-quality option sequences. We evaluate the performance of TSOMFEC by comparing it with four state-of-the-art methods across eight typical embedded programs in terms of solution quality and optimization time. Furthermore, we validate the effectiveness of both OSPM and item interaction graph. The experimental results demonstrate that TSOMFEC not only achieves the best solution quality but also spends the least optimization time. It obtains average energy consumption improvement percentages relative to the -O3 level of 0.075, along with average optimization time of 3178 s. Moreover, the effectiveness of both OSPM and the item interaction graph has been validated.

Streamlining Computational Fragment-Based Drug Discovery through Evolutionary Optimization Informed by Ligand-Based Virtual Prescreening.

Recent advances in computational methods provide the promise of dramatically accelerating drug discovery. While mathematical modeling and machine learning have become vital in predicting drug-target interactions and properties, there is untapped potential in computational drug discovery due to the vast and complex chemical space. This paper builds on our recently published computational fragment-based drug discovery (FBDD) method called fragment databases from screened ligand drug discovery (FDSL-DD). FDSL-DD uses in silico screening to identify ligands from a vast library, fragmenting them while attaching specific attributes based on predicted binding affinity and interaction with the target subdomain. In this paper, we further propose a two-stage optimization method that utilizes the information from prescreening to optimize computational ligand synthesis. We hypothesize that using prescreening information for optimization shrinks the search space and focuses on promising regions, thereby improving the optimization for candidate ligands. The first optimization stage assembles these fragments into larger compounds using genetic algorithms, followed by a second stage of iterative refinement to produce compounds with enhanced bioactivity. To demonstrate broad applicability, the methodology is demonstrated on three diverse protein targets found in human solid cancers, bacterial antimicrobial resistance, and the SARS-CoV-2 virus. Combined, the proposed FDSL-DD and a two-stage optimization approach yield high-affinity ligand candidates more efficiently than other state-of-the-art computational FBDD methods. We further show that a multiobjective optimization method accounting for drug-likeness can still produce potential candidate ligands with a high binding affinity. Overall, the results demonstrate that integrating detailed chemical information with a constrained search framework can markedly optimize the initial drug discovery process, offering a more precise and efficient route to developing new therapeutics.

Two-Stage Neural Network Optimization for Robust Solar Photovoltaic Forecasting

Neural networks (NNs) have shown outstanding performance in solar photovoltaic (PV) power forecasting due to their ability to effectively learn unstable environmental variables and their complex interactions. However, NNs are limited in their practical industrial application in the energy sector because the optimization of the model structure or hyperparameters is a complex and time-consuming task. This paper proposes a two-stage NN optimization method for robust solar PV power forecasting. First, the solar PV power dataset is divided into training and test sets. In the training set, several NN models with different numbers of hidden layers are constructed, and Optuna is applied to select the optimal hyperparameter values for each model. Next, the optimized NN models for each layer are used to generate estimation and prediction values with fivefold cross-validation on the training and test sets, respectively. Finally, a random forest is used to learn the estimation values, and the prediction values from the test set are used as input to predict the final solar PV power. As a result of experiments in the Incheon area, the proposed method is not only easy to model but also outperforms several forecasting models. As a case in point, with the New-Incheon Sonae dataset—one of three from various Incheon locations—the proposed method achieved an average mean absolute error (MAE) of 149.53 kW and root mean squared error (RMSE) of 202.00 kW. These figures significantly outperform the benchmarks of attention mechanism-based deep learning models, with average scores of 169.87 kW for MAE and 232.55 kW for RMSE, signaling an advance that is expected to make a significant contribution to South Korea’s energy industry.

An enhanced stochastic optimization for more flexibility on integrated energy system with flexible loads and a high penetration level of renewables

Full utilization of the potential regulation ability of flexible loads in an integrated energy system (IES) and expanding its structure for more flexibility via integrating auxiliary devices is the key to realizing its high-efficiency operation and high-proportion renewable consumption. The present paper builds the flexible regulation models of thermal and electrical loads and introduces them to the structure expansion planning of IES. A two-stage stochastic probability optimization method integrating the uncertain operation of introducing flexible loads is then proposed to balance the additional costs of device integration and the benefits of performance promotion. Herein, an enhanced sample average approximation based on a stochastic hierarchy scenario generation method is developed to solve the optimization. The regulation mechanisms of flexible loads and their influence on expansion planning are then analyzed by comparing the optimized results. The results show that the path to decreasing the cost via introducing flexible thermal and electrical loads into optimization is increasing renewable consumption and coordinating an increment in renewable consumption and average electrical efficiency, respectively. The regulation between them has synergism on cost reduction and saturation on increasing renewable consumption. The synergism can reduce the cost by 0.62 %. Besides, there is a synergism between electric boiler integration and flexible loads, which further reduces the total cost of the expanded IES by 24.86 %.

Enhancing the waste heat utilization of industrial park: A heat pump-centric network integration approach for multiple heat sources and users

The industrial sector, which is characterized by high energy consumption, primarily using fossil fuels, exhibits significant carbon emissions and severe pollution. Industrial parks generate abundant waste heat with varying flow rates and multiple grades, and also include industrial users with diverse heat demand profiles. Waste heat recovery is an effective method for reducing fossil fuel consumption. However, the current waste heat recovery methods focus on single-heat-source scenarios, making them unsuitable for use in industrial parks with multiple heat sources and heating loads. To achieve efficient matching between different sources and loads, this study developed a heat-pump-centric network system and establishes a two-stage optimization method for networked waste heat utilization. First, based on matrix algebra, a method for matching the generated waste heat with heat pump combinations and heat users was developed to obtain a networked heating path. Second, an optimization model for heat pump combinations was established, and linear integer programming algorithms were employed to obtain the optimal configuration and operational plan for the heating path. Finally, energy flow analysis was conducted to elucidate the optimal energy distribution. The results show that, compared to traditional heating modes, the proposed method achieved a 55 % reduction in energy consumption with a payback period of 4.6 years. The proposed system could enhance the matching between different grades of waste heat and heating demand, thereby improving the thermal energy utilization efficiency. The proposed method demonstrates significant energy saving with efficient utilization and economic benefits and can be applied to different scenarios with multiple sources and loads.

Optimal design of composite grid/skin structures based on deep learning and Double-Double layup strategy

This study introduces a novel two-stage optimization framework combining deep learning and genetic algorithms for the design of composite grid/skin structures. Firstly, an image dataset of 131,022 potential design configurations based on the Double-Double (DD) layup strategy is created. Subsequently, a deep-learning based Auto-encoder model is employed to extract the structural genes from this dataset. These structure genes are then used to establish a surrogate model using transfer learning, which yields accurate predictions of the buckling loads for various grid/skin structures. Finally, the Genetic Algorithm (GA) is employed to explore the optimal design configuration based on the surrogate model, with the objective of maximizing the buckling load while minimizing the weight. Results show that the optimized structure surpasses the traditional Ortho-grid and Iso-grid designs in terms of buckling load by 145 % and 72 %, respectively. Additionally, it improves the structure efficiency by 31 % and 56 %, respectively. These findings emphasize the effectiveness of the two-stage optimization method in addressing complex, multi-objective challenges, offering valuable insights and promising prospects for the optimization design of composite grid/skin structures.

Storage Location Assignment for Improving Human–Robot Collaborative Order-Picking Efficiency in Robotic Mobile Fulfillment Systems

The robotic mobile fulfillment (RMF) system is a parts-to-picker warehousing system and a sustainable technology used in human–robot collaborative order picking. Storage location assignment (SLA) tactically benefits order-picking efficiency. Most studies focus on the retrieval efficiency of robots to solve SLA problems. To further consider the crucial role played by human pickers in RMF systems, especially in the context that the sustainable performance of human workers should be paid attention to in human–robot collaboration, we solve the SLA problem by aiming to improve human–robot collaborative order-picking efficiency. This study specifically makes decisions on assigning multiple items of various products to the slots of pods in the RMF system, in which human behavioral factors are taken into account. To obtain the solution in one mathematical model, we propose the heuristic algorithm under a two-stage optimization method. The results show that assigning correlated products to pods improves the retrieval efficiency of robots compared to class-based assignment. We also find that assigning items of each product to slots of pods, considering behavioral factors, benefits the operation efficiency of human pickers compared to random assignment. Improving human–robot collaborative order-picking efficiency and increasing the capacity usage of pods benefits sustainable warehousing management.

Solving the patient admission scheduling problem using constraint aggregation

Patient admission scheduling (PAS) consists of assigning patients to beds over a planning horizon to maximize treatment efficiency, patient satisfaction, and hospital utilization while meeting all necessary medical constraints and considering patient preferences as much as possible. There are several different variants of the PAS problem in the literature, which differ mainly in the constraints that must be satisfied (hard) or can be violated (soft). Due to the intrinsic difficulty of the PAS problem, solving large integer programming (IP) models to optimality is challenging. In this paper, we consider the widely studied variant of the PAS problem that has the maximum number of soft constraints, and focus on how to reduce the size of IP formulations of the PAS problem to improve the solving efficiency. We employ a two-stage optimization method where the first stage builds reduced models by constraint aggregation to improve the typical formulation of the PAS problem. Experimental results on the 13 benchmark instances in the literature indicate that our method can obtain new improved solutions (new upper bounds) for 6 instances, including one proven optimal solution. For the 5 other instances whose optimal solutions are known, our approach can reach these known optimal solutions in a shorter computation time compared to the existing methods. In addition, we apply our method to the original PAS problem, which has the maximum number of hard constraints, and perform computational experiments on the same 13 benchmark instances. Our method yields 5 new best solutions and proves optimality for 6 instances.

A Two-Stage Optimization Method of High-Power DWPT System for Electric Vehicle

A Two-Stage Optimization Method of High-Power DWPT System for Electric Vehicle

Optimum design method for structural configuration and fiber arrangement for fiber-reinforced composites

Fiber-reinforced composite materials, exemplified by CFRP, offer the possibility of achieving lightweight, high-stiffness, and high-strength structures by continuously and evenly distributing fibers. While topology and orientation optimization methods have been developed for anisotropic materials in the past, there remains a gap in design methods that consider manufacturability, especially for continuous fiber materials. In this study, we propose a design method that takes into account manufacturability, focusing on the aspects of continuity and uniformity in fiber-reinforced composite optimum design. Specifically, we introduce a two-stage optimization approach. In the first stage, we conduct concurrent optimization of topology and fiber orientation. We utilize a level-set function to represent topological configuration, while for orientation, we introduce a “double angle vector”, which enables us to consider fiber properties such as angular periodicity. These design variables are updated by solving partial differential equations based on reaction–diffusion equations. In the second stage, leveraging the optimal orientations obtained in the first stage, we optimize the path-line generation for the manufacture of continuous fiber materials. We introduce a scalar function representing path lines and formulate an optimization problem to ensure that the path lines are both evenly spaced and continuous. The update of design variables in this state is also achieved via solving the partial differential equation. Through the development of this two-stage optimization method, we aim to create an optimal structure with manufacturable continuous fiber materials, incorporating both the topology and fiber orientation that satisfy the requirements of continuity and uniformity.

Planning model for rural distribution networks with integrated energy stations via robust optimization method

With the modernization and intelligent development of agriculture, the energy demand in rural areas continues to increase, which leads to an increased operational burden on the existing rural distribution network. Integrated energy stations (IESs), in rural areas, use renewable energy sources such as biogas, wind power, and photovoltaic as energy inputs, which can fully improve energy efficiency and help reduce the operating load and peak valley difference of rural distribution networks. In this paper, a multistage planning model is proposed for rural distribution networks with IESs based on the robust optimization method. Firstly, a rural distribution network operation framework with IESs is proposed, and a mathematical model of rural IESs is built based on the energy hub (EH). Then, the multistage robust planning model of rural distribution net-works with IESs is developed and typical scenarios of stochastic source and load are generated based on improved k-means. An iterative solution method for a two-stage robust optimization method is proposed based on the nested column constraint generation (NC&CG) algorithm. Finally, the effectiveness of the presented model and solution approach is assessed through case studies on a modified IEEE 33-node distribution network and a real 152-node distribution network.

Integrated scheduling method for fleet wave sorties and maintenance of naval distributed platforms

Managing operational command and maintenance support activities for carrier-based aircraft in a multi-platform system is challenging. This research presents an integrated mathematical model for scheduling deployment, sortie, and maintenance of carrier-based aircraft. The model helps decision-makers formulate fleet allocation plans, create sortie flight schedules, and coordinate repairs for future maritime distributed operations. We have introduced a novel bi-level iteration optimization method that improves traditional manual empirical scheduling methods. An advanced version, a two-stage optimization method, can handle a large number of states and solution spaces while ensuring accuracy. Our statistical validation shows that the two-stage optimization method has an insignificant deviation of 1–2% (with an average of −0.91%) from accurate results. Importantly, this method significantly reduces computational time (with an average of 98.25%), which enhances decision-making accuracy and real-time feasibility. Finally, the research discusses a cross-platform linkage mechanism for distributing aircraft repair tasks. This mechanism aims to enhance mission readiness and operational metrics by avoiding backlogs and reducing inefficiencies caused by concentrating maintenance on a single platform. The results of this study provide a foundation for decision-making regarding future naval distributed systems and their operations.

A robust optimization model for demand response management with source-grid-load collaboration to consume wind-power

To accommodate wind power as safely as possible and deal with the uncertainties of the output power of wind- driven generators, a min-max-min two-stage robust optimization model is presented, considering the unit commitment, source-network load collaboration, and control of the load demand response. After the constraint functions are linearized, the original problem is decomposed into the main problem and subproblem as a matrix using the strong dual method. The minimum-maximum of the original problem was continuously maximized using the iterative method, and the optimal solution was finally obtained. The constraint conditions expressed by the matrix may reduce the calculation time, and the upper and lower boundaries of the original problem may rapidly converge. The results of the example show that the injected nodes of the wind farms in the power grid should be selected appropriately; otherwise, it is easy to cause excessive accommodation of wind power at some nodes, leading to a surge in reserve costs and the load demand response is continuously optimized to reduce the inverse peak regulation characteristics of wind power. Thus, the most economical optimization scheme for the worst scenario of the output power of the generators is obtained, which proves the economy and reliability of the two-stage robust optimization method.

Two-stage robust optimal scheduling method for virtual power plants considering the controllability of electric vehicles

Two-stage robust optimal scheduling method for virtual power plants considering the controllability of electric vehicles

Two-stage optimization method for design of reinforced concrete frames using optimal pre-determined section database and non-revisiting genetic algorithm

Two-stage optimization method for design of reinforced concrete frames using optimal pre-determined section database and non-revisiting genetic algorithm

Utilizing a Two-Stage Taguchi Method and Artificial Neural Network for the Precise Forecasting of Cardiovascular Disease Risk.

The complexity of cardiovascular disease onset emphasizes the vital role of early detection in prevention. This study aims to enhance disease prediction accuracy using personal devices, aligning with point-of-care testing (POCT) objectives. This study introduces a two-stage Taguchi optimization (TSTO) method to boost predictive accuracy in an artificial neural network (ANN) model while minimizing computational costs. In the first stage, optimal hyperparameter levels and trends were identified. The second stage determined the best settings for the ANN model's hyperparameters. In this study, we applied the proposed TSTO method with a personal computer to the Kaggle Cardiovascular Disease dataset. Subsequently, we identified the best setting for the hyperparameters of the ANN model, setting the hidden layer to 4, activation function to tanh, optimizer to SGD, learning rate to 0.25, momentum rate to 0.85, and hidden nodes to 10. This setting led to a state-of-the-art accuracy of 74.14% in predicting the risk of cardiovascular disease. Moreover, the proposed TSTO method significantly reduced the number of experiments by a factor of 40.5 compared to the traditional grid search method. The TSTO method accurately predicts cardiovascular risk and conserves computational resources. It is adaptable for low-power devices, aiding the goal of POCT.

A two-stage distributed optimization method for home energy management systems via multi-modal data-driven algorithm

The home energy management system (HEMS), which utilizes multi-modal data from multiple sensors to generate the knowledge about decision making, is essential to the optimization of home energy management efficiency. Load scheduling based on HEMS can improve the utilization efficiency of multi-modal data and derived knowledge, achieve power supply-demand balance, and reduce users’ electricity costs. This paper proposes a distributed load optimization scheduling method for the load scheduling problem in HEMS based on multi-modal data-driven algorithm. Additionally, a two-stage data-driven optimization method is proposed, including a first-stage optimization model based on minimizing electricity costs and a second-stage optimization model based on minimizing system load fluctuations. In the first stage, cost self-optimization is performed based on energy storage devices. In the second stage, a load optimization instruction is issued by the control center, and each user optimizes the load fluctuations based on the system load data. Compared to centralized control methods, this approach reduces the computational overhead of the control center. Finally, simulation experiments based on load scheduling in the HEMS are conducted. The results of the first optimization stage show that when the battery capacity integrated into the system increases from 3.68 kWh to 6.68 kWh, user costs can be reduced from 57.572 cents to 42.064 cents. It is not only evident that the proposed method can effectively save users on electricity costs, but the introduction of larger capacity batteries also lowers these costs. The second stage of load fluctuation optimization results show that the proposed method can effectively optimize the usage data of a group of users and decrease the absolute peak-valley difference by 8.8%.

A two-stage optimization method for improving the load flexibility of existing district energy systems

Decarbonization of district energy systems is essential for China to meet its carbon neutrality goal by 2060. Most existing district energy systems are missing historical load data and have incomplete information, resulting in a lack of data support for the low-carbon transition. Moreover, demand-side load flexibility has not been fully exploited in the planning stage. In this paper, we developed a two-stage computational approach to optimize district loads. We first established an integrated Python framework, incorporating the TEASER simulation tool and AixLib model library, to efficiently calculate baseline loads through the bottom-up modeling and simulation of district buildings. Then, a price-based integrated demand response strategy was introduced. A mixed-integer nonlinear programming model was formulated to optimize the energy pricing strategy with the objective of minimum load fluctuations. Finally, a case study was employed to illustrate the feasibility of the calculation method, showing a normalized mean bias error of 7.17%. The results further demonstrated that the strategy could reduce the peak electric and heat loads by 3.55% and 9.57%, and increase load rates by 3.85% and 9.48%, respectively. The strategy could assist district energy service providers to optimize equipment capacity configuration and enhance the low-carbon planning potential of energy systems from the demand-side.

An efficient evacuation path optimization for passengers in subway stations under floods

The optimization of passenger evacuation paths in subway stations under flood scenarios plays an important role in improving evacuation efficiency and ensuring escape safety. Considering the impact of evacuation network failures such as gates on path planning, a two-stage passenger evacuation path optimization method under flood scenarios of subway stations is established with the objectives of minimizing total evacuation time, risk, and congestion. The black widow algorithm is proposed to optimize the BP neural network model to predict the travel time of passengers at nodes, which could improve the prediction accuracy of calculating the total evacuation time. The path optimization model is solved by the NSGA-II algorithm, and the optimal Pareto solution is determined based on the minimum total cost. Taking a subway station in Qingdao, China as an example, a passenger evacuation simulation system under flood scenarios is built using PathFinder software. The effect of the path optimization strategy is comprehensively evaluated through comparative experiments. It is found that the overall evacuation optimization degree could be increased by 18.75%, by comparing the evacuation time, congestion, and risk objectives under the situations with and without path optimization strategies.

Modeling the optimal management of land subsidence due to aquifers overexploitation

The study of land subsidence has recently been expanded due to its increased occurrence and magnitude worldwide. This paper develops and applies an optimal control model of groundwater extractions under conditions of land subsidence. We include, in a traditional groundwater management model, two types of negative externalities associated with land subsidence: damage to infrastructure and to economic activities, and the loss of aquifer storage capacity. Using a two-stage optimal control method, characterized by two sub-problems corresponding to the phase before and after the occurrence of subsidence, we find the economically sustainable paths of groundwater extractions and water table levels under the existence of land subsidence impacts. The theoretical results indicate that the presence of land subsidence dictates the optimal paths of groundwater withdrawals and water table levels. The model has been applied to the Alto Guadalentín over-exploited aquifer system in the Segura River Basin of Spain. The empirical outcomes indicate that by following the optimal paths, groundwater extractions should be curtailing to avoid reaching the critical water level at which subsidence takes place. Results suggest that regional net present value of welfare over the planning period, under the two land subsidence scenarios, is reduced by nearly 1–5%, compared to the no land subsidence scenario. Furthermore, under subsidence, even with relatively small impacts of both types of externalities, groundwater optimal extractions are kept at levels that avoid these externalities. These outcomes clearly call for government intervention in order to reduce groundwater withdrawals in aquifers with propensity to face undesirable subsidence effects.