Optimization Model Research Articles

Optimal Allocation of Urban Water Resources Based on Multi-Objective Nutcracker Optimization Algorithm

The imbalance between water supply and demand (WSD) has been growing noticeable as a result of the economy’s fast expansion which can be effectively alleviated using optimal allocation of water resources. An urban water resources allocation (WRA) model based on the innovative Multi-Objective Nutcracker Optimization Algorithm (MONOA) is proposed in this study. Taking into account economic, social and ecological benefits, a comprehensive multi-objective optimization (MOO) model is established. By introducing the opposite learning strategy, non-dominated sorting approach and crowding distance mechanism to a recently reported intelligent optimization algorithm called the Nutcracker Optimization Algorithm (NOA), the novel nature-inspired metaheuristic algorithm MONOA is proposed to solve the multi-objective optimization model. The MONOA is evaluated on ten benchmark test functions, and it exhibits superior distribution and convergence by comparing with some highly cited algorithms. The proposed model is applied to Handan, China, in order to obtain a reasonable water allocation scheme in the planning year. The simulation results reveal that the economic benefit is in the range CNY [1.36, 1.44] × 1011, water shortage is in the range [0.66, 0.98] × 108 m3 and COD emission is in the range [3.70, 3.91] × 104 t in all the obtained Pareto solutions. The water resources management departments might create customized water allocation plans by balancing different goals and taking preferences into account. Moreover, the proposed method is a general approach that can be applied to many other cities. Hence, it is of great significance to the sustainable development and utilization of urban water resources.

Risk−Based Cost−Benefit Optimization Design for Steel Frame Structures to Resist Progressive Collapse

The design of structures to resist progressive collapse primarily focuses on enhancing structural safety and robustness. However, given the low probability of accidental events, such designs often lead to a negative cost–benefit. To address this problem, this paper uses risk analysis to optimize the progressive collapse resistance design of steel frame structures. The elements’ cross-section design for the progressive collapse resistance of steel frame structures is optimized using genetic algorithms and SAP2000 23, which identify the structural model with the minimum robustness index while ensuring safety. The results show that the risk-based robustness index can effectively assess the cost of progressive collapse design. More importantly, the optimization model can rapidly identify the most cost-effective structural design solution that complies with progressive collapse resistance guidelines, enhancing the simplicity and usability of the structure design optimization process. Additionally, the integration of the SAP2000 API with Python 3.8 automation streamlines the parameterization process, minimizes manual errors, and enhances the precision and efficiency of the structural design optimization. Finally, the model’s effectiveness is validated through a case study, where the refined single-frame structure shows a reduction in initial construction and collapse-related costs by 2.4% and 9.1%, respectively. Meanwhile, the three-dimensional frame shows a 2.9% rise in initial costs but a 13.5% decrease in total collapse-resistant design costs, illustrating the model’s ability to balance safety with cost-effectiveness.

Optimal configuration strategy of energy storage for enhancing the comprehensive resilience and power quality of distribution networks

Resilience assessment and enhancement in distribution networks primarily focus on the ability to support and recover critical loads after extreme events. With the increasing integration of new energy sources and power electronics, distribution networks have gained a degree of resilience. However, the impact of power quality issues on these networks has become more severe. In some cases, even networks assessed as highly resilient by users suffer equipment damage and substantial economic losses due to power quality issues. To address this issue, this paper builds upon conventional distribution network resilience assessment methods by supplementing and modifying indices in the dimensions of resistance and recovery to account for power quality issues. Furthermore, an optimized energy storage system (ESS) configuration model is proposed as a technical means to minimize the total operational cost of the distribution network while enhancing comprehensive resilience indices. The proposed nonlinear optimization model is solved using second-order cone relaxation techniques. Finally, the proposed strategy is simulated on the IEEE 33-node distribution network. The simulation results demonstrate that the proposed strategy effectively improves the comprehensive resilience indices of the distribution network and reduces the total operational cost.

Deep Learning Algorithm for Optimized Sensor Data Fusion in Fault Diagnosis and Tolerance

Environmental perception is one of the key technologies to realize autonomous vehicles. The fault diagnosis process involves identifying the fault that occurred or the cause of the out-of-control condition. Here, the major objective is to locate problems in detection by analysing previous data or sequential patterns of data that cause failure. This study evaluates the use of deep learning for improved sensor data fusion in fault identification and tolerance using the KITTI dataset. The input video from the dataset has been transformed to frames through median filtering. Next, feature extraction is applied to a preprocessed image, resulting in the fusion of sensor data. Data fusion is then carried out utilizing an enhanced RPN (region proposal network). The enhanced RPN also has a loss function (object detection loss, bounding box loss and target classification loss), an estimate of ROI and feature extraction network (FEN). Through the use of the COOT connected blue monkey optimization (CCBMO) model, the weight of the optimally enhanced RPN is established. Next, using global non-maximum suppression with both global and local confidence, fault identification and tolerance are carried out. From the analysis, it clearly shows that proposed method accomplished better results in terms of accuracy, precision and specificity of 97.78%, 93.76% and 93.43%, respectively, when compared with various conventional models with respect to diverse performance measures.

A generalized bilevel optimization model for large-scale task scheduling in multiple agile earth observation satellites

Scheduling large-scale tasks within a multi-agile earth observation satellite system poses a formidable challenge. Given the complexity of this optimization problem, the responding solving strategy should exhibit both efficiency and effectiveness in terms of computational time and solution quality. The current strategies can broadly be categorized into all-in-one and two-stage methodologies. The latter, more conducive to real-world scenarios, owing to reducing the problem complexity and practical operational flexibility, dissects this challenge into task allocation and single-satellite scheduling. However, existing two-stage strategies still consider the objectives and constraints at the equivalent level and only adapt to specific algorithms. In this way, the pivotal issues concerning the solution complexity and strategy compatibility remain fundamentally unaddressed. To address this limitation, we proposed a generalized bilevel optimization model called Question-and-Answer model, which establishes two distinct optimization model with different contains and objectives. In this model, the upper questions are highly indispensable in the response from the lower level and constraints are considered separately at two stages. To ascertain the generalization of this framework, we conduct a comprehensive range of experiments employing various proposed strategies and algorithms in two stages. Diverse algorithms ranging from heuristic principles, and evolutionary strategies, to reinforcement learning can be seamlessly combined and integrated within this framework. The results demonstrate that the scale of scenarios does not affect the effectiveness of any amalgamated algorithms within this framework. Furthermore, the transition of upper questions according to the lower answers indeed improves the objectives but concurrently intensify the computational time.

Bi-level optimization of novel distribution network with VPP and flexible load cluster

To satisfy the power requirements of modern industrial parks, while also enhancing energy efficiency and system economy, a bi-level optimization model is proposed for a novel distribution network, which incorporates a virtual power plant (VPP) and flexible load cluster. The proposed optimization model for the distribution network layer considers factors such as minimum voltage offset and operating cost. It accounts for uncertainties associated with new energy sources, control of the soft open point (SOP), as well as dispatching of the static var compensator (SVC). A normalized normal constraint (NNC) method is used to obtain Pareto front. The power flow model is converted into a normalized cone programming model utilizing second-order cone relaxation technique. The VPP optimization layer aims to achieve the lowest operational cost and comprehensively considers the complementarity of multiple types of distributed energy resources. The bi-level iterative solution is obtained using the analytical target cascading (ATC) method. Finally, the enhanced IEEE 33-node system example demonstrates that the proposed bi-level optimization model effectively reduces the system’s operating cost, optimizes the power flow distribution, and minimizes network losses.

Inbound logistics optimization for fresh oranges with waste management

Typical fruit supply chains include several echelons such as farms, primary fruits-processing-facilities to produce main products, secondary fruits-processing-facilities to produce by-products, distribution centers, retailers, and consumers. This paper focuses on the inbound logistics operations that cover the logistics planning for transporting the fruits collected at the farms to the primary fruit processing facilities. Fruit supply chains are considered difficult to manage due the perishable nature of fruits and time constraints to avoid contamination and wastage. The objective of this research is to optimize inbound logistics in fruit supply chains by developing an optimization model that minimizes fruit losses during transportation and identifies optimal waste management practices. This approach not only reduces waste but also lowers greenhouse gas (GHG) emissions associated with fruit wastage. A bi-objective optimization model for the inbound logistics of fresh fruits is presented; the first objective is to minimize the total cost considering the environmental sustainability factors and the second objective is to minimize the carbon footprint and GHG emissions. Fresh fruit losses and wastage caused by changes in temperature, shelf life, and total time spent on transportation during inbound logistics is quantified. The model is applied to original data of fresh Valencia oranges harvested from farms in Egypt and computational results indicate that the fruit loss per month is decreased from 29% to less than 2% during the inbound logistics operations. Three methods are used to solve the bi-objective optimization problem, and the results are compared.

Modelling and optimization of trajectory deviation for compound directional drilling in coal mines

During the sliding mode of compound directional drilling process in coal mines, the inclined angle and azimuth angle need to be changed to minimize the trajectory deviation between the actual trajectory and the designed trajectory. The inclined angle and azimuth angle can be changed by adjusting the tool face angle. In this article, a modelling and optimization method is proposed to obtain optimal tool face angle for sliding mode. Firstly, the gaussian process regression method is employed to build calculation model of trajectory deviation. The optimization model of trajectory deviation consists of the established calculation model of trajectory deviation and the set constraints. Then, the optimal inclination angle and azimuth angle are obtained by solving the constitutive optimization model using an improved particle swarm optimization algorithm. Next, the calculation model of tool face angle is built to represent the relationship between inclination angle, azimuth angle and tool face angle. The optimal tool face angle is calculated based on optimal inclined angle and azimuth angle. Finally, an industrial case study based on the actual drilling data verifies that the proposed method is beneficial to track designed trajectory during drilling process. The proposed method meets the requirements of on-site construction accuracy and ensures the safety and stability of drilling.

Optimum carbon tax rate for emission targets of electricity generation system by life cycle techno-economic-environmental optimization model

Reduction of greenhouse gas emissions from the electricity sector is of special interest for decarbonization of energy systems. Optimum carbon tax as a powerful policy tool is here studied by integrated techno-economic-environmental life cycle analysis in a unit commitment problem. The present model is formulated as a bi-level optimization problem to reach the optimum carbon tax rates for different emission targets. The total life cycle CO2 emissions are estimated to be 20333.90 tons/hr in a real case study of Iran's electricity sector for the peak demand hour. The carbon tax rate for a 2% and a 3% emissions reduction is equal to 15.87 and 24.65 $/ton, respectively. In the business-as-usual scenario, higher carbon taxes will be required each year to meet the same emission target. However, developing the electricity sector with cleaner technologies and strategic plans may decrease the carbon tax rate. The extent of this reduction depends on the type of development program implemented in the green revolution scenario. Therefore, policy makers play a direct role in ensuring the sustainable development of the electricity sector. The present model provides a robust framework to analyze the real carbon tax rates for the whole life cycle of electricity generation dispatch.

Robust and energy-efficient RPL optimization algorithm with scalable deep reinforcement learning for IIoT

The increasing complexity and quantity of the Industrial Internet of Things (IIoT) pose new challenges to the traditional routing protocol for low-power and lossy networks (RPL) in terms of dynamic management, data transmission reliability, and energy efficiency optimization. This paper proposes a scalable deep reinforcement learning (DRL) algorithm with a multi-attention actor double critic model for routing optimization (MADC) to meet the requirements of IIoT for efficient and intelligent routing decisions while improving data transmission reliability and energy efficiency. Specifically, MADC employs the centralized training and decentralized execution (CTDE) learning paradigm to decouple the model’s training and inference tasks, which reduces the difficulty and computational cost of model learning and improves the training efficiency. In addition, a lightweight actor network based on multi-scale convolutional attention mechanism is designed in MADC, which can provide intelligent and real-time decision-making capabilities for resource-constrained nodes with low computational and storage complexities. Moreover, a scalable critic network utilizing multiple attention mechanisms is proposed. It is not only suitable for dynamic and changing network environments but also can more comprehensively and accurately evaluate local observation states, providing more accurate and efficient guidance for model optimization. Furthermore, MADC incorporates a double critic network architecture to mitigate potential overestimation issues during training, thereby ensuring the model’s robustness and reliability. Simulation results demonstrate that MADC outperforms existing RPL optimization algorithms in terms of energy efficiency, data transmission reliability, and adaptability.

Revisiting the traffic flow observability problem: A matrix-based model for traffic networks with or without centroid nodes

This study introduces a graph theory-based model that addresses the link flow observability problem in traffic networks by optimizing passive sensor deployment. The model aims to determine the minimal number of sensors and their optimal placement. It constructs a virtual network and uses isomorphic graph theory to map between the original and virtual networks, ensuring consistency in nodes, links, and link directions. Two formulas are proposed to calculate the minimum number of observable links required across different networks, factoring in links, ordinary nodes, centroid nodes, and added links. Key concepts such as chords, cut sets, and loops, along with their matrices, are analyzed. A matrix-based framework is developed to consider flow conservation conditions. Results show that solving the full link flow observability problem using node flow conservation equations yields a fixed number of sensors with non-unique deployment schemes, Additionally, a resource-constrained sensor network optimization (RSNO) model is presented, employing null space projection (NSP) as an objective function to quantify the impact of budget constraints particularly under the condition if all the link flows cannot be observed. Numerical examples demonstrate the RSNO model's applications.

TGPO-WRHNN: Two-stage Grad-CAM-guided PMRS Optimization and weighted-residual hypergraph neural network for pneumonia detection

Recent studies based on chest X-ray images have shown that pneumonia can be effectively detected using deep convolutional neural network methods. However, these methods tend to introduce additional noise and extract only local feature information, making it difficult to express the relationship between data objects. This study proposes a Two-stage Grad-CAM-guided pre-trained model and removal scheme (PMRS) Optimization and weighted-residual hypergraph neural network model (TGPO-WRHNN). First, our model extracts high-dimensional features using the TGPO module to capture both global and local information from an image. Second, we propose a new distance-based hypergraph construction method (DBHC) to amplify the difference between distances and better distinguish the relation between nearby and distant neighbors. Finally, we introduce a weighted-residual hypergraph convolution module (WRHC) to ensure the model maintains excellent performance, even at deeper levels. Our model was tested on a dataset of chest X-ray images of pediatric patients aged 1 to 5 years at the Guangzhou Women and Children’s Medical Centre by 10-fold cross-validation. The results showed that the method achieved a maximum accuracy of 98.97%, precision of 98.86%, recall of 98.43%, F1 score of 98.64%, and AUC of 99.78%. Compared to other existing models, our model demonstrated improvements of 0.87%, 0.86%, 0.16%, and 0.38% in terms of accuracy, precision, F1 score, and AUC, respectively.

Application of supervised and unsupervised learning for enhancing energy efficiency and thermal comfort in air conditioning scheduling under uncertain and dynamic environments

Air conditioning (AC) plays a major role in building energy management because it generally requires a large amount of energy to maintain indoor thermal comfort. The main objective of this study is to develop a novel method for scheduling AC operations to minimize energy costs and ensure the thermal comfort of occupants under uncertainty. The key challenge is the uncertainty and variability in time-series data and their serial dependence in determining AC operation. To address this challenge, we propose an optimization-informed learning approach that integrates unsupervised and supervised learning techniques with a stochastic optimization model. This method derives energy-efficient and thermal comfort-aware AC operation schedules through a comprehensive interpretation of uncertainties and variabilities in time-series data. Numerical experimental results demonstrate that the proposed approach can reduce energy costs by up to 15.6% and decrease thermal comfort violations by up to 63.6% compared to the Deep Q-learning method, while also reducing energy costs by 1.8% and decreasing thermal comfort violations by 37.5% compared to the forecast data-driven AC scheduling method.

An adaptive material-field series-expansion method for structural topology optimization

The material-field series-expansion (MFSE) method reduces the dimension of design variables in density-based topology optimization and avoids the checkerboard patterns. However, the constant correlation function of the MFSE method only accounts for the spatial dependency between material field points. Accordingly, the expanded material field using the constant correlation function has an obscure topology, which increases the iterations and computation burden of the MFSE method. This paper proposes an adaptive correlation function that considers the spatial dependency and the values of material field points simultaneously. It describes the correlation between material field points more accurately. As a result, the expanded material field based on the adaptive correlation function has a clearer topology than the constant correlation function. Moreover, the adaptive material-field series-expansion (AMFSE) method with dual-loop optimization is introduced leveraging the adaptive correlation function. The outer loop updates the adaptive correlation functions and expanded material fields. The inner loop searches for the optimal solution of the current topology optimization model based on the expanded material field. Finally, several examples of static compliance and dynamic modal loss factor topology optimization validate the effectiveness and applicability of the AMFSE method. Results show that the AMFSE method converges faster with fewer iterations than the MFSE method, despite it increasing the computing time of matrix decomposition in the outer loops. Therefore, the AMFSE method is suitable for topology optimization with complex responses such as modal loss factors to decrease the iterations and computation burden simultaneously.

A rolling horizon heuristic approach for a multi-stage stochastic waste collection problem

In this paper we present a multi-stage stochastic optimization model to solve an inventory routing problem for the collection of recyclable municipal waste. The objective is the maximization of the total expected profit of the waste collection company. The decisions are related to the selection of the bins to be visited and the corresponding routing plan in a predefined time horizon. Stochasticity in waste accumulation is modeled through scenario trees generated via conditional density estimation and dynamic stochastic approximation techniques. The proposed formulation is solved through a rolling horizon approach, providing a rigorous worst-case analysis on its performance. Extensive computational experiments are carried out on small- and large-sized instances based on real data provided by a large Portuguese waste collection company. The impact of stochasticity on waste generation is examined through stochastic measures, showing the importance of adopting a stochastic model over a deterministic formulation when addressing a waste collection problem. The performance of the rolling horizon approach is evaluated, demonstrating that this heuristic provides cost-effective solutions in short computational time. Managerial insights related to different geographical configurations of the instances and varying levels of uncertainty are finally discussed.

A resilient biofuel supply chain design based on Paulownia and Jatropha under uncertainty considering the water-energy nexus

The growth in global population, pollution, and energy demand, in addition to dwindling fossil fuel reserves, are driving scientists and industries toward adopting biomass-based products over non-renewable energy sources. Moreover, the decline of water resources and the importance of conserving water have induced governments to start initiatives to control the consumption of water, especially in the agricultural and industrial sectors. Therefore, the water-energy nexus is a significant issue that has drawn the interest of researchers in recent years. A bi-objective two-stage stochastic multi-product optimization model is presented for designing a resilient second-generation biofuel supply chain under uncertainty, considering the water-energy nexus. In this supply chain, biofuel is yielded from inedible plants Paulownia and Jatropha. Various resilience strategies are adopted to cope with potential disruptions to the supply chain, including multi-sourcing, capacity expansion, imports, multiple transportation modes, and lateral transshipment. The objectives of the model are twofold: maximizing profit and minimizing water consumption. This is achieved by making some key decisions including: facility location, managing the flows of raw materials and finished products among networks, determining production volumes, setting inventory levels, allocating land for biomass crop cultivation, planning production and storage capacities, scaling capacity expansions, the number of vehicles to rent or purchase, and optimizing the amounts of raw materials to import and biomass to export. An actual case study is provided to demonstrate the real-world applicability of the approach, while multiple sensitivity analyses are performed on the problem's main parameters. The study concludes by providing valuable managerial insights that focus on the cost savings and profit increases achievable through resilience strategies. The analysis considers different scenarios and explores effective methods for handling disruptions, emphasizing water resource conservation achieved by integrating the water-energy nexus within the biofuel supply chain.

A data-driven optimization model for the scattered storage assignment with replenishment

Modern warehouses are transitioning from pure storage facilities to order fulfillment centers. To improve order-picking efficiency, picking areas are restricted to small zones to save picker travel distance and thus can only store a limited quantity of SKUs. As a result, replenishment must be frequently carried out which not only causes intensive working efforts but also impacts the order-picking efficiency. Despite of the important role of replenishment, it has been seldom considered in storage assignment planning. This paper proposes a novel optimization model for the storage assignment problem considering both the order-picking and replenishment operations. Instead of the traditional first-extract-then-optimize paradigm, we develop an effective solution method for the problem by integrating the extraction and optimization steps together to avoid the loss of information. Intensive experiments and a case study are presented, the results of which indicate significant advantages of our model against the state-of-the-art counterpart. Several managerial implications are derived: (1) Order data implies substantial useful information for storage assignment planning, including but not limited to the demand correlation of products; (2) The replenishment efforts are intensive and negatively correlated to the order-picking efforts, which therefore should not be neglected in storage assignment planning; (3) To minimize the total working efforts, the optimal replenishment level r of the (r,S) replenishment policy should be more than 0.4S but less than 0.6S with respect to each SKU.

Probabilistic modeling and optimization of microgrids with EV parking lots and dispersed generation

Distributed generation sources provide self-governing power during outages, making microgrids and islanded distribution networks vital for service endurance, superior power quality, reliability, and operative efficiency. However, microgrids structure are difficult to control, particularly in islanded mode where no main power source exists if the main grid fails. Fast responses from discrete generation sources using power electronics can undermine the grid during faults or normal operations without proper regulations. The double-fed induction generator (DFIG) has become the preferred wind turbine generator owing to its low cost and flexibility to varying wind speeds. This paper presents a probabilistic scheduling for day-ahead microgrid programming that includes EV parking lots and dispersed generation resources. The microgrid works in both normal and islanded modes depending on main grid conditions. The uncertainty in EV parking lot usage is modeled hourly using the Z-number method, while wind and solar generation, market prices, and loads are modeled using the Monte Carlo method. Scenario-based incidents in the upstream grid that lead to microgrid islanding are considered, focusing on the time and duration of impact. The optimization model accounts for uncertainty, EV charging/discharging, and operational costs under normal and fault conditions. The fault ride-through (FRT) method for maintaining DFIG stability in islanded microgrids are proposed. In this technique stabilizes terminal voltage during faults by employing a resistor in series with the DFIG stator, enhancing voltage stability and FRT capability. Without these methods, the DFIG may lose stability after clearing transient errors, risking generator loss and threatening microgrid stability, particularly in islanded mode. The effectiveness of these control and protection strategies is validated through comprehensive simulations in MATLAB.

Design optimization of continuous fiber composites with thermo-mechanical coupling and load uncertainties

This paper introduces a theoretical framework for the design optimization of continuous fiber composites reinforced with continuous fiber trajectories subject to thermo-mechanical coupling and load uncertainties. Different uniform temperature variations are applied in the structure to investigate the influence of ambient temperature change on the structural performance. To consider the external load uncertainties, a robust design optimization model is proposed where the loads are modeled as hybrid variables, namely magnitudes as random variables and directions as interval variables, with the robust objective determined through a hybrid orthogonal polynomial expansion method. Furthermore, we use a level-set function to represent the structural boundary, with its evolution driven by shape derivatives calculated based on uncertainty analysis. The continuous fiber paths are subsequently determined by the level-set isoline extracted from the structural boundary, which in turn influences the structural mechanical performance due to the material anisotropy of composites. The continuity of continuous fiber and the equal space between adjacent trajectories largely ensure the additive manufacturability of the composites. Three numerical examples are presented to demonstrate the effectiveness of the developed framework. The results show that the ambient temperature variations and load uncertainties largely impact the optimized topology and fiber infill patterns of composites, thus are important to be considered in the design stage. Moreover, the optimized structure can have a 5-fold stiffness per unit mass compared with the initial design thus largely increasing the material efficiency in carrying external uncertain loads.

Mining Area Production Safety Optimization Based on Multi-objective Particle Swarm Optimization Model

Safe production in metal mines is an important task to ensure the safety of workers and the integrity of production equipment. From the perspective of optimization, this paper establishes an early warning model and a multi-objective particle swarm optimization algorithm model by analyzing the relevant production data affecting the indicator system of mine safety production, and then solves the model through the multi-objective particle swarm optimization algorithm to give an optimization scheme for maximizing the safety production of the relevant mines. For the safety production problems in metal mines, four indicator systems are proposed, namely, production ecological environment safety, production personnel safety standards, production equipment safety and production information security, and then the relevant production data of the four indicator systems are analyzed and the early warning model is established. Based on the relevant production data of the four indicator systems, the mathematical relationship between the production data affecting each indicator system is constructed. Then, a multi-objective particle swarm optimization algorithm is established to construct the relationship between the maximum safe production of the mine and each indicator system, and the index of the maximum safe production production data of the mine is obtained. The feasibility of the mine safety production optimization scheme is given.