Two-level Optimization Method Research Articles

Optimal scheduling of CCHP-based resilient energy distribution system considering active microgrids' multi-carrier energy transactions

This paper introduces a two-stage two-level optimization method for optimal day-ahead and real-time scheduling of multicarrier energy distribution systems and microgrids. The model considers the incentive-based and price-based demand response programs to encourage microgrids to transact electrical, heating, and cooling energy carriers with the energy distribution system, which is named hereafter as the energy system. Further, the model formulates the resilient operation of the energy system considering the energy transactions with the electrical, heating, and cooling markets. The main contribution of this paper is the integration of demand response procedures of microgrids in energy transactions with the energy system considering the switching of electrical switches and heating and cooling control valves. The optimization process is another contribution of this paper that is decomposed into two stages that consist of day-ahead and real-time horizons. The first stage is also decomposed into two levels that determine the optimal scheduling of the energy system and microgrids in day-ahead markets. The second stage is comprised of two levels that commit the energy system and microgrids resources. A resiliency index is proposed to assess the resiliency of the energy system in shock conditions. The proposed method was simulated for the 123-bus test system. Different types of microgrids, incentive-based and price-based demand response processes were considered. Simulation results confirmed that the proposed method can reduce the costs of residential, industrial, and commercial microgrids by about 4.47%, 3.88%, and 5.47% concerning only the real-time pricing process. Further, the model can increase the aggregated benefits of the energy system in the day-ahead and real-time markets by about 0.608 Million Monetary Units (MMUs) and 1.10 MMUs, respectively.

Large-scale mobile users deployment optimization based on a two-stage hybrid global HS-DE algorithm in multi-UAV-enabled mobile edge computing

Multi-UAV (unmanned aerial vehicle)-supported mobile edge computing system deploys multiple UAVs as flight edge clouds for large-scale users. In this system, how to optimize the deployment of UAVs is important for providing good service for all mobile users. Specifically, for each mobile user, we need to determine whether the task can be performed locally or on the drone (i.e., the unload decision) and how much resources should be allocated. In this paper, a new two-level optimization method is proposed for UAV deployment and task scheduling problem to minimize the system energy consumption. The proposed algorithm is named TSHGHSDE algorithm, in which a few features are designed to enhance the algorithm performance. Firstly, a two-stage optimization strategy is proposed based on HS-DE algorithm. In the early stage, HS algorithm is used for the local search in a limited space, and the DE algorithm is employed for the global search in the late stage. Secondly, we design an effective control parameter to adjust the search process, which aims to effectively combine the local search ability of HS algorithm and the global search ability of DE algorithm. Thirdly, a novel encoding mechanism is proposed in the process of the UAV deployment optimization. A global search strategy is designed to enhance the performance of the proposed algorithm. To assess the performance of the proposed algorithm, some well-known algorithms are used for comparison in experiments. The results demonstrate that the proposed algorithm performs better in terms of the search efficiency, search accuracy and stability.

A Two-Level Fuzzy Multi-Objective Design of ATO Driving Commands for Energy-Efficient Operation of Metropolitan Railway Lines

Policies for reducing CO2 and other GHG emissions have motivated an increase in electrification in metropolitan areas, mandating reductions in energy consumption. Metro systems are keystone contributors to the sustainability of cities; they can reduce the energy consumption of cities through the use of the economic driving parameters in their onboard automatic train operation systems (ATO) and through the strategic design of efficient timetables. This paper proposes a two-level optimization method to design efficient, comfortable, and robust driving commands to be programmed in all the interstations of a metro line. This method aims to increase the sustainability of metro operations by producing efficient timetables with economic driving for each interstation while considering comfort restrictions and train mass uncertainty. First, in the eco-driving level, an optimal Pareto front between every pair of successive stations is obtained using a multi-objective particle swarm optimization algorithm with fuzzy parameters (F-MOPSO). This front contains optimized speed profiles for different running times considering train mass variations. The global problem is stated as a multi-objective combinatorial problem, and a fuzzy greedy randomized adaptive search procedure (F-GRASP) is used to perform an intelligent search for the optimal timetables. Thus, a global front of interstation driving commands is computed for the whole line, showing the minimum energy consumption for different travel times. This method is analyzed in a case study with real data from a Spanish metro line. The results are compared with the minimum running time timetable and a typical timetable design procedure. The proposed algorithms achieve a 24% reduction in energy consumption in comparison to the fastest driving commands timetable, representing a 4% increase in energy savings over the uniform timetable design.

Dynamic Spatiotemporal scheduling of hull parts under complex constraints in shipbuilding workshop

ABSTRACT The extremely competitive shipbuilding sector is going through a digital transformation in the context of Industry 4.0. The spatiotemporal problem has gained considerable attention during hull construction, particularly for blocks. There are fewer studies on intermediate products at lower levels, such as the dynamic spatiotemporal scheduling for hull parts under complex constraints in subassembly workshops. Therefore, this paper proposes a multi-queue two-level optimization method along with a dynamic spatiotemporal scheduling model based on the multi-directed acyclic graph (multi-DAG) and queueing theory. Firstly, a mathematical description of the complex constraints imposed by processing tasks and various resource types is provided. Then, a dynamic spatiotemporal scheduling model and an objective function are proposed to minimize the average time for parts in the system. At the sequencing level, different priority determination methods for queue events based on an improved genetic algorithm and the contribution ratio for release space strategy are proposed. At the service level, the allocation strategies for space and workers are constructed to improve utilization. Finally, several simulation experiments are conducted using the data gathered from the workshop. The proposed method is compared with the heuristic rules and combination rules using several queueing indicators and the space utilization vs. time graphs.

Design and Optimization of an Index Finger Exoskeleton With Semi-Wrapped Fixtures and Series Elastic Actuators.

This paper proposes a novel index finger exoskeleton with semi-wrapped fixtures and elastomer-based clutched series elastic actuators. The semi-wrapped fixture is similar to a clip, which improves the convenience of donning/doffing and connection stability. The elastomer-based clutched series elastic actuator can limit the maximum transmission torque and improve passive safety. Second, the kinematic compatibility of the exoskeleton mechanism for the proximal interphalangeal joint is analyzed, and its kineto-statics model is built. To avoid the damage caused by the force along the phalanx, considering the individual difference in the size of the finger segment, a two-level optimization method is proposed to minimize the force along the phalanx. Finally, the performance of the proposed index finger exoskeleton is tested. Statistical results indicate that the donning/doffing time of the semi-wrapped fixture is significantly less than that of the Velcro. Compared with the Velcro, the average value of the maximum relative displacement between the fixture and the phalanx is reduced by 59.7%. Compared with the exoskeleton before optimization, the maximum force along the phalanx generated by the exoskeleton after optimization is reduced by 23.65%. The experimental results show that the proposed index finger exoskeleton can improve the convenience of donning/doffing, connection stability, comfort, and passive safety.

Multi-level design optimization considering uncertainties in configurations and parameters

In this research, a new approach is introduced for multi-level design optimization considering both parameter uncertainties and configuration uncertainties. In this work, an AND-OR tree is used to represent the generic design based on requirements. Nodes of the AND-OR tree are used to model partial design configuration solutions including the solutions considering possible configuration changes in the future. A node is further defined by parameters and their variations due to uncertainties. Design configuration candidates and their possible configuration changes are created from the AND-OR tree through a tree-based search. Each configuration candidate is defined by the parameters of the nodes and variations of these parameters. The optimal design configuration and its parameter values are achieved by a two-level optimization method. Parameter optimization is conducted for each design configuration candidate, while configuration optimization is conducted to obtain the best design configuration. Both the objective function and variation of the objective function due to uncertainties in configurations and parameters are considered in the multi-level optimization.

Failure Analysis and Optimization Design of Wing Skin Unbalanced Lay-Up

To clarify the influence of the unbalanced coefficient and the change in lay-up angle on the failure characteristics of the laminate in the static aeroelastic problem of the aircraft, numerical simulations were performed based on the classical laminate theory and the Tsai-Wu failure criterion, as well as the fluid-structure coupling calculation method. The structure’s stress-strain and failure curves are found to decrease as the unbalanced coefficient increases. The stress curve’s slope is relatively stable, whereas the strain and failure curves’ slopes change three times, indicating that strain may be the primary cause of structural failure. Unbalanced coefficient laminates are classified into three types based on their mechanical properties low unbalanced coefficient laminates (Unbalanced coefficient 0.2 to 0.3), quasi-balanced coefficient laminates (Unbalanced coefficient 0.4 to 0.6, Balanced laminate when the Unbalanced coefficient is 0.5), and high unbalanced coefficient laminates (Unbalanced coefficient 0.7 to 0.8). Within their respective spanning intervals, the mechanical properties of the three types of laminates remain relatively stable. An increase in the ply angle reduces both the elastic deformation of the structure and the failure factor. The variation patterns of structural strain and failure at 45° and 60° ply angles decrease as unbalanced coefficients increase, whereas the opposite is true for 30° ply angles. Finally, a two-level optimization method based on “equalized plies” and “equal-angle plies” was developed, resulting in a 23.93% reduction in elastic deformation and a 37.04% reduction in the laminated structure's failure coefficient when compared to the preoptimization results.

Optimization of Power and Thermal Management System of Hypersonic Vehicle with Finite Heat Sink of Fuel

The scramjet of hypersonic vehicles faces severe high-temperature challenges, but the heat sink available for scramjet cooling is extremely finite. It is necessary to optimize its power and thermal management system (PTMS) with a finite heat sink of hydrocarbon fuel. This paper proposes a two-level optimization method for the PTMS of hypersonic vehicles at Mach 6. The PTMS is based on a supercritical carbon dioxide (SCO2) closed Brayton cycle, and its heat sink is airborne hydrocarbon fuel. System-level optimization aims to obtain the optimal system parameters for the PTMS. The minimum fuel weight penalty and the minimum heat sink consumption of fuel are the optimization objectives. The segmental (SEG) method is used to analyze the internal temperature distribution of fuel–SCO2 heat exchangers in the system-level optimal solution set. This ensures the selected optimal solutions meet the requirement of a pinch temperature difference greater than or equal to 10 °C. Further, the component-level optimization for the fuel–SCO2 heat exchanger is carried out based on the selected optimal solutions. The lightest weight of the heat exchanger and the minimum entropy production are the optimization objectives in this step. Finally, the optimal system parameters and the optimal key component parameters can be searched using this presented two-level optimization method.

Two-level optimization approach to tree-level forest planning

Laser scanning and individual-tree detection are used increasingly in forest inventories. As a consequence, methods that optimize forest management at the level of individual trees will be gradually developed and adopted. The current study proposed a hierarchical two-level optimization method for tree-level planning where the cutting years are optimized at the higher level. The lower-level optimization allocates the trees to the cutting events in an optimal way. The higher-level optimization employed differential evolution whereas the lower-level problem was solved with the simulated annealing metaheuristic. The method was demonstrated with a 30 ​m ​× ​30 ​m sample plot of planted Larix olgensis . The baseline case maximized the net present value as the only management objective. The solution suggested heavy thinning from above and a rotation length of 62 years. The baseline problem was enhanced to mixed stands where species diversity was used as another management objective. The method was also demonstrated in a problem that considered the complexity of stand structure, in addition to net present value. The objective variables that were used to measure complexity were the Shannon index (species diversity), Gini index (tree size diversity), and the index of Clark and Evans, which was used to describe the spatial distribution of trees. The article also presents a method to include natural advance regeneration in the optimization problem and optimize the parameters of simulated annealing simultaneously with the cutting years. The study showed that optimization approaches developed for forest-level planning can be adapted to problems where treatment prescriptions are required for individual trees.

Structural Static/Fatigue/Damage Tolerance Comprehensive Design Optimization of Composite Laminate

This paper develops a structural static/fatigue/damage tolerance comprehensive design method for composite laminated structures under mechanical–thermal coupling environments. The developed design method can finely quantify the additional stress and deformation caused by the mechanical–thermal coupling effect. In addition, a new damage evolution-based fatigue reliability evaluation method is proposed, and the structural fatigue behavior can be described and predicted. The different failure modes of composite material and their correlations are considered during the damage evolution analysis. The structural possible accidental damage can also be taken into account by applying the global preset damage in design stage. Thus, the static requirement, fatigue requirement, and damage tolerance requirement can all be considered simultaneously during the design process. The structural comprehensive design of composite laminate is conducted by virtue of the two-level optimization method. A case of a notched composite laminate is employed to verify the proposed method. In addition, a case of a civil aircraft wing structure is used to explain the feasibility of the developed method in dealing with structural design problems in engineering.

A Two-Level Optimization Method for Hypersonic Periodic Cruise Trajectory

Periodic cruise has the potential to improve the fuel-saving efficiency of hypersonic cruise vehicle but is difficult to optimize. In this paper, a two-level optimization method for the trajectory of periodic cruise is proposed. Due to that the periodic cruise trajectory can be divided into an acceleration phase where engine works and a glide phase where engine is off, the two-level optimization method is proposed to optimize the trajectory in each phase by the corresponding level. In the first level, Downhill Simplex Method (DSM) is employed to find an optimal angle of attack in the acceleration phase. Subsequently, the optimal trajectory in glide phase is obtained by the Pseudo-Spectral Method (PSM) in the second optimization level. Numerical results demonstrate the effectiveness of the proposed method. Finally, through comparing with steady-state cruise, it is concluded that periodic cruise makes full use of the change of atmospheric density and lift-drag ratio; thus, fuel saving is achieved.

Thermal-mechanical coupling-oriented system reliability optimization of composite structures

This paper develops a non-probabilistic system reliability-based design optimization method for composite laminated structures under mechanical - thermal coupling environments. This method improves the traditional method of roughly considering the temperature effect through the humid-thermal amplification factor and precisely considers the thermal stress and temperature effects. In addition, a system reliability analysis method and structural failure criterion for composite laminated structures based on the theory of last-ply failure (LPF) are proposed. The method can calculate the system reliability of composite laminated structures by considering the correlation of multiple failure modes. Finally, non-probabilistic system reliability-based design optimization (NSRBDO) of composite laminated structure system in a thermal–mechanical coupling environment is completed by means of the two-level optimization method. After the proposed optimization strategy is described in detail, two examples of the laminated structure are illustrated, and the results are compared to the traditional design method using the humid-thermal amplification factor, demonstrating the advantages and validity of the proposed method.

Two-stage aerodynamic optimization method based on early termination of CFD convergence and variable-fidelity model

Efficient aerodynamic design optimization method is of great value for improving the aerodynamic performance of little UAV's airfoil. Using engineering or semi-engineering estimation method to analyze aerodynamic forces in solving aerodynamic optimization problems costs little computational time, but the accuracy cannot be guaranteed. However, CFD method ensuring high accuracy needs much more computational cost, which is unfordable for optimization. Surrogate-based optimization can reduce the number of high-fidelity analyses to increase the optimization efficiency. However, the cost of CFD analyses is still huge for aerodynamic optimization due to multiple design variables, multi-optimal and strong nonlinearities. To solve this problem, a two-stage aerodynamic optimization method based on early termination of CFD convergence and variable-fidelity model is proposed. In the first optimization stage, the solutions by early termination CFD convergence and the convergenced CFD solutions are regarded as low-and high-fidelity data respectively for building variable-fidelity model. Then, the multi-island genetic algorithm is used in the global optimization based on the built variable-fidelity model. The modeling efficiency can be greatly improved due to many cheap low-fidelity data. In the second stage optimization, the global optimum from the first optimization stage is treated as the start of the Hooke-Jeeves algorithm to search locally based on convergenced CFD computations in order to acquire better-optimum. The proposed method is utilized in optimizing the aerodynamic performance of the airfoil of little UAV, and is compared with the EGO method based on single-fidelity Kriging surrogate model. The results show that the present two-level aerodynamic optimization method consumes less time.

Integrated Schedule and Trajectory Optimization for Connected Automated Vehicles in a Conflict Zone

The large-scale application of connected automated vehicles (CAVs) provides new opportunities and challenges for the optimization and management of traffic conflict zones. To improve the traffic efficiency of conflict zones and reduce the travel delay and fuel consumption of CAVs, this paper presents a two-level optimization method of scheduling and trajectory planning for CAVs. At the first level, a 0–1 mixed-integer linear program (MILP) is proposed for vehicles entering scheduling. At the second level, a multi-vehicle optimal trajectory control model is developed based on the optimal vehicle schedule from the first level. Then, to reduce the complexity of solving the multi-vehicle optimal trajectory control model, we transform this model into non-linear programming (NLP) based on the infinitesimal method. Moreover, a rolling optimization strategy is developed to facilitate field application. Numerical simulation experiments of different traffic scenarios are conducted, and the results show that the proposed method can effectively reduce vehicle delays and fuel consumption, compared with the first-in-first-out (FIFO) method. The numerical results show that the vehicle delay can be reduced by up to 54% and fuel consumption by up to 34% under different traffic demands. Sensitivity analysis indicates that the performance of the proposed method is mainly determined by the minimum safety time interval of vehicles entering the conflict zone.

Torque Performance Enhancement in Consequent Pole PMSM Based on Magnet Pole Shape Optimization for Direct-Drive EV

Developing a permanent magnet synchronous machine (PMSM) for direct-drive electric vehicle (EV) has challenges such as obtaining high torque density and low torque ripple. The PMSM should have high pole numbers owing to low-speed operation, thereby increasing the use of rare earth magnets and cost. Therefore, in this article a consequent pole (CP) rotor topology is proposed in which the permanent magnet (PM) volume is reduced when compared with conventional surface PMSM (SPMSM). However, replacing south poles in an SPMSM with induced steel poles can increase torque ripple and reduce torque density. In order to improve torque density in a CP PMSM, structural modifications such as multilayer windings and non-ferromagnetic barriers have been proposed in the literature. These modifications increased the torque density while increasing the torque ripple. Therefore, this article proposes a novel two-level optimization method based on gradient descent algorithm, to address the challenges of improving torque density and reducing torque ripple simultaneously in a CP PMSM. Initially, an expression for the magnet pole arc angle is derived for CP PMSM based on magnetic equivalent circuit. A two-level optimization is performed on a baseline CP PMSM to determine the optimal magnet pole arc. The torque production and torque ripples of the optimized design are validated by simulation and experimental results.

Micro-/macro-level optimization of phase change material panel in building envelope

Recently, improving heat transfer performance and latent heat utilization ratio of phase change materials (PCMs) and products is a key focus for energy saving in building. In present study, a PCM panel was optimized at the micro-level (mixing carbon nanotubes) and macro-level (integrating metal fins) simultaneously. Firstly, thermo-physical properties of the composite PCM with different proportions of carbon nanotubes (CNTs) were compared (based on 256 cooling/heating cycles). The optimal proportion was obtained toward improving thermal conductivity, which was used as the input of following numerical simulation. Then, geometric parameters of the fin in the PCM panel were optimized with numerical simulation, by comparing complete melting time of the PCM and temperature difference in the PCM panel’s heating surface. Finally, thermal performance of the composite walls with non-optimized and optimized PCM panels were compared based on the interior surface temperature and heat flux. The results show that the wall with optimized PCM panel had the optimal performance for heat storage and release. The proposed two-level optimization method has been successfully applied for thermal performance improvement of building envelope in Shenzhen (China), which could also provide references for other regions.

Two-level optimization model for water consumption based on water prices in eco-industrial parks

The eco-industrial park (EIP) is universally acknowledged as an important way to achieve resources sustainability by the plant cooperation. As an essential public resource in an EIP, the water resource is a primary research focus for minimizing the water consumption in EIPs. Commonly, the water price was adopted to adjust the plant water consumption; however, this method was relatively single. In this paper, a two-level optimization method was proposed based on the relationship between the water supplier and industrial plants and the interrelationship among plants in the EIP. Two cases were investigated based on the proposed method, and the results of different water prices and profit allocation ratios were presented in detail. Compared to the traditional method, the two-level optimization could produce more effective guide on industrial plants for applying water-saving and new technologies.

Optimal Placement of Remote-Controlled Switches in Distribution Networks in the Presence of Distributed Generators

A two-level optimization method is presented to find the optimal number and location of conventional protective devices to be upgraded to remote-controlled switches (RCSs) for an existing distribution network (DN). The effect of distributed generation (DG) on this problem is considered. In the first level, a nonlinear binary program is proposed to maximize the restored customers subject to technical and topological constraints. All feasible interchanges between protective devices and ties involved in the restoration, when a fault occurs at all possible locations are found considering switching dependencies. In the second level, a nonlinear cost function, combining the expected cost of interruptions (ECOST) and the switch cost, is minimized with respect to the location of RCSs. The expected cost function is computed based on the optimum restoration policies obtained from the first level. The optimum placement of RCSs using the proposed algorithm is tested on a 4-feeder 1069-node test system and compared to the solution obtained with a genetic algorithm (GA) on the same system.

A novel reliability-based two-level optimization method for composite laminated structures

Due to the existence of large number of design variables for large-scale composite laminated structures, such as ply thicknesses and stacking sequence, etc., it has become one of most important concerns to build an efficient optimization design method for composites. In this paper, the purpose is to propose a novel reliability-based two-level optimization design method including thickness and stacking sequence optimizations, where uncertain parameters of composites are taken into account for reliability evaluation. Firstly, by characterizing existing uncertain parameters of composites as random or interval variables, one can carry out uncertainty analysis for structural responses. Then the evaluation models of probabilistic and non-probabilistic reliabilities are separately introduced when treating uncertainties as random and interval variables. Furthermore, by combining the reliabilities with the two-level optimization model, a novel reliability-based two-level optimization model is advanced and the detailed optimization procedures are listed for convenience of understanding. Lastly, two numerical examples including a simple-supported composite plate and a composite wingtip of aerospace plane are given out to demonstrate the validity and availability of the proposed method. The results show that the proposed method can be successfully and efficiently applied in the optimization design of composite structures.

A probabilistic method for cost minimization in a day-ahead electricity market considering wind power uncertainties

During recent decades, using wind power as one of the most substantial renewable energy sources has been vastly intensified in power systems. Increasing wind power penetration in the power grid can have both detrimental and beneficial effects. Due to the uncertain nature of wind power, the system operator is faced with many challenges to make proper decisions for the electricity market. In this paper, a probabilistic method is proposed which not only effectively manages wind power sources along with other producers, but also takes the uncertain behavior of wind power in defined intervals into account. Using wind farm information in each hour, a new approach for calculating the probability density function (PDF) in uncertainty bounds is presented. By utilizing the calculated PDF two objective functions are proposed for minimizing the total expected cost during 24 h without and with considering consumers payments. The proposed objective functions have been minimized through a two-level optimization method using three different heuristic algorithms (Teaching-Learning-Based Optimization (TLBO), Hybrid Particle Swarm Optimization and Gravitational Search Algorithm (PSO-GSA), and Ant Lion Optimization (ALO)) on an 8-bus sample transmission network. The results show the total expected cost has been decreased up to 20% in some scenarios. In addition, the proposed method can satisfy consumers by keeping their payments close to the lowest amount according to the different scenarios.