Coupled Optimization Problem Research Articles

A Bi-Level Optimization of Speed and Energy Management for Diesel-Electric Hybrid Train

Diesel-electric hybrid trains (DEHT) equipped with battery systems can effectively reduce fuel consumption and greenhouse gas emissions. For chasing the best fuel consumption efficiency, the coupled optimization problem of driving strategy and energy management for DEHT is addressed in this paper. We propose a bi-level optimization method that jointly designs driving strategy and energy management for DEHT. The optimal driving strategy is obtained by modeling a particle swarm optimization problem in fuel consumption reduction at the top level. The power allocation for the diesel generator set and the battery is described as a convex optimization problem and solved at the bottom level. The proposed method can converge to an optimal value after cyclic iterations. In each iteration, the top-level outputs the current optimal driving strategy to the bottom problem. Based on this current optimal driving strategy, the bottom level calculates the current best fuel consumption and energy management, then feeds back to the top level to start a new iteration. To verify our introduced method, the proposed optimization is compared with the common problems, such as single energy management optimization, single-speed optimization, and sequence optimization. Results show that the maximum and minimum fuel consumption reduction by the introduced optimization method is 20.0% and 2.7%, respectively.

Energy management for regional microgrids considering energy transmission of electric vehicles between microgrids

As the proliferation of electric vehicles (EVs) continues to accelerate, the inherent attributes of EVs warrant meticulous consideration in the realm of energy dispatch. In order to evaluate the ability of EVs as mobile energy storage, this paper presents an energy management framework for the microgrids' online dispatch, which accounts for the spatio-temporal energy transmission of EVs between microgrids. The energy management framework contains two iterative processes: optimizing charging price and guiding charging dispatch. To sufficiently capture the uncertainties of the renewable energy and load demand, chance-constrained optimization is utilized to determine the charging price by reasonable power allocation. To achieve a continuous and efficient control policy, a normalized advantage function-deep Q learning network (NAF-DQN) is developed for EV dispatch under V2G technology. The above two processes as a coupled optimization problem are solved alternately until convergence. Numerical cases considering energy transmission of EVs between microgrids are studied to demonstrate the superiority of the proposed dispatch framework. The simulation results indicate improved computational efficiency and higher-quality solution.

Stochastic non‐cooperative game for safety control of shared control vehicle in uncertain environments

AbstractThere are great challenges in the driving of human–machine shared control vehicles (HSCVs) in uncertain environments. Aiming at solving the collision avoidance problem of HSCV considering the uncertainty of surrounding vehicles (SVs), a human–machine cooperative control method for collision avoidance based on stochastic non‐cooperative game (SNCG) is proposed. This method realizes the safe driving of HSCV combined with the prediction of surrounding environment and constructs the interaction model between a driver and an automation system based on the game theory. Firstly, a vehicle–driver coupling model with driver's lateral and longitudinal operation characteristics is established. Next, utilizing the prediction equation, the prediction of the SV motion considering uncertainty is realized. Then, the safety constraints of HSCV are established by considering the chance constraints and the saturation characteristics of the actuators. Finally, based on the distributed stochastic model predictive control (DSMPC) method, the coupled optimization problem with chance constraints is constructed. To solve the coupled optimization problem with chance constraints, the idea of Nash equilibrium solution and the method of chance constraints tightening is adopted. The simulation results illustrate that the proposed method ensures the safe driving of HSCV under uncertain environments and realize the cooperative control between the automation system and the driver.

Optimal joint operation of coupled transportation and power distribution urban networks

The number of Electric Vehicles (EVs) and consequently their penetration level into urban society is increasing which has imperatively reinforced the need for a joint stochastic operational planning of Transportation Network (TN) and Power Distribution Network (PDN). This paper solves a stochastic multi-agent simulation-based model with the objective of minimizing the total cost of interdependent TN and PDN systems. Capturing the temporally dynamic inter-dependencies between the coupled networks, an equilibrium solution results in optimized system cost. In addition, the impact of large-scale EV integration into the PDN is assessed through the mutual coupling of both networks by solving the optimization problems, i.e., optimal EV routing using traffic assignment problem and optimal power flow using branch flow model. Previous works in the area of joint operation of TN and PDN networks fall short in considering the time-varying and dynamic nature of all effective parameters in the coupled TN and PDN system. In this paper, a Dynamic User Equilibrium (DUE) network model is proposed to capture the optimal traffic distribution in TN as well as optimal power flow in PDN. A modified IEEE 30 bus system is adapted to a low voltage power network to examine the EV charging impact on the power grid. Our case study demonstrates the enhanced operation of the joint networks incorporating heterogeneous EV characteristics such as battery State of Charge (SoC), charging requests as well as PDN network’s marginal prices. The results of our simulations show how solving our defined coupled optimization problem reduces the total cost of the defined case study by 36% compared to the baseline scenario. The results also show a 45% improvement on the maximum EV penetration level with only minimal voltage deviation (less than 0.3%).

Distributed Optimization of District Heating Networks Using Optimality Condition Decomposition

The optimal operation of District Heating Networks (DHNs) is a challenging task. Current or future optimal dispatch energy management systems attempt to optimize objectives, such as monetary cost minimization, emission reduction, or social welfare maximization. Typically, this requires highly nonlinear models and has a substantial computational cost, especially for large DHNs. Consequently, it is difficult to solve the resulting nonlinear programming problem in real time. In particular, as typical applications allow for no more than several minutes of computation time. However, a distributed optimization approach may provide real time performance. Thereby, the solution of the central optimization problem is obtained by solving a set of small-scale, coupled optimization problems in parallel. At runtime, information is exchanged between the small-scale problems during the iterative solution procedure. A well-known approach of this class of distributed optimization algorithms is Optimality Condition Decomposition (OCD). Important advantages of this approach are the low amount of information exchange needed between the small-scale problems and that it does not require the tuning of parameters, which can be challenging. However, the DHNs model equation structure brings along many difficulties that hamper the application of the OCD approach. Simulation results demonstrate the applicability range of the presented method.

UAV-Enabled Data Collection Over Clustered Machine-Type Communication Networks: AEM Modeling and Trajectory Planning

Machine-type communications (MTC) is a key technology for Internet-of-Things (IoT) services in 5G mobile communications and beyond. An essential design problem for an MTC network is the efficient and scalable data collection from low-power machine-type communication devices (MTCDs). This paper uses unmanned aerial vehicles (UAVs) to facilitate data collection from a clustered MTC network on the ground. The notion of artificial energy map (AEM) is introduced as a novel modeling technique for energy efficiency analysis, which is critical to the subject of investigation here considering the limited energy of battery-powered MTCDs and UAVs. The proposed design framework first determines the number of MTCD clusters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_\mathrm{{opt}}$</tex-math></inline-formula> according to a certain criterion. A greedy learning clustering (GLC) algorithm is then employed to divide the MTCDs into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_\mathrm{{opt}}$</tex-math></inline-formula> clusters. For each MTCD cluster, an AEM is constructed, and the optimal UAV hovering strategy within the cluster can be obtained accordingly. Finally, the UAV stations travel across the clusters and collect data from each cluster while hovering above it. This AEM-based modeling technique leads to a solution that can effectively improve the energy efficiency (EE) of UAV-enabled data collection. However, the MTCD clustering strategy, UAV hovering strategy, and UAV flying strategy all have impacts on the overall energy efficiency, which results in a coupled optimization problem that is difficult to solve. The GLC-AEM method is proposed to decouple the original EE optimization problem into sub-problems that can be handled easily by standard optimization techniques. Simulation results show that the GLC-AEM algorithm can be applied to UAV-enabled data collection scenarios with single and multiple UAV stations, and it can improve the overall EE effectively. Besides, the GLC-AEM algorithm shows good scalability and consistent performance in clustered MTC networks. The more MTCDs, the higher the achieved EE.

A Two-Layer Heterogeneous Ant Colony System With Applications in Part-Picking Planning

Abstract The tape carrier packaging machine with multiple sucking discs is designed for modern, high-speed packaging production line, which is an important part of the electronic manufacturing process. The efficiency of the part-picking can directly affect the efficiency of the packaging production line. The problem involves at least three coupled sub-problems: the number of picking rounds, the matching relationship between the parts and sucking discs, and the picking order. Because the actual industrial production requires real-time or soft real-time scheduling, the challenge is how to efficiently solve this multi-dimensional combinatorial optimization problem within a fairly limited time. The existing advanced algorithms such as the genetic algorithm and the simulated annealing algorithm usually require complex and time-consuming encoding and decoding while solving this problem. In contrast, the ant colony algorithm has advantages in the convergence rate and parallel computing, especially for searching high dimensional paths in dynamic environments. In order to further improve the comprehensive performance of the ant colony algorithm in solving multi-dimensional coupled optimization problems in extremely limited time, we propose a novel two-layer heterogeneous ant colony system based on three strategies: (1) a bottom-up two-layer solution framework to decouple the original tightly coupled problem into a loosely coupled problem composed of two sub-problems; (2) a candidate cluster augmentation strategy based on the Delaunay triangulation to improve the diversity and quality of the clusters; (3) a co-evolution between a pair of heterogeneous colonies by mixing the high-quality pheromone properly as well as a co-evolution based on the prior knowledge. Finally, through a large set of comparisons, the average picking efficiency of Two-layer Heterogeneous Ant Colony System improved by the three proposed strategies is 13–16% higher than that of other popular heuristic algorithms.

Distributed optimal voltage control strategy for AC grid with DC connection and offshore wind farms based on ADMM

A distributed optimal voltage control (DOVC) strategy based on the alternating direction method of multipliers (ADMM) is proposed for the AC grid with voltage source converter (VSC) DC connection and offshore wind farms (OWFs). The proposed DOVC strategy achieves global optimal power distribution inside the AC grid with DC connection to minimize the power losses while minimizing the bus voltage deviation from the rated value as well as power losses inside several OWFs. The optimal power flow (OPF) of the AC grid with VSC DC connection combined with model predictive control (MPC) is relaxed by using the semidefinite programming (SDP) relaxation technique. The MPC-based voltage optimization problem for the OWF is formulated by considering the dynamics of WTs. The ADMM is used to decompose the large-scale strongly coupled optimization problem, which is calculated in AC-DC grid and OWF controllers in parallel while guaranteeing global optimality. Compared to conventional control methods, the control performance of the system is enhanced. A modified IEEE-30 bus system with DC connection incorporating three OWFs consisting of 288 wind turbines (WTs) is used to evaluate the proposed DOVC strategy.

Multi-objective optimization with an integrated electromagnetics and beam dynamics workflow

In particle accelerators, RF cavities are used to accelerate charged particle beams to designed high energy for physical applications. In a typical accelerator design, the optimization of RF cavities and the optimization of beam dynamics are carried out in separate studies. For a more general and unrestricted accelerator design, a coupled optimization of the RF cavities and the beam parameters is required. For this coupled optimization problem, we have developed an integrated electromagnetics and beam dynamics workflow management system. Within this system, the geometries for a set of cavity components are first adjusted; the field modes are then computed with an electromagnetics program, and imported into a beam dynamics program for beam dynamics simulation. This workflow is encapsulated into a parallel multi-objective optimizer to achieve the integrated accelerator design optimization. A multi fidelity strategy is developed to improve the speed of the optimizer. This integrated global optimization capability is illustrated using a photoinjector design example and yields an improved design.

Improving performance specifications of internal combustion engine dedicated to plug-in hybrid electric vehicles based on coupled optimization methodology

In the context of heavy-duty application, this paper introduces a novel methodology for better defining the specifications of the internal combustion engine (ICE) in plug-in hybrid electric vehicles (pHEVs) with energy management-based evaluation. From mathematical modelling of reference engine static efficiency and maximum torque, parametric transformations are performed to explore alternative engine designs. A coupled optimization problem is formulated as a bi-level form with powertrain optimal energy management based on a combinatorial problem formulation solved by Branch&amp;Bound algorithm in the inner loop and exhaustive evaluation of ICE designs in the outer loop. A detailed transmission losses model and limitations on engine torque response dynamics are included in the optimization problem. The number of engine ignition and shutdown phases are also considered in order to better simulate the powertrain. The results show potential fuel reduction of 2.4% on a regional delivery cycle with zero-emission zones, and are intended to be used as specifications to guide further detailed engine development dedicated to hybrid powertrains.

Total Cost of Ownership Optimization of a plug-in Hybrid Electric Truck Operating on a Regional Haul Cycle

Abstract This paper introduces a novel methodology for minimizing the total cost of ownership (TCO) of plug-in Hybrid Electric Vehicles (pHEVs) in the context of heavy duty application. This approach enables the best powertrain components sizing to be determined coupled with the optimal energy management. A detailed financial cost model of the truck is developed to take into consideration the differences in spending from a conventional Diesel vehicle. The introduction of eight design variables enables to explore both internal combustion engine, electrical motor and battery alternative designs. Then, a coupled optimization problem is formulated as a bi-level form with powertrain optimal energy management based on a combinatorial problem formulation solved by Simplex algorithm and Branch & Bound in the inner loop and exhaustive evaluation of the powertrain designs in the outer loop. The results obtained from this new optimization framework show a 2% potential financial savings for a pHEV operating by the end of the decade on a regional haul application while decreasing CO2 emissions by more than 38% compared to a conventional Diesel truck.

Efficient aero-structure coupled wing optimization using decomposition and adaptive metamodeling techniques

This paper proposes an efficient decomposition-based optimization framework using adaptive metamodeling for expensive aero-structure coupled wing optimization problems. First, high-fidelity aero-structure coupled analysis method is presented through spatial interpolations of distributed aerodynamic loads and structural deformation. The proposed optimization framework decomposes the original complex coupled optimization problem into 2-D airfoil optimization (i.e., Stage-I) and 3-D wing optimization (i.e., Stage-II) to alleviate the expensive computational costs. In Stage-II, a two-level optimization strategy is tailored to further decompose the 3-D wing optimization into system-level and subsystem-level for dimension reduction. An adaptive response surface method using intelligent space exploration strategy is used to perform optimization tasks involving CFD simulations (i.e., 2-D airfoil optimization and system-level optimization in Stage-II), while sequential quadratic programming is employed to optimize the massive subsystem structure sizing variables. The effectiveness of two-level optimization strategy is validated on a numerical testing problem and a simplified wing optimization case. Finally, the developed models and proposed methods are successfully applied to aero-structure coupled optimization of a high aspect ratio wing. The optimization results demonstrate the effectiveness of the developed aero-structural analysis models and efficiency of the proposed optimization methods.

Event-Triggered-Based Distributed Cooperative Energy Management for Multienergy Systems

This paper investigates the issues of day-ahead and real-time cooperative energy management for multienergy systems formed by many energy bodies. To address these issues, we propose an event-triggered-based distributed algorithm with some desirable features, namely, distributed execution, asynchronous communication, and independent calculation. First, the energy body, seen as both energy supplier and customer, is introduced for system model development. On this basis, energy bodies cooperate with each other to achieve the objective of maximizing the day-ahead social welfare and smoothing out the real-time loads variations as well as renewable resource fluctuations with the consideration of different timescale characteristics between electricity and heat power. To this end, the day-ahead and real-time energy management models are established and formulated as a class of distributed coupled optimization problem by felicitously converting some system coordinates. Such problems can be effectively solved by implementing the proposed algorithm. With the effort, each energy body can determine its owing optimal operations through only local communication and computation, resulting in enhanced system reliability, scalability, and privacy. Meanwhile, the designed communication strategy is event-triggered, which can dramatically reduce the communication among energy bodies. Simulations are provided to illustrate the effectiveness of the proposed models and algorithm.

Utility maximization for bandwidth allocation in peer-to-peer file-sharing networks

<p style='text-indent:20px;'>Peer-to-peer (P2P) networks have been commonly applied into many applications such as distributed storage, cloud computing and social networking. In P2P networks fairness fosters an incentive so as to encourage peers to offer resources (e.g, upload bandwidth) to the networks. In this paper, we consider fair bandwidth allocation of access links in P2P file-sharing networks and develop a coupled network-wide utility maximization model which aims at achieving several kinds of fairness among requesting peers. We provide a meaningful interpretation of the problem of maximizing social welfare and its sub-problems from an economic point of view. The coupled optimization problem is difficult to resolve in a distributed way because of its non-strict convexity and non-separation. We apply a modified successive approximation method to investigate the coupled problem and propose a distributed bandwidth allocation scheme to solve the approximation problems. Then, we investigate the convergence of the scheme by mathematical analysis and evaluate the performance through numerical examples, which validate that the scheme can achieve the global optimum within reasonable iterations.

Parameter extraction of solar photovoltaic models by means of a hybrid differential evolution with whale optimization algorithm

Parameter extraction of solar photovoltaic (PV) models is a typical complex nonlinear multivariable strongly coupled optimization problem. The original differential evolution (DE) is good at exploring the search space and locating the region of global optimum, but it is slow at exploitation of the solutions. Quite the opposite, the original whale optimization algorithm (WOA) is good at exploiting the population information, but it easily suffers from premature convergence. In such a context, in this paper, an effective hybrid method named DE/WOA by combining the exploration of DE with the exploitation of WOA is proposed for extracting the accurate parameters of PV models. A set of 13 numerical benchmark functions with different characteristics is firstly employed to verify the performance of DE/WOA. Then, DE/WOA is applied to parameter extraction of three PV models, i.e., single diode, double diode, and PV module models. Finally, DE/WOA is implemented to a practical PV power station in the Guizhou Power Grid of China to further validate its effectiveness under different irradiances, temperatures, and dynamic weather conditions. All the experimental results comprehensively demonstrate that DE/WOA performs significantly better than the original DE, WOA, and five advanced variants of them and is highly competitive with some recently-proposed parameter extraction methods.

Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm

Parameter extraction of solar photovoltaic (PV) models is a typical complex nonlinear multivariable strongly coupled optimization problem. In this paper, an improved whale optimization algorithm (WOA), referred to as IWOA, is proposed to accurately extract the parameters of different PV models. The original WOA has good local exploitation ability, but it is likely to stagnate and suffer from premature convergence when dealing with complex multimodal problems. To conquer this concerning shortcoming, IWOA develops two prey searching strategies to effectively balance the local exploitation and global exploration, and thereby enhance the performance of WOA. Three benchmark test PV models including single diode, double diode and PV module models, and two practical PV power station models with more modules in the Guizhou Power Grid of China are employed to verify the performance of IWOA. The experimental and comparison results comprehensively demonstrate that IWOA is significantly better than the original WOA and three advanced variants of WOA, and is also highly competitive with the reported results of some recently-developed parameter extraction methods.

Information Acquisition and Technology Adoption in a Partnership

We study information acquisition and technology adoption decisions in a partnership. Using classical information acquisition and technology adoption results for a single decision-maker (SDM policy; McCardle 1985) as a benchmark, we establish that it could be optimal for the partnership to prematurely adopt/reject the technology. Furthermore, anticipating premature decisions in a later period could trigger unraveling which leads to a series of premature decisions in earlier periods. Finally, for a given precision of the partnership’s belief of the success probability of the technology, the structure of the optimal policy may be non-monotonic in the belief, due to the non-convexity and discontinuity of the associated coupled optimization problem. Thus, the presence of a partner may have a non-trivial and profound impact on the prescribed optimal information acquisition and technology adoption decisions.

Hybrid biogeography-based optimization with brain storm optimization for non-convex dynamic economic dispatch with valve-point effects

Dynamic economic dispatch (DED), mathematically, is a typical highly complex nonlinear multivariable strongly coupled optimization problem with equality and inequality constraints, especially considering valve-point effects. In this paper, a hybrid method named BBOSB by combining biogeography-based optimization (BBO) with brain storm optimization (BSO) is proposed. BBO has good local exploitation ability due to its information sharing mechanism. But it is likely to suffer from premature convergence when dealing with complex multimodal problems. Quite the opposite, BSO possesses excellent global exploration ability owing to its grouping evolution strategy which, however, also can drag its global searching process. In such contexts, the hybrid BBOSB method is able to fully take advantages of both BBO and BSO to conquer premature convergence and to accelerate the global searching process simultaneously. The experimental and comparison results on four non-convex benchmark DED test cases with valve-point effects and a practical provincial power system of China comprehensively demonstrate that BBOSB is highly competitive and can be used as a promising alternative for DED problems. In addition, the effect of population size on the optimization performance is investigated as well.

Orthogonal learning competitive swarm optimizer for economic dispatch problems

Power system economic dispatch (ED), mathematically, is a typical complex nonlinear multivariable strongly coupled optimization problem with equality and inequality constraints, especially considering the valve-point effects. In this paper, a novel variant of competitive swarm optimizer (CSO) referred to as OLCSO is proposed to solve both convex and non-convex ED problems. In the canonical CSO, the loser particle in each pair updates its position by learning from the winner particle. Such a learning strategy is easy to implement, but is not efficient enough because even a bad particle can contain useful information while a good particle may have misleading features. To solve this issue, an orthogonal learning (OL) strategy based on orthogonal experimental design is developed for CSO to quickly discover more useful information that contained in the winner and the loser particles. The OL strategy can easily construct a more promising solution to provide a more systematic search strategy for OLCSO. A set of 24 numerical benchmark functions and three ED cases with diverse complexities and characteristics are used to comprehensively verify the performance of OLCSO. The experimental results and comparison results consistently indicate that OLCSO can be used as a competitive alternative for ED problems.

A Novel Method for Economic Dispatch with Across Neighborhood Search: A Case Study in a Provincial Power Grid, China

Economic dispatch (ED) is of cardinal significance for the power system operation. It is mathematically a typical complex nonlinear multivariable strongly coupled optimization problem with equality and inequality constraints, especially considering the valve‐point effects. In order to effectively solve the problem, a simple yet very young and efficient population‐based algorithm named across neighborhood search (ANS) is implemented in this paper. In ANS, a group of individuals collaboratively navigate through the search space for obtaining the optimal solution by simultaneously searching the neighborhoods of multiple superior solutions. Four benchmark test cases with diverse complexities and characteristics are firstly employed to comprehensively verify the feasibility and effectiveness of ANS. The experimental and comparison results fully demonstrate the superiority of ANS in terms of the final solution quality, convergence speed, robustness, and statistics. In addition, the sensitivities of ANS to variations of population size and across‐search degree are studied. Furthermore, ANS is applied to a practical provincial power grid of China. All the comparison results consistently indicate that ANS is highly competitive and can be used as a promising alternative for ED problems.