Conventional Optimization Methods Research Articles

Robust optimal triple event-triggered intermittent control for uncertain input-constrained nonlinear systems

This paper investigates the concept of finite time (FT) optimal event-triggered intermittent (ETI) control for nonlinear systems with input constraints and dynamic uncertainty. Firstly, we address a key challenge faced by existing controllers, wherein the unbounded nature of the signal function renders it impractical to handle the input-constrained FT control problem. To overcome this limitation, we derive a novel lemma of semiglobal practical finite-time stability (SGPFTS) specifically for intermittent control with the additional constant terms. By leveraging the lemma and the Hamilton–Jacobi–Bellman (HJB) equation, we obtain the optimal FT guaranteed cost intermittent control law and establish FT stability criteria for uncertain nonlinear systems. Recognizing that the general HJB theory is ill-equipped to address input-constrained optimal control problems, We introduce the model predictive control (MPC) algorithm, which has been proven to be an effective online optimization method in handling robust optimal control and constrained problems. Moreover, conventional ETI optimal control methods struggle to address intermittent control for nonlinear systems with input constraints and dynamic uncertainty. To address this limitation, we propose a triple ETI Lyapunov-based MPC strategy, which not only enhances intermittent control performance but also resolves input constraints and dynamic uncertainty issues. Finally, we present two straightforward examples of uncertain nonlinear systems to demonstrate the effectiveness of the developed strategy in practice.

A self-adapting woven net trap based on the evolution mechanism of orb-web topology

The development of structures that can adapt spontaneously to achieve desired functions in complex environments is crucial for new unmanned countermeasures, such as prey capture or net-recovery. Conventional structural optimization methods based on a singular net–like configuration may lead to functional limitations and fail to achieve specific objectives. In this study, we utilized an evolutionary algorithm that incorporated mechanical features and biological corrections to construct spider threads with advanced properties capable of efficient and reliable trapping behavior in arbitrary boundary conditions. We employed distinct thread types in different components, which achieved distinguished stiffness and strength that could not be accomplished by a single kind of thread. By assembling prestress reinforcement threads, we developed an orb-web-like trap that demonstrated effective trapping performance in experiments. The adaptive evolutionary method could be applied to design intelligent intercepting devices suited to particular functions and extreme environments, with wide application prospects in net-recovery system of UAV. Statement of significanceStructures that adapt spontaneously to perform desired functions in difficult environments are crucial for rising unmanned countermeasures. Conventional structural optimization methods based on a singular net–like configuration may lead to functional limitations and fail to achieve specific objectives. We used an evolutionary algorithm that combined mechanical features and biological corrections to create spider threads in arbitrary boundary circumstances in this work. The adaptive evolutionary method could be applied to design intelligent intercepting devices suited to particular functions and extreme environments, with wide application prospects in net-recovery system of UAV.

Anti-fatigue optimization of the twisting force arm of landing gear based on Kriging approximate sequential optimization method

ABSTRACT The twisting force arm (TFA) is an important part of the pillar landing gear, anti-fatigue optimization on its structure can improve the reliability of the landing gear. However, the optimization accuracy of the conventional optimization method is limited by the basic topological structure from the views of topological theory. Besides that, the optimization efficiency of the conventional method is also relatively low because of the high computational cost of the fatigue life estimation. In this paper, an anti-fatigue optimization method of the TFA was developed to improve the optimization accuracy and efficiency by using the approximate sequential optimization method after an optimal basic topological structure was obtained. To verify its effectiveness, the proposed method was introduced to the anti-fatigue optimization of a pillar landing gear TFA. The results show that the optimization accuracy of the proposed method is higher than the conventional method, and the computational cost can be reduced 82.35%. This indicates that the proposed method can improve the optimization accuracy and efficiency of the anti-fatigue optimization.

Performance enhancement of segmented annular thermoelectric generator based on multi-parameter and multi-objective optimization

The excellent performance of annular thermoelectric generator (ATEG) is crucial for its commercial application, and it has been validated that the segment configuration can effectively enhance the ATEG performance. Nevertheless, owing to the limitations in conventional optimization methods which fail to simultaneously consider the co-influence of multiple parameters, further exploration is required for achieving optimal design of segmented annular thermoelectric generator (SATEG). In this study, we present a novel approach combining multi-objective genetic algorithm (MOGA) with finite element method to implement the multi-parameter and multi-objective optimization of SATEG. This approach not only reduces the computational cost but also ensures precise control on SATEG temperature below its maximum acceptable operation temperature. Furthermore, the optimization results highlight the importance of emphasizing diversity between p- and n- type TE legs as well as recognizing the different optimal geometrical structures for two types of TE legs, which have been always overlooked in previous researches. By adopting the optimal geometrical structure at a hot end temperature of 600 K, significant improvements in output power of 32.839 % and efficiency of 61.915 % are achieved for SATEG.

Applying real options with reinforcement learning to assess commercial CCU deployment

Carbon capture and utilization (CCU), which emerged as a means to reduce anthropogenic carbon emissions, has been highlighted to close the carbon cycle and combat climate change. CCU involves utilizing or converting captured CO2 to create value-added products that can replace or supplement fossil fuel-derived products. In order to meet climate goals, commercial-scale CCU facilities need to be built and their capacities increased, but barriers to large-scale CCU deployment still exist, primarily caused by large uncertainties in product/energy prices, markets, technologies, and policies. Conventional techno-economic analysis (TEA) methods cannot appropriately assess viability of CCU deployment projects which include dynamic uncertainties and deployment strategies. More flexible methods that can account for both time-varying uncertainties and dynamic capacity building are needed. We propose a systematic framework for the evaluation of commercial CCU deployment using the theory of real options and reinforcement learning (RL). RL is needed as considering options of adding capacities or delaying/abandoning the project at multiple time points under dynamic uncertainties lead to a large-scale stochastic optimal control problem which cannot be solved using conventional optimization methods like stochastic programming. The framework consists of three steps: surrogate modeling, uncertainty modeling, and assessment modeling. The framework is dependent on the type of CCU technology, uncertainties, real options and RL algorithm. We demonstrate the application of the framework through a case study of CO2 hydrogenation-to-methanol process in Europe, which is a late-stage, i.e., high technology readiness level (TRL), technology.

Deep reinforcement learning based model-free optimization for unit commitment against wind power uncertainty

Solving the unit commitment (UC) problem in a computationally efficient manner has become increasingly crucial, especially in the context of high renewable energy penetration. This paper tackles this challenge by employing the offline training of a model-free deep reinforcement learning (DRL) framework, thereby enhancing the optimization efficiency of the UC problem. The complex modeling of random variables is avoided by reformulating the UC problem as a Markov decision process, where the DRL-based method extracts knowledge regarding wind output forecasting errors from historical data. Finally, a discrete proximal policy optimization (PPO-D) algorithm is developed to generate UC solutions under the discrete action spaces necessitated by unit start-up/shut-down variables. Simulation results on the 5-unit system demonstrate that the proposed DRL-based UC model can yield an optimal solution with higher computational efficiency compared to the conventional mathematical optimization methods, while hedging against the wind power uncertainty. In addition, the case study on the IEEE 118-bus system involving 31 testing days further validates the generalization ability of the proposed DRL-based UC model.

Hybrid Quantum-Enhanced Machine Learning for Supply Chain Optimization

Abstract: Modern supply chains face intricate challenges demanding sophisticated optimization strategies.This research presents a pioneering approach, combining quantum computing and machine learning, to revolutionize supply chain optimization. A hybrid framework harmonizes the power of quantum computing, including quantum annealers and gate-based quantum devices, with classical machine learning techniques. This synthesis aims to surmount the limitations of conventional optimization methods. Through rigorous experimentation on real-world supply chain scenarios, our approach demonstrates substantial efficiency gains and enhanced solution quality in comparison to classical methods. The implications are far- reaching, promising substantial cost reductions, streamlined resource allocation, and sustainability improvements for industries relying on supply chain management. Our study contributes to the burgeoning field of quantum machine learning and offers immediate value to supply chain professionals grappling with complexity. As supply chains evolve, our research sets the stage for innovative solutions in the quest for optimization.

An Effective Dose Rate Optimization Algorithm for Efficient Conventional-Dose-Rate Proton Therapy and Ultra-High-Dose-Rate FLASH Proton Therapy

The treatment delivery with high dose rate is desirable for efficient conventional-dose-rate proton therapy (IMPT and proton ARC) and essential for achieving biological sparing effect to normal tissues for ultra-high-dose-rate FLASH proton therapy. The minimum-monitor-unit (MMU) problem is mathematically fundamental to these high-dose-rate proton therapy problems, since the dose rate is proportionally associated with the MMU threshold. However, the MMU problem is nonconvex and larger MMU threshold that leads to higher dose rate makes the nonconvex problem more difficult to solve, for which the conventional optimization methods (e.g., alternating direction method of multipliers (ADMM) or proximal gradient descent (PGD) usually cannot satisfactorily solve. This work will develop an effective dose rate optimization algorithm for the MMU problem. The new method is based on orthogonal matching pursuit (OMP), and consists of two essential components. First, the iterative convex relaxation method is used to determine the active sets for dose-volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non-zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non-zero spots localized via OMP will be adaptively added to or removed from the optimization objective. The new method via OMP is validated in comparison with conventional methods (ADMM and PGD) and a recently proposed new method (called stochastic coordinate descent (SCD) method) for high-dose-rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). A brain case is provided in the table: compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC. A new dose rate optimization algorithm via OMP is developed to solve the MMU problem with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from conventional methods (ADMM and PGD) and a recently proposed new method SCD.

A multi-area intra-day dispatch strategy for power systems under high share of renewable energy with power support capacity assessment

Long-distance power support through High-voltage Direct Current (HVDC) has provided feasible solutions for power dispatch and control problems in multi-area power systems under high share of renewable energy. In this paper, an advanced multi-area intra-day dispatch strategy for power systems with high penetration of renewable energy considering power support capacity is established to increase the accommodation of wind power and enhance the stability of the power system. At first, a novel assessment method of regional active power support capacity is carried out in this paper, which can sufficiently quantify the regional power margin (RPM), the DC dispatchable power (DCDP), and the regional power support distance (RPSD) of a power system. Subsequently, a multi-area intra-day dispatch strategy based on power support capacity analysis is proposed, where constraints on conventional units, wind farms, transmission lines, and RPSD are developed. Finally, to enable the development of the dispatch model, a model predictive control (MPC) scheme is used to update the power support capacity indicators dynamically and improve model reliability. The effectiveness and superiority of the proposed strategy are verified by case studies. Numerical results show a 7.02% cost reduction and overload risk reduction by using the proposed strategy compared to conventional global optimization methods.

Design of a silicon Mach–Zehnder modulator via deep learning and evolutionary algorithms

As an essential block in optical communication systems, silicon (Si) Mach–Zehnder modulators (MZMs) are approaching the limits of possible performance for high-speed applications. However, due to a large number of design parameters and the complex simulation of these devices, achieving high-performance configuration employing conventional optimization methods result in prohibitively long times and use of resources. Here, we propose a design methodology based on artificial neural networks and heuristic optimization that significantly reduces the complexity of the optimization process. First, we implemented a deep neural network model to substitute the 3D electromagnetic simulation of a Si-based MZM, whereas subsequently, this model is used to estimate the figure of merit within the heuristic optimizer, which, in our case, is the differential evolution algorithm. By applying this method to CMOS-compatible MZMs, we find new optimized configurations in terms of electro-optical bandwidth, insertion loss, and half-wave voltage. In particular, we achieve configurations of MZMs with a 40~text {GHz} bandwidth and a driving voltage of 6.25~text {V}, or, alternatively, 47.5~text {GHz} with a driving voltage of 8~text {V}. Furthermore, the faster simulation allowed optimizing MZM subject to different constraints, which permits us to explore the possible performance boundary of this type of MZMs.

Deep Reinforcement Learning Empowers Wireless Powered Mobile Edge Computing: Towards Energy-Aware Online Offloading

Deep integration of wireless power transmission and mobile edge computing (MEC) promotes wireless powered MEC to become a new research hotspot in the field of Internet of Things. In this paper, we focus on the joint optimization problem of online offloading decision and charging resource allocation for minimizing task accomplishing time in dynamic time-varying wireless channel scenarios. The optimal solution involves addressing a mixed integer programming problem in real time, which is proved to be NP-hard, and imposes nontrivial challenges to design with conventional optimization methods. To efficiently address this problem, we leverage the deep reinforcement learning (DRL) technology to propose an energy-aware online offloading algorithm called EAOO. EAOO algorithm learns empirically the online offloading decision policies via a well-designed DRL framework, and adopts the feasible solution region analysis method to implement the charging resource allocation. We further propose a novel feasible decision vector generation method, and incorporate the crossover and mutation technology to expand the offloading vector search space with the provable feasibility guarantee. Extensive experimental results show that, our EAOO algorithm outperforms existing baseline algorithms, and achieves near-optimal performance with low CPU execution latency, which well satisfies the practical requirements of real-time and efficiency.

Mixed topology optimization: A self-guided boundary-independent approach for power sources

As the use of electrochemical devices becomes more prevalent, advanced optimization techniques, such as topology optimization, are being employed to improve their performance. Among various electrochemical systems, power sources have an intrinsic best operating point that corresponds to the maximum output power. This study proposes a mixed topology optimization approach to enhance the performance of these systems by a simultaneous modification of electrode structure and the working condition. In contrast to the conventional approaches, the proposed method focuses on enhancement of the maximum power point. Thanks to its self-guidance feature, this technique outperforms conventional topology optimization methods and eliminates the need for a prior decision on the optimization starting point. Therefore, the proposed approach has a significant potential for adapting the material distribution to the best working condition. The proposed approach enables more effective topological optimization and takes the utilization of topology optimization in power sources to the next level.

Three-dimensional plasticity-based topology optimization with smoothed finite element analysis

AbstractThis paper presents a novel plasticity-based formulation for three-dimensional (3D) topology optimization of continuum structures. The proposed formulation addresses the optimization problem by combining mixed rigid-plastic analysis with density-based topology optimization, resulting in a volume minimization approach. Unlike conventional stress-constrained topology optimization methods that rely on linear elastic structural analysis, our developed formulation focuses on enhancing the loading capacity of the designed structures based on the plastic limit theory, leading to more cost-effective designs. To improve computational efficiency, we employ the smoothed finite element technique in our proposed method, enabling the utilization of linear tetrahedral elements for 3D mesh refinement. Moreover, the final formulation of our developed method can be efficiently solved using the advanced primal–dual interior point method, eliminating the need for a separate nonlinear finite element structural analysis. Numerical examples are presented to demonstrate the effectiveness of the proposed approach in offering enhanced design possibilities for continuum structures.

Performance investigation of state-of-the-art metaheuristic techniques for parameter extraction of solar cells/module

One of the greatest challenges for widespread utilization of solar energy is the low conversion efficiency, motivating the needs of developing more innovative approaches to improve the design of solar energy conversion equipment. Solar cell is the fundamental component of a photovoltaic (PV) system. Solar cell’s precise modelling and estimation of its parameters are of paramount importance for the simulation, design, and control of PV system to achieve optimal performances. It is nontrivial to estimate the unknown parameters of solar cell due to the nonlinearity and multimodality of search space. Conventional optimization methods tend to suffer from numerous drawbacks such as a tendency to be trapped in some local optima when solving this challenging problem. This paper aims to investigate the performance of eight state-of-the-art metaheuristic algorithms (MAs) to solve the solar cell parameter estimation problem on four case studies constituting of four different types of PV systems: R.T.C. France solar cell, LSM20 PV module, Solarex MSX-60 PV module, and SS2018P PV module. These four cell/modules are built using different technologies. The simulation results clearly indicate that the Coot-Bird Optimization technique obtains the minimum RMSE values of 1.0264E-05 and 1.8694E−03 for the R.T.C. France solar cell and the LSM20 PV module, respectively, while the wild horse optimizer outperforms in the case of the Solarex MSX-60 and SS2018 PV modules and gives the lowest value of RMSE as 2.6961E−03 and 4.7571E−05, respectively. Furthermore, the performances of all eight selected MAs are assessed by employing two non-parametric tests known as Friedman ranking and Wilcoxon rank-sum test. A full description is also provided, enabling the readers to understand the capability of each selected MA in improving the solar cell modelling that can enhance its energy conversion efficiency. Referring to the results obtained, some thoughts and suggestions for further improvements are provided in the conclusion section.

Sensitivity Region-Based Optimization for Maximizing Renewable Generation Hosting Capacity of an Islanded Microgrid

Renewable energy based distributed generators are key components in islanded microgrids. However, their power intermittency and uncertainty may impair power quality and cause system operating constraint violations. It is imperative to evaluate and maximize the hosting capacity of an islanded mi-crogrid for renewable generation. Besides, conventional optimi-zation methods focus on improving the solution robustness on constraints under uncertainties but ignoring that on the optimi-zation objective. To address these unsolved issues, a sensitivity region (SR) based optimization method for maximizing renewa-ble generation hosting capacity of an islanded microgrid is pro-posed. This paper firstly proposes an optimization model consid-ering microgrid frequency variation and microturbine droop control functionality. Secondly, SR and feasibility-SR are adopt-ed to quantify solution robustness against uncertainties of renew-able generation and load. It is expected to enlarge these two re-gions to cover all the possible uncertainty realizations, thus providing robust solutions. Last, this paper develops an SR based optimization method with a new solution algorithm. Through comprehensive numerical simulations, the proposed SR based hosting capacity maximization method is verified with high solu-tion robustness on both objective and operating constraints.

Adaptive User Pairing in Multi-IRS-Aided Massive MIMO-NOMA Networks: Spectral Efficiency Maximization and Deep Learning Design

In this paper, we propose an adaptive user pairing (AUP) scheme in multi-intelligent reflecting surface (IRS)-aided massive multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) networks. In the AUP scheme, two users with different channel conditions are selected for user pairing while multiple IRSs assist to improve received signal quality at users. We consider the problem of jointly optimizing the precoding matrix, the phase shift of IRSs, and the user pairing element to maximize the overall spectral efficiency (SE) subject to the maximum power budget at the base station (BS) and user-specific quality-of-service (QoS). The SE problem formulated as the maximization of non-concave functions involves a mixed-integer program, which is very challenging to solve optimally. To tackle this problem, we first relax the user pairing elements to be continuous and then transform the formulated problem into an equivalent non-convex problem with a more tractable form. We then apply the iterative algorithm (IA) with low complexity to guarantee convergence at a relative optimum. Towards real-time optimization, we propose a deep learning (DL) framework to predict the optimal solution of the precoding matrix, the phase shift of IRSs, and user pairing elements according to the user’s locations and channel gains. Compared to the conventional optimization method, the DL-based optimization framework can achieve the optimal solution within a very short time via an efficient inference process. Numerical results verify that the proposed algorithm improves the SE over state-of-the-art approaches. Moreover, the effects of essential parameters such as the total BS transmit power, the number of UEs, IRSs, and BS’s antennas on the system are discussed and evaluated to show the effectiveness of the proposed scheme in balancing resource utilization.

An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions.

The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback-Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback-Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.

Topology optimization for near-junction thermal spreading of electronics in ballistic-diffusive regime

Hotspots in electronic devices can cause overheating and reduce performance. Enhancing the thermal spreading ability is critical for reducing device temperature to improve the reliability. However, as devices shrink, phonon ballistic effects can increase thermal resistance, making conventional optimization methods less effective. This paper presents a topology optimization method that combines the phonon Boltzmann transport equation with solid isotropic material with penalization method to optimize high thermal conductivity (HTC) material distributions for thermal spreading problems. Results show that the contraction-expansion structure can effectively reduce thermal resistance. Optimal distributions differ from that based on Fourier's heat conduction law, and only the trunk structure appears in optimized layouts due to the size effect. Additionally, HTC material with longer mean free paths tends to be filled around the heat source with a gap in a ballistic-diffusive regime. This work deepens understanding of thermal spreading and aids in thermal optimization of microelectronic chips.

Multiple parameter optimization methodology by integrating a game theory principle into priority-based decision making

Mathematical model development for multivariate decision-making problems (i.e., multiple parameter and response optimization problems) has received significant attention and has been investigated by many researchers and practitioners. Although many different optimization models and methods, including priority and weight allocation problems, have been proposed in the literature, there is significant room for improvement. The majority of existing optimization methods may have difficulties in determining reliable priorities and weights for practical industrial situations. In addition, because they often focus on tradeoffs only among multiple output responses, these methods may not incorporate the multiple priority and/or weight effects directly from input factors to output responses (i.e., quality characteristics). To address these problems, the primary objective of this research is to propose a new multi-objective optimization approach by integrating a game theory principle (i.e., the Stackelberg leadership game) into a robust parameter design model to determine the optimal factor settings. First, a multi-response robust design optimization (RDO) problem was formulated using a mean squared error model and response surface methodology. A Stackelberg leadership game is then integrated into this RDO problem, where multiple responses play the role of game participants. Second, the integrated RDO model using the Stackelberg game-based multi-response (SGMR) formulation approach is analyzed by decomposition into various sequential optimization models in terms of different leader–follower relationships. Finally, non-dominated solutions are obtained from the proposed model by evaluating the overall quality loss (OQL). A pharmaceutical numerical example was performed to demonstrate the proposed integrated model and to examine whether this model can determine the most efficient solutions when the relative importance among multiple responses is unidentified. In addition, a comparative study associated with the conventional multi-objective optimization methods and the newly proposed RDO model is presented, and the proposed RDO model provided significantly better solutions than the conventional methods in the relevant comparative study.

Robust Optimization of UOE Forming Process Considering Inhomogeneity of Material Properties

Abstract The properties inhomogeneity of steel plates will result in uncertainty of forming quality of large diameter UOE oil pipes and increase the risk of pipeline failure. In this paper, a robust design method for UOE forming process based on support vector machine and sequential response surface modeling and considering the variation of steel plates′ properties is proposed. A hundred of mechanical experiments are first carried out and the variation of X80 steel's properties is statistically evaluated. The varied properties are assigned to partitioned steel segments and taken as the noise factor in process design. The ovality of the UOE pipe is employed as the optimization objective, and the forming quality indicators including convex amount, mean outside diameter, yield strengths and Ys/Uts7, O-forming gap, the width of the U-shaped plate, inclined angle of straight arm of the U-shaped plate, etc., are taken as the constraints. Based on the semi-analytical computation of C-, U- and O-forming processes and finite element simulation of expanding process, a sequential response surface model is established by using the support vector machine method. Finally, a Monte Carlo sampling is performed to demonstrate the effectiveness of the proposed method. Compared to conventional optimization method, the robust optimization performs obviously better in reducing the ovality and increasing the robustness of UOE forming process.