Expensive Optimization Algorithms Research Articles

Graph neural networks for power grid operational risk assessment under evolving unit commitment

This article investigates the ability of graph neural networks (GNNs) to identify risky conditions in a power grid over the subsequent few hours, without explicit, high-resolution information regarding future generator on/off status or power dispatch decisions. The GNNs are trained using supervised learning to predict the power grid’s aggregated bus-level (either zonal or system-level) or individual branch-level state under different power supply and demand conditions. The variability of the stochastic grid variables (wind/solar generation and load demand), and their statistical correlations, are considered while generating the inputs for the training data. The outputs in the training data include system-level, zonal and transmission line-level quantities of interest (QoIs). The ground truth of QoIs are obtained by numerically solving deterministic optimization problems (e.g., security-constrained unit commitment) with the same inputs. The GNN predictions are used to conduct hours-ahead, sampling-based reliability and risk assessment w.r.t. zonal and system-level (load shedding) as well as branch-level (overloading) failure events. The proposed methodology is demonstrated for three synthetic grids with sizes ranging from 118 to 2848 buses. Our results demonstrate that GNNs are capable of providing fast and accurate prediction of QoIs and can be good proxies for computationally expensive optimization algorithms. The excellent accuracy of GNN-based reliability and risk assessment suggests that GNN models can substantially improve situational awareness by enabling quick, high-resolution reliability and risk estimation.

Efficient Surrogate Model Assisted Estimation of Distribution Algorithm for Expensive Optimization

Efficient Surrogate Model Assisted Estimation of Distribution Algorithm for Expensive Optimization

A Hybrid Regressor and Classifier-Assisted Evolutionary Algorithm for Expensive Optimization With Incomplete Constraint Information

Surrogate-assisted evolutionary algorithms (SAEAs) have become a popular tool to solve expensive optimization problems and have been gradually used to deal with expensive constraints. To handle inequality expensive constraints, existing SAEAs need both the information of constraint violation and satisfaction to construct surrogate models for constraints. However, many problems only feedback whether the candidate solution is feasible or how much degree it violates constraints. There is no detailed information of how much degree the candidate satisfies constraints. The performance of most existing SAEAs decreases a lot in solving expensive constrained optimization problems (ECOPs) with such incomplete constraint information. To solve the problem, this article proposes a hybrid regressor and classifier-assisted evolutionary algorithm (HRCEA). HRCEA adopts a radial basis function regression model to approximate the degree of constraint violation. In order to make a more credible prediction, a logistic regression classifier (LRC) is constructed for the offspring rectification. The classifier works in cooperation with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -cut strategy, in which the high confidence level can significantly improve the prediction reliability. Besides, the LRC is built based on the boundary training data selection strategy, which is devised to select samples around feasible boundaries. This strategy is helpful for the LRC to fit the local feasibility structure. Extensive experiments on commonly used benchmark functions in CEC2006 and CEC 2010 demonstrate that HRCEA has satisfactory performance in found results and execution efficiency when solving ECOPs with incomplete constraint information. Furthermore, HRCEA is utilized to solve ceramic formula design optimization problem, which shows its promising application in real-world optimization problems.

Efficient wave type fingerprinting and filtering by six-component polarization analysis

SUMMARYWe present a technique to automatically classify the wave type of seismic phases that are recorded on a single six-component recording station (measuring both three components of translational and rotational ground motion) at the Earth’s surface. We make use of the fact that each wave type leaves a unique ’fingerprint’ in the six-component motion of the sensor (i.e. the motion is unique for each wave type). This fingerprint can be extracted by performing an eigenanalysis of the data covariance matrix, similar to conventional three-component polarization analysis. To assign a wave type to the fingerprint extracted from the data, we compare it to analytically derived six-component polarization models that are valid for pure-state plane wave arrivals. For efficient classification, we make use of the supervised machine learning method of support vector machines that is trained using data-independent, analytically derived six-component polarization models. This enables the rapid classification of seismic phases in a fully automated fashion, even for large data volumes, such as encountered in land-seismic exploration or ambient noise seismology. Once the wave-type is known, additional wave parameters (velocity, directionality and ellipticity) can be directly extracted from the six-component polarization states without the need to resort to expensive optimization algorithms. We illustrate the benefits of our approach on various real and synthetic data examples for applications such as automated phase picking, aliased ground-roll suppression in land-seismic exploration and the rapid close-to real-time extraction of surface wave dispersion curves from single-station recordings of ambient noise. Additionally, we argue that an initial step of wave type classification is necessary in order to successfully apply the common technique of extracting phase velocities from combined measurements of rotational and translational motion.

Decision space partition based surrogate-assisted evolutionary algorithm for expensive optimization

In expensive optimization, function evaluations are based on expensive physical experiments or time consuming simulations. Moreover, the gradient for the objective is not readily available. Therefore, it is a challenge task to deal with expensive optimization. In this work, a decision space partition based surrogate-assisted evolutionary algorithm (DSP-SAEA) is proposed for expensive optimization. In DSP-SAEA, a two-stage search strategy is introduced, where the global search and the local search are seamlessly integrated. In the global search stage, a decision space partition based global search strategy is proposed. In this strategy, all the exactly evaluated points are clustered into a set of clusters. Thus, the decision space can be partitioned into several regions based on the formed clusters. Furthermore, in each region, the surrogate model is constructed. The algorithm will search for these regions simultaneously with the help of the built surrogate models. As a result, several promising points distributed in different regions are able to be obtained. In the local search stage, a model adaptive selection strategy and the trust region local search are integrated. The model adaptive selection strategy is introduced to accurately assist the trust region local search, where the local elite surrogate model is adaptively chosen from the local surrogate model pool. Experimental results on benchmark problems and the parameter estimation for frequency-modulated sound waves problem demonstrate that DSP-SAEA performs competitively compared with some state-of-the-art algorithms.

A surrogate-assisted bi-swarm evolutionary algorithm for expensive optimization

A surrogate-assisted bi-swarm evolutionary algorithm for expensive optimization

A classification surrogate-assisted multi-objective evolutionary algorithm for expensive optimization

Surrogate-assisted multi-objective evolutionary algorithms (SAMOEAs) have been developed for solving expensive optimization problems. According to the roles that the surrogate models play in SAMOEAs, they can be divided into two categories: prediction-based and classification-based algorithms. Though prediction-based SAMOEAs are the mainstream methods, classification-based ones are gaining their fast developments. In this article, a classification surrogate-assisted multi-objective evolutionary algorithm (CSA-MOEA) is proposed for expensive optimization. The algorithm adopts a classification tree as the surrogate model to predict promising offsprings, which may be non-dominated solutions with good convergence. Then based on two effective infilling strategies, some of these promising individuals are added to the sample archive. By repeating the above steps iteratively, valuable solutions can be obtained. To evaluate the performance of CSA-MOEA, it is compared with several state-of-the-art surrogate-assisted evolutionary algorithms on three sets of multi-objective optimization test problems and an engineering shape optimization problem. The experimental results demonstrate the competitiveness of CSA-MOEA.

A Three-Level Radial Basis Function Method for Expensive Optimization.

This article proposes a three-level radial basis function (TLRBF)-assisted optimization algorithm for expensive optimization. It consists of three search procedures at each iteration: 1) the global exploration search is to find a solution by optimizing a global RBF approximation function subject to a distance constraint in the whole search space; 2) the subregion search is to generate a solution by minimizing an RBF approximation function in a subregion determined by fuzzy clustering; and 3) the local exploitation search is to generate a solution by solving a local RBF approximation model in the neighborhood of the current best solution. Compared with some other state-of-the-art algorithms on five commonly used scalable benchmark problems, ten CEC2015 computationally expensive problems, and a real-world airfoil design optimization problem, our proposed algorithm performs well for expensive optimization.

A Stability Criterion for Networked Control Systems With Packetized Transmissions

A stability criterion for networked feedback loops with time-varying measurement delays is proposed. It allows to check stability under the presence of different packetized network transmission policies where, e.g., newer packets may arrive at the same time or before older packets. The criterion is based on the small gain theorem and explicitly takes into account a packet selection and hold mechanism at the receiver side. It can easily be checked in frequency domain and does not involve any computationally expensive optimization algorithms.

Modeling, Optimization, and Operation of Large-Scale Air Traffic Flow Management on Spark

The nationwide air traffic flow management problem often encounters computational difficulty because it is generally modeled as an integer programming problem that requires computationally expensive optimization algorithms. This paper introduces a customized Spark-based optimization architecture for such large-scale integer programming problems to further speed up the modeling and optimization process, where Spark is a big data cluster-computing platform. First, a novel layered aggregate model is developed for handling flexible rerouting problem, which is not well handled in a previous link transmission model. As an aggregate linear model, the layered aggregate model has the nice features of computational efficiency and scalability, which make it suitable for Apache Spark. By applying a dual decomposition method, the original large-scale problem is decomposed into a number of small subproblems. The optimization proceeds by iteratively solving subproblems and updating Lagrange multipliers. This paper encapsulated the process into the Spark-based data processing model such that the optimization is automatically scheduled to run in parallel. Spark gains efficiency by means of in-memory computing and dynamic schedule allocation. This is demonstrated in the experimental results that are compared to an earlier Hadoop MapReduce-based model, where Hadoop MapReduce is a basic cloud computing framework; the Spark-based model is solved twice as fast as the Hadoop MapReduce-based model.

A metamodel-assisted evolutionary algorithm for expensive optimization

Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive o...

A metamodel-assisted evolutionary algorithm for expensive optimization

Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems.

Sum Throughput Enhancements in Quality of Service Constrained Multiuser MIMO OFDM Systems

In many wireless applications, such as video streaming, data transfer or mobile Internet, user satisfaction is directly related to the transmission rates of the wireless channels in the physical layer. If the transmission rate of one user undercuts a certain level, the quality of the application becomes unacceptable. Furthermore network operators are interested in maximizing overall system throughput. However, this aim can usually not be achieved without violating these minimum rate constraints. In this article we therefore consider a practical resource allocation scheme for MIMO OFDM systems that achieves both aims without requiring computationally expensive optimization algorithms. The main part consists of a user classification. Users in one group will only be served with their minimum required rates. The remaining users can exploit the additional system resources more effectively for strong throughput increases and are therefore put in the other group. An iterative application of the proposed scheme enables additional throughput increases and the consideration of maximum transmission rates.

On the computational aspects of Gibbs-Markov random field modeling of missing-data in image sequences

Gibbs-Markov random field (GMRF) modeling has been shown to be a robust method in the detection of missing-data in image sequences for a video restoration application. However, the maximum a posteriori probability (MAP) estimation of the GMRF model requires computationally expensive optimization algorithms in order to achieve an optimal solution. The continuous relaxation labeling (RL) is explored in this paper as an efficient approach for solving the optimization problem. The conversion of the original combinatorial optimization into a continuous RL formulation is presented. The performance of the RL formulation is analyzed and compared with that of other optimization methods such as stochastic simulated annealing, iterated conditional modes, and mean field annealing. The results show that RL holds out promise as an optimization algorithm for problems in image sequence processing.