Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run.Currently,the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs.By contrast,problem domain knowledge of NESs is investigated in this study,where we propose the incorporation of a variable reduction strategy(VRS)into EAs to solve NESs.The VRS makes full use of the systems of expressing a NES and uses some variables(i.e.,core variable)to represent other variables(i.e.,reduced variables)through variable relationships that exist in the equation systems.It enables the reduction of partial variables and equations and shrinks the decision space,thereby reducing the complexity of the problem and improving the search efficiency of the EAs.To test the effectiveness of VRS in dealing with NESs,this paper mainly integrates the VRS into two existing state-of-the-art EA methods(i.e.,MONES and DR-JADE)according to the integration framework of the VRS and EA,respectively.Experimental results show that,with the assistance of the VRS,the EA methods can produce better results than the original methods and other compared methods.Furthermore,extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.

A Data-driven Variable Reduction Approach for Transmission-constrained Unit Commitment of Large-scale Systems

This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment(TCUC).Lagrangian relaxation(LR)and mixed-integer linear programming(MILP)are popular approaches to solving TCUC.However,with many binary unit commitment variables,LR suffers from slow convergence and MILP presents heavy computation burden.The proposed data-driven variable reduction approach consists of offline and online calculations to accelerate computational performance of the MILP-based large-scale TCUC problems.A database including multiple nodal net load intervals and the corresponding TCUC solutions is first built offline via the data-driven and all-scenario-feasible(ASF)approaches,which is then leveraged to efficiently solve new TCUC instances online.On/off statuses of considerable units can be fixed in the online calculation according to the database,which would reduce the computation burden while guaranteeing good solution quality for new TCUC instances.A feasibility proposition is proposed to promptly check the feasibility of the new TCUC instances with fixed binary variables,which can be used to dynamically tune parameters of binary variable fixing strategies and guarantee the existence of feasible UC solutions even when system structure changes.Numerical tests illustrate the efficiency of the proposed approach.

Variable Reduction Strategy Integrated Variable Neighborhood Search and NSGA-II Hybrid Algorithm for Emergency Material Scheduling

Developing a reasonable and efficient emergency material scheduling plan is of great significance to decreasing casualties and property losses.Real-world emergency material scheduling(EMS)problems are typically large-scale and possess complex constraints.An evolutionary algorithm(EA)is one of the effective methods for solving EMS problems.However,the existing EAs still face great challenges when dealing with large-scale EMS problems or EMS problems with equality constraints.To handle the above challenges,we apply the idea of a variable reduction strategy(VRS)to an EMS problem,which can accelerate the optimization process of the used EAs and obtain better solutions by simplifying the corresponding EMS problems.Firstly,we define an emergency material allocation and route scheduling model,and a variable neighborhood search and NSGA-II hybrid algorithm(VNS-NSGAII)is designed to solve the model.Secondly,we utilize VRS to simplify the proposed EMS model to enable a lower dimension and fewer equality constraints.Furthermore,we integrate VRS with VNS-NSGAII to solve the reduced EMS model.To prove the effectiveness of VRS on VNS-NSAGII,we construct two test cases,where one case is based on a multi-depot vehicle routing problem and the other case is combined with the initial 5∙12 Wenchuan earthquake emergency material support situation.Experimental results show that VRS can improve the performance of the standard VNS-NSGAII,enabling better optimization efficiency and a higher-quality solution.

Variable-fidelity optimization with design space reduction

Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.

Reducing deep learning network structure through variable reduction methods in crop modeling

Crop models are widely used to predict plant growth,water input requirements,and yield.However,existing models are very complex and require hundreds of variables to perform accurately.Due to these shortcomings,large-scale applications of crop models are limited.In order to address these limitations,reliable crop models were developed using a deep neural network(DNN)–a new approach for predicting crop yields.In addition,the number of required input variables was reduced using three common variable selection techniques:namely Bayesian variable selection,Spearman's rank correlation,and Principal Component Analysis Feature Extraction.The reduced-variableDNN modelswere capable of estimating future crop yields for 10,000,000 differentweather and irrigation scenarios while maintaining comparable accuracy levels to the original model that used all input variables.To establish clear superiority of the methodology,the results were also compared with a very recent feature selection algorithm called min-redundancy max-relevance(mRMR).The results of this study showed that the Bayesian variable selection was the best method for achieving the aforementioned goals.Specifically,the final Bayesian-based DNN model with a structure of 10 neurons in 5 layers performed very similarly(78.6%accuracy)to the original DNN cropmodel with 400 neurons in 10 layers,even though the size of the neural network was reduced by 80-fold.This effort can help promote sustainable agricultural intensifications through the large-scale application of crop models.