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.

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.

Control and Implementation of 2-DOF Lower Limb Exoskeleton Experiment Platform

In this study,a humanoid prototype of 2-DOF(degrees of freedom)lower limb exoskeleton is introduced to evaluate the wearable comfortable effect between person and exoskeleton.To improve the detection accuracy of the humanrobot interaction torque,a BPNN(backpropagation neural networks)is proposed to estimate this interaction force and to compensate for the measurement error of the 3D-force/torque sensor.Meanwhile,the backstepping controller is designed to realize the exoskeleton's passive position control,which means that the person passively adapts to the exoskeleton.On the other hand,a variable admittance controller is used to implement the exoskeleton's active followup control,which means that the person's motion is motivated by his/her intention and the exoskeleton control tries best to improve the human-robot wearable comfortable performance.To improve the wearable comfortable effect,serval regular gait tasks with different admittance parameters and step frequencies are statistically performed to obtain the optimal admittance control parameters.Finally,the BPNN compensation algorithm and two controllers are verified by the experimental exoskeleton prototype with human-robot cooperative motion.

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.