Global Convergence Research Articles

Optimization of vehicle conceptual design problems using an enhanced hunger games search algorithm

Abstract Electric vehicles have become a standard means of transportation in the last 10 years. This paper aims to formalize design optimization problems for electric vehicle components. It presents a tool conceptual design technique with a hunger games search optimizer that incorporates dynamic adversary-based learning and diversity leader (referred to as HGS-DOL-DIL) to overcome the local optimum trap and low convergence rate limitations of the Hunger Games search algorithm to improve the convergence rate. The performance of the proposed algorithms is studied on six widely used engineering design problems, complex constraints, and discrete variables. For the HGS-DOL-DIL practical feasibility analysis, a case study of shape optimization of an electric car suspension arm from the industry is carried out. Overall, the inclusion of the OL strategy has proven its superiority in solving real-world problems, especially in solving real-world problems such as shape optimization of an electric vehicle automobile suspension arm, showing that the algorithm improves the search space improves the solution quality, and reflects its potential to find global optimum solutions in a well-balanced exploration and exploitation phase.

Distributed robust tracking control for multiple unmanned aerial vehicles: theory and experimental verification

The distributed trajectory tracking problem for multiple UAVs under unknown external disturbance is investigated. A new nonlinear robust trajectory tracking strategy for multiple UAVs is proposed. The dynamic model for the UAVs' formation is illustrated in the Tangent frame. For the trajectory tracking problem, a Robust formation tracking control strategy based on robust integral of the signum of error (RISE) is designed to compensate for the effects of unknown external disturbances, which improves the robustness of the UAVs' formation system. Based on the Lyapunov stability analysis, it is proved that the global asymptotic convergence of the coordination errors and the semi-global asymptotic convergence of the UAVs' position tracking errors are achieved. The proposed formation control strategy is validated via real-time experiments that are performed on the self-build UAVs' formation flight control testbed. Flights without wind disturbance and flights with disturbance are all performed. The performance comparison experiment with the conventional sliding mode control algorithm is performed. The experimental results show that the designed control strategy can achieve good coordinated trajectory tracking of multiple UAVs, and has better control performance compared with normal sliding mode control law.

Energy-Efficient Passivity-Based Sliding Mode Controller for Small-Scale Quadrotor UAV for Trajectory Tracking

Quadrotor unmanned aerial vehicles (UAVs) have emerged as versatile platforms applicable to various fields such as surveillance, reconnaissance, and mapping. However, the limited energy capacity inherent in these vehicles poses a significant challenge. This limitation is a critical concern hindering their widespread adoption across diverse applications. Despite various proposed technological solutions addressing the energy consumption issue, the central challenge for the control community lies in developing controllers that ensure stability, robustness, and energy efficiency. In this paper, we present a passivity-based sliding mode controller (P-SMC) designed specifically for quadrotor UAVs. The suggested controller capitalizes on the robustness of the SMC and the energy efficiency of passivity-based control theory. Feedback passification is employed to create a sliding surface with passivity, ensuring stability. The inclusion of a noncontinuity term in the proposed P-SMC guarantees global asymptotic convergence to the sliding surface. To address the multi-faceted nature of the problem, a multi-objective optimization criterion is introduced. This criterion, which combines tracking error and control energy, is solved using the ant colony optimization (ACO) algorithm. The optimization process aims to identify control parameters that strike a balance between tracking accuracy and energy efficiency. Additionally, a conventional sliding mode method is developed to respond to conditions of attempted reach and sliding. Finally, the effectiveness of the proposed method is demonstrated through simulation results considering piecewise constant external disturbances. The outcomes based on the proposed control strategy indicate a notable reduction in energy consumption (ranging from [Formula: see text] to [Formula: see text]), faster reaching times (5–8 times), higher accuracy approximately ([Formula: see text]), and reduced chattering compared to the conventional sliding mode technique.

Hybridized Brazilian–Bowein type spectral gradient projection method for constrained nonlinear equations

This paper proposes a hybridized Brazilian and Bowein derivative-free spectral gradient projection method for solving systems of convex-constrained nonlinear equations. The method avoids solving any subproblems in each iteration. Global convergence is established under appropriate assumptions on the functions involved. Additionally, numerical experiments are conducted to evaluate the algorithm’s performance, providing evidence of its efficiency compared to similar algorithms from the existing literature. The results demonstrate that the method outperforms some existing approaches in terms of the number of iterations, function evaluations, and time required to obtain a solution based on the examples considered.

A novel highly efficient alternating direction method of multipliers for large-scale trimmed concave SVM

Support vector machine (SVM) is widely utilized for classification in diverse fields thanks to its superior performance. However, when tackling large-scale SVM problems, it encounters high computational complexity. To address this issue, we develop a novel trimmed concave loss SVM model called Ltri-SVM, which achieves sparsity and robustness simultaneously. The new optimality theory for the nonconvex and nonsmooth Ltri-SVM is developed by our new constructed proximal stationary point. Based on which, a new fast alternating direction method of multipliers (ADMM) with working set and low computational complexity is established for addressing Ltri-SVM. Based on our new established optimality theory, our proposed algorithm will divides the training dataset into two distinct categories: the non-working and the working sets. In every training iteration, the algorithm modifies the parameters associated with the working set, while ensuring that the parameters belonging to the non-working set remain unchanged. This algorithm enables the updating of parameters on smaller datasets, which in turn decreases computational complexity and improves the efficiency of runtime. Further, we prove that our algorithm is global convergence. Numerical experiments have confirmed the excellent performance of our algorithm in terms of accuracy in classification, number of support vector and computational speed, surpassing nine other leading solvers. For instance, when solving the real dataset with over 107 samples, our algorithm is able to complete the task in just 18.92 s, which is much faster than other solvers that take at least 650.4 s.

A Quasi-Newton Subspace Trust Region Algorithm for Nonmonotone Variational Inequalities in Adversarial Learning over Box Constraints

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In this paper, we propose a quasi-Newton subspace trust region (QNSTR) algorithm for the least squares problems defined by the smoothing approximation of nonsmooth equations. Based on the structure of the nonmonotone VI, we use an adaptive quasi-Newton formula to approximate the Hessian matrix and solve a low-dimensional strongly convex quadratic program with ellipse constraints in a subspace at each step of the QNSTR algorithm efficiently. We prove the global convergence of the QNSTR algorithm to an ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document}-first-order stationary point of the min-max optimization problem. Moreover, we present numerical results based on the QNSTR algorithm with different subspaces for a mixed generative adversarial networks in eye image segmentation using real data to show the efficiency and effectiveness of the QNSTR algorithm for solving large-scale min-max optimization problems.

Convergence of a class of algorithms with the level-set subdifferential error bound

In this paper, we study the convergence of algorithms for a class of nonconvex and nonsmooth optimization problems via an level-set subdifferential error bound. Many algorithms (cf. forward-backward splitting algorithm and alternating proximal minimization algorithm) satisfy sufficient descent and relative error conditions. We also find that these algorithms satisfy a quadratic error condition. Under these conditions and the level-set subdifferential error bound, we study the global convergence and the convergence rates of these algorithms without the Kurdyka-Łojasiewicz property which is stronger than the level-set subdifferential error bound. Two examples are given to illustrate the broader applicability of our findings across these algorithms.

Coordinated planning and operation of PV- hydrogen integrated distribution network incorporating daily-seasonal green hydrogen storage and EV charging station

The current study introduces an optimal planning and operational framework for a Distribution Network (DN) that integrates Photovoltaic (PV)-green Hydrogen (H2)-based energy system with Electric Vehicle Charging Station (EVCS). An efficient operational strategy is proposed considering both short-term H2 storage (STHS) and long-term H2 storage (LTHS), ensuring uninterrupted power supply. Besides, a novel Improved Harris Hawk Optimization method is developed to enhance the global search capabilities and convergence rate in optimizing the capacity of Solar module, Electrolyzer, and Fuel cells. The objective of the proposed model is to minimize the device costs, energy loss, and carbon emissions, adhering to all operational constraints. The proposed work is tested on 33-bus radial DN and 51-bus real Indian DN considering the time frame of 10 years. The analysis reveals that the PV-STHS-LTHS configuration, reduces total planning costs by 12% and 15% as compared to the base case in the 33-bus and 51-bus systems, respectively. Additionally, the integration of both daily and seasonal storage facilities with PV systems leads to a reduction in carbon emissions by 76% and 81% in the 33-bus and 51-bus systems, respectively. Besides the carbon reduction, the incorporation of daily and cross-seasonal H2 storage increases oxygen release into the environment by 13% for the 33-bus system and 15% for the 51-bus system.

Global Convergence of Natural Policy Gradient with Hessian-Aided Momentum Variance Reduction

Global Convergence of Natural Policy Gradient with Hessian-Aided Momentum Variance Reduction

An efficient weighted slime mould algorithm for engineering optimization

In engineering applications, optimal parameter design is crucial. While Slime Mould Algorithm (SMA) excels in parameter discovery under constrained conditions, it faces challenges in achieving global convergence and avoiding local opsecttimal traps in complex tasks. This paper introduces an enhanced variant of SMA, termed CCHSMA, which integrates a Chaotic Local Search (CLS) mechanism to improve initial population diversity and combines Covariance Matrix Adaptation (CMA) and Harris Hawks Optimization (HHO) strategies to enhance global search efficiency. CCHSMA aims to improve search quality and reduce the likelihood of getting trapped in local optima. We evaluated CCHSMA's effectiveness by benchmarking it against the standard SMA and its variants using 30 CEC2017 test functions, and compared its performance with seven notable meta-heuristic algorithms and ten advanced swarm intelligence variants. The experimental results demonstrate that CCHSMA outperforms the other algorithms tested on the benchmark functions. To further validate its practical utility, CCHSMA's performance was also benchmarked against leading algorithms in real-world engineering applications. This paper uses detailed statistical methods, including the Wilcoxon signed-rank test and the Friedman test, to validate the comparative results. Our findings show that CCHSMA outperforms other algorithms in solving complex engineering optimization problems such as tension/compression spring design, pressure vessel design, and three-bar truss design, proving to be a robust tool for complex engineering optimization. Its enhanced initial population diversity and improved global search efficiency are essential for effectively addressing diverse engineering challenges.

Improving the Global Convergence of Inexact Restoration Methods for Constrained Optimization Problems

Improving the Global Convergence of Inexact Restoration Methods for Constrained Optimization Problems

DG-IMEX method for a two-moment model for radiation transport in the [formula omitted] limit

We consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to O(v/c), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct O(v/c) Eulerian-frame number density and is consistent, to O(v/c), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. [1] and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical fluxes; (iii) a realizability-preserving implicit collision update; and (iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a “spectral redistribution” scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems

Conjugate gradient methods are widely used and attractive for large-scale unconstrained smooth optimization problems, with simple computation, low memory requirements, and interesting theoretical information on the features of curvature. Based on the strongly convergent property of the Dai–Yuan method and attractive numerical performance of the Hestenes–Stiefel method, a new hybrid descent conjugate gradient method is proposed in this paper. The proposed method satisfies the sufficient descent property independent of the accuracy of the line search strategies. Under the standard conditions, the trust region property and the global convergence are established, respectively. Numerical results of 61 problems with 9 large-scale dimensions and 46 ill-conditioned matrix problems reveal that the proposed method is more effective, robust, and reliable than the other methods. Additionally, the hybrid method also demonstrates reliable results for some image restoration problems.

A diffusive predator-prey system with hunting cooperation in predators and prey-taxis: II stationary pattern formation

This paper is a continuation of the study conducted by Ko and Ryu (2024) [5], which introduces and analyzes a generalized predator-prey reaction-diffusion system incorporating (repulsive) prey-taxis and a hunting cooperation effect in predators, under homogeneous Neumann boundary conditions. In the study, the existence and uniqueness of global and classical solutions for the time- and space-dependent system are analytically examined. Furthermore, the study examines the local and global stability and convergence rate at the constant predator-extinction and coexistence states. In our paper, we analyze the stationary system corresponding to the system in [5], with a specific focus on examining the existence and nonexistence of positive and nonconstant solutions. The nonexistence occurs when the diffusion rate of prey is sufficiently high. On the other hand, the existence occurs when the prey-tactic rate is sufficiently high, indicating a strong repulsive prey-taxis, and the diffusion rate of prey is sufficiently low. For this investigation, we separately employ the energy method and the Leray-Schauder degree theory.

Neural network algorithm with transfer learning and dropout for using a UAV to search the lost target in motion

When performing the rescue mission, how to find a lost target in motion as soon as possible is a very valuable and interesting research topic. To find the optimal flight path of the UAV used to search the lost target in motion under different prior knowledge and interference intensity, this paper proposes a novel optimization technique called neural network algorithm with transfer learning and dropout (TLDNNA), which is a variant of neural network algorithm (NNA) inspired by artificial neural networks. To improve the global search ability and convergence performance of NNA, the multiple transfer mechanism, the generalized mean transfer position, and the random dropout operator driven by the principles of transfer learning and dropout are introduced to TLDNNA. To investigate the performance of TLDNNA, TLDNNA and 12 powerful population-based optimization algorithms are applied to the problem of using a UAV to search the lost target in motion in the designed 9 scenarios. Experimental results show that TLDNNA is remarkably better than the other 12 algorithms in most of the scenarios in terms of solution quality, stability, and convergence performance. In addition, TLDNNA can improve the overall search performance by 18.14% and overall computational efficiency by 3.41 times compared to NNA. The source code of TLDNNA can be obtained by https://github.com/jsuzyy/TLDNNA.

A Modified Wei-Yao-Liu Stochastic Conjugate Gradient Algorithm in Machine Learning

Abstract The Wei-Yao-Liu (WYL) Conjugate Gradient (CG) algorithm exhibits favourable attributes, notably sufficient descent and trust domain characteristics, in the context of solving unconstrained optimization problems. The exploration and enhancement of computational methodologies for stochastic optimization problems have garnered significant attention. In this study, our objective is to improve the Wei-Yao-Liu (WYL) CG algorithm and introduce an effective optimization method tailored for solving stochastic optimization problems. We will present a comprehensive framework for analysing the convergence of this algorithm and, under suitable conditions, establish its sufficient descent properties, trust region features, and global convergence of stationary points. We will also give an improved CG algorithm to calculate a framework for variance reduction. Additionally, we will conduct experimental comparisons to showcase the competitiveness of our proposed algorithm.

A Modified Three-terms CG Method with the MWWP Line Search and its Application to Image Restoration

Abstract In this article, an innovative method, which integrates the optimized three-term Polak–Ribière–Polyak (PRP) conjugate gradient (CG) method with the improved WWP line search rule, is presented and applied in the field of image restoration. The proposed search direction exhibits sufficient descent and trust region characteristics, maintaining its effectiveness regardless of the specific line search rule employed. We established the global convergence of the presented algorithm and eliminated the dependence on the Lipschitz continuity assumption. The numerical comparisons with the PRP CG method revealed the superior performance of the designed algorithm in the field of image restoration. This research outcome provides strong support for further advancements in the field of image recovery.

Probability density function based adaptive ensemble learning with global convergence for wind power prediction

Probability density function based adaptive ensemble learning with global convergence for wind power prediction

A New Hybrid Conjugate Gradient Method with Global Convergence Properties

This work introduces a novel hybrid conjugate gradient (CG) technique for tackling unconstrained optimisation problems with improved efficiency and effectiveness. The parameter is computed as a convex combination of the standard conjugate gradient techniques using and . Our proposed method has shown that when using the strong Wolfe-line-search (SWC) under specific conditions, it achieves global theoretical convergence. In addition, the new hybrid CG approach has the ability to generate a search direction that moves downward with each iteration. The quantitative findings obtained by applying the recommended technique about 30 functions with varying dimensions clearly illustrate its effectiveness and potential. This work introduces a novel hybrid conjugate gradient (CG) technique for tackling unconstrained optimisation problems with improved efficiency and effectiveness. The parameter is computed as a convex combination of the standard conjugate gradient techniques using and . Our proposed method has shown that when using the strong Wolfe-line-search (SWC) under specific conditions, it achieves global theoretical convergence. In addition, the new hybrid CG approach has the ability to generate a search direction that moves downward with each iteration. The quantitative findings obtained by applying the recommended technique about 30 functions with varying dimensions clearly illustrate its effectiveness and potential.

Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions

AbstractIn this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka–Łojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.