Local Minima Research Articles

3D-AMM: a 3D artificial moment method for path planning of manipulator in multiple obstacles scenario

Purpose In response to the issue of traditional algorithms often falling into local minima or failing to find feasible solutions in manipulator path planning. The purpose of this paper is to propose a 3D artificial moment method (3D-AMM) for obstacle avoidance for the robotic arm's end-effector. Design/methodology/approach A new method for constructing temporary attractive points in 3D has been introduced using the vector triple product approach, which generates the attractive moments that attract the end-effector to move toward it. Second, distance weight factorization and spatial projection methods are introduced to improve the solution of repulsive moments in multiobstacle scenarios. Third, a novel motion vector-solving mechanism is proposed to provide nonzero velocity for the end-effector to solve the problem of limiting the solution of the motion vector to a fixed coordinate plane due to dimensionality constraints. Findings A comparative analysis was conducted between the proposed algorithm and the existing methods, the improved artificial potential field method and the rapidly-random tree method under identical simulation conditions. The results indicate that the 3D-AMM method successfully plans paths with smoother trajectories and reduces the path length by 20.03% to 36.9%. Additionally, the experimental comparison outcomes affirm the feasibility and effectiveness of this method for obstacle avoidance in industrial scenarios. Originality/value This paper proposes a 3D-AMM algorithm for manipulator path planning in Cartesian space with multiple obstacles. This method effectively solves the problem of the artificial potential field method easily falling into local minimum points and the low path planning success rate of the rapidly-exploring random tree method.

CFD modelling of Close-Coupled Gas Atomisation (CCGA) process by employing the Euler-Lagrange approach to understand melt flow instabilities

This paper presents a CFD analysis of the melt and flow-field instabilities in a close-coupled gas atomisation process (CCGA) caused by the gas–melt interactions. The melt mass flow is coupled to the atomiser internal pressure, which varies over time due to the unsteady flow field. A two-phase flow of Argon gas and melt particles is modelled using a coupled Euler-Lagrange framework. Three different initial gas-to-melt ratios (GMRs) of 5.5, 2.6 and 1.32 are considered to study the gas–melt interaction. The results show that in the case GMR = 1.32, sustained instability both in the melt and in the flow-field are distinctly observed, resembling physical atomisation process. This melt fluctuation corresponded to an alternating flow-field fluctuation; alternating between open- to closed-wake condition, where the local maxima of the melt corresponded to an open-wake condition, and the local minima of the melt corresponded to a closed-wake condition.

NURBs Based Multi-robots Path Planning with Obstacle Avoidance

The primary problem for multi-robot displacement and motion phase solving requires that the robots prevent themselves from colliding with each other as well as stationary obstacles. In certain situations, robot conflict is unavoidable if one robot views its neighbors as immovable obstacles. Hence, this paper proposes a new NURBs (Non-Uniform Rational B-spline) based algorithm for multi-robot path planning in a crowded environment. First, the proposed technique finds each robot's free, smooth, optimal path while avoiding collision with the existing obstacles. Secondly, the prospect of possible collision between the preplanned trajectories will be computed to allow the robots to navigate in the same workspace and coordinate between them. Then, each robot's time to arrive at potential collision sites is computed based on its speed. As a result, the robots involved in the collision must choose whether to use the robot priority technique to prevent the collision. Simulation results under different scenarios and comparisons with previous works are provided to validate the work. The obtained results prove that the proposed approach is accurate (as the robot's instantaneous speed is taken into consideration), fast (as there is no need to broadcast the robots’ positions), the robots’ paths are optimal and smooth (to avoid jerk movements), and the approach ensures that the robots will not be trapped by local minima problem.

Feasibility Verification and Upper Bound Computation in Global Minimization Using Approximate Active Index Sets

We propose a new upper bounding procedure for global minimization problems with continuous variables and possibly nonconvex inequality and equality constraints. Upper bounds are crucial for standard termination criteria of spatial branch-and-bound (SBB) algorithms to ensure that they can enclose globally minimal values sufficiently well. However, whereas for most lower bounding procedures from the literature, convergence on smaller boxes is established, this does not hold for several methods to compute upper bounds even though they often perform well in practice. In contrast, our emphasis is on the convergence. We present a new approach to verify the existence of feasible points on boxes, on which upper bounds can then be determined. To this end, we resort to existing convergent feasibility verification approaches for purely equality and box constrained problems. By considering carefully designed modifications of subproblems based on the approximation of active index sets, we enhance such methods to problems with additional inequality constraints. We prove that our new upper bounding procedure finds sufficiently good upper bounds so that termination of SBB algorithms is guaranteed after a finite number of iterations. Our theoretical findings are illustrated by computational results on a large number of standard test problems. These results show that compared with interval Newton methods from the literature, our proposed method is more successful in feasibility verification for both, a full SBB implementation (42 instead of 26 test problems) and exhaustive sequences of boxes around known feasible points (120 instead of 29 test problems). History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0162 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0162 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Optimal control problem with state constraints via penalty functions

In this paper, we derive necessary conditions of optimality for problems with state constraints using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., de Pinho et al., 2022). Our aim is to provide a proof of the Maximum Principle that can be easily followed by those with basic knowledge of classical optimal control and elementary functional analysis. We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact.

Application of a mild data-driven technique to Lippmann–Schwinger inverse scattering in variable-exponent Lebesgue spaces for microwave imaging

A mild data-driven approach for microwave imaging is considered in this paper. In particular, the developed technique relies upon the use of a Newton-type inversion scheme in variable-exponent Lebesgue spaces, which has been modified by including a data-driven operator to enforce the available a-priori information about the class of targets to be investigated. In this way, the performance of the method is improved, and the problems related to the possible convergence to local minima are mitigated. The effectiveness of the approach has been evaluated through numerical simulations involving the detection of defects inside (partially) known objects, showing good results.

Solution of engineering design and truss topology problems with improved forensic-based investigation algorithm based on dynamic oppositional based learning

AbstractThe forensic-based investigation (FBI) is a metaheuristic algorithm inspired by the criminal investigation process. The collaborative efforts of the investigation and pursuit teams demonstrate the FBI’s involvement during the exploitation and exploration phases. When choosing the promising population, the FBI algorithm’s population selection technique focuses on the same region. This research aims to propose a dynamic population selection method for the original FBI and thereby enhance its convergence performance. To achieve this objective, the FBI may employ dynamic oppositional learning (DOL), a dynamic version of the oppositional learning methodology, to dynamically navigate to local minima in various locations. Therefore, the proposed advanced method is named DOLFBI. The performance of DOLFBI on the CEC2019 and CEC2022 benchmark functions is evaluated by comparing it with several other popular metaheuristics in the literature. As a result, DOLFBI yielded the lowest fitness value in 18 of 22 benchmark problems. Furthermore, DOLFBI has shown promising results in solving real-world engineering problems. It can be argued that DOLFBI exhibits the best convergence performance in cantilever beam design, speed reducer, and tension/compression problems. DOLFBI is often utilized in truss engineering difficulties to determine the minimal weight. Its success is comparable to other competitive MAs in the literature. The Wilcoxon signed-rank and Friedman rank tests further confirmed the study’s stability. Convergence and trajectory analyses validate the superior convergence concept of the proposed method. When the proposed study is compared to essential and enhanced MAs, the results show that DOLFBI has a competitive framework for addressing complex optimization problems due to its robust convergence ability compared to other optimization techniques. As a result, DOLFBI is expected to achieve significant success in various optimization challenges, feature selection, and other complex engineering or real-world problems.

Molecular structure, optical, first-order hyper polarizability, electronic properties, reactivity (ELF and LOL) − computational analysis using DFT and Multiwfn for 2, 3-diaminopyridinium selenate

A detailed study on the first principle calculations of 2,3-diaminopyridinium selenite (2,3-DAPS) – an organometallic salt has been performed using B3LYP/6–311++G(d,p). Single crystal X-ray diffraction (XRD) analysis confirms that the crystal formed exhibits a monoclinic crystal structure, specifically belonging to the centrosymmetric space group P21/c. The obtained primitives and interfacial angles are as follows: a = 7.4978(15)Å, b = 7.6681(15) Å, c = 14.314(3) Å, α = γ = 90°, β = 93.75(3)°, and the volume of the unit cell V = 821.2(3) (Å)3. The structure was optimized with a global minimum. The natural bonding orbital charge transfer studies between the cation and anion was performed to gain insights into their electronic interactions. Energy gap and other global chemical reactivity descriptors have been computed with the aid of molecular orbital studies. The influence of solvent on the absorption spectra provided the evidence of solvent–solute interactions and their impact on the electronic transitions within the molecule. The presence of electrophilic and nucleophilic reactivity in the chemical is indicated by the molecular electrostatic potential (MEP) map. From the nonlinear optical (NLO) studies, it has been found that the first-order hyperpolarizability value is 30.771 × 10−31 esu, which is 8.252 times that of urea. This suggests that the compound may be a better non-linear optical material and suitable for laser applications. To calculate the proportion of intermolecular interactions and examine the distribution compound's electrostatic potential, a Hirshfeld surface analysis was conducted. The analysis provided insights into the spatial arrangement of molecules and their interactions. Additionally, topology path calculations elucidated the intrinsic connectivity between critical points, shedding light on the bonding characteristics within the compound. The likelihood of electron density at bonding and anti-bonding sites was also determined using the Electron Localization Function (ELF) and Localised Orbital Locator (LOL) plots. These analyses aided in understanding the electron distribution and the nature of chemical bonding within the compound, providing valuable information about its electronic structure and reactivity.

Inversion of 2D Magnetotelluric (MT) Data with Axial Anisotropy using Adaptive Particle Swarm Optimization (PSO)

In the presence of anisotropic resistivity structures, Magnetotelluric (MT) data inversion based on an isotropic resistivity model will be insufficient. Recent work on anisotropic MT inversions is primarily conducted using gradient-based, deterministic methods which may converge towards local minima and in general, suffer from ill-posedness of the inversion problem. Alternatively, meta-heuristical methods, such as Particle Swarm Optimization (PSO), are able to find the global minima of cost function. At the same time, they are easy to implement and do not require access to the dense Jacobian (and Hessian) matrix as needed by deterministic inversion methods. In this paper we propose PSO inversion for the anisotropic MT inversion problem using an adaptive inertia weights control strategy to balance exploration and exploitation during the PSO search. Higher order differential regularization is introduced with a Gaussian filter, where the conventional first order, Occam-like regularization term is replaced by a variance term. We investigate the performance of the proposed PSO inversion for an isotropic as well as an axial anisotropic synthetic case to demonstrate improvements over an Occam-like regularization. For the COPROD2 benchmark data set, the proposed PSO inversion can not only reproduce the extend of the North American Central Plains (NACP) conductive anomaly, but also to predict an anisotropy ratio of two orders of magnitude, which is in accordance with laboratory findings.

Artificial intelligence warm-start approach: optimizing the generalization capability of QAOA in complex energy landscapes

To address the issue of the quantum approximate optimization algorithm frequently encountering local minima and the cost of parameter optimization within complex non-convex optimization energy landscapes, we consider a warm-start method. This approach leverages the characteristics of transition states in the enhanced optimizer, specifically descending along unique negative curvature directions, to find smaller local minima. Our research results indicate that with the assistance of an enhanced pre-training structure of the AlphaZero AI model, the initialization generalization ability of the new optimizer is significantly enhanced across various test sets. We train on 2-SAT training sets with clause densities between α ≈ 2.6 and α ≈ 2.89, and transfer to more complex test sets. Additionally, the average residual energy density in transfer learning consistently remains below 0.01, even achieving a high transfer success probability of 98% in hard instances with α ≈ 3.7. The search efficiency, pre-trained by ensemble learning, was significantly enhanced, while only requiring simple interpolation of a few transition points to transfer on the global optimal solutions at higher sample clause densities.

Sound absorption model of thin woven fabric with tortuosity effects by equivalent circuit method

The fabric has been widely used as a noise-reduction material. This paper presents a revised equivalent circuit model to simulate the acoustical behavior of woven fabric with backing an air gap, with a special focus on including a tortuosity parameter. The simulated sound absorption of three fabrics with and without the tortuosity parameter was experimentally validated. The equivalent circuit model including the tortuosity parameter predicts the absorption curve better, particularly at the local minima in comparison to the existing models without the tortuosity effects. It is beneficial to the structural design of woven fabric with enhanced sound absorption.

Predictor‐based collision‐free and connectivity‐preserving resilient formation control for multi‐agent systems under sensor deception attacks

AbstractMalicious attack is a potential threat to collision‐free and connectivity‐preserving formation. In this article, a predictor‐based collision‐free and connectivity‐preserving resilient formation control strategy is proposed for a class of multi‐agent systems under sensor deception attacks. The predictor states are constructed to replace original states in the control strategy, and a novel attack compensator is constructed to suppress sensor deception attacks. Prediction errors, instead of compromised errors, are introduced to update weights of radial basis function neural networks (RBFNNs). To achieve collision avoidance and connectivity preservation, a transformation function in logarithmic form is introduced. To avoid static and dynamic obstacles, an improved artificial potential function (APF) combined with their velocity information is constructed. Furthermore, to solve the local minimum problem in the combining of transformation function and APF, a virtual force is added. Based on the Lyapunov function, all closed‐loop signals are bounded and collision‐free and connectivity‐preserving formation is achieved. The simulation related to a group of quadrotors verifies the effectiveness of the proposed resilient control strategy.

ANÁLISIS COMPARATIVO DE METAHEURÍSTICAS DE BASE BIOLÓGICA

This article reviews the metaheuristics published in the literature, emphasizing their usefulness in solving complex optimization problems. The review highlights inspiration's relevance in the metaheuristics design, being the main classification in multiple taxonomies existing in the literature. After reviewing the state of the art, six of the most relevant metaheuristics used to solve problems of various types (engineering, logistics, economics, data science, ...) were selected. This selection of metaheuristics will be subjected to an analysis of their performance using a set of problems selected from different authors. The problems selected for this analysis include problems with a single minimum or multiple minima, different sizes in terms of dimensions, and different types of mathematical functions such as polynomial, trigonometric, or exponential. The analysis offers a discussion of which scenarios are the best for each metaheuristic, analyzing aspects such as the ability of metaheuristics to explore and escape local minima. The article concludes by summarizing which metaheuristic is best for each type of problem. Keywords: Metaheuristics, benchmark, optimization problems, biological-based metaheuristics

Regularizing Scale-Adaptive Central Moment Sharpness for Neural Networks.

In deep learning, finding flat minima of loss function is a hot research topic in improving generalization. The existing methods usually find flat minima by sharpness minimization algorithms. However, these methods suffer from insufficient flexibility for optimization and generalization due to their ignorance of loss value. This article theoretically and experimentally explores the sharpness minimization algorithms for neural networks. First, a novel scale-invariant sharpness which is called scale-adaptive central moment sharpness (SA-CMS) is proposed. This sharpness is not only scale-invariant but can characterize the nature of loss surface clearly. Based on the proposed sharpness, this article further derives a new regularization term by integrating the different orders of the sharpness. Particularly, a host of sharpness minimization functions such as local entropy can be covered by this regularization term. Then the central moment sharpness generating function is introduced as a new objective function. Moreover, theoretical analyses indicate that the new objective function has a smoother landscape and prefer converging to flat local minima. Furthermore, a computationally efficient two-stage algorithm is developed to minimize the objective function. Compared with other algorithms, the two-stage loss-sharpness minimization (TSLSM) algorithm offers a more flexible optimization target for different training stages. On a variety of learning tasks with both small and large batch sizes, this algorithm is more universal and effective, and meanwhile achieves or surpasses the generalization performance of the state-of-the-art sharpness minimization algorithms.

A convex level-set method with multiplicative-additive model for image segmentation

The existing active contour models (ACMs) based on bias field (BF) correction mostly rely on a single BF assumption and lack in-depth discussion on the convexity of the energy functional, often leading to the problem of local minima. To address this issue, this paper introduces a dual BF and proposes a convex level-set (LS) method based on multiplicative-additive (MA) model to achieve global minima. Firstly, a MA model is adopted as the fidelity term, and a kernel function is introduced to adjust the size of the intensity inhomogeneous neighborhood, enhancing the adaptability to intensity inhomogeneity. Then, the convex LS function is embedded in the variational framework to ensure convexity of each variable in the energy functional. This transformation turns the segmentation problem into a convex optimization problem. By introducing the total variation regularization term to smooth the LS function, the model's resistance to noise is effectively enhanced. Finally, by minimizing the proposed energy functional, image segmentation and BF correction are successfully achieved. Experimental results validate the global minima property of our model, while also demonstrating good flexibility in the initial contour. The proposed model achieves superior segmentation results compared to other classical ACMs on various types of images.

Bilinear optimization of protein structure prediction: An exact approach via AB off-lattice model

Protein structure prediction (PSP) remains a central challenge in computational biology due to its inherent complexity and high dimensionality. While numerous heuristic approaches have appeared in the literature, their success varies. The AB off-lattice model, which characterizes proteins as sequences of A (hydrophobic) and B (hydrophilic) beads, presents a simplified perspective on PSP. This work presents a mathematical optimization-based methodology capitalizing on the off-lattice AB model. Dissecting the inherent non-linearities of the energy landscape of protein folding allowed for formulating the PSP as a bilinear optimization problem. This formulation was achieved by introducing auxiliary variables and constraints that encapsulate the nuanced relationship between the protein’s conformational space and its energy landscape. The proposed bilinear model exhibited notable accuracy in pinpointing the global minimum energy conformations on a benchmark dataset presented by the Protein Data Bank (PDB). Compared to traditional heuristic-based methods, this bilinear approach yielded exact solutions, reducing the likelihood of local minima entrapment. This research highlights the potential of reframing the traditionally non-linear protein structure prediction problem into a bilinear optimization problem through the off-lattice AB model. Such a transformation offers a route toward methodologies that can determine the global solution, challenging current PSP paradigms. Exploration into hybrid models, merging bilinear optimization and heuristic components, might present an avenue for balancing accuracy with computational efficiency.

Energetics and electronic structure of Janus WSSe formation by continuous chalcogen substitutions

Abstract We investigated the energetics and the electronic structure of Janus WSSe when formed by continuous sulfurization and selenization of WSe$_2$ and WS$_2$, respectively, using density functional theory combined with the effective screening medium method. The total energy of WS$_{2-x}$Se$_x$ is sensitive to the stoichiometry. The total energy increases monotonically as the substitutional surface selenization of WS$_2$ increases. The sulfurization of WSe$_2$ causes complex energetics with respect to the number of S atoms involved. Competition between the energy cost of polarization and the energy gain through S-W bond formation produces the compound WS$_{0.445}$Se$_{1.445}$, which is a metastable structure that gives the local minimum in the energy landscape. The electronic structures of the partially substituted structures are interpolated smoothly from those of Janus WS$_2$ and WSe$_2$. 

Binary matrix factorization via collaborative neurodynamic optimization

Binary matrix factorization is an important tool for dimension reduction for high-dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

Desingularization of 2D elliptic free-boundary problem with non-autonomous nonlinearity

In this paper, we consider the existence and limiting behaviour of solutions to a semilinear elliptic equation arising from confined plasma problem in dimension two \[ \begin{cases} -\Delta u=\lambda k(x)f(u) & \text{in}\ D,\\ u= c & \displaystyle\text{on}\ \partial D,\\ \displaystyle - \int_{\partial D} \frac{\partial u}{\partial \nu}\,{\rm d}s=I, \end{cases} \] where $D\subseteq \mathbb {R}^2$ is a smooth bounded domain, $\nu$ is the outward unit normal to the boundary $\partial D$ , $\lambda$ and $I$ are given constants and $c$ is an unknown constant. Under some assumptions on $f$ and $k$ , we prove that there exists a family of solutions concentrating near strict local minimum points of $\Gamma (x)=({1}/{2})h(x,\,x)- ({1}/{8\pi })\ln k(x)$ as $\lambda \to +\infty$ . Here $h(x,\,x)$ is the Robin function of $-\Delta$ in $D$ . The prescribed functions $f$ and $k$ can be very general. The result is proved by regarding $k$ as a $measure$ and using the vorticity method, that is, solving a maximization problem for vorticity and analysing the asymptotic behaviour of maximizers. Existence of solutions concentrating near several points is also obtained.

A Two-stage Method for Damage Detection in Z24 Bridge Based on K-nearest Neighbor and Artificial Neural Network

In this paper, we propose an effective approach for identifying damages in the Z24 bridge, a large-scale bridge in Switzerland. The dataset of the Z24 bridge is evaluated as a benchmark, reflecting the behavior of a real structure that has been used for numerous studies. However, most of the previous studies have only addressed the issues of updating the model or estimating the location and severity of damages. The core idea behind our proposed approach is to leverage the strengths of two effective Machine Learning (ML) algorithms: K-Nearest Neighbor (KNN) and Artificial Neural Network (ANN), to assess both the location and severity of damages in the Z24 bridge. First, we employ KNN, an unsupervised learning algorithm, for pinpointing the damage location. This strategy proves highly efficient, significantly reducing computation time by circumventing the need for a loss function during KNN training. By adopting this approach, KNN effectively mitigates the risk of encountering local minima in the ANN optimization process. Subsequently, we deploy ANN to determine the damage severity. When compared to previous studies on the Z24 bridge, our proposed method (KNN-ANN) exhibits promising results. Furthermore, our results illustrate that KNN-ANN consistently outperforms traditional ANN methodologies.