Local Minima Research Articles

Unraveling the Mechanical Response of Short-Chain Branched Amorphous Polyethylene: Insights from Molecular Dynamics Simulations

The deformation behavior of short-chain branched, amorphous polyethylene (PE) was investigated using united atom molecular dynamics (MD) simulations under uniaxial stretching. Our research reported in this paper examined the internal mechanisms underlying the mechanical response of the PE by analyzing potential energies, dihedral angle distributions, chain orientation and entanglements. The findings indicated that the short-chain branching generally enhanced Young’s modulus, except for sample B60 with a critical ethyl branch content of 60/1000 (60 ethyl branches per 1000 backbone carbons). The Young’s modulus of B60 was the local minimum value in the various samples. Analysis of the evolution of dihedral angles shows that the short-chain branching hinders the transition from gauche to trans configurations, leading to a decrease in the trans population as the branch content increases. Regarding the sample B60 with critical branch content 60/1000, the orientation parameter and entanglement parameter of the molecular chains along the backbone were lowest in the initial structure, and the efficiency of chain disentanglement was at its lowest during deformation. The simulation results elucidated the deformation mechanism related to the conformational evolution of the molecular chains, which can provide atomic-scale insights into the mechanical properties and processability of branched polyethylene, thereby allowing for optimization in its design and application.

Development and simulation of two novel indoor odor source localization methods using a modified shark smell optimization algorithm

Aiming to solve the problem of odor source localization (OSL) in the presence of interference sources, this paper presents two methods based on swarm intelligence algorithms. We initially introduced the shark smell optimization (SSO) algorithm and modified it for OSL tasks. Subsequently, mechanisms for collective information sharing and preventing falling into local minima were incorporated, leading to the development of the Improved Shark Smell Optimization (I-SSO) algorithm. We tested both algorithms in a computational fluid dynamics (CFD) simulated environment with a single interference source and compared them to the particle swarm optimization (PSO) algorithm and whale optimization algorithm (WOA). In scenarios with one and two interference sources. The results showed that the I-SSO algorithm outperformed the other three algorithms in both environment settings, demonstrating a higher success rate and superior search distance efficiency.

Characteristic reflection wavefield-based wave equation traveltime inversion

Introducing a high-precision deep-depth velocity model is essential for accurately imaging seismic data in complex areas such as deepwater and deep depth in oil and gas exploration. Conventional methods, such as reflection full-waveform inversion (RFWI), face challenges, notably the cycle-skipping issue, especially when the initial velocity model is far away from the true model. To address this, we develop a novel wave equation traveltime inversion (WETI) using the characteristic reflection wavefield (CRW) to update the low-wavenumber components of the velocity model. The CRWs are primary reflections in seismic data that contribute significantly to velocity model updates. We implement a multistep approach, including migration, characteristic reflector structure (CRS) picking, and demigration to extract the CRW. This extraction, constrained by CRS, ensures accurate matching between the observed and the simulated CRWs, even with an inaccurate initial velocity model, thus enabling an accurate traveltime shift estimation during inversion. Unlike conventional methods that use all reflection data simultaneously, CRW-WETI strategically selects fewer CRWs, enhancing inversion convexity and avoiding local minima from the cycle-skipping problem. This selective inversion begins with a limited number of CRWs to ensure stability and progressively incorporates more as the WETI process advances, eventually transitioning into conventional RFWI. Moreover, with the CRS constraint, CRW can be selected based on the target region. The target-oriented velocity inversion can also be implemented easily to update a local anomalous velocity model. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of our method.

Dynamic Structural Fluxionality in a Planar Tetracoordinate Carbon Cluster Stabilized by Boron Ligands.

The design of boron-based molecular rotors stems from boron-carbon binary clusters containing multiple planar hypercoordinate carbons (phCs, such as C2B8). However, the design of boron-coordinated phCs is challenging due to boron's tendency to occupy hypercoordinate centers more than carbon. Although this challenge has been addressed, the designed clusters of interest have not exhibited dynamic fluxionality similar to that of the initial C2B8. To address this issue, we report a σ/π doubly aromatic CB2H5 + cluster, the first global minimum containing a boron-coordinated planar tetracoordinate carbon atom with dynamic fluxionality. Dynamics simulations show that two ligand H atoms exhibit alternate rotation, resulting in an intriguing dynamic fluxionality in this cluster. Electronic structure analysis reveals the flexible bonding positions of the ligand H atoms because they do not participate in π delocalized bonding nor bond to any other non-carbon atom, highlighting this rotational fluxionality. Unprecedentedly, the fluxional process involves not only the usual conversion of the number of bonding atoms, but also the type of bonding (3c π bonds ↔4c σ bonds), which is an uncommon fluxional mechanism. The cluster represents an effort to apply phC species to molecular machines.

Phase sensitivity of entanglement in the Quantum Phase Estimation algorithm

We study entanglement in the steps before Quantum Fourier Transform (pre-QFT) part of the Quantum Phase Estimation and the Quantum Counting algorithms (QPEA—QCA) with the use of three entanglement detection tools. In particular we focus on the sensitivity of entanglement to the input value (the phase ϕ and the ratio of marked elements MN ) in some basic cases. One starts from numerical observations and deduce some general results in particular regarding the classes of entanglement. More precisely, when the second register of both algorithms (i.e. the register on which a specific unitary operator act, see section ) is initialized in the non-entangled superposition of two (separable) eigenvectors, one proves that the QPEA and QCA curves of entanglement evolution are the same up to a scalar multiplication of the parameter ϕ. One demonstrates that a local minimum is obtained and corresponds to an EPR (Einstein-Podolsky-Rosen) state and finally one proves that, up to Stochastic Local Operation and Classical Communication (SLOCC), all states, except for a few values of ϕ, are equivalent to the product of a separable state and a generalized GHZ (Greenberger-Horen-Zeilinger) state , i.e. GHZn+1=12(00...0+11...1) .

An improved nutcracker optimization algorithm for discrete and continuous optimization problems: Design, comprehensive analysis, and engineering applications

This study is presented to examine the performance of a newly proposed metaheuristic algorithm within discrete and continuous search spaces. Therefore, the multithresholding image segmentation problem and parameter estimation problem of both the proton exchange membrane fuel cell (PEMFC) and photovoltaic (PV) models, which have different search spaces, are used to test and verify this algorithm. The traditional techniques could not find approximate solutions for those problems in a reasonable amount of time, so researchers have used metaheuristic algorithms to overcome those shortcomings. However, the majority of metaheuristic algorithms still suffer from slow convergence speed and stagnation into local minima problems, which makes them unsuitable for tackling these optimization problems. Therefore, this study proposes an improved nutcracker optimization algorithm (INOA) for better solving those problems in an acceptable amount of time. INOA is based on improving the performance of the standard algorithm using a newly proposed convergence improvement strategy that aims to improve the convergence speed and prevent stagnation in local minima. This algorithm is first applied to estimating the unknown parameters of the single-diode, double-diode, and triple-diode models for a PV module and a solar cell. Second, four PEMFC modules are used to further observe INOA's performance for the continuous optimization challenge. Finally, the performance of INOA is investigated for solving the multi-thresholding image segmentation problem to test its effectiveness in a discrete search space. Several test images with different threshold levels were used to validate its effectiveness, stability, and scalability. Comparison to several rival optimizers using various performance indicators, such as convergence curve, standard deviation, average fitness value, and Wilcoxon rank-sum test, demonstrates that INOA is an effective alternative for solving both discrete and continuous optimization problems. Quantitively, INOA could solve those problems better than the other rival optimizers, with improvement rates for final results ranging between 0.8355 % and 3.34 % for discrete problems and 4.97 % and 99.9 % for continuous problems.

Existence, concentration and multiplicity of solutions for (p,N)-Laplacian equations with convolution term

In this paper, we concern some qualitative properties of the following [Formula: see text]-Laplacian equations with convolution term: [Formula: see text] where [Formula: see text] is a positive parameter, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] satisfies the critical exponential growth. By using the variational methods and the penalization method, we prove the existence of solutions for the above equations which concentrates at a local minimum of [Formula: see text] in the semi-classical limit as [Formula: see text]. Moreover, we obtain the multiplicity of solutions for the above equations by the Morse theory.

Safe path planning of mobile robot based on improved particle swarm optimization

Path planning is a fundamental aspect of mobile robot navigation, playing a crucial role in enabling robots to autonomously navigate while avoiding obstacles. Nevertheless, traditional path planning algorithms face navigation challenges, including obstacle avoidance and the potential for getting stuck in local minima or deadlocks along the path. To tackle these challenges, the study proposes an enhanced path planning method based on control barrier function (CBF). This approach introduces a safety velocity adjustment mechanism based on CBF and combines it with the particle swarm optimization (PSO), adjusting the safe speed in global planning and addressing the issue of local minima. Experimental simulations are conducted to validate the flexibility and global optimization performance of the proposed path planning method across various obstacle scenarios.

Minimum wage and internal labor migration: Evidence from China

We study the geographical allocation consequences of minimum wage, using individual-level migration data and the substantial variation over time in minimum wages across 262 counties in China. Our preferred specification shows that a 10% increase in the local minimum wage decreases the probability of outmigration by 1.52 percentage points. Using data from a major online recruitment platform, we further corroborate the main finding by showing that workers are less likely to search for a job in other cities when their city of residence experiences an increase in minimum wage.

Energetics and spectroscopic studies of clusters and the temperature dependencies of the isomers: An approach based on a combined recipe of parallel tempering and quantum chemical methods.

A system associated with several number of weak interactions supports numerous number of stable structures within a narrow range of energy. Often, a deterministic search method fails to locate the global minimum geometry as well as important local minimum isomers for such systems. Therefore, in this work, the stochastic search technique, namely parallel tempering, has been executed on the quantum chemical surface of the system for -8 to generate global minimum as well as several number of local minimum isomers. IR spectrum can act as the fingerprint property for such system to be identified. Thus, IR spectroscopic features have also been included in this work. Vertical detachment energy has also been calculated to obtain clear information about number of water molecules in several spheres around the central anion. In addition, in a real experimental scenario, not only the global but also the local minimum isomers play an important role in determining the average value of a particular physically observable property. Therefore, the relative conformational populations have been determined for all the evaluated structures for the temperature range between 20K and 400K. Further to understand the phase change behavior, the configurational heat capacities have also been calculated for different sizes.

Self-learning Markov prediction algorithm based aging-oriented gradient drop power control strategy for the transient modes of fuel cell hybrid electric vehicles

The power transients caused by switching from drive mode to brake mode in fuel cell hybrid electric vehicles (FCHEV) can result in significant degradation cost losses to the fuel cell. To address this issue, this study proposes a self-learning Markov prediction algorithm based aging-oriented gradient drop power control strategy. First, a real-time self-learning Markov predictor (SLMP) based on the traditional offline training Markov improvement is designed to predict the demand power and combined with the sequential quadratic programming (SQP) optimization algorithm to solve for the inner optimal demand power based on its global cost function minimization characteristic. On this basis, the fuel cell gradient drop power (FGDP) strategy is proposed to optimize the operating state of the vehicle powertrain under vehicle mode switching. This involves establishing a power gradient drop step based on considering the fuel cell hydrogen consumption cost and its lifetime degradation cost to further obtain the outer fuel cell demand power at the optimal step. And three execution modes are designed to trigger the FGDP strategy. Finally, by combining the above efforts, the SLMP-FGDP optimization control strategy is constructed. The numerical verification and hardware in loop experiments results show that the proposed improved SLMP can predict the vehicle demand power more accurately. Compared with the non-FGDP system, the SLMP-FGDP strategy can effectively near-eliminate the fuel cell power transient due to any braking scenario, thus effectively controlling the fuel cell lifetime degradation cost in a lower range and realizing a reduction of up to 52.21% of the fuel cell usage costs without significantly sacrificing the hydrogen fuel economy.

Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: A Way Out of Multiple Minima and Symmetry Breaking.

The Perdew-Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, the PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which the PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al. J. Chem. Theory Comput. 2016, 12, 3195]. The PZ-SIC is often implemented with Fermi-Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al. J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of the PZ-SIC─the ensemble PZ-SIC (E-PZ-SIC) method─which shares the asymptotic computational scaling of the PZ-SIC (albeit with an additional prefactor). The E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of the E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of the FLO-SIC. We show that the E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of the PZ-SIC and its FLO-SIC versions.

Hydrophobic Residues Promote Interfacial Activation of Candida rugosa Lipase: A Study of Rotational Dynamics.

Microbial lipases constitute a class of biocatalysts with the ability to cleave ester linkages of long-chain triglycerides. This property makes them particularly attractive for industrial applications ranging from food processing to pharmaceutical preparation. Among such enzymes, Candida rugosa lipase (CRL) is one of the most frequently used in biotransformation. A notable feature of CRL, among many lipases, is its propensity for interfacial activation: these enzymes exhibit elevated catalytic rates when acting at the interface between aqueous and hydrophobic phases. Notably, this phenomenon can be attributed to the presence of a mobile lid domain, which in its closed state occludes the enzyme active site. To advance our understanding of interfacial activation, we explore the dynamics of CRL rotation at the octane-water interface in this work. To do so, we employ molecular dynamics and umbrella sampling to evaluate the free energy of rotation of the enzyme at the interface. We identify a global minimum in the rotational landscape that coincides with lid opening at the interface. Additionally, we investigate the role of surface residues outside the lid domain as they serve to instigate rotation of the lid toward the aqueous phase. In doing so, we identify a patch of leucine residues which when mutated to glycine impose a barrier to rotation that maintains the enzyme in the inactive (closed lid) state on the order of 1 μs. Importantly, this study presents a novel quantification of the rotational free energy corresponding to CRL lid opening at the octane-water interface. The accompanying mutagenesis study likewise clarifies the role of hydrophobic surface residues in the transition. As such, this work provides valuable insight into the phenomenon of interfacial activation that might open up new avenues for manipulating the microenvironment of industrially relevant lipases, affording enhanced control over the enzyme state.

Horizontal rearrangement frequency domain chirplet transform: algorithm and applications

Abstract Based on the idea of optimal time–frequency analysis (TFA) theory, a time–frequency post-processing method called horizontal rearrangement frequency domain chirplet transform (HRFCT) is proposed. The proposed method is designed to analyze non-stationary transient signals with nonlinear group delay (GD), aiming at obtaining energy-concentrated and accurate time–frequency representation (TFR). First, based on the image characteristics of the constructed amplitude function, the selection criteria of GD are defined, that is, the local maximum of amplitude function and the local minimum of absolute value of derivative of amplitude function are calculated. Next, according to the calculated GD, the coefficients on the GD trajectory are adaptively extracted, and the coefficients that cause the TFR to be blurred are discarded. Finally, the analysis result of a two-component simulation signal demonstrates the satisfactory performance of the HRFCT, and compared with four advanced TFA methods, the competitiveness of the HRFCT is verified. Additionally, the application of the HRFCT in the processing of constant and variable speed bearing signals highlights its prospects in transient signal analysis and rotating machinery condition monitoring.

A class of one-parameter filled functions with the same local minima as the objective function for global optimization problems

As an effective global optimization method, the filled function algorithm obtains the optimal solution of optimization problems by alternately minimizing the objective function and filled function. One development direction of the filled function method is to construct the filled function with good properties, which directly affects the efficiency of the algorithm and has attracted the attention of scholars. This paper presents a class of one-parameter filled function that is easy to adjust. It is proved theoretically that the filled function is continuously differentiable and has the same local minimizers as the objective function, and these minimizers are all better than the current local minimizer of the objective function. Meanwhile, some natures of the constructed filled function are conducted as followed by a new algorithm is presented. The new filled function algorithm optimizes the iterative framework of the conventional filled function method, improving the efficiency and decreasing the computational cost. The numerical experiments of the new algorithm on several optimization issues are reported with satisfactory computational results, verifying the feasibility and efficiency of the algorithm.

Tabular and Deep Learning for the Whittle Index

The Whittle index policy is a heuristic that has shown remarkably good performance (with guaranteed asymptotic optimality) when applied to the class of problems known as Restless Multi-Armed Bandit Problems (RMABPs). In this article, we present QWI and QWINN, two reinforcement learning algorithms, respectively tabular and deep, to learn the Whittle index for the total discounted criterion. The key feature is the use of two time-scales, a faster one to update the state-action Q -values, and a relatively slower one to update the Whittle indices. In our main theoretical result, we show that QWI, which is a tabular implementation, converges to the real Whittle indices. We then present QWINN, an adaptation of QWI algorithm using neural networks to compute the Q -values on the faster time-scale, which is able to extrapolate information from one state to another and scales naturally to large state-space environments. For QWINN, we show that all local minima of the Bellman error are locally stable equilibria, which is the first result of its kind for DQN-based schemes. Numerical computations show that QWI and QWINN converge faster than the standard Q -learning algorithm, neural-network based approximate Q-learning, and other state-of-the-art algorithms.

GPU accelerated sparse curvelet-constrained wavefield reconstruction inversion with source estimation: Application to Chevron Benchmark 2014 blind test data set

Full-waveform inversion (FWI) is a pivotal tool in seismic exploration and seismology but encounters a persistent challenge known as “cycle-skipping,” causing it to frequently converge to local minima. Wavefield reconstruction inversion (WRI) has emerged as a potential solution to mitigate the risk of cycle skipping. Researchers have provided numerical examples indicating that WRI is less prone to being ensnared in local minima caused by the absence of low-frequency component data and the absence of a well-defined initial model compared with conventional FWI. Despite its potential, the computational demands of WRI have hindered its widespread application, especially in scenarios involving ocean towed streamer seismic acquisition and unknown sources, where the augmented systems differ from source to source. In our study, we introduce a novel approach — sparse curvelet-constrained WRI with source estimation (WRI-SE-CC) — accelerated by graphics processing unit (GPU). Real-time source function estimation is achieved through the variable projection method, and noise-related artifacts are suppressed using sparse curvelet constraints. By optimizing the utilization of hundreds of computation processors within a GPU for parallel computing of matrix-vector multiplications, we present a GPU-based grouped conjugate gradient method to accelerate the computation of WRI-SE-CC. Numerical experiments demonstrate a significant 240-fold acceleration compared with the preconditioned conjugate gradient using one CPU core for computations involving multiple sources. Inversion experiments with the overthrust model demonstrate the capability of our method in mitigating local minima and suppressing noise-related artifacts. Furthermore, we validate the framework on the Chevron 2014 blind test data set, showcasing its effectiveness in addressing practical challenges in the field.

Cl©Li5Cl5-: A Star-like Superhalogen Anion Featuring a Planar Pentacoordinate Chlorine at the Center.

Among the known planar pentacoordinate atoms, chlorine is missing due to its large radius and high electronegativity. Herein, we report the first star-like superhalogen anion D5h Cl©Li5Cl5- (1), which contains a planar pentacoordinate chlorine (ppCl) at the center. Computer structural searches and high-level calculations reveal that 1 is a true global minimum (GM) on the potential energy surfaces. Molecular dynamics simulations indicate it is kinetically stable against isomerization or decomposition. Although detailed chemical bonding analyses reveal one delocalized 6c-2e σ bond over the Cl©Li5 central unit and five delocalized 3c-2e σ bonds along the periphery, while aromaticity has very little beneficial effect on stability, instead, ionic interaction dominates the stability of the system. More encouragingly, with the large HOMO-LUMO energy gap of 7.66 eV and vertical detachment energy of 7.87 eV, the highly chemically inert 1 can be viewed as a typical superhalogen anion and is possible to be synthesized and characterized in future experiments.

A two-phase sequential algorithm for global optimization of the standard quadratic programming problem

AbstractWe introduce a new sequential algorithm for the Standard Quadratic Programming Problem (StQP), which exploits a formulation of StQP as a Linear Program with Linear Complementarity Constraints (LPLCC). The algorithm is finite and guarantees at least in theory a $$\delta $$ δ -approximate global minimum for an arbitrary small $$\delta $$ δ , which is a global minimum in practice. The sequential algorithm has two phases. In Phase 1, Stationary Points (SP) with strictly decreasing objective function values are computed. Phase 2 is designed for giving a certificate of global optimality for the last SP computed in Phase 1. Two different Nonlinear Programming Formulations for LPLCC are proposed for each one of these phases, which are solved by efficient enumerative algorithms. New procedures for computing a lower bound for StQP are also proposed, which are easy to implement and give tight bounds in general. Computational experiments with a number of test problems from known sources indicate that the two-phase sequential algorithm is, in general, efficient in practice. Furthermore, the algorithm seems to be an efficient way to study the copositivity of a matrix by exploiting an StQP with this matrix.

Improved Osprey Optimization Algorithm Based on Two-Color Complementary Mechanism for Global Optimization and Engineering Problems.

Aiming at the problem that the Osprey Optimization Algorithm (OOA) does not have high optimization accuracy and is prone to falling into local optimum, an Improved Osprey Optimization Algorithm Based on a Two-Color Complementary Mechanism for Global Optimization (IOOA) is proposed. The core of the IOOA algorithm lies in its unique two-color complementary mechanism, which significantly improves the algorithm's global search capability and optimization performance. Firstly, in the initialization stage, the population is created by combining logistic chaos mapping and the good point set method, and the population is divided into four different color groups by drawing on the four-color theory to enhance the population diversity. Secondly, a two-color complementary mechanism is introduced, where the blue population maintains the OOA core exploration strategy to ensure the stability and efficiency of the algorithm; the red population incorporates the Harris Hawk heuristic strategy in the development phase to strengthen the ability of local minima avoidance; the green group adopts the strolling and wandering strategy in the searching phase to add stochasticity and maintain the diversity; and the orange population implements the optimized spiral search and firefly perturbation strategies to deepen the exploration and effectively perturb the local optimums, respectively, to improve the overall population diversity, effectively perturbing the local optimum to improve the performance of the algorithm and the exploration ability of the solution space as a whole. Finally, to validate the performance of IOOA, classical benchmark functions and CEC2020 and CEC2022 test sets are selected for simulation, and ANOVA is used, as well as Wilcoxon and Friedman tests. The results show that IOOA significantly improves convergence accuracy and speed and demonstrates high practical value and advantages in engineering optimization applications.