Local Minima Research Articles

A Divide-and-Conquer Approach to Nanoparticle Global Optimisation Using Machine Learning.

Global optimization of the structure of atomic nanoparticles is often hampered by the presence of many funnels on the potential energy surface. While broad funnels are readily encountered and easily exploited by the search, narrow funnels are more difficult to locate and explore, presenting a problem if the global minimum is situated in such a funnel. Here, a divide-and-conquer approach is applied to overcome the issue posed by the multifunnel effect using a machine learning approach, without using a priori knowledge of the potential energy surface. This approach begins with a truncated exploration to gather coarse-grained knowledge of the potential energy surface. This is then used to train a machine learning Gaussian mixture model to divide up the potential energy surface into separate regions, with each region then being explored in more detail (or conquered) separately. This scheme was tested on a variety of multifunnel systems and yielded significant improvements to the times taken to locate the global minima of Lennard-Jones (LJ) nanoparticles, LJ75 and LJ104, as well as two metallic systems, Au55 and Pd88. However, difficulties were encountered for LJ98, providing insight into how the scheme could be further improved.

Impact localization of CFRP laminate based on FBG sensing and GWO-BP neural network

Carbon fiber reinforced plastic (CFRP) structures are susceptible to external energy impact during service, resulting in invisible damage. Therefore, accurate localization of these impact sites is crucial for the maintenance and safety of CFRP structures. In this paper, the strain data of the impact response of the CFRP laminate is obtained by using the fiber grating (FBG) sensor, and the data are mapped to the impact location by BP neural network. However, the traditional BP neural network is susceptible to local minima and slow convergence speed. Therefore, Grey Wolf optimization algorithm (GWO) is introduced in this study to optimize the BP neural network, which improves the convergence speed and positioning accuracy of the model. The experimental results show that the GWO-BP neural network model has excellent performance in impact positioning, with the maximum positioning error of 17.01 mm and the average positioning error of 13.05 mm. Compared with other machine learning methods, it has higher accuracy and efficiency.

INNV-11. DELIVERY OF TTFIELDS TO THE INFRATENTORIAL BRAIN USING HFE ARRAYS

Abstract INTRODUCTION Tumor Treating Fields (TTFields) therapy is a noninvasive, locoregional treatment comprising alternating electric fields delivered to the tumor via two pairs of skin-placed transducer arrays. TTFields physically disrupt cancer cell viability through a multimodal mechanism that includes antimitotic and antitumor immune effects. TTFields therapy is FDA-approved for glioblastoma (GBM) and CE marked for WHO grade 4 glioma. While clinically approved array layouts for GBM target supratentorial tumors, TTFields distribution depends on the arrays’ locations and dedicated layouts are needed to target infratentorial tumors. To increase patient comfort, Novocure developed HFE arrays that are thinner and lighter than existing INE arrays. Here, we evaluate innovative HFE array layouts for TTFields delivery to infratentorial tumors at therapeutic intensities (~1 V/cm). METHODS TTFields delivery was simulated using Sim4Life v6.2 in a male computational model. 32 layouts of HFE arrays were placed on the model’s scalp, neck, and scapulae, with one placed at a standard cerebral location. Local Average Field Intensity (LAFI) and Local Minimum Power Density (LMiPD) were calculated in the cerebrum, cerebellum and brainstem. RESULTS Standard cerebral layout provided LAFI of 2.47 V/cm to the cerebrum, while providing 1.50 and 1.10 V/cm to the cerebellum and brainstem, respectively (LMiPD 2.22, 1.34 and 0.64 mW/cm3). Layouts comprising arrays on the scapulae (right and left) paired in cross configuration with arrays on either the temples or forehead, provided LAFI of 1.87-2.17 V/cm (LMiPD 1.05-2.20 mW/cm3) to the cerebrum, while providing 1.64-2.13 V/cm (LMiPD 1.77-2.26 mW/cm3) to the cerebellum and 1.74-1.89 V/cm (LMiPD 2.28-2.89 mW/cm3) to the brainstem. CONCLUSION Lower array placement provides higher levels of field intensity in the cerebellum and brainstem versus standard cerebral layout, while still providing adequate field intensity to the cerebrum. This simulation-based study suggests feasibility of delivering therapeutic TTFields intensities to infratentorial tumors using dedicated HFE array layouts.

Bad Local Minima Exist in the Stochastic Block Model

AbstractWe study the disassortative stochastic block model with three communities, a well-studied model of graph partitioning and Bayesian inference for which detailed predictions based on the cavity method exist (Decelle et al. in Phys Rev E 84:066106, 2011). We provide strong evidence that for a part of the phase where efficient algorithms exist that approximately reconstruct the communities, inference based on maximum a posteriori (MAP) fails. In other words, we show that there exist modes of the posterior distribution that have a vanishing agreement with the ground truth. The proof is based on the analysis of a graph colouring algorithm from Achlioptas and Moore (J Comput Syst Sci 67:441–471, 2003).

Mean-Field-Type Transformers

In this article, we present the mathematical foundations of generative machine intelligence and link them with mean-field-type game theory. The key interaction mechanism is self-attention, which exhibits aggregative properties similar to those found in mean-field-type game theory. It is not necessary to have an infinite number of neural units to handle mean-field-type terms. For instance, the variance reduction in error within generative machine intelligence is a mean-field-type problem and does not involve an infinite number of decision-makers. Based on this insight, we construct mean-field-type transformers that operate on data that are not necessarily identically distributed and evolve over several layers using mean-field-type transition kernels. We demonstrate that the outcomes of these mean-field-type transformers correspond exactly to the mean-field-type equilibria of a hierarchical mean-field-type game. Due to the non-convexity of the operators’ composition, gradient-based methods alone are insufficient. To distinguish a global minimum from other extrema—such as local minima, local maxima, global maxima, and saddle points—alternative methods that exploit hidden convexities of anti-derivatives of activation functions are required. We also discuss the integration of blockchain technologies into machine intelligence, facilitating an incentive design loop for all contributors and enabling blockchain token economics for each system participant. This feature is especially relevant to ensuring the integrity of factual data, legislative information, medical records, and scientifically published references that should remain immutable after the application of generative machine intelligence.

UN Tax Pillars to Address Capital Concentration (through Inheritance Levies) and Wealth Flight (through Exit Taxes) – Implications for the European Union

The article investigates the rising concentration of capital ownership, drawing evidence from the United States, Germany and other European states, and its impact on widening wealth inequality. It warns of modern economies morphing into an “inheritocracy”, where corporate equity and financial assets concentrate across generations. The analysis sheds light on the limitations of income tax systems in addressing wealth inequality in the context of high capital mobility. To tackle these challenges and building on the OECD’s experience with a global minimum tax for large corporations, the article advocates for a UN-led multilateral approach supporting Global Minimum Inheritance Taxes and a Global Minimum Exit Tax to prevent a race to the bottom in taxing high-net-worth individuals and deter wealth flight. By coordinating these taxes at a supranational level, the article supports a fairer tax burden distribution and emphasizes the revenue potential of inheritance levies. Additionally, drawing from the US Expatriation Tax, it explores the legal feasibility of the European Union harmonizing an EU-wide exit tax to mitigate capital flight. Ultimately, these measures have the potential to enhance progressivity across tax systems.

Revisiting the global minimum of Au10 clusters.

This study employs high-level quantum chemical calculations to determine the global minimum structure of Au10 clusters definitively. Contrary to previous reports, coupled-cluster singles and doubles with perturbative triples [CCSD(T)] calculations with sizable quadruple-ζ basis sets incorporating the spin-orbit (SO) effect reveal that the planar 10.b structure is the true global minimum for Au10, not the three-dimensional 10.a structure. Two-component spin-orbit density functional theory calculations demonstrate that the SO effect is minimal for most Au10 isomers, except for the 10.f structure. A straightforward diagnostic tool is proposed for identifying Au cluster structures with strong spin-orbit coupling based on 6p orbital occupation. The calculated IR spectra based on Boltzmann averaging the six Au10 isomers show good agreement with recent experimental spectra although minor discrepancies are noted potentially due to interactions with Kr. The results suggest that the transition point to non-planar global minimum structures for Au clusters lies beyond Au10 but is nearby.

OnionVQE optimization strategy for ground state preparation on NISQ devices

Abstract The Variational Quantum Eigensolver (VQE) is one of the most promising and widely used algorithms for exploiting the capabilities of current Noisy Intermediate-Scale Quantum (NISQ) devices. However, VQE algorithms suffer from a plethora of issues, such as barren plateaus, local minima, quantum hardware noise, and limited qubit connectivity, thus posing challenges for their successful deployment on hardware and simulators. In this work, we propose a VQE optimization strategy that builds upon recent advances in the literature, and exhibits very shallow circuit depths when applied to the specific system of interest, namely a model Hamiltonian representing a cuprate superconductor. These features make our approach a favorable candidate for generating good ground state approximations on current NISQ devices. Our findings illustrate the potential of VQE algorithmic development for leveraging the full capabilities of NISQ devices.

Soft Actor-Critic Approach to Self-Adaptive Particle Swarm Optimisation

Particle swarm optimisation (PSO) is a swarm intelligence algorithm that finds candidate solutions by iteratively updating the positions of particles in a swarm. The decentralised optimisation methodology of PSO is ideally suited to problems with multiple local minima and deceptive fitness landscapes, where traditional gradient-based algorithms fail. PSO performance depends on the use of a suitable control parameter (CP) configuration, which governs the trade-off between exploration and exploitation in the swarm. CPs that ensure good performance are problem-dependent. Unfortunately, CPs tuning is computationally expensive and inefficient. Self-adaptive particle swarm optimisation (SAPSO) algorithms aim to adaptively adjust CPs during the optimisation process to improve performance, ideally while reducing the number of performance-sensitive parameters. This paper proposes a reinforcement learning (RL) approach to SAPSO by utilising a velocity-clamped soft actor-critic (SAC) that autonomously adapts the PSO CPs. The proposed SAC-SAPSO obtains a 50% to 80% improvement in solution quality compared to various baselines, has either one or zero runtime parameters, is time-invariant, and does not result in divergent particles.

Improved intelligent model predictive controller for the nuclear power reactor system

Abstract Over the last two decades, extensive research has been conducted to enhance the control performance of reactor power. Various methodologies have been suggested and implemented to achieve optimal power control in nuclear reactors. However, due to the diverse characteristics and inherent uncertainties in the models, devising optimal controllers for nuclear systems remains a complex task. To address this, numerous approaches have been adopted to ensure controllability and resilience, aiming for an optimal nuclear power reactor controller. The Model Predictive Control (MPC) algorithm has garnered significant attention as a viable approach to boost operational efficiency and overall system utility. In this research, Particle Swarm Optimization (PSO) method and MPC controller are combined together to form a novel algorithm termed PSO-MPC, aiming to amplify the system’s performance and overcomes the local minima problem that basically happens when using MPC controller. First, MPC controller is applied to the nuclear reactor model, then the suggested technique PSO-MPC also is applied to the system and a comparison of the outcomes using both techniques is done. The results demonstrate enhanced system response using the innovative technique.

Curing monitoring of adhesive layers between metal adherends by ultrasonic resonance technique

Abstract Layer resonance induced by ultrasonic wave incidence is applied to monitor the viscoelastic properties of a curing adhesive layer between metal plates. The theoretical analysis shows that when the adhesive layer is modeled as a linear viscoelastic material, the ultrasonic reflection spectrum takes local minima at the layer resonance frequencies depending on the wave velocity of the adhesive. On the other hand, the local minima of the reflection spectrum can be expressed as a function of the loss factor of the adhesive. Based on these results, a characterization technique for the wave velocity and the loss factor of a curing adhesive layer is proposed. This technique enables the evaluation of the viscoelastic properties even if the reflected waves from both faces of a bond layer cannot be separated. The proposed method is employed to investigate the curing behavior of bi-component epoxy adhesives. As a result, it is shown that the bonding condition affects the variation of the wave velocity and loss factor. The estimated wave velocity increases as the curing proceeds, while the loss factor sometimes takes a local maximum depending on the bonding condition and the frequency range. When the mixing ratio of the main and curing agents is imbalanced, the variation of the wave velocity becomes gradual. Furthermore, the increase in the curing temperature leads to fast changes in the wave velocity and loss factor. The proposed technique has the potential to provide insight into the curing behavior of the adhesive layer by incorporating it into other measurement methods and theories.

Two-Positron-bonded Dihalides: Ps2XY (X, Y=F, Cl, Br).

This study explores the energetic stability and physical properties of complexes formed by two halide anions (X-, Y-=F-, X-, Br-), and two positrons (Ps: positron-electron pair). We combine electronic coupled cluster (CCSD(T)) calculations with positronic multicomponent renormalized partial third-order propagator (MC-REN-PP3) calculations to effectively recover correlation energies. Analysis of potential energy curves confirms the energetic stability of these positronic molecules, with optimized structures identified as global minima. Further investigation of electron and positron densities reveals stabilization owing to the formation of two-positron bonds. The global stability of the complexes contrasts with the metastable two-positron-bonded (PsH)2, which energetically favors the emission of Ps2. Comparative analysis of one- and two-positron dihalides indicates that the addition of a positron to PsXY- generally results in shorter bond distances, higher force constants, and lower dissociation energies, with exceptions due to differences in positron affinities of PsXY- and Y-. We explore the analogy between two-positron-bonded dihalide systems and two-electron-bonded dialkali molecules AB, (A, B=Na, K, Rb). The bonding properties in two-positron dihalides and their electronic dialkali analogs are comparable, displaying identical periodic trends. However, compared to their isoelectronic AB counterparts, the positron bonds in have shorter bond lengths, higher force constants, and higher bond energies.

Structure Prediction and Mechanical Properties of Tantalum Carbide (TaC) on ab initio Level

AbstractTantalum carbide (TaC) is an extremely hard, brittle, refractory ceramic material with excellent physical properties, which makes it a desirable material in e. g. aerospace industries. In order to explore the range of feasible modifications of TaC, we have executed a crystal structure prediction study of the TaC chemical system using a multi‐methodological approach, via enthalpy landscape explorations of pristine TaC at different pressures, supplemented by data mining searches in the ICSD database. Local structure relaxations have been accomplished by using Density Functional Theory (DFT). The global minimum is found to correspond to the equilibrium rock salt (NaCl) type modification. Additionally, eight new phases of tantalum carbide are predicted to be feasible: the WC‐type, the NiAs‐type, the 5‐5‐type, the ZnS‐type, the RingTaC‐type, the CsCl‐type, the OrthoTaC‐type, and the TetraTaC‐type. Furthermore, the elastic and mechanical properties of the predicted TaC modifications were explored on the DFT level of computation. The promising values of some of the mechanical properties of the proposed tantalum carbide modifications suggest that various scientific, industrial, and technological applications of TaC should be possible.

Application of the Gray Wolf Optimization Algorithm and Neural Networks for Solving Discrete Problems

Relevance. In recent decades, metaheuristic optimization methods have become popular for solving complex problems that require searching for global extrema. Algorithms such as genetic algorithm (GA), ant colony optimization (ACO), particle swarm optimization (PSO), as well as more modern approaches such as cat pack optimization (CSO) and gray wolf pack optimization (GWO) demonstrate high efficiency, but their application is often limited by the conditions of continuity and differentiability of the objective functions. This is a challenge when solving problems with discrete data, where such requirements are not met. In this context, the search for methods that allow adapting metaheuristic algorithms to work with discrete functions is of particular relevance.Aim. The study is aimed at testing the hypothesis about the possibility of using a neural network trained on a limited set of discrete data as an approximation of a function sufficient for the correct execution of the GWO algorithm when searching for a global minimum. The implementation of this hypothesis can significantly expand the scope of GWO, making it available for a wider range of problems where functions are defined on discrete sets.Methods. The study is based on the analysis of existing approaches and experimental verification of the hypothesis on two test functions: a linear function and a Booth function, which are widely used as standards for evaluating the performance of optimization algorithms. Numerical experiments were conducted using neural networks as an approximating model to obtain the results. Solution. During the experiments, an analysis of the applicability of neural networks for approximating discrete functions was carried out, which showed the success of this approach. It was found that neural networks can approximate discrete functions with high accuracy, creating conditions for a successful search for a global minimum using the GWO algorithm.Novelty. For the first time, a hypothesis was proposed and tested on the use of neural networks for approximating objective functions in metaheuristic optimization problems on discrete data. This direction has not previously received due coverage in the scientific literature, which adds significance to the obtained results and confirms the effectiveness of the proposed approach.Practical significance. The results of the study open up new prospects for the application of algorithms such as GWO in optimization problems based on discrete data, expanding the capabilities of metaheuristic methods and facilitating their implementation in a wider class of applied problems, including problems where the use of other methods is limited.

Nuclear norm regularized loop optimization for tensor network

We propose a loop optimization algorithm based on nuclear norm regularization for the tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to the standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, ] for the critical two-dimensional Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion. Published by the American Physical Society 2024

Artificial intelligence-based optimization techniques for optimal reactive power dispatch problem: a contemporary survey, experiments, and analysis

The optimization challenge known as the optimal reactive power dispatch (ORPD) problem is of utmost importance in the electric power system owing to its substantial impact on stability, cost-effectiveness, and security. Several metaheuristic algorithms have been developed to address this challenge, but they all suffer from either being stuck in local minima, having an insufficiently fast convergence rate, or having a prohibitively high computational cost. Therefore, in this study, the performance of four recently published metaheuristic algorithms, namely the mantis search algorithm (MSA), spider wasp optimizer (SWO), nutcracker optimization algorithm (NOA), and artificial gorilla optimizer (GTO), is assessed to solve this problem with the purpose of minimizing power losses and voltage deviation. These algorithms were chosen due to the robustness of their local optimality avoidance and convergence speed acceleration mechanisms. In addition, a modified variant of NOA, known as MNOA, is herein proposed to further improve its performance. This modified variant does not combine the information of the newly generated solution with the current solution to avoid falling into local minima and accelerate the convergence speed. However, MNOA still needs further improvement to strengthen its performance for large-scale problems, so it is integrated with a newly proposed improvement mechanism to promote its exploration and exploitation operators; this hybrid variant was called HNOA. These proposed algorithms are used to estimate potential solutions to the ORPD problem in small-scale, medium-scale, and large-scale systems and are being tested and validated on the IEEE 14-bus, IEEE 39-bus, IEEE 57-bus, IEEE 118-bus, and IEEE 300-bus electrical power systems. In comparison to eight rival optimizers, HNOA is superior for large-scale systems (IEEE 118-bus and 300-bus systems) at optimizing power losses and voltage deviation; MNOA performs better for medium-scale systems (IEEE 57-bus); and MSA excels for small-scale systems (IEEE 14-bus and 39-bus systems).

Planar Pentacoordinate Halogens

Planar hypercoordinate motifs represent an intriguing frontier in chemistry, challenging traditional bonding norms. As electronegativity of the central atom increases, achieving planar hypercoordination becomes more difficult due to restricted delocalization, making the design of planar hypercoordinate halogens particularly puzzling. Here, we conduct an extensive computational survey of LinXn+1– (n = 4, 5, 6; X = F, Cl, Br, I) clusters, revealing a starlike D5h‐symmetry global minimum in Li5X6– (X = F, Cl, Br) with a planar pentacoordinate halogen (ppX), where X– is located at the center of Li5X5 crown. The clusters are stabilized predominantly through electrostatic interactions between X– and Li5X5, complemented by weak covalent bonding from dative interaction. Due to the weak orbital overlap, ppX clusters exhibit localized diatropic ring currents around X and Li.

Less is more: adjusting convergence of Cooper’s algorithm in the continuous location-allocation problem

This paper proposes a variant of the well-known heuristic by Cooper for continuous location-allocation problems in general, and in particular, the continuous p-median problem. This algorithm alternates between a location phase where the allocations are fixed and an allocation phase where the locations of the p new facilities are fixed. The main idea of the proposed variant is to partially solve the p independent one-median problems in the location phase (instead of solving optimally) in order to induce a larger number of cycles of location-allocation. In effect, we are trying to alter the descent path of the algorithm by slowing the convergence rate using smaller descent steps in the location phase. Computational experiments show that this approach is highly effective in finding alternate descent paths that lead to “deeper” local minima. The best improvements are obtained with random starting locations of the p facilities, and the larger values of p that were tested.

Phase transitions of ice VIII-VII-X: A potential energy landscape perspective

Water ice, an archetypal molecular system, exhibits a complex phase diagram characterized by numerous phase transitions under varying pressure-temperature conditions. However, it remains a significant challenge to theoretical modeling of these transitions owing to the high dimensionality in representing the potential energy landscapes (PEL) of ice crystalline phases. In an attempt to deeply understand the mechanisms of phase transitions between ice VII, VIII, and X, a graph-based stationary-point network was employed to simplify the representation of the PEL and locally constructed the PEL of ice at different pressures by our developed high-index saddle dynamic scheme. The stationary-point networks at 40 and 80 GPa indicate a pronounced flattened PEL of ice over a wide range of pressure (up to at least 80 GPa), where multiple structures (i.e., local minima) are energetically degenerate with phase VIII and separated by low-energy barriers (∼10 meV/atom at 40 GPa). These features indicate the disordered VII phase is more favorable at finite temperatures, in agreement with previous experimental observations. Additionally, we demonstrated that the PEL topology undergoes a fundamental alteration at higher pressures, with a single funnel emerging at 120 GPa, facilitating the crystallization of phase X. This work serves as a proof of concept for using the stationary-point network to explicitly represent the PEL, highlighting their potential in elucidating complex phase transitions. Published by the American Physical Society 2024

Ensembled snake optimiser to solve multiobjective mixed energy generation scheduling

This paper presents Ensembled Snake Optimiser (ESO), to optimise the scheduling of mixed energy generation from coordinated thermal, hydro, pumped-storage hydro, and solar units. It tackles operational constraints while minimising non-convex and non-linear objectives. To reduce the pollutants emitted and operating cost of thermal and solar units, the mixed energy generation scheduling problem uses committed hydro, thermal, and solar units to generate power, pumped-storage hydro units to maintain water levels, and hydro units to maximise available water volume. Utilising the water volume and actively exceeding the power-generating limit are the primary obstacles to satisfy the load requirement. The heuristics are utilised to satisfy the load demand and water volume constraints. The binary-optimistic approach commits solar units. The snake optimisation algorithm tends to get trapped in the local minima while solving complex engineering optimisation problems, which leads to sluggish convergence behaviour. A local search, simplex search, and extended opposition-based learning are investigated to improve its exploitation aspect, convergence behaviour, and procure good solutions. Three electric power systems are undertaken for the simulation studies. ESO gives better results. The significant cost savings for integrated energy scheduling are ranging from 10–15%. The rapid convergence behaviour and whisker box plots justify ESO’s robustness.