Global Optimizations Research Articles

Consensus-based optimisation with truncated noise

Abstract Consensus-based optimisation (CBO) is a versatile multi-particle metaheuristic optimisation method suitable for performing non-convex and non-smooth global optimisations in high dimensions. It has proven effective in various applications while at the same time being amenable to a theoretical convergence analysis. In this paper, we explore a variant of CBO, which incorporates truncated noise in order to enhance the well-behavedness of the statistics of the law of the dynamics. By introducing this additional truncation in the noise term of the CBO dynamics, we achieve that, in contrast to the original version, higher moments of the law of the particle system can be effectively bounded. As a result, our proposed variant exhibits enhanced convergence performance, allowing in particular for wider flexibility in choosing the noise parameter of the method as we confirm experimentally. By analysing the time evolution of the Wasserstein- $2$ distance between the empirical measure of the interacting particle system and the global minimiser of the objective function, we rigorously prove convergence in expectation of the proposed CBO variant requiring only minimal assumptions on the objective function and on the initialisation. Numerical evidences demonstrate the benefit of truncating the noise in CBO.

Numerically Optimized Fourier Transform-Based Beamforming Accelerated by Neural Networks

Conventional beamforming methods for reconfigurable reflector antennas assume full control over the amplitude and phase of the reflected field. Here, we develop a novel beamforming methodology for reflecting Programmable Metasurfaces (PMS) with capacitive memory. Although utilizing such fully reactive PMS simplifies antenna design and reduces energy consumption, the PMS reflection magnitude is unity and thus a global optimization of the reflection phases over the PMS unit cells is required in each beamforming scenario. We propose an implementation of such an optimization method rooted in the traditional Fourier transform-based beamforming and evaluate its performance. Additionally, we show that a pair of trained feed-forward neural networks (FFNN) with one input, one hidden, and one output layer can replace time-consuming global optimizations in the case of a PMS comprising 3×10 unit cells. We train the FFNNs on a dataset obtained for typical single- and dual-beam beamforming scenarios. After training, the FFNNs perform requested beamforming tasks within a fraction of second and with about the same accuracy as the original optimization algorithm. The proposed methodology may find applications in future mobile telecommunication systems that require real-time beamforming on low-end hardware. The same beamforming methodology can be also employed in short-range wireless power transfer systems.

Federated Causality Learning with Explainable Adaptive Optimization

Discovering the causality from observational data is a crucial task in various scientific domains. With increasing awareness of privacy, data are not allowed to be exposed, and it is very hard to learn causal graphs from dispersed data, since these data may have different distributions. In this paper, we propose a federated causal discovery strategy (FedCausal) to learn the unified global causal graph from decentralized heterogeneous data. We design a global optimization formula to naturally aggregate the causal graphs from client data and constrain the acyclicity of the global graph without exposing local data. Unlike other federated causal learning algorithms, FedCausal unifies the local and global optimizations into a complete directed acyclic graph (DAG) learning process with a flexible optimization objective. We prove that this optimization objective has a high interpretability and can adaptively handle homogeneous and heterogeneous data. Experimental results on synthetic and real datasets show that FedCausal can effectively deal with non-independently and identically distributed (non-iid) data and has a superior performance.

On the brink of self-hydration: the water heptadecamer.

For pure, neutral, isolated molecular clusters, (H2O)17 marks the transition from structures with all water molecules on the cluster surface to water self-hydration, i.e., cluster structures around one central water molecule. Getting this right with water model potentials turns out to be challenging. Even the best water potentials currently available, which reproduce collective properties very well, still deliver contradicting results for (H2O)17, when different low-energy isomers from global structure optimizations are examined. Interestingly, ab initio quantum chemistry also struggles with the only seemingly simple question if (H2O)17 is all-surface or water-centered. Hence, although the long history of water potential development may be entering its final phase, it is not quite finished yet.

Leveraging memory effects and gradient information in consensus-based optimisation: On global convergence in mean-field law

Abstract In this paper, we study consensus-based optimisation (CBO), a versatile, flexible and customisable optimisation method suitable for performing nonconvex and nonsmooth global optimisations in high dimensions. CBO is a multi-particle metaheuristic, which is effective in various applications and at the same time amenable to theoretical analysis thanks to its minimalistic design. The underlying dynamics, however, is flexible enough to incorporate different mechanisms widely used in evolutionary computation and machine learning, as we show by analysing a variant of CBO which makes use of memory effects and gradient information. We rigorously prove that this dynamics converges to a global minimiser of the objective function in mean-field law for a vast class of functions under minimal assumptions on the initialisation of the method. The proof in particular reveals how to leverage further, in some applications advantageous, forces in the dynamics without loosing provable global convergence. To demonstrate the benefit of the herein investigated memory effects and gradient information in certain applications, we present numerical evidence for the superiority of this CBO variant in applications such as machine learning and compressed sensing, which en passant widen the scope of applications of CBO.

Modeling and optimization of liquid-based battery thermal management system considering battery electrochemical characteristics

In this research, a novel multi-physics model is proposed to facilitate battery thermal management system (BTMS) design and optimization. For parametric simulations and optimization, a new optimization framework is developed for BTMS by utilizing numerical simulations, artificial intelligence and multi-objective genetic algorithm. It is found that BTMS is inadequate in addressing thermal issues that arise in aged battery pack, primarily because of the increased total heat generation rate resulting from battery aging effect. Besides, it has also been observed that BTMS plays a significant role in managing battery electrochemical performance. Meanwhile, optimizing mini-channel geometrical parameters, mini-channel arrangement and nanoparticle volume fraction are found to be an effective method to further control battery thermal issues. However, it is observed that reducing battery temperature invariably incurs a reduction in battery average potential. Therefore, multi-variables global optimizations are conducted based on various combinations of weighted coefficients and optimization strategies. It is found that all obtained optimization schemes can achieve the trade-offs among battery thermal behaviors, pressure loss and electrochemical performance, with meeting the desired temperature requirements even during long-term operation. Furthermore, the selection about weighted coefficient and optimization strategy can be tailored to meet the specific demands and prerequisites of various engineering applications.

Simultaneous and Global Optimizations of LNG-Fueled Hybrid Electric Ship for Substantial Fuel Cost, CO2, and Methane Emission Reduction

Natural gas (NG) is a promising low-carbon fuel to replace diesel for heavy-duty marine propulsion with prominent fuel cost and carbon dioxide equivalent (CDE) emissions reduction potential. However, using NG in compression ignition (CI) engines presents several inherent drawbacks. This research addresses the central issue of an NG-diesel CI engine with increased methane emissions, resulting in minor CDE emission reduction. The hydrocarbon (HC), carbon monoxide (CO), and nitrogen oxides (NOx) emissions are minimized in addition to fuel consumption and carbon dioxide emission reduction as in the current practice. The simultaneous optimizations of powertrain component sizes and the NG-engine hybrid electric propulsion control are introduced to minimize NG fuel consumption and CDE emissions globally. The top-level powertrain component sizing and bottom-level optimal power control and energy management are conducted simultaneously to achieve global optimization with balanced fuel cost and CDE emissions reductions. The new method reduced the fuel cost by about 75 percent and well-to-wake CDE emissions by about 40 percent over the traditional diesel-mechanical propulsion for the test ferry running under an actual operation profile. The research opened a new path to the global design and control optimization of the NG-diesel CI engine-powered hybrid electric marine propulsion system.

A synthetic machine learning framework for complex crystallization processes: The case study of the second-order asymmetric transformation of enantiomers

Improving the flexibility and capabilities of pharmaceutical technologies and lowering the process development time while satisfying regulatory constraints translate to highly desired resilient supply chains. Generating and validating the necessary knowledge in-silico before experimentation or plant-scale intervention with minimized human implications is the dream this paper aims to contribute to. The idea is demonstrated through the case study of particle size-controlled second-order asymmetric transformation of enantiomers (SOAT), a crystallization and racemization-based resolution technique. The fundamental processes form a complex network, to which we propose a crystallization-integrated wet milling system, which is promising but has limited general, and no SOAT-specific operation experience. The developed computational framework has three steps: (1) skilled scientists draft potential technologies to solve a well-defined problem; (2) all alternatives are modeled with high fidelity first-principle models, followed by high throughput parametric optimizations (3) data mining is deployed to extract key information from the synthetic database of optimal solutions and take the effectiveness of process design and operation to the next level. In this work, population balance-based models were applied to describe the crystallization, fragmentation, and chemical reaction in the crystallizer and wet mill. The efficient implementation enabled the execution of nearly 1300 global multiobjective process optimizations. Carefully trained classifiers consistently predicted the with or without milling and with or without T-cycling decisions (AUC score exceeding 0.85). Regression methods estimated the product property profile with Pearson coefficients over 0.95. The results agree with the existing SOAT literature based on a literature meta-analysis, but some of the conclusions point beyond the state-of-the-art.

Global Optimization: A Soft Computing Perspective

Tackling the problem of global optimization is one of the most important domains that physicists and chemists are working on. The use of soft computing (SC) techniques has made this easier by reducing nonlinearity and instability and making it technologically rich. This Perspective aims at explaining the basic mathematical models of the most efficient and commonly used SC techniques in computational chemistry for finding the global minimum (GM) energy structures of chemical systems. In this Perspective, we discuss the global optimizations of several chemical systems that our group has worked on using CNN, PSO, FA, ABC, BO, and some hybrid techniques, two of which are interfaced to achieve better-quality results.

Advanced machine learning based global optimizations for Pt nanoclusters

Pt-nanoclusters have attracted attention due to their extensive use as catalysts in various sectors and their catalytic capabilities, instigating a theoretical investigation to correlate structure and property. On the other hand, it is challenging to find stable and reliable structures to support experimental results at the nanoscale due to their fluxional nature at ambient temperature. The major objective of this work is to test the capability of stable and reliable structure findings at the nanocluster region by Gaussian Process Regression (GPR) model potentials on-the-fly within the evolutionary framework using the Bayesian optimization approach. The entire algorithm is called Global Optimizations by GPR (GO-GPR) learning. In this regard, the GO-GPR algorithm examined the potential energy surfaces of bare Ptn-nanoclusters of sizes (n = 3–6, 7, 8, 10, 13). GO-GPR identified new low-lying isomers and global minimum structures are in correlation with earlier studies. In the case of Pt13 and Pt8 nano-clusters, the global minimum structure is close to the second lowest energy structure, implying that these clusters can have fluxional nature. In fact, a few experimental studies have shown that Pt8 and Pt13 are effective in catalyzing reactions.

An enhanced vortex search algorithm based on fluid particle density transfer for global and engineering optimization

The vortex search algorithm is a new meta-heuristic algorithm for solving optimization problems. However, it has some disadvantages such as weak stability, tendency to trap into local minima, and high iterations. To overcome these disadvantages, this paper proposes a density transfer vortex search algorithm based on Cauchy distribution and Archimedean spiral surrounding for global and engineering optimization. The algorithm is divided into two populations. In the first population, the mutual action of the Cauchy random step and Gaussian step is introduced to improve the searchability. To improve the exploitation ability of the algorithm in the current optimal solution, an Archimedean spiral surrounding mechanism is introduced in the second population. Moreover, we introduce the vortex flow mechanism, which mimics the physical characteristics of the vortex flow. With the number of iterations increasing, candidate solutions of the first population are gradually affected by the vortex, and their density continuously shifts to the second population. The relationship between the exploration and exploitation in different iteration periods is reasonably adjusted through the density transfer of two populations. In the experiment, the performance of the proposed algorithm and six competitive algorithms are tested on the IEEE CEC2021 global optimization benchmark suite, eight real-world engineering optimizations and a scheduling problem for automated storage and retrieval systems (AS/RS). The experimental results show that the proposed algorithm has significant improvements in convergence precision, speed and stability. The proposed algorithm not only solves complex global optimizations and real-world engineering optimizations with good convergence performance, but also improves efficiency and reduces energy consumption when solving the scheduling problem of AS/RS.

Machine Learning Assisted Clustering of Nanoparticle Structures.

We propose a scheme for the automatic separation (i.e., clustering) of data sets composed of several nanoparticle (NP) structures by means of Machine Learning techniques. These data sets originate from atomistic simulations, such as global optimizations searches and molecular dynamics simulations, which can produce large outputs that are often difficult to inspect by hand. By combining a description of NPs based on their local atomic environment with unsupervised learning algorithms, such as K-Means and Gaussian mixture model, we are able to distinguish between different structural motifs (e.g., icosahedra, decahedra, polyicosahedra, fcc fragments, twins, and so on). We show that this method is able to improve over the results obtained previously thanks to the successful implementation of a more detailed description of NPs, especially for systems showing a large variety of structures, including disordered ones.

Data Alignment Design for Robotic Programming by Demonstration Based on IMU and Optical Tracker

This study proposes a data alignment design for sensor fusion of an optical target (OT) and an inertial measurement unit (IMU) to track the trajectory of a handheld tool for robot programming by demonstration (PbD). A novel method is proposed for coordinate and temporal alignment between the OT and the IMU sensor to increase the tracking accuracy. The IMU measurements are aligned with the corresponding angular velocities and accelerations derived from the OT to calibrate the IMU-OT relationship. Global and local optimizations are combined to reduce the computation time for the temporal alignment and coordinate calibration. Experimental results show that the proposed method provides improved calibration results with shorter calculation time compared with two existent methods. The sensor fusion experiments verify the accuracy of trajectory tracking of 1.3mm using the calibration result, an improvement from 1.4mm of the data alignment using ruler measurement. Integrated PbD experiments by using a 6-DOF manipulator were carried out to evaluate the proposed method. The manipulator imitated the hand motion of a bottle transfer task with the trajectory error of 0.66mm. Practical robotic experiments demonstrate that the method is suitable for robot programming applications.

Obtaining Feasible Minimum Side Lobe Level for Narrow Beam Width Using Convex Optimization in Linear, Planar, and Random Antenna Arrays

In many applications, the radiating elements of the used antenna may be configured in the form of a one-dimensional linear array, or two-dimensional planar array or even random array. In such applications, a simple optimization algorithm is highly needed to optimally determine the excitation amplitudes and phases of the array elements to maximize the system’s performance. This paper uses a convex optimization instead of other complex global stochastic optimizations to synthesize a linear, planar, and random array patterns under pre-specified constraint conditions. These constraints could be either fixed beam width with the lowest possible sidelobe levels or fixed sidelobe level with narrower possible beam width. Two approaches for array pattern optimization have been considered. The first one deals with the problem of obtaining a feasible minimum sidelobe level for a given beam width, while the second one tries to obtain a feasible minimum beam width pattern for a given sidelobe level. Both optimization approaches were applied to the linear, planar, and random arrays. Simulation results verified the effectiveness of both optimization approaches and for all considered array configurations.

Structure and dynamics of 38-atom Ag-Pt nanoalloys using ANN based-interatomic potential

Silver–platinum nanoalloys are potential candidates as effective and less expensive catalysts than pure platinum-based catalysts. The reactivity of these nanoalloys depends crucially on their size, composition, and ordering of the constituent Ag and Pt atoms. Moreover, the presence of a second metal atom in these nanoalloys results in a variety of structural configurations in comparison to their pure counterparts. To explore the structural aspects further, in this paper, we developed an interatomic potential for Ag–Pt nanoalloys based on an artificial neural network model. We systematically carried out structural and energetic analysis of Ag38−nPtn (n = 1 −8) nanoalloys. Using neural network-based interatomic potential, we have also performed molecular dynamics simulations and global optimizations to search the global minimum structures as well as to investigate the effect of temperature on the structures of silver–platinum nanoalloys. We find the lowest energy isomers of Ag38−nPtn nanoalloys are a core–shell structure in which the Pt atoms occupy the core region while the Ag atoms are located in the surface region. The relative stability of nanoalloys has been investigated using excess energy and second-order energy difference calculations. The charge distribution over Pt and Ag atoms is determined for all the lowest energy isomers of Ag38−nPtn nanoalloys. Furthermore, the probability of the presence of a Pt atom on the surface sites in Ag38−nPtn nanoalloys has been calculated at finite temperatures. We find that at 360K, at least one Pt atom moves from the core to the surface region of the Ag38−nPtn nanoalloys.

Born This Way: A Self-Organizing Evolution Scheme With Motif for Internet of Things Robustness

The span of Internet of Things (IoT) is expanding owing to numerous applications being linked to massive devices. Subsequently, node failures frequently occur because of malicious attacks, battery exhaustion, or other malfunctions. A reliable and robust network topology can alleviate the cascading collapse caused by local node failures. Existing optimization methods for fixed topologies enhance the robustness of the IoT topology by reconstructing the connections among the devices. However, the application of existing algorithms requires global topology optimizations or local adjustments when new nodes are added, which leads to high computational complexity. To address this problem, based on neuroevolution and network motifs, this study proposes an evolutionary algorithm to generate a robust IoT topology called “Born This Way: a self-organizing evolution scheme with Motif” (BTW-Motif). Using novel mutation and crossover operators, BTW-Motif generates an IoT topology with intrinsic robustness when new nodes are added. We design an adaptive edge density control mechanism to avoid an increase in energy consumption resulting from redundant connections. Specifically, BTW-Motif innovatively introduces network motif as a guide structure which has been proven to have a positive effect on the network robustness. Experiments indicate that BTW-Motif can effectively produce a robust topology. With different network sizes and edge densities, BTW-Motif can generate more robust topologies compared with the existing topology optimization algorithms. And the time consumption for the large-scale topology to achieve similar robustness is reduced by 50%.

Optimum Synthesis of Pencil Beams with Constrained Dynamic Range Ratio

In antenna array design, low dynamic range ratio (DRR) of excitation coefficients is important because it simplifies array’s feeding network and enables better control of mutual coupling. Optimization-based synthesis of pencil beams allows explicit control of DRR. However, incorporating DRR into an optimization problem leads to nonconvex constraints, making its solving challenging. In this paper, a framework for global optimization of linear pencil beams with constrained DRR is presented. By using this framework, the methods for synthesis of pencil beams with minimum sidelobe level and minimum sidelobe power are developed. Both methods utilize convex problems suitable for the synthesis of pencil beams whose coefficients’ signs are known in advance. By incorporating these problems into a branch and bound algorithm, the procedures for global optimizations are formed which systematically search the space of all coefficient signs. The method for minimization of sidelobe power is further analyzed in the context of beam efficiency. It is shown that this method can be utilized in an approximate and at the same time global design of pencil beam arrays with maximum beam efficiency and constrained DRR. Based on this approach, a method for the design of pencil beam arrays with minimum DRR and specified beam efficiency is proposed.

Photocatalytic activity of MoS2 with water monolayers: Global optimization.

Atomically thin MoS2 has emerged to be promising for photocatalytic water splitting benefiting from its suitable geometrical and electronic structure for light harvesting. A better understanding of how water molecules affect the band edge levels of MoS2 is critical for promoting the interfacial reactivity. Here, we determine the structures of water monolayers on MoS2 using global optimizations achieved by molecular dynamics in combination with local minimization. It is shown that cyclic water clusters are formed on a surface through a hydrogen-bonding network. The absolute band edge positions are explored taking into account the derivative discontinuity of the exchange-correlation functional. Shifts in band edges are observed with the increase in H2O coverage, while bandgaps tend to be slightly decreased. In particular, the band alignment relative to water redox potentials has been investigated in detail. We find that the dimer configuration is likely to suppress the hydrogen evolution reaction (HER), while the polygon clusters lift the conduction band by 0.2-0.7eV, and thus, they would enhance HER. This effect is explained in terms of the linear dependence of the band edge offset on an interface electric dipole arising from water assemblies.

Integrated Optimal Design for Hybrid Electric Powertrain of Future Aircrafts

This paper presents the integrated optimal design of the powertrain of a hybrid regional aircraft using multidisciplinary design optimization (MDO). The sizing of the main components of the propulsion chain is performed over the flight mission under various scenarios regarding energy management strategies and technological assessments. For that purpose, a complete set of multidisciplinary surrogate models are integrated into the MDO process, taking account not only of the main electrical, thermal and mechanical aspects but also of environmental constraints such as partial discharges in electric motors regarding flight conditions. Several MDO formulations are investigated comparing local (i.e., motor mass minimization) and global optimizations (i.e., powertrain mass then fuel burn minimization at aircraft level). Results emphasize main systemic couplings showing that despite future technological progress, the series hybrid architecture is heavier than a conventional thermal aircraft. Nevertheless, thanks to the whole aircraft optimization, potential gains related to kerosene consumption can be reached, reducing the environmental footprint. The “energy gains” focused on in this paper may be added with aerodynamic gains potentially involved in more electric powertrain. This work has been carried out in the frame of the HASTECS project under the Clean Sky II program which aims at reducing CO2 emissions and environmental impacts of the aviation sector.

High-Temperature Ferromagnetism in a Two-Dimensional Semiconductor with a Rectangular Spin Lattice

Atomically thin two-dimensional (2D) ferromagnetic (FM) semiconductors with a high Curie temperature (TC) are essential and highly desired for nanoscale spintronic devices. However, the recently discovered 2D FM semiconductors show rather low TC (≤45 K), which limits their practical application. An important reason for the low TC is the lack of effective spin interactions. Here, we reveal that increasing the number of effective spin interactions by constructing a rectangular spin–lattice can significantly improve the TC of FM semiconductors. Based on this mechanism, we design a rectangular lattice of the CrO2 monolayer (denoted as R-CrO2) by performing global structural optimizations. The first-principles calculations show that the R-CrO2 is energetically more stable than the previously reported H- and T-CrO2. As expected, the R-CrO2 monolayer is an intrinsic FM semiconductor with TC up to ∼370 K, which is more than twice that of the T-CrO2 monolayer (∼150 K). This is because the R-CrO2 monolayer possesses four effective spin interactions between adjacent Cr sites, more than that of the T-CrO2 monolayer (3). These findings give rise to a new and efficient design principle for realizing high-temperature 2D FM semiconductors.