Quasi-random Research Articles

Machine learning-assisted multi-objective optimization of battery manufacturing from synthetic data generated by physics-based simulations

The optimization of the electrodes manufacturing process is critical to ensure high-quality Lithium-Ion Battery (LIB) cells, in particular for automotive applications. LIB electrode manufacturing is a complex process involving multiple steps and parameters. We have shown in our previous works that 3D-resolved physics-based models constitute very useful tools to provide insights into the impact of the manufacturing process parameters on the textural and performance properties of the electrodes. However, their high-throughput application for electrode properties optimization and inverse design of manufacturing parameters is limited due to the high computational cost associated with these models. In this work, we tackle this issue by proposing a generalizable and innovative approach, supported by a deterministic machine learning (ML)-assisted pipeline for multi-objective optimization of LIB electrode properties and inverse design of its manufacturing process. Firstly, the pipeline generates a synthetic dataset from physics-based simulations with low discrepancy sequences, that allows to sufficiently represent the manufacturing parameters space. Secondly, the generated dataset is used to train deterministic ML models to implement a fast multi-objective optimization, to identify an optimal electrode and the manufacturing parameters to adopt in order to fabricate it. Lastly, this electrode was successfully fabricated experimentally, proving that our modeling pipeline prediction is physical-relevant. Here, we demonstrate our pipeline for the simultaneous minimization of the electrode tortuosity factor and maximization of the effective electronic conductivity, the active surface area, and the density, all being parameters that affect the Li+ (de-)intercalation kinetics, ionic, and electronic transport properties of the electrode.

A random walk algorithm to estimate a lower bound of the star discrepancy

Abstract In many Monte Carlo applications, one can substitute the use of pseudorandom numbers with quasirandom numbers and achieve improved convergence. This is because quasirandom numbers are more uniform that pseudorandom numbers. The most common measure of that uniformity is the star discrepancy. Moreover, the main error bound in quasi-Monte Carlo methods, called the Koksma–Hlawka inequality, has the star discrepancy in the formulation. A difficulty with this bound is that computing the star discrepancy is very costly. The star discrepancy can be computed by evaluating a function called the local discrepancy at a number of points. The supremum of these local discrepancy values is the star discrepancy. If we have a point set in [ 0 , 1 ] s {[0,1]^{s}} with N members, we need to compute the local discrepancy at N s {N^{s}} points. In fact, computing star discrepancy is NP-hard. In this paper, we will consider an approximate algorithm for a lower bound on the star discrepancy based on using a random walk through some of the N s {N^{s}} points. This approximation is much less expensive that computing the star discrepancy, but still accurate enough to provide information on convergence. Our numerical results show that the random walk algorithm has the same convergence rate as the Monte Carlo method, which is O ( N - 1 2 {O(N^{-\frac{1}{2}}} ).

Convergence of Uniformity Criteria and the Application in Numerical Integration

Quasi-Monte Carlo (QMC) methods have been successfully used for the estimation of numerical integrations arising in many applications. In most QMC methods, low-discrepancy sequences have been used, such as digital nets and lattice rules. In this paper, we derive the convergence rates of order of some improved discrepancies, such as centered L2-discrepancy, wrap-around L2-discrepancy, and mixture discrepancy, and propose a randomized QMC method based on a uniform design constructed by the mixture discrepancy and Baker’s transformation. Moreover, the numerical results show that the proposed method has better approximation than the Monte Carlo method and many other QMC methods, especially when the number of dimensions is less than 10.

Improving the accuracy of estimators for the two-point correlation function

Aims. We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. Methods. We quantify the error of the pair-counts and of the Landy & Szalay estimator by comparing them with exact reference values. The standard method, using random point sets, is compared to geometrically motivated estimators and estimators using quasi-Monte Carlo integration. Results. In the standard method, the error scales proportionally to 1/√Nr, with Nr being the number of random points. In our improved methods, the error scales almost proportionally to 1/Nq, where Nq is the number of points from a low-discrepancy sequence. We study the run times of the new estimator in comparison to those of the standard estimator, keeping the same level of accuracy. For the considered case, we always see a speedup ranging from 50% up to a factor of several thousand. We also discuss how to apply these improved estimators to incompletely sampled galaxy catalogues.

Reliability Sensitivity Analysis by the Axis Orthogonal Importance Sampling Method Based on the Box-Muller Transformation

The axis orthogonal importance sampling method proves to be one version of efficient importance sampling methods since the quasi-Monte Carlo simulation is its basic ingredient, in which it is now a common practice to transform low-discrepancy sequences from the uniform distribution to the normal distribution by the well-known inverse transformation. As a valid transformation method for low-discrepancy sequences, the Box-Muller transformation is introduced into the axis orthogonal importance sampling method and compared with the inverse transformation in this paper for structural reliability sensitivity analysis. Three representative quasi-random sequences with low discrepancy are presented to generate samples following the target distribution and explore the interaction with the transformation method, which is used as a sample plan along the tangent plane at the most probable failure point in the axial orthogonal importance sampling for structural reliability analysis and reliability sensitivity analysis. The numerical experiments show that the reliability sensitivity analysis method by means of the Box-Muller transformation is a good alternative to the inverse transformation to generate samples from low-discrepancy sequences to the normal distribution. In particular, the scheme of the Box-Muller transformation combined with the Sobol sequence needs fewer samples with more accuracy and is more applicable for solving reliability sensitivity analysis in various nonlinear problems.

PENGGUNAAN METODE SIMULASI QUASI MONTE CARLO DENGAN BARISAN QUASI ACAK VAN DER COURPUT DALAM MENENTUKAN HARGA OPSI EROPA

An option is a right by a person or institution to sell or buy an investment instrument at a certain price for a certain period. The point of view for way an option is exercised, there are two types of options known today, namely European options and American options. European options are characterized by option contracts that can only be exercised at the expiration date of the option. American options are indicated by option contracts that can be exercised at any time within the validity of the option contract. There are several methods that can be used in determining option prices, including the Black Scholes method which can be used to calculate the standard price of options. Monte Carlo simulation is a method that gives all possible values of a variable using the average as an estimator of its exact value. Quasi Monte Carlo simulation is an alternative to Monte Carlo simulation which uses quasi-random sequences instead of random numbers. In this article, the quasi-random sequence used is Van der Courput. Calculate option prices with Monte Carlo simulation and Quasi Monte Carlo simulation using MATLAB.

Optimal Performance and Application for Seagull Optimization Algorithm Using a Hybrid Strategy.

This paper aims to present a novel hybrid algorithm named SPSOA to address problems of low search capability and easy to fall into local optimization of seagull optimization algorithm. Firstly, the Sobol sequence in the low-discrepancy sequences is used to initialize the seagull population to enhance the population’s diversity and ergodicity. Then, inspired by the sigmoid function, a new parameter is designed to strengthen the ability of the algorithm to coordinate early exploration and late development. Finally, the particle swarm optimization learning strategy is introduced into the seagull position updating method to improve the ability of the algorithm to jump out of local optimization. Through the simulation comparison with other algorithms on 12 benchmark test functions from different angles, the experimental results show that SPSOA is superior to other algorithms in stability, convergence accuracy, and speed. In engineering applications, SPSOA is applied to blind source separation of mixed images. The experimental results show that SPSOA can successfully realize the blind source separation of noisy mixed images and achieve higher separation performance than the compared algorithms.

Improved Fitness-Dependent Optimizer for Solving Economic Load Dispatch Problem.

Economic load dispatch depicts a fundamental role in the operation of power systems, as it decreases the environmental load, minimizes the operating cost, and preserves energy resources. The optimal solution to economic load dispatch problems and various constraints can be obtained by evolving several evolutionary and swarm-based algorithms. The major drawback to swarm-based algorithms is premature convergence towards an optimal solution. Fitness-dependent optimizer is a novel optimization algorithm stimulated by the decision-making and reproductive process of bee swarming. Fitness-dependent optimizer (FDO) examines the search spaces based on the searching approach of particle swarm optimization. To calculate the pace, the fitness function is utilized to generate weights that direct the search agents in the phases of exploitation and exploration. In this research, the authors have used a fitness-dependent optimizer to solve the economic load dispatch problem by reducing fuel cost, emission allocation, and transmission loss. Moreover, the authors have enhanced a novel variant of the fitness-dependent optimizer, which incorporates novel population initialization techniques and dynamically employed sine maps to select the weight factor for the fitness-dependent optimizer. The enhanced population initialization approach incorporates a quasi-random Sabol sequence to generate the initial solution in the multidimensional search space. A standard 24-unit system is employed for experimental evaluation with different power demands. The empirical results obtained using the enhanced variant of the fitness-dependent optimizer demonstrate superior performance in terms of low transmission loss, low fuel cost, and low emission allocation compared to the conventional fitness-dependent optimizer. The experimental study obtained 7.94E−12, the lowest transmission loss using the enhanced fitness-dependent optimizer. Correspondingly, various standard estimations are used to prove the stability of the fitness-dependent optimizer in phases of exploitation and exploration.

Some connections between discrepancy, finite gap properties, and pair correlations

A generic uniformly distributed sequence (x_n)_{n in mathbb {N}} in [0, 1) possesses Poissonian pair correlations (PPC). Vice versa, it has been proven that a sequence with PPC is uniformly distributed. Grepstad and Larcher gave an explicit upper bound for the discrepancy of a sequence given that it has PPC. As a first result, we generalize here their result to the case of alpha -pair correlations with 0< alpha < 1. Since the highest possible level of uniformity is achieved by low-discrepancy sequences it is tempting to assume that there are examples of such sequences which also have PPC. Although there are no such known examples, we prove that every low-discrepancy sequence has at least alpha -pair correlations for 0< alpha <1. According to Larcher and Stockinger, the reason why many known classes of low-discrepancy sequences fail to have PPC is their finite gap property. In this article, we furthermore show that the discrepancy of a sequence with the finite gap property plus a condition on the distribution of the different gap lengths can be estimated. As a concrete application of this estimation, we re-prove the fact that van der Corput and Kronecker sequences are low-discrepancy sequences. Consequently, it follows from the finite gap property that these sequences have alpha -pair correlations for 0< alpha < 1.

MatBuilder

Many applications ranging from quasi-Monte Carlo integration over optimal control to neural networks benefit from high-dimensional, highly uniform samples. In the case of computer graphics, and more particularly in rendering, despite the need for uniformity, several sub-problems expose a low-dimensional structure. In this context, mastering sampling uniformity over projections while preserving high-dimensional uniformity has been intrinsically challenging. This difficulty may explain the relatively small number of mathematical constructions for such samplers. We propose a novel approach by showing that uniformity constraints can be expressed as an integer linear program that results in a sampler with the desired properties. As it turns out, complex constraints are easy to describe by means of stratification and sequence properties of digital nets. Formalized using generator matrix determinants, our new MatBuilder software solves the set of constraints by iterating the linear integer program solver in a greedy fashion to compute a problem-specific set of generator matrices that can be used as a drop-in replacement in the popular digital net samplers. The samplers created by MatBuilder achieve the uniformity of classic low discrepancy sequences. More importantly, we demonstrate the benefit of the unprecedented versatility of our constraint approach with respect to low-dimensional problem structure for several applications.

Image Encryption Using a Spectrally Efficient Halton Logistics Tent (HaLT) Map and DNA Encoding for Secured Image Communication.

With the advancement of technology worldwide, security is essential for online information and data. This research work proposes a novel image encryption method based on combined chaotic maps, Halton sequence, five-dimension (5D) Hyper-Chaotic System and Deoxyribonucleic Acid (DNA) encoding. Halton sequence is a known low-discrepancy sequence having uniform distribution in space for application in numerical methods. In the proposed work, we derived a new chaotic map (HaLT map) by combining chaotic maps and Halton sequence to scramble images for cryptography applications. First level scrambling was done by using the HaLT map along with a modified quantization unit. In addition, the scrambled image underwent inter- and intra-bit scrambling for enhanced security. Hash values of the original and scrambled image were used for initial conditions to generate a 5D hyper-chaotic map. Since a 5D chaotic map has complex dynamic behavior, it could be used to generate random sequences for image diffusion. Further, DNA level permutation and pixel diffusion was applied. Seven DNA operators, i.e., ADD, SUB, MUL, XOR, XNOR, Right-Shift and Left-Shift, were used for pixel diffusion. The simulation results showed that the proposed image encryption method was fast and provided better encryption compared to ‘state of the art’ techniques. Furthermore, it resisted various attacks.

ESTIMASI VALUE AT RISK PORTOFOLIO MENGGUNAKAN METODE QUASI MONTE CARLO DENGAN PEMBANGKIT BILANGAN ACAK HALTON

Estimating the value at risk (VaR) is an important aspect of investment. VaR is a standard method of measuring risk defined as the maximum loss over a certain period of time at a certain level of confidence. The purpose of this study is to estimate the risk of a portfolio represented as a VaR where the volatilities were simulated by th the Monte Carlo and Quasi Monte Carlo methods. The Monte Carlo method involves generating random numbers and the Quasi Monte Carlo method uses Halton's quasi-random sequences. This study uses secondary data, namely daily stock price closing data. Based on the calculation, the VaR of the Quasi Monte Carlo Portfolio produces a maximum loss greater than that of the Monte Carlo Portfolio. This is due to randomization performed with different random number generators for each method and the number of simulations performed. It can be concluded that the Quasi Monte Carlo method is a better method than the Monte Carlo method in estimating the risk of portfolio losses in stocks in the telecommunications sector.

A Review of the Use of Quasi-random Number Generators to Initialize the Population in Meta-heuristic Algorithms

A Review of the Use of Quasi-random Number Generators to Initialize the Population in Meta-heuristic Algorithms

Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain

We present a machine learning based model that can predict the electronic structure of quasi-one-dimensional materials while they are subjected to deformation modes such as torsion and extension/compression. The technique described here applies to important classes of materials such as nanotubes, nanoribbons, nanowires, miscellaneous chiral structures and nano-assemblies, for all of which, tuning the interplay of mechanical deformations and electronic fields is an active area of investigation in the literature. Our model incorporates global structural symmetries and atomic relaxation effects, benefits from the use of helical coordinates to specify the electronic fields, and makes use of a specialized data generation process that solves the symmetry-adapted equations of Kohn-Sham Density Functional Theory in these coordinates. Using armchair single wall carbon nanotubes as a prototypical example, we demonstrate the use of the model to predict the fields associated with the ground state electron density and the nuclear pseudocharges, when three parameters - namely, the radius of the nanotube, its axial stretch, and the twist per unit length - are specified as inputs. Other electronic properties of interest, including the ground state electronic free energy, can then be evaluated with low-overhead post-processing, typically to chemical accuracy. We also show how the nuclear coordinates can be reliably determined from the pseudocharge field using a clustering based technique. Remarkably, only about 120 data points are found to be enough to predict the three dimensional electronic fields accurately, which we ascribe to the symmetry in the problem setup, the use of low-discrepancy sequences for sampling, and presence of intrinsic low-dimensional features in the electronic fields. We comment on the interpretability of our machine learning model and discuss its possible future applications.

On graph norms for complex‐valued functions

For any given graph H $H$ , one may define a natural corresponding functional ∥ . ∥ H $\Vert .\Vert _H$ for real-valued functions by using homomorphism density. One may also extend this to complex-valued functions, once H $H$ is paired with a 2-edge-colouring α $\alpha$ to assign conjugates. We say that H $H$ is real-norming (respectively complex-norming) if ∥ . ∥ H $\Vert .\Vert _H$ (respectively ∥ . ∥ H , α $\Vert .\Vert _{H,\alpha }$ for some α $\alpha$ ) is a norm on the vector space of real-valued (respectively complex-valued) functions. These generalise the Gowers octahedral norms, a widely used tool in extremal combinatorics to quantify quasi randomness. We unify these two seemingly different notions of graph norms in real- and complex-valued settings. Namely, we prove that H $H$ is complex-norming if and only if it is real-norming and simply call the property norming. Our proof does not explicitly construct a suitable 2-edge-colouring α $\alpha$ but obtains its existence and uniqueness, which may be of independent interest. As an application, we give various example graphs that are not norming. In particular, we show that hypercubes are not norming, which resolves the last outstanding problem posed in Hatami's pioneering work on graph norms.

Monte Carlo and quasi-Monte Carlo methods for Dempster's rule of combination

One of the challenges in Dempster-Shafer theory is that the data fusion calculation resulting from the popular Dempster's rule of combination is #P-complete. This imposes a computational constraint on the number of belief functions and the number of focal sets that can be combined using Dempster's rule. In this paper we develop Monte Carlo algorithms to approximate Dempster's rule of combination. The algorithms incorporate importance sampling and low-discrepancy sequences. Numerical results suggest the algorithms make it possible to apply Dempster's rule to a much larger number of belief functions and focal sets, and consequently widen the scope of applications of Dempster-Shafer theory.

Numerical Probabilistic Load Flow Analysis in Modern Power Systems with Intermittent Energy Sources

Renewable resources integration through distributed generation (DG) affects conventional consideration of power system performance and confronts deterministic load flow (DLF) analysis with serious challenges. The DLF gives a snapshot of the system state neglecting all of the uncertainties arising from intermittent DG driven by variable weather conditions or volatile consumption. Therefore, with the aim of finer tracking and presentation of system variables, a probabilistic load flow (PLF) approach should be adopted. First, this article gives a literature overview of different PLF techniques. It focuses on numerical techniques examining them for simple random and Latin Hypercube sampling, vastly applied in previous works, and proposes a method combining Monte Carlo simulations with Halton quasi-random numbers. Stochastic modelling is performed for solar and wind power output. For method comparison and confirmation of the applicability of suggested PLF method with Halton sequences, different IEEE test cases were used, all modified by attaching DGs. More profound method assessment is conducted through discussing different renewables penetration levels and processing time. The overall simulation outcomes have shown that results of Halton method are of similar precision as the generally used Latin Hypercube method and therefore indicated the relevance of the proposed method and its potential for application in contemporary system analysis.

Generation of address sequences with specified switching activity and address repeatability

Objectives. The problem of developing a methodology for generating address sequences with a given switching activity and repeatability of addresses widely used in testing modern computing systems is being solved. The relevance of this problem lies in the fact that the main characteristic of the difference and their effectiveness for address sequences is the switching activity of both individual address bits and their sequences.Methods. Presented results are based on a universal method for generating quasi-random Sobol sequences, which are effectively used to generate targeted test sequences. As an initial mathematical model, a modification of the indicated generation method proposed by Antonov and Saleev is used. The main idea of proposed approach is based on the use of rectangular (m + k) × m generating matrices V of arbitrary rank r to generate address sequences.Results. The main properties of sequences generated in accordance with the new mathematical model are determined. A number of statements are given that substantiate the requirements for generator matrices to ensure the maximum period of generated sequences and the multiplicity of repetition of used addresses. The problem of synthesizing the sequences with given values of switching activity F(A) and F(ai) is solved. It is shown that in order to find a generating matrix for generating such sequences, it is necessary to solve the problem of decomposing an integer into terms. This decomposition represents the value of switching activity in the (m + k)-ary mixed number system, in which the weights of the digits are represented as powers of two from 20 to 2m+k-1, and the values of the digits w(vi) lie in the range from 0 to m+k-1. On the basis of proposed restrictions, the notion of an integer decomposition diagram similar to the Young diagram is introduced, and the operation of its modification is defined.Conclusion. The proposed mathematical model expands the possibilities of generating test address sequences with the required values of switching activity of both test sets and their individual bits. The use of generating matrices of non-maximal rank makes it possible to formalize the method of generating address sequences with even repetition of addresses.

Initialisation Approaches for Population-Based Metaheuristic Algorithms: A Comprehensive Review

A situation where the set of initial solutions lies near the position of the true optimality (most favourable or desirable solution) by chance can increase the probability of finding the true optimality and significantly reduce the search efforts. In optimisation problems, the location of the global optimum solution is unknown a priori, and initialisation is a stochastic process. In addition, the population size is equally important; if there are problems with high dimensions, a small population size may lie sparsely in unpromising regions, and may return suboptimal solutions with bias. In addition, the different distributions used as position vectors for the initial population may have different sampling emphasis; hence, different degrees of diversity. The initialisation control parameters of population-based metaheuristic algorithms play a significant role in improving the performance of the algorithms. Researchers have identified this significance, and they have put much effort into finding various distribution schemes that will enhance the diversity of the initial populations of the algorithms, and obtain the correct balance of the population size and number of iterations which will guarantee optimal solutions for a given problem set. Despite the affirmation of the role initialisation plays, to our knowledge few studies or surveys have been conducted on this subject area. Therefore, this paper presents a comprehensive survey of different initialisation schemes to improve the quality of solutions obtained by most metaheuristic optimisers for a given problem set. Popular schemes used to improve the diversity of the population can be categorised into random numbers, quasirandom sequences, chaos theory, probability distributions, hybrids of other heuristic or metaheuristic algorithms, Lévy, and others. We discuss the different levels of success of these schemes and identify their limitations. Similarly, we identify gaps and present useful insights for future research directions. Finally, we present a comparison of the effect of population size, the maximum number of iterations, and ten (10) different initialisation methods on the performance of three (3) population-based metaheuristic optimizers: bat algorithm (BA), Grey Wolf Optimizer (GWO), and butterfly optimization algorithm (BOA).

Star discrepancy subset selection: Problem formulation and efficient approaches for low dimensions

Motivated by applications in instance selection, we introduce the star discrepancy subset selection problem, which consists of finding a subset of m out of n points that minimizes the star discrepancy. First, we show that this problem is NP-hard. Then, we introduce a mixed integer linear formulation (MILP) and a combinatorial branch-and-bound (BB) algorithm for the star discrepancy subset selection problem and we evaluate both approaches against random subset selection and a greedy construction on different use-cases in dimension two and three. Our results show that the MILP and BB are efficient in dimension two for large and small m/n ratio, respectively, and for not too large n. However, the performance of both approaches decays strongly for larger dimensions and set sizes.As a side effect of our empirical comparisons we obtain point sets of discrepancy values that are much smaller than those of common low-discrepancy sequences, random point sets, and of Latin Hypercube Sampling. This suggests that subset selection could be an interesting approach for generating point sets of small discrepancy value.