Simulated Annealing Method Research Articles

Hybrid Population-Based Hill Climbing Algorithm for Generating Highly Nonlinear S-boxes

This paper introduces the hybrid population-based hill-climbing (HPHC) algorithm, a novel approach for generating cryptographically strong S-boxes that combines the efficiency of hill climbing with the exploration capabilities of population-based methods. The algorithm achieves consistent generation of 8-bit S-boxes with a nonlinearity of 104, a critical threshold for cryptographic applications. Our approach demonstrates remarkable efficiency, requiring only 49,277 evaluations on average to generate such S-boxes, representing a 600-fold improvement over traditional simulated annealing methods and a 15-fold improvement over recent genetic algorithm variants. We present comprehensive experimental results from extensive parameter space exploration, revealing that minimal populations (often single-individual) combined with moderate mutation rates achieve optimal performance. This paper provides detailed analysis of algorithm behavior, parameter sensitivity, and performance characteristics, supported by rigorous statistical evaluation. We demonstrate that population size should approximate available thread count for optimal parallel execution despite smaller populations being theoretically more efficient. The HPHC algorithm maintains high reliability across diverse parameter settings while requiring minimal computational resources, making it particularly suitable for practical cryptographic applications.

Comparative study of deterministic and stochastic optimization algorithms applied to the absorption of CO2 by alkanolamine solution

Abstract A model based on simulated annealing approach is used with e-UNIQUAC model as well as two other algorithms to study the absorption of carbon dioxide by monoethanolamine solutions. In this work, we propose to compare the performance (through the knowledge of RMSD values) of two stochastic methods, namely the GA (genetic algorithm) and SA (simulated annealing) methods and a deterministic method that is the simplex method. These methods were applied to the absorption of carbon dioxide by an alkanolamine solution using a chemical equilibrium model and a thermodynamic equilibrium model. The latter is based on the use of the modified-UNIQUAC (UNIQUAC-electrolyte) model instead of e-NRTL model for the liquid phase and a fugacity model for the vapor phase. The chemical equilibrium in this work represents the absorption of CO2 by monoethanolamine solution at different temperatures. Solving the coupled system of material and charge balances gives us the carbon dioxide pressure while taking into account the non-ideality of the system. The three-optimization methods show good agreement with the experimental data with a better performance of the simulated annealing method..

Using data-driven models to simulate the performance of surfactants in reducing heavy oil viscosity

There is a substantial body of literature exploring the challenges associated with exploring and exploiting these underground resources. Unconventional resources, particularly heavy oil reservoirs, are critical for meeting ever-increasing global energy demand. By injecting surfactants into heavy oil, chemically enhanced oil recovery (EOR) may enable emulsification, which may reduce the viscosity of heavy oil and facilitate extraction and transportation. In this work, a large experimental dataset, containing 2020 data points, was extracted from the literature for modeling oil-in-water (O/W) emulsion viscosity using machine learning (ML) methods. The algorithms used pressure, temperature, salinity, surfactant concentration, type of surfactant, shear rate, and crude oil density as inputs. For this purpose, five ML algorithms were selected and optimized, including adaptive boosting (AB), convolutional neural network (CNN), ensemble learning (EL), artificial neural network (ANN), and decision tree (DT). A combined simulated annealing (CSA) method was utilized to optimize all algorithms. With AARE, R2, MAE, MSE, and RMSE values of 8.982, 0.996, 0.004, 0.0002, and 0.0132, respectively, the ANN predictor exhibited higher accuracy in predicting O/W emulsion viscosity for total data (train and test subsets combined). A Monte-Carlo sensitivity analysis was also performed to determine the impact of input features on the model output. By using the proposed ML predictor, expensive and time-consuming experiments can be eliminated and emulsion viscosity predictions can be expedited without the need for costly experiment.

Decomposition and Growth Pathways for Ammonium Nitrate Clusters and Nanoparticles.

Understanding the formation and decomposition mechanisms of aerosolized ammonium nitrate species will lead to improvements in modeling the thermodynamics and kinetics of aerosol haze formation. Studying the sputtered mass spectra of cation and anion ammonium nitrate clusters can provide insights as to which growth and evaporation pathways are favored in the earliest stages of nucleation and thereby guide the development and use of accurate models for intermolecular forces for these systems. Simulated annealing Monte Carlo optimization followed by density functional theory optimizations can be used reliably to predict minimum-energy structures and interaction energies for the cation and anion clusters observed in mass spectra as well as for neutral nanoparticles. A combination of translational and rotational mag-walking and sawtooth simulated annealing methods was used to find optimum structures of the various heterogeneous clusters identifiable in the mass spectra. Following these optimizations with ωB97X-D3 density functional theory calculations made it possible to rationalize the pattern of peaks in the mass spectra through computation of the binding energies of clusters involved in various growth and dissociation pathways. Testing these calculations against CCSD(T) and MP2 predictions of the structures and binding energies for small clusters demonstrates the accuracy of the chosen model chemistry. For the first time, the peaks corresponding with all detectable species in both the positive and negative ion mass spectra of ammonium nitrate are identified with their corresponding structures. Thermodynamic control of particle growth and decomposition of ions due to loss of ammonia or nitric acid molecules is indicated. Structures and interaction energies for larger (NH4NO3)n nanoparticles are also presented, including the prediction of new particle morphologies with trigonal pyramidal character.

Model and Energy Bounds for a Two-Dimensional System of Electrons Localized in Concentric Rings.

We study a two-dimensional system of interacting electrons confined in equidistant planar circular rings. The electrons are considered spinless and each of them is localized in one ring. While confined to such ring orbits, each electron interacts with the remaining ones by means of a standard Coulomb interaction potential. The classical version of this two-dimensional quantum model can be viewed as representing a system of electrons orbiting planar equidistant concentric rings where the kinetic energy may be discarded when one is searching for the lowest possible energy. Within this framework, the lowest possible energy of the system is the one that minimizes the total Coulomb interaction energy. This is the equilibrium energy that is numerically determined with high accuracy by using the simulated annealing method. This process allows us to obtain both the equilibrium energy and position configuration for different system sizes. The adopted semi-classical approach allows us to provide reliable approximations for the quantum ground state energy of the corresponding quantum system. The model considered in this work represents an interesting problem for studies of low-dimensional systems, with echoes that resonate with developments in nanoscience and nanomaterials.

Improved Sparse Mean Reverting Portfolio Selection Using Simulated Annealing and Extreme Learning Machine

We study the problem of selecting a sparse, mean reverting portfolio from a universe of assets using simulated annealing (SA). Assuming that assets follow a first order vector autoregressive process (VAR(1)), we make a number of improvements in existing methods. First, we extend the underlying asset dynamics to include a time-independent additive term, thereby enriching the model’s applicability. Second, we introduce Extreme Learning Machine (ELM) to decide whether to apply SA or settle for the much faster greedy solution. Finally, we improve the SA method by better calibration of the initial temperature and by determining the exact value of the weights within a selected dimension using the Rayleigh quotient. On real data, these changes result in more than 90% improvement in run time on average and 4.78% improvement in optimized mean reversion in our simulations. We also test the trading performance of our method on both simulated and real data and managed to achieve positive mean trading results in both cases.

High-Resolution Dipole Remote Detection Logging Based on Optimal Nonlinear Frequency Modulation Excitation.

In order to improve the detection range and imaging resolution of dipole remote detection logging, an optimal nonlinear frequency modulation (ONLFM) excitation method is proposed in this paper. In this method, the optimal waveform model of the sound source is designed with objective functions of SNR and resolution to obtain the highest resolution under the condition of the required SNR. This optimal model is a multi-constraint optimization problem, and the simulated annealing method has been used to solve it. Solving the optimal model can obtain the optimal spectrum, and the ONLFM waveform can be designed by using the stationary phase principle. Compared with the electric pulse sound source used in traditional technology, this ONLFM sound source can improve the energy and extend the frequency band range of the reflected wave, which can provide the higher resolution and SNR. The simulation results show that the ONLFM sound source can effectively improve the SNR and resolution of the reflected wave, and the detection range and imaging resolution of dipole shear wave remote detection will be improved.

Horizon picking algorithm using global optimization and coherence measurement in poststacked seismic data

Accurate horizon recognition within poststack seismic sections is important in seismic interpretation. Horizon picking techniques influence diverse seismic structural analyses and inversion methodologies. Despite encountering challenges such as computational demands and time constraints, the past few years have witnessed the development of numerous 2D and 3D methods. With the progress of modern computing, more robust and efficient techniques, harnessing artificial intelligence, have come to the fore. In this context, we develop an innovative cost-effective algorithm grounded in a global optimization framework. This algorithm combines the very fast simulated annealing method with a set of stability parameters and coherence measurements between neighboring seismic traces, which is used as the objective function. The search is executed on continuous and sequential clusters of seismic traces, with a focus on maximizing coherence amidst the presented events. We evaluate the algorithm’s efficacy by applying it to two distinct input data sets — enveloped and nonenveloped seismic traces. The initial application is to the time-migrated Marmousi data set, a synthetic marine data set originated from a complex geologic sedimentary basin situated in Angola, Africa. Subsequently, we apply the algorithm to depth-migrated land data extracted from a past survey conducted in the Tacutu Basin in northern Brazil. Outcomes arising from the application to 2D synthetic and field data sets underscore the method’s viability as a compelling alternative for seismic horizon picking within the time or depth domain.

Structural elucidation of the dichloridodioxido-[(4,7-dimethyl)-1,10-phenanthroline]molybdenum(VI) (C14H12Cl2MoN2O2)

In this work, the synthesis, characterization, and X-ray powder diffraction data for dichloridodioxido-[(4,7-dimethyl)-1,10-phenanthroline]molybdenum(VI) are reported. The crystal structure of this compound was solved from powder diffraction data using the simulated annealing method with a subsequent refinement using the Rietveld method. The dioxo-molybdenum (VI) complex C14H12Cl2MoN2O2 crystallizes in a monoclinic system with space group C2/c (N° 15) with refined unit-cell parameters a = 12.9495 (5) Å, b = 9.7752 (4) Å,c = 12.0069 (6) Å, β = 101.702 (3) °, unit-cell volume V = 1488.27 (11) Å3, and values of Z′ = 0.5 and Z = 4. The molecules are organized into chains diagonally along the a and c axis. Parallel polyhedra are observed along these axes formed by the interactions of Mo, Cl, O, and N atoms present in the coordination sphere. The crystalline packing of this dioxo-molybdenum (VI) complex is dominated by five intermolecular hydrogen bonds, two intramolecular hydrogen bonds, and the four interactions between the centroids (CgI⋯CgJ) of the aromatic rings. An analysis of the Hirshfeld surface revealed that the greatest contributions of the attractive forces are given by H⋯Cl/Cl⋯H, H⋯C/C⋯H, H⋯O/O⋯H, and H⋯H interactions.

Optimization by linear kinetic equations and mean-field Langevin dynamics

One of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al. in the middle of last century. In this paper, we show how the tools of linear kinetic theory allow the description of this gradient-free algorithm from the perspective of statistical physics and how convergence to the global minimum can be related to classical entropy inequalities. This analysis highlights the strong link between linear Boltzmann equations and stochastic optimization methods governed by Markov processes. Thanks to this formalism, we can establish the connections between the simulated annealing process and the corresponding mean-field Langevin dynamics characterized by a stochastic gradient descent approach. Generalizations to other selection strategies in simulated annealing that avoid the acceptance–rejection dynamic are also provided.

A comparison of meta-heuristic and hyper-heuristic algorithms in solving an urban transit routing problems

<p class="p1">Public transport is a serious problem that is difficult to solve in many countries. Public transport routing optimization problem also known as urban transit routing problem (UTRP) is time-consuming process, therefore effective approches are urgently needed. UTRP aims to minimize cost passenger and operator from a combination of route set. UTRP can be optimize with heuristics, meta-heuristics, and hyper-heuristics methods. In several previous studies, UTRP can be optimized with any meta-heuristics and hyper-heuristics methods. In this study we compare the performance of meta-heuristic methods, i.e. ill-climbing, simulated annealing, and hyper-heuristics method based on modified particle swarm optimization algorithm. The experimental results showed that the proposed methods could solve UTRP effectively. Regarding their performance, the results show that despite the generality of hyper-heuristics, their performance are competitive. More specifically, hyper-heuristics method is the best method compared to the other two methods in each dataset. In addition, compared to prior studies results, he proposed hyper-heuristics could outperform them in term of cost passenger of small dataset Mandl. The main contribution of this paper is that to best of our knowledge, it is the first study comparing the performance of meta-heuristics and hyper-heuristics approaches over UTRP.</p>

Optimization of Weibull Distribution Parameters with Application to Short-Term Risk Assessment and Strategic Investment Decision-Making

Accurate parameter estimation is fundamental in financial modeling, especially in investment analysis, where the Modified Internal Rate of Return (MIRR) plays a key role in evaluating investment performance. This study aims to enhance risk and return predictions in Sharia-compliant property investments by exploring the efficacy of various optimization techniques for estimating Weibull distribution parameters within the MIRR framework. To achieve this, we employed a comparative analysis of optimization methods, including Simulated Annealing (SA), Differential Evolution (DE), Genetic Algorithm (GA), and traditional Numerical Methods (NM). Performance was assessed through metrics such as Root Mean Squared Error (RMSE), Akaike Information Criterion (AIC), R-squared (R2) values, and Kolmogorov-Smirnov (KS) statistics. The results reveal that metaheuristic algorithms (SA, DE, GA) significantly outperform traditional numerical methods in terms of parameter estimation accuracy. Specifically, SA achieved the lowest RMSE of 0.042, with a Weibull shape parameter estimate of 1.254 and variance of 0.004, followed closely by DE with an RMSE of 0.048, and GA with 0.046. In contrast, NM exhibited a higher RMSE of 0.067, with a shape parameter estimate of 1.310 and a variance of 0.006. The AIC values for metaheuristic methods ranged from 14.25 to 14.68, compared to 15.12 for NM, and R2 values for metaheuristic methods ranged from 0.932 to 0.945, compared to 0.910 for NM. KS statistics further underscored the superior model fit of metaheuristics, with SA showing the lowest KS value of 0.045. The study underscores the critical role of metaheuristic optimization in improving the accuracy of parameter estimation based on MIRR models. This enhancement provides more reliable risk assessments and returns predictions, offering valuable insights for informed investment decision-making and contributing to optimized financial outcomes in the property sector.

The imprint of conservation laws on correlated particle production

The study of event-by-event fluctuations of net-baryon number in a subspace of full phase space is a promising direction for deciphering the structure of strongly interacting matter created in collisions of relativistic heavy nuclei. Such fluctuations are generally suppressed by exact baryon number conservation. Moreover, the suppression is stronger if baryon number is conserved locally. In this report we present a conceptually new approach to quantify correlations in rapidity space between baryon-antibaryon, baryon-baryon, and antibaryon-antibaryon pairs and demonstrate their impact on net-baryon number fluctuations. For the special case of Gaussian rapidity distributions, we use the Cholesky factorization of the covariance matrix, while the general case is introduced by exploiting the well-known Metropolis and Simulated Annealing methods. The approach is based on the use of the canonical ensemble of statistical mechanics for baryon number and can be applied to study correlations between baryons as well as strange and/or charm hadrons. It can also be applied to describe relativistic nuclear collisions leading to the production of multi-particle final states. One application of our method is the search for formation of proton clusters at low collision energies emerging as a harbinger of the anticipated first-order chiral phase transition. In a first step, the results obtained are compared to the recent measurements from the CERN ALICE collaboration. Such investigations are key to explore the phase diagram of strongly interacting matter and baryon production mechanisms at energy scales from several GeV to several TeV.

Metaheuristic algorithms for capacitated controller placement in software defined networks considering failure resilience

SummarySoftware‐defined networking (SDN) has revolutionized network architectures by decoupling the control plane from the data plane. An intriguing challenge within this paradigm is the strategic placement of controllers and the allocation of switches to optimize network performance and resilience. In the event of a controller failure, the switches are disconnected from the controller until they are reassigned to other active controllers possessing sufficient spare capacity. The reassignment could lead to a significant rise in propagation latency. This correspondence presents a mathematical model for capacitated controller placement, strategically designed to anticipate failures and prevent a substantial increase in worst‐case latency and disconnections. The aim is to minimize the worst‐case latency between switches and their backup controllers and among the controllers. Four metaheuristic algorithms are proposed including, an enhanced genetic algorithm (CCPCFR‐EGA), particle swarm optimization (CCPCFR‐PSO), a hybrid particle swarm optimization and simulated annealing algorithm (CCPCFR‐HPSOSA), and a grey wolf optimization algorithm (CCPCFR‐GWO). These algorithms are compared with a simulated annealing method and an optimal method. Evaluation conducted on four network datasets demonstrates that the proposed metaheuristic methods are faster than the optimal method. The experimental outcome indicates that CCPCFR‐HPSOSA and CCPCFR‐GWO outperform the other methods, consistently providing near‐optimal solutions. However, CCPCFR‐GWO is preferred over CCPCFR‐HPSOSA due to its faster execution time. Specifically, CCPCFR‐GWO achieves an average speed‐up of 3.9 over the optimal for smaller networks and an average speed‐up of 31.78 for larger networks, while still producing near‐optimal solutions.

Modeling and simulation of optical system error transmission in the laser tracker

The optical system of the laser tracker utilizes plane mirrors to construct a reflective path, reducing its size and weight. However, maintaining the alignment of the laser with the ideal optical axis during its propagation in the optical system poses significant challenges in the design, fabrication, and assembly of the optical system. This paper explores the principle of error propagation during the assembly process of the optical system and improves the accuracy of the output laser through a numerical simulation and optimization methods. A general error model for the optical system is established to understand the principle of error propagation. A Monte Carlo numerical simulation and sensitivity analysis are used to study the influence of various errors on the accuracy of the output laser. The machining errors are optimized using a simulated annealing method to balance the manufacturing difficulty and system accuracy. The assembly process is also optimized to reduce the degrees of freedom and the number of optical parts required, and verified by experiments. The experimental results indicate that the average position error of the output laser is 15.743 µm, and the average angle error is 1.427′′. This study provides what we believe is a novel approach and methodology for the design and alignment of optical systems.

Optimum Cutting Parameters for Carbon-Fiber-Reinforced Polymer Composites: A Synergistic Approach with Simulated Annealing and Genetic Algorithms in Drilling Processes

This paper presents a unique approach to generate a number of cutting knowledge blocks for the surface roughness analysis of the drilling process for carbon-fiber-reinforced polymer composite (CFRP) materials. The influence of drilling on the surface quality of woven CFRP materials was investigated experimentally. The CFRP material (0/90° fiber orientation) was drilled at different cutting parameters and the surface roughness of the hole was measured. A set of tests was carried out using carbide drills of 8 mm in diameter at 50, 70, and 90 m/min cutting speeds, 2, 3, and 4 flute numbers, and 0.2, 0.3, and 0.4 mm/rev feed rates. The Simulated Annealing (SA) and Genetic Algorithm (GA) methods were used for optimization. Based on the experimental findings and optimization techniques applied, optimal cutting parameters were derived, which were subsequently adjusted to enhance surface quality. Overall, the cutting parameters are carefully optimized to achieve good surface roughness quality in the drilling of CFRP.

Molecular dynamics simulation and experimental study of the material machinability characteristics and crack propagation mechanisms for fused silica double nanoscratches

Fused silica is a high-purity, hard and brittle, difficult-to-machine amorphous material that is widely used in the aerospace, optical instruments, semiconductors, microelectronics and other important fields. However, the influence of adjacent scratches on material deformation and subsurface damage during ultraprecision machining by abrasive particles is not well understood. This study aims to investigate the influence of micron-spaced double scratches on the deformation and damage for fused silica through molecular dynamics simulations and double nanoscratch experiments. An amorphous model of fused silica is created using a two-step simulated annealing method with three-directional periodic boundary conditions. Variable loaded double scratches with different nanometer distances are simulated on the surface of the model, and variable loaded double scratch experiments with varying micron-sized distances between scratches are conducted for fused silica wafers. The simulation and experimental results reveal that the deformation of fused silica during nanoscale double scratching involves both elastic and plastic deformation, and the surface and subsurface damage primarily consists of radial, lateral, Hertzian, and median cracks. The distance between the double scratches affects the load variation, surface and subsurface crack propagation, extent of material damage and removal rate, and surface roughness. Examination of the material subsurfaces using the FIB-TEM sample preparation and testing technique shows that the distance between the double scratches also influences the subsurface damage to the material.

Neuron grouping and mapping methods for 2D-mesh NoC-based DNN accelerators

Deep Neural Networks (DNNs) have gained widespread adoption in various fields; however, their computational cost is often prohibitively high due to the large number of layers and neurons communicating with each other. Furthermore, DNNs can consume a significant amount of energy due to the large volume of data movement and computation they require. To address these challenges, there is a need for new architectures to accelerate DNNs. In this paper, we propose novel neuron grouping and mapping methods for 2D-mesh Network-on-Chip (NoC)-based DNN accelerators considering both fully connected and partially connected DNN models. We present Integer Linear Programming (ILP) and simulated annealing (SA)-based neuron grouping solutions with the objective of minimizing the total volume of data communication among the neuron groups. After determining a suitable graph representation of the DNN, we also apply ILP and SA methods to map the neurons onto a 2D-mesh NoC fabric with the objective of minimizing the total communication cost of the system. We conducted several experiments on various benchmarks and DNN models with different pruning ratios and achieved an average of 40-50% improvement in communication cost.

Zigzag phase transition of electrons confined within a thin annulus region

We consider a semiclassical approach to study the possible stabilization of a zigzag phase for a system of interacting electrons confined within a thin annulus region with infinite inner/outer walls. The electrons are considered spinless and interact via the standard Coulomb interaction potential. The classical minimum energy configuration of the system due to the Coulomb repulsion between electrons is accurately determined by using the simulated annealing method. As the number of electrons increases we see the appearance and stabilization of a two-ring structure with zigzag patterns. Further increase of the number of electrons appears to eventually lead to the collapse of the two-ring zigzag structure. A simple quantum treatment of the nodal features of the free many-particle wave function shows the appearance of nodal domain patterns that are consistent with the zigzag features that were observed in the classical model.

Shell with Striped, Helical, and Bipolar Lamellae Structures from Soft Confinement-Induced Self-Assembly of AB Diblock Copolymers on a Nanocylinder.

The soft confinement-induced self-assembly of AB diblock copolymers on a nanocylinder is studied via a simulated annealing method. The formation of multiple copolymer shells was predicted by varying the interfacial interaction, the size of confinement, and the height and diameter of the nanocylinder. The competition between solvent repulsion and nanocylinder attraction determined the degree of encapsulation of the copolymer shell. The formation of a helical copolymer shell was induced by the maximization of conformational entropy. The preferential distribution position of copolymers on anisotropic nanocylinder surfaces was induced by interfacial energy minimization. Our study contributes to the understanding of the formation mechanism of the helical structure in block copolymer aggregates and the fabrication of copolymer shells with predesigned morphologies.