Simple Optimization Technique Research Articles

Gegenbauer Graph Neural Networks for Time-Varying Signal Reconstruction.

Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series forecasting. Accurately capturing the spatio-temporal information inherent in these signals is crucial for effectively addressing these tasks. However, existing approaches relying on smoothness assumptions of temporal differences and simple convex optimization techniques that have inherent limitations. To address these challenges, we propose a novel approach that incorporates a learning module to enhance the accuracy of the downstream task. To this end, we introduce the Gegenbauer-based graph convolutional (GegenConv) operator, which is a generalization of the conventional Chebyshev graph convolution by leveraging the theory of Gegenbauer polynomials. By deviating from traditional convex problems, we expand the complexity of the model and offer a more accurate solution for recovering time-varying graph signals. Building upon GegenConv, we design the Gegenbauer-based time graph neural network (GegenGNN) architecture, which adopts an encoder-decoder structure. Likewise, our approach also uses a dedicated loss function that incorporates a mean squared error (MSE) component alongside Sobolev smoothness regularization. This combination enables GegenGNN to capture both the fidelity to ground truth and the underlying smoothness properties of the signals, enhancing the reconstruction performance. We conduct extensive experiments on real datasets to evaluate the effectiveness of our proposed approach. The experimental results demonstrate that GegenGNN outperforms state-of-the-art methods, showcasing its superior capability in recovering time-varying graph signals.

(Invited) 3D Printing of 2D Materials for Optimized Electrochemical Performance

Electrochemical energy storage (EES) and conversion devices (e.g. batteries, supercapacitors, and reactors) are emerging as primary methods for global efforts to shift energy dependence from limited fossil fuels towards sustainable and renewable resources. These devices, while showing great potential for meeting some key metrics set by conventional technologies, still face significant limitations. For example, an EES device tends to exhibit large energy density (e.g. lithium-ion battery) or power density (e.g. supercapacitor), but not both. This inability of a single device to simultaneously achieve both metrics represents a major obstacle to widespread adoption of EES devices. Similarly, many catalytic processes depend on expensive platinum group metals (PGM) because non-PGM materials have poor performance or durability. Though the integration of 2D materials (e.g. graphene, dichalcogenides, MXene, etc.) into electrochemical devices has yielded some exciting results towards tackling these issues, significant improvements are still needed. One approach to optimizing the performance of these devices is to focus on one of the fundamental processes that occur in these systems: mass (or charge) transport. The efficient transport of ions within EES and conversion devices is critical to realizing better performance and durability. The pore structure of the electrode is a key factor in determining this transport phenomena, but in many cases, engineering the pore structure in a highly deterministic fashion can be challenging. In this work, we explore a number of additive manufacturing methods (e.g. direct ink write, projection microstereolithography, etc.) to engineer the pore structure of device electrodes. We also determine effective electrode geometries using both simple theory and topology optimization techniques. The topology optimization couples the solution of the forward electrochemical problem over the full electrode domain with gradient-based optimization. The output of our code is a three-dimensional CAD representation which optimizes over specific performance metrics and which can be used to print functional electrodes. This work provides a systematic path toward automated design and fabrication of engineered electrodes with precise control over the fluid and species distribution.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Size Optimization of Truss Structures Based on Genetic Algorithm by Developing Single-point Crossover with Bit-wise Mutation Using FORTRAN Programming

A truss is a collection of axially loaded structural elements connected through pin joints. Optimization of truss structures indicates the determination of best possible conditions that are necessary for achieving the most economical design in terms of lowest possible weights of the truss elements. According to recent studies, Size, Topology and Shape based optimizations are the three possible independent optimization scopes for finding the optimum weight of a truss. The current study focuses on the size optimization of truss structure and aims to identify the most cost-effective sections of the truss using a powerful evolutionary optimization technique named as Genetic Algorithm (GA). Here single point cross over method and bit wise mutation operator are adopted for expanding the search space with the assigned displacement and stress constraints. Fortran based sub routines are developed for each individual steps of GA such as fitness evaluation, selection, cross-over and mutation. Finaly the complete program is run for validation of its outcome. While comparing with the solution of an existing literature regarding a minimization of objective function having two design variables the outcomes tend to show a good correlation. Further, the study is extended for the weight minimization of two widely used truss having 10 members and 17 members respectively with standard Finite Element Method of analysis. Minimum weight of each truss is obtained via convergence plot and compared with the existing literatures. With this simple but efficient global optimization technique optimum weight of truss structure can easily be achieved.

A simple and fast split-model optimization technique for RF couplers of helix traveling-wave tubes

A simple and fast split-model optimization technique for RF couplers of helix traveling-wave tubes

A Mayfly-Based Approach for CMOS Inverter Design with Symmetrical Switching

This paper presents a novel approach to designing a CMOS inverter using the Mayfly Optimization Algorithm (MA). The MA is utilized in this paper to obtain symmetrical switching of the inverter, which is crucial in many digital electronic circuits. The MA method is found to have a fast convergence rate compared to other optimization methods, such as the Symbiotic Organisms Search (SOS), Particle Swarm Optimization (PSO), and Differential Evolution (DE). A total of eight different sets of design parameters and criteria were analyzed in Case I, and the results confirmed compatibility between the MA and Spice techniques. The maximum discrepancy in fall time across all design sets was found to be 2.075711 ns. In Case II, the objective was to create a symmetrical inverter with identical fall and rise times. The difference in fall and rise times was minimized based on Spice simulations, with the maximum difference measuring 0.9784731 ns. In Case III, the CMOS inverter was designed to achieve symmetrical fall and rise times as well as propagation delays. The Spice simulation results demonstrated that symmetry had been successfully achieved, with the minimum difference measuring 0.312893 ns and the maximum difference measuring 1.076540 ns. These Spice simulation results are consistent with the MA results. The results conclude that the MA is a reliable and simple optimization technique and can be used in similar electronic topologies.

On a Geometric Programming Approach to Profit Maximization: The Case of CES Technology

The profit maximization problem takes a central place in the theory of the firm, especially when conditions for perfect competition hold. In this paper, we solve the profit maximization problem of a perfectly competitive firm when the constant elasticity of substitution (CES) production function with n≥2 inputs describes its technology. Commonly, this problem is solved by using multivariable differential calculus. However, to avoid tedious algebraic manipulations and bypass checking nontrivial necessary and sufficient conditions, we employ geometric programming (GP), and the power mean inequality (PMI) as an elegant complementary tool to multivariable calculus. Since the GP and the PMI are simple optimization techniques without derivatives, they can provide new insights into the given problem to managers, students, and other audiences who may be unfamiliar with multivariable differential calculus. Additionally, by using the properties of limits, we show that the solution to the profit maximization problem with Cobb-Douglas technology is a limiting case of our result.

Improving genetic algorithms for solving the SVP: focusing on low memory consumption and high reproducibility

The shortest vector problem (SVP) is absolutely essential in lattice-based cryptography. In this paper, we significantly improve genetic algorithms (GAs) for solving the SVP. GAs, which are simple and powerful optimization techniques, that have the potential to eliminate the limitations of the existing fast SVP algorithms. We improve the entire phase of the GA construction. Our proposed method is based on the concept of low memory consumption and high reproducibility, and this is the main and significant difference between our algorithm and the other SVP algorithms. Our contributions are twofold. First, we developed a new GA for solving the SVP and achieved a considerable improvement in the running time performance. Second, we interpreted certain genetic operations, such as mutation and crossover, in the context of lattices, which has not been done in previous studies. The general result of this paper is that we showed the potential of GAs in the field of lattices.

An adaptive multilevel thresholding method with chaotically-enhanced Rao algorithm.

Multilevel image thresholding is a well-known technique for image segmentation. Recently, various metaheuristic methods have been proposed for the determination of the thresholds for multilevel image segmentation. These methods are mainly based on metaphors and they have high complexity and their convergences are comparably slow. In this paper, a multilevel image thresholding approach is proposed that simplifies the thresholding problem by using a simple optimization technique instead of metaphor-based algorithms. More specifically, in this paper, Chaotic enhanced Rao (CER) algorithms are developed where eight chaotic maps namely Logistic, Sine, Sinusoidal, Gauss, Circle, Chebyshev, Singer, and Tent are used. Besides, in the developed CER algorithm, the number of thresholds is determined automatically, instead of manual determination. The performances of the developed CER algorithms are evaluated based on different statistical analysis metrics namely BDE, PRI, VOI, GCE, SSIM, FSIM, RMSE, PSNR, NK, AD, SC, MD, and NAE. The experimental works and the related evaluations are carried out on the BSDS300 dataset. The obtained experimental results demonstrate that the proposed CER algorithm outperforms the compared methods based on PRI, SSIM, FSIM, PSNR, RMSE, AD, and NAE metrics. In addition, the proposed method provides better convergence regarding speed and accuracy.

Hybrid Method Implementation Fuzzy K-Nearest Neighbor (FK-NN) And Particle Swarm Optimization (PSO) for Classification of Liver Disease

Liver disease is a disease that attacks the liver or liver where this disease is caused by viral infections, toxic materials and bacteria, causing inflammation of the liver and causing the liver to not function properly. Therefore, the author will conduct research to make a Liver Disease Classification program. This research will use Fuzzy K-Nearest Neighbor (FK-NN) and Particle Swarm Optimization (PSO) methods. Fuzzy K-Nearest Neighbor is a classification method that combines fuzzy and k-nearest neighbor algorithms. Particle Swarm Optimization is a simple optimization technique to apply and modify several parameters. This research will implement the application design to the lines of web-based program code using the Python language and the Django framework. This study resulted in the value of the accuracy range obtained by the PSO-FKNN hybrid method is 66 to 74 (in percent) compared to the range of accuracy values ??of FKNN without the hybrid method is 64.90% to 68.29% (in percent), the difference in the accuracy values ??obtained by PSO-FKNN FKNN is affected by changes in the position of the training and testing data in each test

(Invited) 3D Printing of 2D Materials for Optimized Electrochemical Performance

Electrochemical energy storage (EES) and conversion devices (e.g. batteries, supercapacitors, and reactors) are emerging as primary methods for global efforts to shift energy dependence from limited fossil fuels towards sustainable and renewable resources. These electric-based devices, while showing great potential for meeting some key metrics set by conventional technologies, still face significant limitations. For example, an EES device tends to exhibit large energy density (e.g. lithium-ion battery) or power density (e.g. supercapacitor), but not both. This inability of a single device to simultaneously achieve both metrics represents a major obstacle to widespread adoption of EES devices. Improvements in materials, such as the integration of 2D materials (e.g. graphene, dichalcogenides, MXene, etc.) into electrochemical devices has yielded some exciting results towards tackling this issue, but significant improvements are still needed. Our approach to simultaneously achieving high energy and power density is to focus on one of the fundamental processes that occur in these systems: mass (or charge) transport. The efficient transport of ions within EES devices is critical to realizing both large power and energy densities. The pore structure of the electrode is a key factor in determining this transport phenomena, but in many cases, engineering the pore structure in a highly deterministic fashion is not pursued or even possible for many electrode materials. In this work, we explore a number of additive manufacturing methods (e.g. direct ink write, projection microstereolithography, etc.) to engineer the pore structure of device electrodes. We also determine effective electrode geometries using both simple theory and topology optimization techniques. The topology optimization couples the solution of the forward electrochemical problem over the full electrode domain with gradient-based optimization. The output of our code is a three-dimensional CAD representation which optimizes over specific performance metrics and which can be used to print functional electrodes. This work provides a systematic path toward automatic design and fabrication of engineered electrodes with precise control over the fluid and species distribution.

Free vibration analysis and optimization of doubly-curved stiffened sandwich shells with functionally graded skins and auxetic honeycomb core layer

A review of the literature reveals a dearth of works on functionally graded material sandwich shells having an auxetic core layer. This study contributes an analytical approach for the free vibration analysis of doubly curved stiffened sandwich shells with the face sheets of functionally graded materials and the core layer of the auxetic honeycomb material. The theoretical formulation is established based on first-order shear deformation theory associated with the smeared stiffener method. The free vibration solution of simply supported shallow shells with the rectangular platform is derived using Navier’s form. The proposed methodology is general and can be applied to examine the natural frequencies of various shell types, including flat, cylindrical, spherical, and hyperbolic paraboloidal panels. Numerical results indicate that the fundamental frequency is largely influenced by the relative proportion of the constituent materials of the face layers, the geometrical parameters of the auxetic honeycomb core layer, as well as the stiffeners. Additionally, a simple optimization technique based on Rao algorithms is introduced to obtain the maximum fundamental frequency of the shell. It is shown that the shell parameters, particularly the thickness of the auxetic core and the number of stiffeners, can be tailored to maximize the natural frequency. Moreover, the optimal solutions are fully dependent on the material proportion of the functionally graded material, the geometry of the shell, and the geometrical parameters of the auxetic honeycomb core.

A comparison of minimum variance and maximum Sharpe ratio portfolios for mainstream investors

PurposeMotivated by the recent theoretical rehabilitation of mean-variance analysis, the authors revisit the question of whether minimum variance (MinVar) or maximum Sharpe ratio (MaxSR) investment weights are preferable in practical portfolio formation.Design/methodology/approachThe authors answer this question with a focus on mainstream investors which can be modeled by a preference for simple portfolio optimization techniques, a tendency to cling to past asset characteristics and a strong interest in index products. Specifically, in a rolling-window approach, the study compares the out-of-sample performance of MinVar and MaxSR portfolios in two asset universes covering multiple asset classes (via investable indices and their subindices) and for two popular input estimation methods (full covariance and single-index model).FindingsThe authors find that, regardless of the setting, there is no statistically significant difference between MinVar and MaxSR portfolio performance. Thus, the choice of approach does not matter for mainstream investors. In addition, the analysis reveals that, contrary to previous research, using a single-index model does not necessarily improve out-of-sample Sharpe ratios.Originality/valueThe study is the first to provide an in-depth comparison of MinVar and MaxSR returns which considers (1) multiple asset classes, (2) a single-index model and (3) state-of-the-art bootstrap performance tests.

NAVAL ARCHITECTURAL CONSIDERATIONS IN THE DESIGN OF FLOATING DOCK

A brief introduction about floating docks, its advantages and types have been described. The naval architectural considerations which play a significant role in the design of floating dock have been explained. Typical ratios of L/B and L/D as a function of Dock’s lifting capacity have been presented. Empirical formulation for the same have also been indicated wherever applicable. Intact stability and its criterion as applicable for a floating dock have been described. Critical positions during evolution of docking operation and important considerations while performing stability calculations have been highlighted. Attention has also been drawn to the damage stability of floating dock. Aspects of longitudinal and transverse bending moment, which are the governing aspects in the scantling calculations have been described. Also typical methods for securing and mooring of floating dock, without compromising on flexibility for docking operations have been described. Methodology and consideration which has to be kept in mind while using design software (such as NAPA) have been indicated. Simple size optimization techniques which result in steel / ballast volume reduction have also been explained.

Prediction and analysis of penetration rate in drilling operation using deterministic and metaheuristic optimization methods

AbstractThe rate of penetration (ROP) optimization is one of the most important factors in improving drilling efficiency, especially in the downturn time of oil prices. This process is crucial in the well planning and exploration phases, where the selection of the drilling bits and parameters has a significant impact on the total cost and time of the drilling operation. Thus, the optimization and best selection of the drilling parameters are critical. Optimization of ROP is difficult due to the complexity of the relationship between the drilling variables and the ROP. For this reason, the development of high-performance computer systems, predictive models, and algorithms will be the best solution. In this study, a new investigation approach for ROP optimization has been done regarding different ROP models (Maurer, Bingham, Bourgoyne and Young models), algorithms (Multiple regression, ant colony optimization (ACO), fminunc, fminsearch, fsolve, lsqcurvefit, lsqnonlin), and different objective functions. The well-known data from the Louisiana field in an offshore well have been used to compare the used parameter estimation approach with other techniques. Indeed, datasets from an onshore well in the Hassi Messaoud Algerian field are explored. The results confirmed the superiority and the effectiveness of B&Y models compared to Bingham and Maurer models. Fminsearch, lsqcurvefit, ACO, and Excel (GRG) algorithms give the best results in ROP prediction while the application of the MNLR approach. Using the mean squared error (MSE) and the determination coefficient (R$$^{2}$$2) as objective functions significantly increases the accuracy prediction where the results given are ($$R=0.9522$$R=0.9522,$$RMSE=2.85$$RMSE=2.85) and ($$R= 0.9811$$R=0.9811,$$RMSE=4.08$$RMSE=4.08) for Wells 1 and 2, respectively. This study validates the application of B&Y model in both onshore and offshore wells. The findings reveal to deal with data limitation problems in ROP prediction. Simple and effective optimization techniques that require less memory space and computational time have been provided.

Aviation Turbine Fuel Thermal Conductivity: A Predictive Approach Using Entropy Scaling-Guided Machine Learning with Experimental Validation.

Although typical aircraft fuel thermal management analysis relies upon temperature-dependent thermodynamic and transport properties of aviation turbine fuel, the variation in properties associated with compositional variation in fuels and the subsequent impacts on system performance are not well established. With this in mind, the present work aimed to develop a predictive model of aviation turbine fuel thermal conductivity which utilized only compositional (hydrocarbon) and state (temperature and pressure) inputs and had errors within the bounds of typical uncertainty of the associated test data (3%). A novel modeling approach was developed to predict thermal conductivity using pseudo-component entropy scaling techniques with a machine learning-developed intermediate step in the overall model. Simple hyper-parameter optimization techniques were developed to promote model stability, computational efficiency, and long-term repeatability of the novel architecture. Validation data were gathered which included four fuel samples (3 JP-5 and 1 F-24), which underwent two-dimensional gas chromatography compositional testing and temperature-dependent density, viscosity, thermal conductivity, and specific heat testing. Model performance on the validation data set assembled from the literature data and present efforts showed an average deviation of 1% and an absolute average deviation of 2.5%. Model outputs outside the validation range are well-behaved and are expected to perform well on a large range of liquid hydrocarbon mixtures with the overall process expected to be well suited to prediction of other properties.

Black-Hole Optimization Applied to the Parametric Estimation in Distribution Transformers Considering Voltage and Current Measures

The problem of parametric estimation in single-phase transformers is addressed in this research from the point of view of metaheuristic optimization. The parameters of interest are the series resistance and reactance as well as the magnetization resistance and reactance. To obtain these parameters considering only the voltage and the currents measured in the terminals of the transformer, a nonlinear optimization model that deals with the minimization of the mean square error among the measured and calculated voltage and current variables is formulated. The nonlinear programming model is solved through the implementation of a simple but efficient metaheuristic optimization technique known as the black-hole optimizer. Numerical simulations demonstrate that the proposed optimization method allows for the reduction in the estimation error among the measured and calculated variables when compared with methods that are well established in the literature such as particle swarm optimization and genetic algorithms, among others. All the simulations were carried out in the MATLAB programming environment.

Multi-Objective Energy Management and Charging Strategy for Electric Bus Fleets in Cities Using Various ECO Strategies

The paper presents use case simulations of fleets of electric buses in two cities in Europe, one with a warm Mediterranean climate and the other with a Northern European (cool temperate) climate, to compare the different climatic effects of the thermal management strategy and charging management strategy. Two bus routes are selected in each city, and the effects of their speed, elevation, and passenger profiles on the energy and thermal management strategy of vehicles are evaluated. A multi-objective optimization technique, the improved Simple Optimization technique, and a “brute-force” Monte Carlo technique were employed to determine the optimal number of chargers and charging power to minimize the total cost of operation of the fleet and the impact on the grid, while ensuring that all the buses in the fleet are able to realize their trips throughout the day and keeping the battery SoC within the constraints designated by the manufacturer. A mix of four different types of buses with different battery capacities and electric motor specifications constitute the bus fleet, and the effects that they have on charging priority are evaluated. Finally, different energy management strategies, including economy (ECO) features, such as ECO-comfort, ECO-driving, and ECO-charging, and their effects on the overall optimization are investigated. The single bus results indicate that 12 m buses have a significant battery capacity, allowing for multiple trips within their designated routes, while 18 m buses only have the battery capacity to allow for one or two trips. The fleet results for Barcelona city indicate an energy requirement of 4.42 GWh per year for a fleet of 36 buses, while for Gothenburg, the energy requirement is 5 GWh per year for a fleet of 20 buses. The higher energy requirement in Gothenburg can be attributed to the higher average velocities of the bus routes in Gothenburg, compared to those of the bus routes in Barcelona city. However, applying ECO-features can reduce the energy consumption by 15% in Barcelona city and by 40% in Gothenburg. The significant reduction in Gothenburg is due to the more effective application of the ECO-driving and ECO-charging strategies. The application of ECO-charging also reduces the average grid load by more than 10%, while shifting the charging towards non-peak hours. Finally, the optimization process results in a reduction of the total fleet energy consumption of up to 30% in Barcelona city, while in Gothenburg, the total cost of ownership of the fleet is reduced by 9%.

(Invited) Additively Manufactured Graphene Aerogel Supercapacitors

Electrochemical energy storage (EES) and conversion devices (e.g. batteries, supercapacitors, and reactors) are emerging as primary methods for global efforts to shift energy dependence from limited fossil fuels towards sustainable and renewable resources. These electric-based devices, while showing great potential for meeting some key metrics set by conventional technologies, still face significant limitations. For example, an EES device tends to exhibit large energy density (e.g. lithium-ion battery) or power density (e.g. supercapacitor), but not both. This inability of a single device to simultaneously achieve both metrics represents a major obstacle to widespread adoption of EES devices. Improvements in materials, such as the integration of 2D materials (e.g. graphene, dichalcogenides, MXene, etc.) into electrochemical devices has yielded some exciting results towards tackling this issue, but significant improvements are still needed. Our approach to simultaneously achieving high energy and power density is to focus on one of the fundamental processes that occur in these systems: mass (or charge) transport. The efficient transport of ions within EES devices is critical to realizing both large power and energy densities. The pore structure of the electrode is a key factor in determining this transport phenomena, but in many cases, engineering the pore structure in a highly deterministic fashion is not pursued or even possible for many electrode materials. In this work, we explore a number of additive manufacturing methods (e.g. direct ink write, projection microstereolithography, etc.) to engineer the pore structure of device electrodes. We also determine effective electrode geometries using both simple theory and topology optimization techniques. The topology optimization couples the solution of the forward electrochemical problem over the full electrode domain with gradient-based optimization. The output of our code is a three-dimensional CAD representation which optimizes over specific performance metrics and which can be used to print functional electrodes. This work provides a systematic path toward automatic design and fabrication of engineered electrodes with precise control over the fluid and species distribution.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Enhanced fusidic acid transdermal delivery achieved by newly isolated and optimized Bacillus cereus Keratinase

The expanding interest in bioremediation of poorly degradable wastes has led to the discovery of many microbial enzymes capable of degrading recalcitrant substances such as keratinaceous wastes that are produced in vast quantities on daily basis. Such enzymes don’t only work as a bioremediation tool but also have multiple beneficial applications. Hence, environmental samples were collected from sewage water, soils, animal bodies and feces in order to isolate keratinase producing organisms. Keratinolytic isolates were isolated from sewage water; soils; animal bodies; animal feces, and identified both traditionally and molecularly through 16S-rRNA sequencing to be Bacillus cereus strain. Produced keratinase was purified by centrifugation, ammonium sulfate precipitation, and HPLC, then assayed using Azokeratine based analysis. keratinase quantification yielded a 420 ± 1.63 U/mL. Optimum production was obtained at 40 °C, pH 7, 3 days incubation, 0.5 % substrate, 0.4 g/l magnesium ion, 2% v/v inoculum, 0.5 g/l NaCl, 0.4 g/l K2HPO4, and 0.3 g/l KH2PO4. Production was increased by 1.9 fold after acclimatization to reach 809 ± 2.49 U/mL in only 2 days. Thermal and pH stability testing revealed the effectiveness of the isolated keratinase over a wide range of temperatures at neutral pH. Finally, isolated keratinase enhanced fusidic acid topical penetration to treat induced deep skin bacterial infection in mice. A 1.4 fold decrease in treatment period and a 2 log cycle reduction in the viable count of Staphylococcus aureus were noticed in keratinase/fusidic acid treated mice compared to mice treated with fusidic acid alone. This study shed some light on a simple keratinase production optimization technique and suggested a promising medical application of this enzyme as a drug delivery agent.

Forecasting with full use of data without interpolation on logistic curve model with missing data

We propose a forecasting method based on a logistic curve model with missing data, which are a ubiquitous problem in social science forecasting, especially in marketing. The method completely recovers parameters of the difference equation when data are on an exact solution curve because it uses an unequal step difference equation that has an exact solution. It makes full use of data without wasting any data or generating plausible data for the missing data. It only requires regression analysis and a simple optimization technique and showed better fitting than two conventional methods for three actual datasets.