Simplex Technique Research Articles

Advanced Applications and Methodologies in Mathematical Optimization and Operations Research: Insights into Linear Programming, Nonlinear Programming, and Decision-Making Frameworks

Mathematical optimization and operations research are pivotal disciplines in solving complex decision-making problems across industries. This research delves into advanced methodologies within these fields, with a focus on linear programming (LP), nonlinear programming (NLP), and their applications in optimizing processes and resource allocation. Linear programming, with its capacity to model and solve large-scale problems, remains a cornerstone for optimization, particularly in logistics, finance, and manufacturing. Nonlinear programming, characterized by its ability to handle complex, real-world systems with non-convex functions, expands the scope of optimization to include dynamic and intricate challenges such as energy management and machine learning. This study investigates state-of-the-art algorithms, including interior-point methods, dual simplex techniques, and gradient-based approaches, to enhance the efficiency and accuracy of solutions. By addressing theoretical advancements and practical implementations, this research bridges the gap between mathematical rigor and real-world applications. The insights gained are expected to contribute significantly to operational efficiency, strategic planning, and decision-making in diverse fields.

Breast cancer diagnosis using hybrid AlexNet-ELM and chimp optimization algorithm evolved by Nelder-mead simplex approach

This study proposes a Hybrid AlexNet-Extreme Learning Machine (ELM) approach for breast cancer diagnosis using mammography images. Batch normalization is applied to improve AlexNet's performance, and the chimp optimization algorithm (ChOA) is utilized to avoid sub-optimal solutions in ELM. The Nelder-mead simplex (NEMS) technique is then employed to enhance the convergence behavior of ChOA. The study's main contributions are the proposed hybrid model and the application of ChOA and NEMS techniques to improve the performance of ELM. The proposed model is evaluated using the CBIS-DDSM dataset, with wiener and CALHE filters used as preprocessors. The effectiveness of the classification is examined using five optimization algorithms, and several metrics. The outcomes demonstrate that CALHE filter offered the best performance overall, and AlexNet-BN-ELM-CHOA-NEMS was the most accurate of the five models, with a sensitivity of 96.03 %, a specificity of 94.60 %, and an overall accuracy of 95.32 %. The findings demonstrate the effectiveness of the proposed model in breast cancer diagnosis.

A Novel Algorithm to Find the Best Solution for Pentagonal Fuzzy Numbers with Linear Programming Problems

Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking function (RF) approaches for solving fuzzy linear programming problems (FLPP) with a pentagonal fuzzy number (PFN) have been proposed, based on new ranking functions (N RF). The simplex method (SM) is very easy to understand. Finally, numerical examples (NE) are used to demonstrate the suggested approach's computing process.

Adaptive infinite impulse response system identification using an enhanced golden jackal optimization

Golden jackal optimization (GJO) is inspired by the cooperative attacking behavior of golden jackals and mainly simulates searching for prey, stalking and enclosing prey, and pouncing on prey to solve complicated optimization problems. However, the basic GJO has the disadvantages of premature convergence, a slow convergence rate and low computation precision. To enhance the overall search and optimization abilities, an enhanced golden jackal optimization (EGJO) method with the elite opposition-based learning technique and the simplex technique is proposed to address adaptive infinite impulse response system identification. The intention is to minimize the error fitness value and obtain the appropriate control parameters. The elite opposition-based learning technique boosts population diversity, enhances the exploration ability, extends the search range and avoids search stagnation. The simplex technique accelerates the search process, enhances the exploitation ability, improves the computational precision and increases the optimization depth. EGJO can not only achieve complementary advantages to avoid search stagnation but also balance exploration and exploitation to arrive at the best value. Three sets of experiments are used to verify the effectiveness and feasibility of EGJO. The experimental results clearly demonstrate that the optimization efficiency and recognition accuracy of EGJO are superior to those of AOA, GTO, HHO, MDWA, RSO, WOA, TSA and GJO. EGJO has a faster convergence rate, higher computation precision, better control parameters and better fitness value, and it is stable and resilient in solving the IIR system identification problem.

Production Optimization Using Fuzzy Linear programming Method (Case Study: UMKM Untir-untir and Raja Manis Factory)

Production efficiency and performance optimization in a company can be achieved by using an optimization model. An optimisation model can be written in a function of equation and equation known as a Linear Program. A Linear program can be combined with a fuzzy value to adjust a production problem model that is heavily dependent on an unstable supply. This modeling is known as Fuzzy Linear programming. Using Fuzzy Linear programming, the production problems of micro, small and medium-sized enterprises Untir-untir and King Sweet are analyzed and solved with the heLP of simulation programs. Fuzzy Linear programming solutions use simplex methods using POM-QM software to complete complex calculations. Completion with the fuzzy simplex method consists of several steps namely calculating the optimal bottom and upper boundaries with the maximizing simplex technique, modifying the initial equation by adding the variable λ, and finishing it with the two-phase simplex approach. Results of completion with the simulation program showed the estimated amount of profit using the Linear Program equation of Rp. 1,378,723 and using the Fuzzy Linear programming equation with a 10% tolerance of Rp. 1,447,470.

A novel global maximum power point tracking algorithm based on Nelder-Mead simplex technique for complex partial shading conditions

In this study, a novel global maximum power point tracking (GMPPT) algorithm for photovoltaic generation system (PGS) operating under complex partial shading conditions is proposed. The presented GMPPT technique is based on Nelder-Mead (NM) simplex technique, which is commonly used to solve complicated optimization problems and has advantages such as simple implementation, derivative-free nature, fast convergence, and high accuracy. In this study, simulation results of 252 shading patterns with non-repeatable irradiance levels and 243 shading patterns under repeatable irradiance levels are provided to validate the effectiveness of the proposed GMPPT methods. According to the simulated and experimental results, the presented NM-based GMPPT approach has the highest success rate and tracking accuracy under all the tested shading patterns compared with other GMPPT methods.

New Approach to Solve Cubic Objective Function Programming Problem

In this paper, a cubic objective programming problem (COPP) is defined. Introduced a new modification to solve a cubic objective programming problem. Suggested an algorithm for its solution. Also reported the algorithm of the usual simplex method. Application talks about how the developed algorithm can be used to unravel non-linear. The proposed technique, modification simplex technique, can be used with the constructed numerical examples an illustrative numerical problems are given to demonstrate the algorithms.

Improved Preisach Model for the Vector Hysteresis Property of Soft Magnetic Composite Materials Based on the Hybrid Technique of SA-NMS

The two-dimensional hysteresis property of the soft magnetic composite (SMC) material under circular rotational excitation was measured by the experimental platform. The first-order reversal curves and the corresponding scalar Everett functions can be numerically generated by the measured major hysteresis loops along the orthogonal easy axis and hard axis. Different from the classical model, an improved vector Preisach hysteresis model that considers the anisotropic property of the SMC materials under vector magnetic excitation was put forward by introducing two parameters w and z. The two parameters were used to identify the vector Everett functions and adjust the shape of hysteresis curves under different magnitudes of the magnetic flux density. Furthermore, an efficient hybrid algorithm that combines simulated annealing with Nelder-Mead simplex technique was proposed for the accurate extraction of optimal parameters. The simulated results based on the improved model agree well with the measured ones; thus, the effectiveness and accuracy of the proposed method were verified.

Evaluation of constraint in photovoltaic models by exploiting an enhanced ant lion optimizer

Parameter estimation of photovoltaic models is a critical step in the control and management of photovoltaic equipment. In this study, to estimate photovoltaic model parameters efficiently and accurately, an enhanced Ant Lion Optimizer is designed, which is on account of the opposition-based learning mechanism and the Nelder-Mead simplex technique. This optimizer has a mediocre performance and suffers from high uncertainty in finding global optima, immature convergence, and imbalanced exploration and exploitation inclinations. Hence, the opposition-based learning mechanism is used to ensure in-depth exploration and achieve a better balance between diversification and intensification. The Nelder-Mead simplex is adapted to enable a smooth transition from extensive exploration to intensified exploitation. The proposed methodology is utilized to determine the parameters of photovoltaic solar cells using three diode models (i.e., single diode, double diode, and photovoltaic module). Besides, the performance of the proposed approach is validated based on three practical manufacturers’ datasets. The extensive experimental results show that the enhanced optimizer can estimate the parameters efficiently. It significantly outperforms a variety of well-known algorithms as a potential tool for parameter estimation of photovoltaic models and shows promising capability. A public online service supports this research for any question and application of the proposed tool at http://aliasgharheidari.com.

MULTIOBJECTIVE PIG IRON COST OPTIMIZATION USING SIMPLEX PROJECTION

This work presents a multiobjective optimization model to support the assembly of the raw materials budget for blast furnaces consumption in the production of pig iron, the main material for steelmaking. Given a set of materials and fabrication constraints, such as materials availability, their chemical compositions, the required features for the final product, etc, the objective of the model is to determine the amount of each material that generates the lowest cost solution with minimum wasteful. Due to conflicting objectives, defined by fabrication cost and slag rate, and based on characteristics of decision variables that formulate the problem, some of them in percentage form, an evolutionary multi-objective model has been developed associated with a projection onto a simplex technique aiming to improve the encoding of the genetic solutions. This projection is used in the genetic algorithm-based evolutionary model, wherein each new generated individual, their genes with percentage values are projected onto a simplex, a Euclidean space where the sum of all variables is the unit. The projection allows an intrinsic strategy to deal with percentage constraint of the model variables, increasing significantly the number of feasible individuals generated by the evolutionary procedure. The model has shown to be very effective and useful in determining several scenarios to support decisions making for the raw materials budget.

The periodic pulse photothermal radiometry technique within the front face configuration

The front face photothermal radiometry technique has been improved in order to estimate the thermal conductivity of thin films with better accuracy compared to existing techniques. The experimental procedure is based on the front face response to a nanoseconds laser pulse repeated periodically at high frequency, i. e., a Dirac comb waveform. Averaging the thermal response by considering thousands successive pulses allows improving largely the signal noise ratio. The unknown thermal properties and related experimental parameters are identified by minimizing the gap between the measured signal and the theoretical response that accounts with the pulse waveform, the repetition frequency and the detector transfer function. Minimization is first achieved by implementing first a simplex technique that gives an initial set of values to start the Metropolis–Hastings algorithm in a second step. Application of the proposed methodology is done considering amorphous GeTe film deposited on a Si wafer. It is shown that this experimental method as well as the implementation of the Bayes minimization technique allows to identify the thin film intrinsic thermal conductivity with high accuracy considering some uncertainty on the other parameters assumed to be known.

Stochastic Dual Simplex Algorithm: A Novel Heuristic Optimization Algorithm.

A new heuristic optimization algorithm is presented to solve the nonlinear optimization problems. The proposed algorithm utilizes a stochastic method to achieve the optimal point based on simplex techniques. A dual simplex is distributed stochastically in the search space to find the best optimal point. Simplexes share the best and worst vertices of one another to move better through search space. The proposed algorithm is applied to 25 well-known benchmarks, and its performance is compared with grey wolf optimizer (GWO), particle swarm optimization (PSO), Nelder-Mead simplex algorithm, hybrid GWO combined with pattern search (hGWO-PS), and hybrid GWO algorithm combined with random exploratory search algorithm (hGWO-RES). The numerical results show that the proposed algorithm, called stochastic dual simplex algorithm (SDSA), has a competitive performance in terms of accuracy and complexity.

Surviving or thriving: The role of learning for the resilient performance of small firms

Building on a longitudinal dataset of 245 small firms covering the period of the Global Financial Crisis, this study uses, in combination with fuzzy clustering, the N-State Classification and Ranking Belief Simplex (NCaRBS) technique. This technique, able to deal with ambiguous outcome variables, small datasets, incomplete data and relationships that have the potential to be non-linear, is used to explore the relationship between learning and the resilient performance of small firms. Our findings provide a fine-grained picture of the complex relationships between strategic, cognitive and behavioural learning mechanisms and three resilient performance clusters – sustained performance, stability, and survival – which has implications for theory, as well as practice. By examining learning at the level of the individual owner-manager and also the organisation, we contribute to a better understanding of the role of specific learning mechanisms, a role that is still not well understood.

SME development strategy and product/service innovation intention: A NCaRBS analysis of the role of uncertainty

Small and medium-sized enterprises (SME) are tasked with driving economic recovery globally, in terms of contribution to economic growth. Understanding the determinants of SME innovation is essential in clarifying this phenomena. This study investigates the link between SME strategies and intention to undertake future innovation, using Federation of Small Businesses data. The analysis employs the novel N-State Classification and Ranking Belief Simplex (NCaRBS) technique, investigating relationships between changes in SME strategies, including staffing levels, importing/exporting and client base, and future (including uncertain) innovation intentions. NCaRBS can analyse an incomplete data set, with missing values in the considered characteristic variables, without the need to manage their presence. NCaRBS can also generate results providing insights into SME behaviour regarding strategy and innovation, while also increasing learning about potential reasons behind SMEs uncertainty regarding innovation intention. The study provides novel perspectives into how SMEs develop innovation intentions and the strategies required to support/exploit such intentions, of value to academia, enterprise support agencies and policymakers.

Data-driven multi-objective optimization via grid compatible simplex technique and desirability approach for challenging high throughput chromatography applications.

Recently, a grid compatible Simplex variant has been demonstrated to identify optima consistently and rapidly in challenging high throughput (HT) applications in early bioprocess development. Here, this method is extended by deploying it to multi‐objective optimization problems. Three HT chromatography case studies are presented, each posing challenging early development situations and including three responses which were amalgamated by the adoption of the desirability approach. The suitability of a design of experiments (DoE) methodology per case study, using regression analysis in addition to the desirability approach, was evaluated for a large number of weights and in the presence of stringent and lenient performance requirements. Despite the adoption of high‐order models, this approach had low success in identification of the optimal conditions. For the deployment of the Simplex approach, the deterministic specification of the weights of the merged responses was avoided by including them as inputs in the formulated multi‐objective optimization problem, facilitating this way the decision making process. This, and the ability of the Simplex method to locate optima, rendered the presented approach highly successful in delivering rapidly operating conditions, which belonged to the Pareto set and offered a superior and balanced performance across all outputs compared to alternatives. Moreover, its performance was relatively independent of the starting conditions and required sub‐minute computations despite its higher order mathematical functionality compared to DoE techniques. These evidences support the suitability of the grid compatible Simplex method for early bioprocess development studies involving complex data trends over multiple responses. © 2018 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 34:1393–1406, 2018

An approach for the Pasternak elastic foundation parameters estimation of beams using simulated frequencies

As a first attempt, a mix of differential quadrature (DQ) and simplex (S) method for the Pasternak elastic foundation parameters estimation of beams using simulated frequencies is presented. The method is applied for the parameters estimation of functionally graded (FG) beams. The first-order shear deformation theory is employed to derive governing equations of FG beam on the Pasternak elastic foundation. The equations are discretized by utilizing the DQ method and frequencies of the beam are calculated. Then, the simulated frequencies are obtained by applying random error to the calculated frequencies. The simulated frequencies are used as input data for estimating parameters of the problem. An objective function as a root-mean-square error between the calculated and simulated frequencies is defined. The DQ method and simplex technique as a classical optimization technique are coupled to minimize the function via finding the best foundation parameters, iteratively. Some examples are solved to show applicability, robustness and accuracy of the mixed method for elastic foundation parameters estimation of the beam. Also, it has been found that using only the first simulated frequency of the beam cannot give correct parameters of the foundation.

Simplex filter: A novel heuristic filter for nonlinear systems state estimation

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters.

Treatment of a Young Permanent Maxillary First Molar with Two Palatal Roots

Background: Klebsiella spp. are Enterobacteriaceae frequently isolated from pathological specimens during urinary tract infections, bloodstream infection, and pus. They are becoming more and more resistant to antibiotics and challenging treatment options. β-lactamases are a great variety of enzymes capable of inducing resistance to β- lactams. The objective of this study was to identify extended-spectrum-β-lactamase (ESBL) genes in Klebsiella spp. strains isolated from various specimens in Lome, Togo. Methods: Sixty-four strains of Klebsiella spp. were isolated from different pathological specimens. They were then further characterized and tested against 3rd generation cephalosporin (ceftazidime, ceftriaxone, cefotaxime) and aztreonam. The detection of blaTEM, blaSHV and blaCTX-M was performed on these strains using simplex and multiplex PCR techniques. Results: Fifty five (85.94%) Klebsiella pneumoniae and 9 (14.06%) Klebsiella oxytoca were isolated. These strains derived from urine (n=33; 51.56%), vaginal swabs (n=21; 32.81%), pus (n=8; 12.5%) and sperm samples (n=2; 3.13%). All strains were resistant to cefepime. The resistance rate to other β-lactams was 29.69% (19/64) for piperacillin-tazobactam, 23.08% (12/52) for cefoxitin and 1.56% (1/64) for imipenem. Other inactive antibiotics were trimethoprim-sulfamethoxazole 96.72% (59/61), doxycycline 92.06% (58/63), ciprofloxacin 90.63% (58/64), nalidixic acid 80.95% (51/63), chloramphenicol 77.42% (48/62) and gentamicin 76.69% (51/64). Amikacin and fosfomycin remained the most active antibiotics with 1.56% (1/64) and 4.69% (3/64) resistance rates respectively. ESBL genes were detected in 63/64 (98.44%) strains. TEM/SHV/CTX-M was predominant 61.90% (39/63) followed by TEM/SHV 20.63% (13/63), SHV/CTX-M 11.11% (7/63), TEM/SHV 4.76% (3/63) and TEM 1.59% (1/63). Conclusion: ESBL genes occur more by combination 96.88% (62/64) than singularly 1.59% (1/63). These strains were also very resistant to quinolones and trimethoprim-sulfamethoxazole. These findings are of high importance in a medical and scientific perspective and may motivate decision makers towards a better monitoring and control of antimicrobial resistance in Togo.

The application of NCaRBS to the Trendelenburg test and total hip arthroplasty outcome.

This paper compares the frontal plane hip function of subject’s known to have had hip arthroplasty via either the lateral (LA) or posterior (PA) surgical approaches and a group of subjects associated with no pathology (NP). This is investigated through the Trendelenburg test using 3D motion analysis and classification. Here, a recent development on the Classification and Ranking Belief Simplex (CaRBS) technique, able to undertake n-state classification, so termed NCaRBS is employed. The relationship between post-operative hip function measured during a Trendelenburg Test using three patient characteristics (pelvic obliquity, frontal plane hip moment and frontal plane hip power) of LA, PA and NP subjects are modelled together. Using these characteristics, the classification accuracy was 93.75% for NP, 57.14% for LA, 38.46% for PA. There was a clear distinction between NP and post-surgical function. 3/6 LA subjects and 6/8 PA subjects were misclassified as having NP function, implying that greater function is restored following the PA to surgery. NCaRBS achieved a higher accuracy (65.116%) than through a linear discriminant analysis (48.837%). A Neural Network with two-nodes achieved the same accuracy (65.116%) and as expected was further improved with three-nodes (69.767%). A valuable benefit to the employment of the NCaRBS technique is the graphical exposition of the contribution of patient characteristics to the classification analysis.

An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems

In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with a dual-consistent output evaluation for elliptic interface problems on interface-conforming meshes, and then extend the method to handle multi-physics interface problems, in particular conjugate heat transfer (CHT) problems. The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process. No assumption is made on the interface shape (other than Lipschitz continuity). We then equip our strategy with an output-based adaptive scheme for an accurate output prediction. Through numerical examples, we demonstrate high-order convergence for elliptic interface problems and CHT problems with both smooth and non-smooth interface shapes.