Simplex Method Research Articles

Fast Quantum Subroutines for the Simplex Method

What would Dantzig do with a quantum computer? It is unlikely we will ever find out the answer to this question. However, we can try to understand if the simplex method can be implemented on a quantum computer, and this might have piqued Dantzig’s interest. The paper “Fast Quantum Subroutines for the Simplex Method” gives a quantum implementation of an iteration of the simplex method, in which the basis inverse is never explicitly computed: the quantum computer takes as input the current basis and certifies optimality or outputs the next basis. Because computing the basis inverse is expensive, this can lead to an asymptotically faster algorithm in terms of the problem size: in the best case, the quantum algorithm can identify pivots in essentially linear time! This, however, comes at the cost of worse dependence on some numerical parameters: all these tradeoffs are discussed in the full article.

Carbon dioxide spectrophotometric determination in whole roasted coffee beans using a total analysis system after super-modified simplex optimization

In this work an automated methodology for the spectrophotometric determination of carbon dioxide in whole roasted coffee beans was developed. The analytical flow system was based on a reaction vessel featuring a lab-made gas diffusion flow cell. The coffee beans, without any pre-treatment, were poured in a vessel into which an acidic solution was added to promote carbon dioxide evolution from the sample. By pervaporation, the gas was thereafter trapped in a gas diffusion flow cell containing an acceptor solution which was afterwards analyzed by spectrophotometry. To enhance the sensitivity of the methodology, an experimental design based on super-modified simplex method was carried out to adjust the chemical composition of the acceptor solution. The developed methodology showed to be suitable to determine carbon dioxide in roasted coffee samples, and present as main advantages a higher determination rate (ca. 7 h−1) and reduced labor comparing with usually followed methodologies. Under the selected experimental conditions, the minimum quantity of carbon dioxide detected was of 4.62 × 10−7 mol. The results obtained by the developed methodology were correlated with those provided by the Hinman methodology.

DC Bus Voltage Stabilization and SOC Management Using Optimal Tuning of Controllers for Supercapacitor Based PV Hybrid Energy Storage System

The global initiative of decarbonization has led to the popularity of renewable energy sources, especially solar photovoltaic (PV) cells and energy storage systems. However, standalone battery-based energy storage systems are inefficient in terms of the shelf and cycle life, reliability, and overall performance, especially in instantaneous variations in solar irradiance and load. In order to overcome this, a combination of a supercapacitor and battery-based hybrid energy storage system (HESS) is considered as an emerging and viable solution. The present work proposes an optimally tuned tilt-integral (TI) controller to develop an efficient power management strategy (PMS) to enhance the overall system performance. The controller parameters are tuned by optimization of the time-domain design specifications using a gradient-free simplex search technique. The robustness of the proposed TI controller is demonstrated in comparison to PI and fractional-order PI (FOPI) controllers. Furthermore, extensive experimentation was carried out to analyze the effectiveness of the proposed approach for DC bus voltage stabilization and state-of-charge (SOC) management under varying operating conditions such as solar irradiance, load, temperature, and SOC consumption by battery.

A Novel Interval Programming Method and Its Application in Power System Optimization Considering Uncertainties in Load Demands and Renewable Power Generation

This paper expresses the output power of renewable generators and load demand as interval data and develops the interval economic dispatch (IED), as well as interval reactive power optimization (IRPO) models. The two models are generalized into a specific type of linear interval programming (LIP) and nonlinear interval programming (NLIP), respectively. A security limits method (SLM) is proposed to solve LIP and NLIP problems. As for the LIP, the maximum radii of the interval variables are first calculated by the optimizing-scenarios method (OSM) for defining security limits, and the LIP is transformed into deterministic linear programming (LP), for which its constraints are the security limits, which can be solved by the simplex method. As for the NLIP, Monte Carlo simulations were used to obtain the maximum radii of the interval variables, and the average interval ratio of the interval variables is defined to compute the security limits for transforming the NLIP to deterministic nonlinear programming (NLP), which can be solved by using the interior point method. Finally, the IED and IRPO are used to verify the effectiveness and engineering of the proposed SLM.

MGPM Methods for Rectangular Single-Size Printed Circuit Board Orthogonal Packing Problems

Printed circuit board (PCB) orthogonal packing problems derive from the massive circuit board production process in the electronic industry. In the early stage, it mainly relied on human experiences to make decisions on how to make the most of each sheet while meeting customers’ orders. Up till now, researchers in enterprises and academic circles are still trying to explore effective mathematical models and feasible optimization methods. In most cases, what PCB companies generally face is the orthogonal layout decision, which considers positioning each rectangle PCB piece (PCB-P) on a rectangle sheet board (panel) in an ideal way so that each panel has the minimal remains with the most PCB-Ps. In this paper, multi-round gradual packing methods (MGPMs) are proposed based on the idea of combinatorial optimization and dynamic programming. MGPMs include the depth priority-based method (MGPM-DP) and breadth priority-based branch-and-prune method (MGPM-BC). The former has the advantage of finding better solutions, while the latter has the advantage of consuming short computational time. Through extensive computational tests on real data from a PCB production enterprise in China, both MGPM-DP and MGPM-BC have achieved noticeable and satisfactory results compared with the simplex method, dynamic programming method, and a widely used industrial software (Yuanbo) in China.

Selection and Identification of a Model of Elasto-Viscoplasticity of the Filled Fluorocomposite according to Free and Constrained Compression Tests

Introduction. Properties of filled composites based on polytetrafluoroethylene allow them to work at high contact pressures, reciprocating nature of shear loads, and in a wide temperature range. Due to this, they are used as antifriction layers of bearing parts with ball segment. To simulate the mechanical behavior of such materials under operating conditions, adequate constitutive equations of elasto-viscoplasticity and methods of their identification according to the data of basic experiments are needed.Materials and Methods. The tensor-linear model of elasto-viscoplasticity should be identified according to the data of tests on free compression of samples. They were subjected to loading up to a maximum deformation of 10 %, allowed to remain, unloaded, and then, a similar loading cycle up to 160 MPa under constrained compression was carried out. The experiment with a composite based on polytetrafluoroethylene filled with 40 wt. % fine bronze, was conducted at room temperature. Tests for constrained compression were performed for two values of the strain rate, and for free compression – for three values of the strain rate in the range of 10-6 – 10-3 s-1. For the description, two models of elasto-viscoplasticity were considered, representing modifications of Swain and Kletschkowski’s models and corresponding to the connection of a viscoelastic or elastic nonlinear viscous element with a plastic or endochronic element. An integral operator with a Kohlrausch kernel was considered as a viscoelastic element.Results. The results of the constrained compression tests made it possible to separate the elastic relationship of volumetric deformations and average stresses from the constitutive relations. The data of free compression cycles at different strain rates were used to determine the material constants of the model. For this purpose, an efficient search algorithm based on the simplex method of minimizing the discrepancy was implemented. Both models discovered the importance of the plastic component (independent of the deformation rate) for a qualitative description of the stress cycling that accompanied the cyclic deformation, as well as their dependence on the strain rate.Discussion and Conclusions. Both models of elasto-viscoplasticity described correctly the behavior of the studied fluorocomposite under loading conditions close to the operating conditions of the antifriction layers of the bearing parts with ball segment. They can be considered as a basis for their further generalization, taking into account the dependence on temperature.

Effects of environmental factors on anthocyanin accumulation in the fruits of Lycium ruthenicum Murray across different desert grasslands

Anthocyanins can help plants adapt and resist adverse environments and have important nutritional and medicinal effects on human beings. However, how environmental factors affect the anthocyanins accumulation of plants and how to improve the anthocyanins content of plants in different soils needs further exploration. Hence, this study aimed to investigate the effects of environmental factors on the accumulation of cyanidin, petunidin, malvidin, and delphinidin in the fruits of Lycium ruthenicum in sandy desert grassland (SS), gravel desert grassland (GD), and saline-alkali desert grassland (SD) in the lower reaches of the Shiyang River Basin. The variable importance screened the key environmental factors affecting anthocyanin accumulation in projection (VIP) and multiple stepwise regressions. The structural equation model (SEM) was established to understand how the climate and soil factors affect the total anthocyanin accumulation. For establishing soil nutrient optimization schemes by partial least squares regression (PLS) and the simplex algorithm used to improve the anthocyanin content in different types of desert grassland. In SS, electrical conductivity (EC) and microbial biomass carbon (SMBC) showed highly significant and positive effects on the content of total anthocyanin, cyanidin, and petunidin. In GD, soil moisture and microbial biomass nitrogen (SNBN) significantly negatively affected total anthocyanin content. In SD, catalase (CAT), phosphatase (PHO), and total potassium (TK) had the greatest impact on total anthocyanin content. It is indicated that the targeted improvement measures are necessary to increase anthocyanin content in the fruit of Lycium ruthenicum.

Efficient Ranking Function Methods for Fully Fuzzy Linear Fractional Programming problems via Life Problems

In this paper, we propose two new ranking function algorithms to solve fully fuzzy linear fractional programming (FFLFP) problems, where the coefficients of the objective function and constraints are considered to be triangular fuzzy numbers (TrFN) s. The notion of a ranking function is an efficient approach when you want to work on TrFNs. The fuzzy values are converted to crisp values by using the suggested ranking function procedure. Charnes and Cooper’s method transforms linear fractional programming (LFP) problems into linear programming (LP) problems. The suggested ranking functions methods' applicability to actual problems of daily life, which take data from a company as an example, is shown, and it presents decision-making and exact error with the main value problem. The study aims to find an efficient solution to the FFLFP problem, and the simplex method is employed to determine the efficient optimal solution to the original FFLFP problem.

Particle Swarm Optimization with a Simplex Strategy to Avoid Getting Stuck on Local Optimum

Heuristic methods, for global optimization, have been receiving much interest in the last years, among which Particle Swarm Optimization (PSO) algorithm can be highlighted. However, the application of heuristic methods can lead to premature convergence. In this work, the addition of a step on the PSO algorithm is proposed. This new step, based in Nelder–Mead simplex search method (NM), consists of repositioning the current particle with global best solution, not for a better position, but away from the current nearest local optimum, to avoid getting stuck on this local optimum. There are other PSO-NM algorithms, but the one we are proposing, has a different strategy. The proposed algorithm was also tested with the repositioning strategy in other particles beyond the current global best particle, depending on the repositioning probability. To evaluate the effectiveness of the proposed methods, and study its better parameters, were used various test functions, and for each test function, various number of particles were used in combination with various probabilities of particles repositioning. A thousand runs were performed for each case, resulting in more than two millions runs. The computational studies showed that the repositioning of of global best particle increases the percentage of success on reaching the global best solution, but better results can be obtained applying the repositioning strategy to other particles with repositioning probabilities between 1–5%.

Quantification of the asynchronous gas diffusivity in macro-/micropores using a Nelder-Mead simplex algorithm and its application on predicting desorption-based indexes

Accurate and intelligent calculation of diffusion coefficient not only helps reduce greenhouse gas emissions, but also conduces to CO2 geological storage and CH4 displacement in coal seams. In this study, a kind of object-oriented software for conveniently and quickly obtaining bidisperse (i.e., macro-pore and micro-pore) diffusion coefficients and grasping main controlling factors of macroscopic desorption curves was designed based on the Nelder-Mead simplex algorithm. Furthermore, the gas desorption characteristics under different pressures were analyzed by performing conventional desorption experiments. The results show that the apparent diffusion coefficient obtained by the bulk technique displays three different trends as the pressure rises, namely a rising, falling and constant diffusion coefficient respectively. The three variation trends mainly result from the difference in deformation caused by adsorption swelling and mechanical compression. As desorption continues, the gas diffusion coefficient values in the macro-pores and micro-pores fluctuate for a short time, but increase in the long term. This is because the early stage corresponds to intense mechanical expansion and a flow boundary effect, while the later stage corresponds to an increasingly intense effect of desorption-induced shrinkage. Moreover, the time-dependent contribution law of macro-pore diffusion and micro-pore diffusion affects the reliability of outburst risk index, making △h2 more stable than K1. The conclusions provide theoretical guidance for the selection of rational gas drainage methods for diffusion-controlled coal seams.

A cash crop combination for maximum net income: A case study of a small-scale cash crop farmer in Vhembe, Limpopo province, South Africa

This paper investigates the optimal cash crop combination at a small-scale cash crop farm in Vhembe District, Limpopo Province, South Africa in which green maize, cabbages, tomatoes, spinach, mustard, butternut and sweet potatoes are grown. To get optimum farm outputs, decisions on crop combination and operational activities in crop production are crucial. Proper farm planning and resource allocation play a significant role in optimising farm revenues. It was observed that the farmer used traditional methods of allocating resources, which lead to a less profitable crop mix. In view of this, in this study, linear programming model was formulated using data collected from a farm concerning the past crop combinations and allocation of resources in crop planning and production to determine the best crop combination that maximizes net income given limited resources such as land, labour, capital, and others. The simplex method of linear programming works by first locating a feasible solution and then relocating to any vertex of the feasible set that improves the cost function. Eventually, a point is reached beyond which no further movement improves the cost function. The results of the developed linear programming model were compared to past farming practices based on experience, leading to the conclusion that crops and limited resources were not optimally allocated. The results clearly demonstrate the optimal crop combination and allocation of scarce resources that the farm could have considered to yield maximum returns. It is observed that the proposed linear programming model is appropriate for finding the optimal land allocation criteria for the cash crops in the study area. The optimal crop mix from the linear programming two phase simplex method show that the farmer should grow the following crop mix, 1.16 ha of green mealies, 2.64 ha of cabbages, 0.8 ha of tomatoes, 1.2 ha of mustard, 0.4 ha spinach, 0.4 ha of butternut and 0.4 ha of sweet potatoes with the gross income of R 740 800. The linear programming model resulted in a 37.8 percent increase in profit margin. Based on the results obtained from this study, it is recommended that the small-scale cash crop farmer should invest more in producing crops that give maximum profit. MATLAB software was used to determine the optimal values of the decision variables. Key words: Cash crops allocation, crop combination, net income, linear programming (LP), resource allocation.

Analisis Keuntungan dan Penugasan dengan Metode Simpleks dan Metode Hungarian (Studi Kasus UMKM Nasi Goreng Kencur)

MSME Nasi Goreng Kencur is one of the developing MSMEs. With a variety of products for sale. Of the various variants that are sold, of course, they have different advantages. So we need a problem solving tool to find out which product has the maximum benefit. Research is able to find out how feasible and optimal solutions are from various problem models. Implementation of operational research on the completion of the case study in Nasi Goreng Kencur SMEs, to obtain optimal benefits. This research was conducted in 2022 using the interview method and direct observation, where MSME owners become the data source for conducting research. To optimize the profit can be solved by using the Integer Linear Programming problem model using the Simplex method. Then for the assignment analysis at the Nasi Goreng Kencur SMEs using the Hungarian method. In the data processing that is carried out using these two models, manual data processing is carried out, and calculations using POM-QM software. So that the results of the study become more accurate, because in addition to using manual calculations. Calculations are also used using the POM-QM application.

Ameliorated artificial hummingbird algorithm for coordinated wind-solar-thermal generation scheduling problem in multiobjective framework

This paper proposed an optimization technique, namely ameliorated artificial hummingbird algorithm (AAHA), that blends artificial hummingbird algorithm (AHA) with simplex search strategy (SSS) to solve the coordinated wind-solar-thermal generation scheduling problem. The AAHA simulates the foraging behaviour of hummingbirds for food, including guided, territorial, and migration foraging. Guided foraging helps in the higher exploration in the initial stages, and territorial foraging performs the exploitation in its neighbourhood. Migration foraging explores the search space. The SSS enhances the weak territorial and migration foraging of AHA by improving the exploitation mechanism. The proposed method is simple and has less dependency on parameters to adjust. The solar and wind units are committed to ascertaining their share for uninterrupted supply. The price penalty method is applied to unify the emission of gaseous pollutants due to thermal generation with operating costs. To reduce the use of coal, renewable energy sources have been considered in this problem which results in reducing the pollutants’ emissions and saving in fuel costs. To solve the dynamic multivariable constrained optimization problem, the forward approach has been implemented. The performance of the proposed algorithm is tested on different electric test systems, and a statistical test justifies the results.

An Efficient Direct Search Method for Simulation Optimization With Conditional-Expectation- Based Objectives

In order to generalize the applicability of Conditional Value at Risk, one of the most widely used measurements used in financial risk management, we develop a solution methodology for the conditional expectation (CE)-based simulation optimization problems. To optimize CE-based objective functions in a highly generalized context, we propose a gradient-free, direct search optimization method, called SNM-CE, which inherits the search framework of Stochastic Nelder-Mead (SNM) Simplex Method but further incorporates effective mechanisms designed for handling problems with CE-based objective functions. As we assume the underlying problem is complicated enough that no closed-form expression can represent the objective function, stochastic simulation is applied to estimate CE. We apply Importance Sampling (IS) as a variance reduction technique, which, combined with a newly-developed methodology, called SOCBA-mn, ensures that simulation resources are used with great efficiency. We show that SNM-CE can converge to the true global optimum with probability one (w.p.1) like SNM. An extensive numerical study and a communication system-based empirical study are both conducted to demonstrate the effectiveness, efficiency and viability of this research in both theoretical and practical settings. Note to Practitioners—This paper develops a direct search algorithm, called SNM-CE, used for solving conditional expectation-based simulation optimization problems. By tackling conditional expectation-based problems, SNM-CE fills a gap in the stochastic optimization literature which has traditionally focused on expectation- or quantile-based objective functions. SNM-CE possesses a high degree of flexibility and generalizability which users can benefit from in solving real-world applications. For example, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> value in the CE-based simulation optimization formulation can be freely adjusted. In other words, the quantile value above which the CE is estimated and optimized can be set according to the needs of the practitioner and/or characteristics of the problem to be solved. Also, SNM-CE is designed such that instead of setting the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> value, the user may choose to utilize a particular numerical value of the objective function as the threshold for the CE estimation and optimization. SNM-CE is also simple in terms of implementation and, being a direct search method, does not impose many assumptions about the structure of the underlying objective function and does not necessitate the use of gradient information in the search process. As one application example, SNM-CE can be utilized to select the operational parameters which minimize the average delay in the manufacturing of semiconductors given that the delay exceeds the 90th percentile of simulated delay times.

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.

Eyebox uniformity optimization over the full field of view for optical waveguide displays based on linked list processing.

Eyebox uniformity is an important indicator to evaluate the performance of optical waveguide displays. However, there is currently no standard design approach that achieves ideal uniformity over the full field of view (FOV) within the eyebox. Here, a novel method for eyebox uniformity optimization based on linked list processing is proposed. The linked list processing method can fast record the light trajectory and calculate the optimal numerical diffraction efficiency distribution of the coupler. We use the linked list method for an L-shaped diffractive optical waveguide and solve the matched coupler structure by combining rigorous coupled-wave analysis (RCWA) and the simplex method. By building the model on LightTools and demonstrating the illuminance uniformity, the feasibility of the method is verified. In the FOV range of 15°× 15°, the eyebox uniformity reaches 0.9 at the central viewing angle and the overall eyebox uniformity is 0.617.

An Approach to Compute the Multi-Objective Programming Problem Under Triangular Fuzzy Numbers

The most important one advantages of the operation research (OR) theory is displayed of this paper for tackling multi-objective function programming problems (MOFPP). In this study, we present an approach for multi-objective fractional programming problems (MOFrPP) using fuzzy numbers (FN) coefficients in the objective functions (OF). The objective functions' (OF) parameters are all considered to be fuzzy triangular fuzzy numbers (FTrFN). This problem's multi-objective function (MOF) case was resolved by transforming the MOF to a linear programming problem (LnPP) that could be resolved using the simplex method (SM). The problem is being solved using algorithms. Then the value is compared with a result, which obtained by simplex method (SM). These techniques are illustrated with numerical examples (NE). This study shows the reliability of our methods and their utility to this specific set of multi-objective functions (MOF).

Automatic modeling of dynamic drug-hERG channel interactions using three voltage protocols and machine learning techniques: A simulation study

BackgroundAssessment of drug cardiac safety is critical in the development of new compounds and is commonly addressed by evaluating the half-maximal blocking concentration of the potassium human ether-à-go-go related gene (hERG) channels. However, recent works have evidenced that the modelling of drug-binding dynamics to hERG can help to improve early cardiac safety assessment. Our goal is to develop a methodology to automatically generate Markovian models of the drug-hERG channel interactions. MethodsThe training and the test sets consisted of 20800 and 5200 virtual drugs, respectively, distributed into 104 groups with different affinities and kinetics to the conformational states of the channel. In our system, drugs may bind to any state (individually or simultaneously), with different degrees of preference for a conformational state and the change of the conformational state of the drug bound channels may be restricted or allowed. To model such a wide range of possibilities, 12 Markovian chains are considered. Our approach uses the response of the drugs to our three previously developed voltage clamp protocols, which enhance the differences in the probabilities of occupying a certain conformational state of the channel (open, closed and inactivated). The computing tool is comprised of a classifier and a parameter optimizer and uses linear interpolation, support vector machines and a simplex method for function minimization. ResultsWe propose a novel methodology that automatically generates dynamic drug models using Markov model formulations and that elucidates the states where the drug binds and unbinds and the preferential binding state using data obtained from simple voltage clamp protocols that captures the preferential state-dependent binding properties, the relative affinities, trapping and non-trapping dynamics and the onset of IKr block. Overall, the tool correctly predicted the class of 92.04% of the drugs and the model provided by the tool accurately fitted the response of the target compound, the mean accuracy being 97.53%. Moreover, generation of the dynamic model of an IKr blocker from its response to our voltage clamp protocols usually takes less than an hour on a common desktop computer. ConclusionOur methodology could be very useful to model and simulate dynamic drug–hERG channel interactions. It would contribute to the improvement of the preclinical assessment of the proarrhythmic risk of drugs that inhibit IKr and the efficacy of antiarrhythmic IKr blockers.

Cutting-plane algorithms and solution whitening for the vertex-cover problem.

The phase-transition behavior of the NP-hard vertex-cover (VC) combinatorial optimization problem is studied numerically by linear programming (LP) on ensembles of random graphs. As the basic Simplex (SX) algorithm suitable for such LPs may produce incomplete solutions for sufficiently complex graphs, the application of cutting-plane (CP) methods is sought. We consider Gomory and {0,1/2} cuts. We measure the probability of obtaining complete solutions with these approaches as a function of the average node degree c and observe transition between typically complete and incomplete phase regions. While not generally complete solutions are obtained for graphs of arbitrarily high complexity, the CP approaches still advance the boundary in comparison to the pure SX algorithm, beyond the known replica-symmetry breaking (RSB) transition at c=e≈2.718. In fact, our results provide evidence for another algorithmic transition at c≈2.90(2). Besides this, we quantify the transition between easy and hard solvability of the VC problem also in terms of numerical effort. Further we study the so-called whitening of the solution, which is a measure for the degree of freedom that single vertices experience with respect to degenerate solutions. Inspection of the quantities related to clusters of white vertices reveals that whitening is affected, only slightly but measurably, by the RSB transition.

A Simplex Method-Based Bacterial Colony Optimization Algorithm for Data Clustering Analysis

Data clustering is the task of separating data samples into a set of clusters. [Formula: see text]-means is a popular partitional clustering algorithm. However, it has a lot of weaknesses, including sensitivity to initialization and the ability to become stuck in local optima. Hence, nature-inspired optimization algorithms were applied to the clustering problem to overcome the limitations of the [Formula: see text]-means algorithm. However, due to the high-dimensionality of a search space, the nature-inspired optimization algorithm suffers from local optima and poor convergence rates. To address the mentioned issues, this paper presents a simplex method-based bacterial colony optimization (SMBCO) algorithm. The simplex method is a stochastic variant approach that improves population diversity while increasing the algorithm’s local searching ability. The potential and effectiveness of the proposed SMBCO clustering algorithm are assessed using a variety of benchmark machine learning datasets and the generated groups were evaluated using different performance measures. When compared to several well-known nature-inspired algorithms, the experimental results reveal that the SMBCO model produces superior clustering efficiency and a faster convergence rate.