Simplex Method Research Articles

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

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

ANALISIS NILAI TAMBAH DAN OPTIMASI KEUNTUNGAN PRODUKSI OLAHAN KERANG KAMPAK (STUDI KASUS PADA UMKM BUNDA SURABAYA)

This research was conducted at UMKM Bunda Surabaya, Surabaya City, with a focus on value-added analysis and profit optimization of processed shellfish production. The research method used was a case study with non-probability sampling, and data collection through interviews, questionnaires, observation, and secondary data. Data analysis was carried out descriptively and quantitatively, including the calculation of production costs, revenues, and profits. The Hayami method was used to calculate added value, while the simplex method was used for production profit optimization. The results showed that Bunda Surabaya MSMEs earned profits from the production of shredded clams, clam sticks, and clam chili sauce, with a fairly high added value. The highest profit was obtained from the clam sauce product amounting to Rp. 775,201 per one production process. The added value of shredded clams is Rp. 94,726 per kg of raw material with a value-added ratio of 63.15%. This research is expected to provide benefits for the shellfish processing industry and improve the welfare of the fishing community.

Ensembled snake optimiser to solve multiobjective mixed energy generation scheduling

This paper presents Ensembled Snake Optimiser (ESO), to optimise the scheduling of mixed energy generation from coordinated thermal, hydro, pumped-storage hydro, and solar units. It tackles operational constraints while minimising non-convex and non-linear objectives. To reduce the pollutants emitted and operating cost of thermal and solar units, the mixed energy generation scheduling problem uses committed hydro, thermal, and solar units to generate power, pumped-storage hydro units to maintain water levels, and hydro units to maximise available water volume. Utilising the water volume and actively exceeding the power-generating limit are the primary obstacles to satisfy the load requirement. The heuristics are utilised to satisfy the load demand and water volume constraints. The binary-optimistic approach commits solar units. The snake optimisation algorithm tends to get trapped in the local minima while solving complex engineering optimisation problems, which leads to sluggish convergence behaviour. A local search, simplex search, and extended opposition-based learning are investigated to improve its exploitation aspect, convergence behaviour, and procure good solutions. Three electric power systems are undertaken for the simulation studies. ESO gives better results. The significant cost savings for integrated energy scheduling are ranging from 10–15%. The rapid convergence behaviour and whisker box plots justify ESO’s robustness.

Analyzing the Characteristic of Simplex Algorithm

Simplex algorithm is a kind of iterated algorithm which is used to solve linear programming problems. It is raised by George Dantzig in 1974 and is still a valid tool especially when the scale of problem is relatively small or secondary. Simplex algorithm starts at an initializing feasible solution, and constantly approach to the optimal solution until the optimal solution is found or unbounded. Serving as a classical algorithm solving linear programming problem, it plays an important role in both theoretical. With the continuous development of computing technology, the simplex method and its varieties will continue in optimization. This research aims to help people make better decisions in optimization problems by summarizing the formula, characteristics and problem solutions of simplex algorithm. The summary is come from existing literature and including the condition of using simplex algorithm, all kind of different solutions, an example of simplex tableau method and the future of simplex algorithm.

Optimizing Transportation Logistics for Cost Efficiency in a Garment Factory: A Linear Programming Approach Using LINDO

The garment industry in Bangladesh plays a pivotal role in the nation's economy, yet it faces significant challenges in optimizing transportation logistics to minimize costs and enhance efficiency. This paper uses linear programming techniques to negotiate the optimization of transportation logistics in a garment factory located in Gazipur, Bangladesh. The primary objective is to develop an optimized transportation plan that reduces costs while satisfying supply and demand constraints across multiple suppliers, production facilities, and distribution centers. The study formulates the transportation problem as a linear programming model and employs the simplex method to determine the optimal solution. LINDO software is utilized for model implementation and optimization. The model incorporates real data from the garment factory, including supply capacities, demand requirements, and transportation costs. Results from the LINDO optimization reveal a detailed transportation plan that minimizes total transportation costs, demonstrating significant cost savings compared to existing practices. The optimized plan improves operational efficiency and provides a robust decision-support tool for logistics managers. Sensitivity analysis is conducted to ensure the model's robustness under varying conditions. The methodologies and findings are scalable and adaptable to other industrial settings, offering valuable insights for enhancing logistical efficiency in the garment industry. The study also highlights potential areas for future research, including integrating environmental considerations and advanced optimization techniques. Through this research, the garment factory in Gazipur can achieve substantial cost reductions and operational improvements, enhancing its competitiveness in the global market.

Centralised Control and Energy Management of Multiple Interconnected Standalone AC Microgrids

When microgrids operate autonomously, they must curtail the surplus of renewable energy sources (RES) while minimising reliance on gas. However, when interconnected, microgrids can collaboratively minimise RES curtailment and gas consumption due to the ability of exchanging power. This paper presents a centralised controller and energy management of multiple standalone AC microgrids interconnected to a common AC bus using back-to-back converters. Each microgrid consists of RES, a battery, a gas-powered auxiliary unit, and a load. The battery’s state of charge (SOC) is controlled and is used in the AC bus frequency to indicate whether the microgrid has a surplus or shortage of power. High-level global droop control exchanges power between the microgrids. The optimisation problem for this interconnected system is modelled cooperatively to determine the optimal dispatch solution that minimises the energy cost from the auxiliary unit. The optimal dispatch is solved in three cases using the Nelder–Mead simplex algorithm under different settings: one-variable optimisation, three-variable optimisation with the standard droop equation, and three-variable optimisation with a modified droop equation. The optimised performance results are compared with those of the non-optimised benchmark to determine the percentage of optimal performance. The simulation results show that the total energy cost from the auxiliary unit is minimised by 8.98%.

Bi-Functional Materials for Sulfur Cathode and Lithium Metal Anode of Lithium-Sulfur Batteries: Status and Challenges.

Over the past decade, the most fundamental challenges faced by the development of lithium-sulfur batteries (LSBs) and their effective solutions have been extensively studied. To further transfer LSBs from the research phase into the industrial phase, strategies to improve the performance of LSBs under practical conditions are comprehensively investigated. These strategies can simultaneously optimize the sulfur cathode and Li-metal anode to account for their interactions under practical conditions, without involving complex preparation or costly processes. Therefore, "two-in-one" strategies, which meet the above requirements because they can simultaneously improve the performance of both electrodes, are widely investigated. However, their development faces several challenges, such as confused design ideas for bi-functional sites and simplex evaluation methods (i. e. evaluating strategies based on their bi-functionality only). To date, as few reviews have focused on these challenges, the modification direction of these strategies is indistinct, hindering further developments in the field. In this review, the advances achieved in "two-in-one" strategies and categorizing them based on their design ideas are summarized. These strategies are then comprehensively evaluated in terms of bi-functionality, large-scale preparation, impact on energy density, and economy. Finally, the challenges still faced by these strategies and some research prospects are discussed.

Optimization and modelling of bioethanol production by the fermentation of CCN‐51 cocoa mucilage using the sequential simplex method and the modified Gompertz model

AbstractThis work deals with the optimization of bioethanol production through a fermentation process of CCN‐51 cocoa mucilage, based on increased concentrations of the Saccharomyces cerevisiae yeast. Cocoa mucilage, considered biomass waste, was selected for its high productivity and the large volumes generated in the cocoa industrial chain in Ecuador. The optimization of the fermentation process was performed using the sequential simplex method with two variables, and the results were experimentally confirmed by quantifying bioethanol through the microdiffusion method. The best operational conditions corresponded to a temperature of 35°C and a pH of 4. Regarding the concentration of yeast, it was found that the optimal value was 8 g/L, since lower concentrations led to low productivities, while higher concentrations resulted in inadequate functioning of the bioreactor. The best results reached a productivity of 1.35 ± 0.04 g/L · h and a maximum bioethanol concentration of 28.3 ± 0.8 g/L for a processing time of 21 h. The production of bioethanol was modelled using the modified Gompertz equation and simulated in MATLAB®, yielding a bioethanol production rate of 2.42 g/L · h with a correlation coefficient (R2) of 0.95. These results contribute to the knowledge of bioethanol production using cocoa mucilage and seek to add a positive value to this residue, whose management and final disposition have both undesirable environmental and economic effects.

Linear fractional transportation problem in bipolar fuzzy environment

This article proposes a solution methodology for the Linear Fractional Transportation Problem (LFTP) by incorporating bipolar fuzzy sets (BFSs) to accommodate both positive and negative judgmental perspectives. The approach explores Zimmermann's extension within bipolar fuzzy environment to compare outcomes. In this context, the cost function and constraint coefficients are depicted using interval-valued trapezoidal bipolar fuzzy numbers (IVTrBFNs) and defuzzified by (s, t)-cut. The initial approach employs the simplex method and fuzzy optimization method, renowned for its effectiveness in obtaining optimal solutions. In the alternative method, Bipolar fuzzy programming approach (BFPA) is utilized for better outcome. In this method the LFTP is altered to a Multi-Objective Transportation Problem (MOTP), and BFPA extends Zimmermann's technique under suitable positive and negative membership functions, converting MOTP to a one-objective transportation problem (TP) and solved using LINGO software. Supporting this proposed method some theorems are formulated to demonstrate that the most effective solution of the single-objective TP is a Pareto optimal solution for the corresponding MOTP. A quantitative example is provided for better understanding of the proposed BFPA method alongside two other approaches.

Method for robot kinematic parameters identification based on position and orientation data obtained with laser tracker.

How to quickly and accurately identify the kinematic parameter errors is an important prerequisite for robot accuracy compensation. The laser tracker is used to measure and identify the kinematic parameters of the robot. The influence of laser tracker layout in robot pose measurement is analyzed, and the evaluation function of laser tracker layout is constructed to determine the optimal layout position. Then, the mapping relationship between the position and orientation deviation of the robot end and the deviation of each kinematic parameter is established, and the kinematic parameter identification model integrating the position and orientation information is constructed. The identification model is compared to the identification model based on position information to clarify the intrinsic reason of high accuracy. Next, aiming at the problem that the genetic algorithm is easy to prematurely converge to the local optimal solution, a hybrid genetic algorithm is constructed by introducing the simplex method to determine the optimal calibration pose set of the robot. On this basis, the results of robot kinematics parameter identification based on position measurement data, pose measurement data, and optimal calibration pose set are compared and analyzed through experiments, which verifies the effectiveness of the robot kinematics parameter identification model based on pose measurement data and optimization strategy.

Pareto-critical equilibrium condition for non-linear multiobjective optimization problems with applications

The new (necessary) Pareto-critical equilibrium condition (PCEC) discussed in this study is based on the Pareto-critical condition for non-linear optimization problems. The proposed condition is evaluated by defining a multiobjective optimization problems (MOOPs) subject to a set of constraints. Then this MOOPs is converted to a single objective optimization problem by using the available optimization techniques, for instance, the weighted sum method, and solved by the non-linear Nelder-Mead simplex method. The obtained solution points satisfy the proposed PCEC of an unconstrained multiobjective optimization problem (MOOPs) under the convexity assumption. This PCEC is evaluated in a search that either results in a point inside the feasible region or a point for which the PCEC holds. The resulting Pareto-critical equilibrium condition is globally valid for convex problems. Numerical experiments are carried out in order to clarify the proposed condition's validity. Moreover, the proposed PCEC is used to place a downlink transmit beamforming system base station in an ideal position as a first application and is also employed in situations where there are multiple agents working towards a common goal as a second application.

Aerodynamic optimization design and experimental verification of a high-load axial flow compressor

The performance and stable operating range of compressors are critical to the efficient operation of various turbomachinery systems. This paper proposes a multi-level optimization strategy combining the uni-uniform direct free deformation method, Linux partitioned CPU accelerated parallel computing technology, multi-objective particle swarm optimization algorithm and downhill simplex algorithm, which improves design efficiency. Numerical results show that after optimization design, the average value of peak efficiency and stall margin increases. The flow mechanism of compressor performance improvement after optimization lies in the reduction of a low-velocity separation zone in stator hub region. Moreover, the experiment study confirms the reliability and accuracy of the optimization design method and found that flow instability triggering mode, propagation characteristics of the stall cell, and surge frequency are changed after optimization design. Setting a probability distribution threshold for autocorrelation coefficient and cross-correlation coefficients can be used to predict the arrival of the surge condition.

Harvesting Ancient Wisdom: Mathematical Modeling of Agricultural Technology in Sangam Literature and its Comparative Study with Modern Techniques

Agriculture has been the backbone of human civilization since its inception. While modern technology has revolutionized agricultural practices, the ancient texts of the Tamil literary corpus, particularly the Sangam literature, offer invaluable insights into the agricultural techniques and wisdom of the past. This essay delves into the agricultural practices detailed in the Sangam texts, namely Naṟṟiṇai, Kuṟuntokai, Aingurunūṟu, Patiṟṟuppattu, Paripāṭal, Kalittokai, Akanāṉūṟu, and Puranāṉūṟu, and uses mathematical modeling, specifically simplex methods, to analyze and compare these techniques with contemporary agricultural technology.

An Enhanced Symmetric Sand Cat Swarm Optimization with Multiple Strategies for Adaptive Infinite Impulse Response System Identification

An infinite impulse response (IIR) system might comprise a multimodal error surface and accurately discovering the appropriate filter parameters for system modeling remains complicated. The swarm intelligence algorithms facilitate the IIR filter’s parameters by exploring parameter domains and exploiting acceptable filter sets. This paper presents an enhanced symmetric sand cat swarm optimization with multiple strategies (MSSCSO) to achieve adaptive IIR system identification. The principal objective is to recognize the most appropriate regulating coefficients and to minimize the mean square error (MSE) between an unidentified system’s input and the IIR filter’s output. The MSSCSO with symmetric cooperative swarms integrates the ranking-based mutation operator, elite opposition-based learning strategy, and simplex method to capture supplementary advantages, disrupt regional extreme solutions, and identify the finest potential solutions. The MSSCSO not only receives extensive exploration and exploitation to refrain from precocious convergence and foster computational efficiency; it also endures robustness and reliability to facilitate demographic variability and elevate estimation precision. The experimental results manifest that the practicality and feasibility of the MSSCSO are superior to those of other methods in terms of convergence speed, calculation precision, detection efficiency, regulating coefficients, and MSE fitness value.

Improved Parameter Estimation of Three-Phase Squirrel-Cage Induction Motors Using the Nelder-Mead Simplex Algorithm

This work presents a technique for precisely determining the characteristics of a squirrel-cage three-phase induction motor using the Nelder-Mead simplex algorithm. This approach is a frequently employed numerical optimization technique for determining the minimal value of a multi-dimensional objective function. An advantageous feature of the Nelder-Mead simplex algorithm is its independence from the need to calculate partial derivatives of the objective function. Nevertheless, similar to several optimization techniques, the Nelder-Mead simplex approach can also exhibit sensitivity to the initial conditions. Thus, the initial estimation of the parameters of the approximated equivalent circuit of the induction motor was used as the starting point for the Nelder-Mead optimization approach. The experiment's results are compared to those obtained using the polynomial regression approach to demonstrate the efficacy of the proposed method.

Methods of Multi-Criteria Optimization of Technological Processes in a Fuzzy Environment Based on the Simplex Method and the Theory of Fuzzy Sets

Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production.

Linear programming with infinite, finite, and infinitesimal values in the right-hand side

The goal of this work is to propose a new type of constraint for linear programs: inequalities having infinite, finite, and infinitesimal values in the right-hand side. Because of the nature of such constraints, the feasible region polyhedron becomes more complex, since its vertices can be represented by non-purely finite coordinates, and so is the optimum of the problem. The introduction of such constraints enlarges the class of linear programs, where those described by finite values only become a special case. To tackle optimization problems over such polyhedra, there is a need for an ad-hoc solving routine: this work proposes a generalization of the Simplex algorithm, which is able to solve common linear programs as corner cases. Finally, the study presents three relevant applications that can benefit from the use of these novel constraints, making the use of the extended Simplex algorithm essential. For each application, an exemplifying benchmark is solved, showing the effectiveness of the proposed routine.

A multiscale approach to optimize off-grid hybrid renewable energy systems for sustainable rural electrification: Economic evaluation and design

This article thoroughly investigates the design and optimization of an off-grid hybrid renewable energy system for a remote town in the province of Ankara, whose traditional power infrastructure is lacking. The goal is to provide an efficient and cost-effective energy system that can supply the village's power needs indefinitely. The optimization process entails selecting the best mix of renewable energy sources and sizing components to obtain the best economic and technical performance. To handle the complexity of the optimization problem, the Nelder-Mead simplex search method is used, taking into account the stochastic nature of renewable energy generation and the nonlinear features of RES-based power plants. The simulation results show that the suggested hybrid system outperforms traditional diesel power generators in terms of economic viability and environmental sustainability. The system assures consistent power supply by using reserve energy devices such as batteries, thereby minimizing the intermittent nature of renewable sources. With a competitive energy cost of €0.63/kWh, the optimized hybrid system ensures a dependable and continuous power supply, fulfilling the village's electrical requirement for an amazing 16 years.

Orientation optimization of the Halbach PMG for the levitation and guidance performance of the HTS maglev system

High-temperature superconducting maglev technology has great application potential in rail transit applications due to its advantages such as passive stable levitation and green environmental protection. As one of the key components of the HTS maglev system, the Halbach-type permanent magnet guideway (PMG) enhances the magnetic field on one side of the guideway and weakens that on the other side. Optimizing the PMG, including the geometry and magnetic properties of the magnet, is an effective method to improve the levitation and guidance performance of the system. In addition, since NdFeB permanent magnets are expensive, optimizing the design of the PMG for the HTS maglev system is also an important work to reduce the application cost. In this paper, the Nelder–Mead Simplex method (NMS) in the optimization solver in COMSOL software is used to optimize the geometric parameters of the Halbach PMG according to the different objective requirements of the HTS maglev system. The optimization objectives include the maximum levitation force and guidance force under the constraint of the maximum cross-sectional area of the PMG, as well as the minimum cross-sectional area of the PMG with a minimum levitation force constraint. The results indicate that the NMS method is effective. By comparing four PMGs during the optimization process, it is found that this method can fully improve the utilization of the magnetic field by changing the geometric parameters of the Halbach PMG. This study can provide a valuable reference for the optimal design of the PMG for HTS maglev systems in the future.

Comparative study of kernel- and deep learning-based proxy models for nonlinearly constrained life-cycle production optimization

This study presents a comparative study for the application of deep learning–based and kernel-based proxy models in hydrocarbon production optimization with nonlinear constraints, comparing their performance against high-fidelity simulators (HFS) in terms of computational efficiency and the quality of the results achieved. One of the proxy models employed is referred to as embed to control and observe (E2CO), a deep learning–based model. The other model is a kernel-based proxy model known as least-squares support-vector regression (LS-SVR). Both proxy models can predict production/injection outputs for each well. We use the sequential quadratic programming (SQP) method for nonlinearly constrained production optimization. Our optimization objective revolves around the net present value (NPV), while the nonlinear state constraints involve field liquid production rate (FLPR) and field water production rate (FWPR). NPV, FLPR, and FWPR are estimated using two different types of proxy models. The gradient of the objective function and the Jacobian matrix of constraints are computed analytically for LS-SVR. In contrast, the method of stochastic simplex approximated gradient (StoSAG) is employed for optimization with E2CO and HFS. The reservoir model considered in this study is a two-phase, three-dimensional reservoir characterized by channelized and heterogeneous permeability, sourced from the SPE10 benchmark case. We optimize well controls to maximize NPV in an oil-water waterflooding scenario. All proxy models can achieve optimal NPV results like those obtained through HFS but with significantly lower computational resources. Both proxy models are found to be approximately 15-fold more efficient than using HFS when the number of simulation runs is compared. Forward prediction results show that both proxy models outperform numerical simulator, and the E2CO can predict up to 2400 times faster than HFS whereas speedups gained over HFS go up to 5000-fold with LS-SVR. The training time required for E2CO is at least an order of magnitude longer than that for LS-SVR. The main contributions of the paper are (i) development of a novel methodology that uses an E2CO proxy model within a gradient-based iterative retraining proxy approach for life-cycle production optimization with nonlinear state constraints, (ii) comparison of this methodology in terms of computational cost and accuracy with an LS-SVR proxy model, and (iii) new insights into the accuracy and prediction performances of these machine learning-based proxy models for 3D oil-water systems as well as their efficiency in nonlinearly constrained production optimization for waterflooding applications.