Nelder-Mead Simplex Optimization Algorithm Research Articles

Multidisciplinary design of a guided flying vehicle using simplex nondominated sorting genetic algorithm II

This paper presents design of a typical Guided Flying Vehicle (GFV) using the multidisciplinary design optimization (MDO). The main objectives of this multi-disciplinary design are maximizing the payload’s weight as well as minimizing the miss distance. The main disciplines considered for this design include aerodynamics, dynamic, guidance, control, structure, weight and balance. This design of GFV is applied to three and six Degree of Freedom (DOF) to show comparison of simulation results. The hybrid scheme of optimization algorithm is based on Nelder-Mead Simplex optimization algorithm and Nondominated Sorting Genetic Algorithm II (NSGA II), called Simplex-NSGA II. This scheme is implemented for finding an optimal solution through the MDO. The Simplex-NSGA II method is a heuristic optimization algorithm that applies to multi-objective functions and the results are then compared with the most famous algorithms, like Nondominated Sorting Genetic Algorithm II (NSGA II) and Multi-Objective Particle Swarm Optimization (MOPSO). Simulation results demonstrate the superior performance of the Simplex-NSGA II over NSGA II and MOPSO. Also, it is used in this study in order to achieve an optimal solution using MDO in both 3DOF and 6DOF simulations of GFV to reach desirable performance index.

Optimization and robustness analysis of hybridoma cell fed-batch cultures using the overflow metabolism model

The maximization of biomass productivity in fed-batch cultures of hybridoma cells is analyzed based on the overflow metabolism model. Due to overflow metabolism, often attributed to limited oxygen capacity, lactate and ammonia are formed when the substrate concentrations (glucose and glutamine) are above a critical value, which results in a decrease in biomass productivity. Optimal feeding rate, on the one hand, for a single feed stream containing both glucose and glutamine and, on the other hand, for two separate feed streams of glucose and glutamine are determined using a Nelder-Mead simplex optimization algorithm. The optimal multi exponential feed rate trajectory improves the biomass productivity by 10 % as compared to the optimal single exponential feed rate. Moreover, this result is validated by the one obtained with the analytical approach in which glucose and glutamine are fed to the culture so as to control the hybridoma cells at the critical metabolic state, which allows maximizing the biomass productivity. The robustness analysis of optimal feeding profiles obtained with different optimization strategies is considered, first, with respect to parameter uncertainties and, finally, to model structure errors.

Optimal Operation of Hybridoma Cell Fed-Batch Cultures Using the Overflow Metabolism Model: Numerical and Analytical Approach

The maximization of biomass productivity in fed-batch cultures of hybridoma cells is analyzed based on the overflow metabolism model. Due to overflow metabolism, often attributed to limited oxygen capacity, lactate and ammonia are formed when the substrate concentrations (glucose and glutamine) are above a critical value, which results in a decrease in biomass productivity. Optimal feeding rate, on the one hand, for a single feed stream containing both glucose and glutamine and, on the other hand, for two separate feed streams of glucose and glutamine are determined using a Nelder-Mead simplex optimization algorithm. The optimal multi exponential feed rate trajectory improves the biomass productivity by 10% as compared to the optimal single exponential feed rate. Moreover, this result is validated by the one obtained with the analytical approach in which glucose and glutamine are fed to the culture such as to control the hybridoma cells at the critical metabolism state, which allows maximizing the biomass productivity.

From molecular weight distribution to linear viscoelastic properties and back again: application to some commercial high-density polyethylenes

The aim of this study was to predict broad molecular weight distribution (MWD) of commercial high-density polyethylene (HDPE) samples from their linear viscoelastic (LVE) responses using a tube-based model. In the first step, a forward model based on time-dependent reptation mechanism was applied to predict LVE properties from MWD. Material parameters of the considered tube-based model were adjusted by comparing experimental and theoretical dynamic storage and loss moduli values. Adjusted parameters were compared with previously reported values and the effects of important parameters on the LVE properties were studied. It was found that higher polydispersity may lead to more relaxation which will be reflected in model by increase of mixing exponent. In the second step, the adjusted material parameters of one of the samples were used for prediction of MWD of all samples from their dynamic storage and loss moduli values. Two standard distribution functions were used for prediction of MWDs and the results were compared. It was shown that the Gaussian distribution function is suitable for prediction of broad unimodal MWD specimens, as they regularly appear in Ziegler–Natta catalyzed polyolefins, but the GEX function brings about optimal combination of flexibility and generality and is more appropriate for samples with asymmetric MWD curves. Considered combination of modeling elements including a Gaussian distribution function, a time-dependent diffusion relaxation function, a double-reptation mixing rule and the Nelder–Mead simplex optimization algorithm offers a practical tool for prediction of broad MWD of the commercial HDPE samples which can be used for online measurements.

Band-gap engineering in CIGS solar cells using Nelder–Mead simplex optimization algorithm

Band-gap grading in a CIGS absorber and a conduction band offset at n/p hetero-interface are two important parameters of band-gap engineering aiming at high efficient CIGS solar cells. To obtain optimal CIGS absorber's band-gap grading profile an automatic optimization loop based on Nelder–Mead simplex optimization algorithm has been implemented. The optimization problem is described with an objective function, which—by varying the input parameters—is minimized or maximized. In our study two types of objective functions are used; optical and electrical. As the most optimal profile a parabolic, double graded band-gap profile with a positive or nearly zero conduction band offset at n/p hetero-interface is calculated. Structures with different CIGS absorber thicknesses and bulk and/or hetero-interface recombination lifetimes are examined and their optimized parameters are discussed in the light of experimental achievements.

Synthesis of fiber Bragg grating parameters from experimental reflectivity: a simplex approach and its application to the determination of temperature-dependent properties

A simple, accurate, and fast method to synthesize the physical parameters of a fiber Bragg grating numerically from its reflectivity is proposed and demonstrated. Our program uses the transfer matrix method and is based on a Nelder-Mead simplex optimization algorithm. It can be applied to both uniform and nonuniform (apodized and chirped) fiber Bragg gratings. The method is then used to synthesize a uniform Bragg grating from its reflectivity taken at different temperatures. It gives a good estimate of the thermal expansion coefficient and the thermo-optic coefficient of the fiber.

A CONTROL ARCHITECTURE FOR MULTIPLE SUBMARINES IN COORDINATED SEARCH MISSIONS

A control architecture for executing multi-vehicle search algorithms is presented. The proposed hierarchical structure consists of three control layers: maneuver controllers, vehicle supervisors and team controllers. The system model is described as a dynamic network of hybrid automata in the programming language Shift and allows reasoning about specification and dynamical properties in a formal setting. The particular search problem that is studied is that of finding the minimum of a scalar field using a team of autonomous submarines. As an illustration, a coordination scheme based on the Nelder-Mead simplex optimization algorithm is presented and illustrated through simulations.

Prediction of East African Seasonal Rainfall Using Simplex Canonical Correlation Analysis

Abstract A linear statistical model, canonical correlation analysis (CCA), was driven by the Nelder–Mead simplex optimization algorithm (called CCA-NMS) to predict the standardized seasonal rainfall totals of East Africa at 3-month lead time using SLP and SST anomaly fields of the Indian and Atlantic Oceans combined together by 24 simplex optimized weights, and then “reduced” by the principal component analysis. Applying the optimized weights to the predictor fields produced better March–April–May (MAM) and September–October–November (SON) seasonal rain forecasts than a direct application of the same, unweighted predictor fields to CCA at both calibration and validation stages. Northeastern Tanzania and south-central Kenya had the best SON prediction results with both validation correlation and Hanssen–Kuipers skill scores exceeding +0.3. The MAM season was better predicted in the western parts of East Africa. The CCA correlation maps showed that low SON rainfall in East Africa is associated with cold SST...