The use of optimization software requires that the function f is defined in a suitable programming language and connected at compile or run time to the optimization software. The optimization software will deliver input values in A, the software module realizing f will deliver the computed value f(x) and, in some cases, additional information about the function like derivatives.
In this manner, a clear separation of concerns is obtained: different optimization software modules can be easily tested on the same function f, or a given optimization software can be used for different functions f.
AMTS.Farm.Cattle(Pro) is sold on subscription basis and includes free support and free updates. Updates are made continuously and new versions are released regularly (3-4 times annually). The ability to perform least cost optimization using a linear optimizer is standard with .Cattle(Pro).
You are busy. Our cattle feeding software is designed to be efficient. We believe that users should only have to enter data once. Digital data (such as feed library analyses) can be electronically imported. Templates allow you to load data for common inputs. Using AMTS.FBM, AMTS.Farm.Cattle dairy and beef ration formulation software products can share data with major mill formulation programs.
AMTS.Farm.Cattle offers two optimizers. Customers can choose to remain with the basic least-cost ration optimization that comes standard with the software or upgrade to the AMTS.Farm.Cattle(ao). Customers can also upgrade the Mixes function to allow linear optimization of ingredients in AMTS.Farm.Cattle(mo). To unlock full optimization power they can bundle into AMTS.Farm.Cattle(ao+).
This includes so called hard-to-change factors (for split-plot designs ) and optimization of chemical formulations or mixture designs as well as combined designs which handle mixture and process factors in a single experiment.
Designed as a specialized DOE software package, Design-Expert offers features for ease of use, functionality and power that you won't find in general statistical packages. You'll discover a wide variety of designs, the flexibility to modify designs, unique evaluation capabilities, tools for response modeling, graphics to simplify interpretation, multiple response optimization, POE capabilities, an intuitive interface and a greatly expanded help system.
A powerful formulation and correction software designed to bring confidence and speed to those working in the textile industries, our Match Textile Software provides fast and accurate matches with the lowest-cost recipes for exhaust and continuous dyers alike.
The software makes it easy to manage accurate nutritional values, production parameters and recipe specifications, under any conditions and at any time. This means that you can instantly adapt to volatile material costs, ingredient stocks and purchasing positions. BESTMIX® Recipe Management effortlessly translates recipes into practical products, while always maintaining the highest standards in formulation, legal requirements and labeling.
The aquafeed industry deals with specific challenges such as sustainability, moisture control, reaching optimal density and dealing with the volatility of ingredients while searching for alternative ones. This requires powerful formulation software.
Prototypes are stored and can be easily shared for comparison and approval. R&D staff can send a set of prototypes to Marketing, R&D and Quality managers for comparison of recipe prototypes based on ingredient lists, allergen lists, nutritional specifications, health claims and costs so you can select the one closest to the original brief. As your iterations progress, the formulation software stores the history of your prototypes so that the Research & Development team can easily access and capitalize on past experience.
We have designed and optimized the formulations of highly thermosensitive liposomes by control of DPPC, DSPC, DSPE-PEG, cholesterol, and ELP-lipid conjugates. During the optimization of formulation, we found that the concentration and balance of cholesterol and ELP-lipid conjugates were the main factors in the amount and temperature of drug release. The characteristics of selected formulations were investigated in vitro drug release, cryo-TEM analysis, simulation study, DOX accumulation study, and antitumor efficacy study. The results demonstrated that, in our system, e-TSL was very versatile for the modulation of amount and temperature of drug release, as we intended. Our liposome system was confirmed to be highly stable in physiological environments. It is expected that mild hyperthermia before i.v. injection and lag time after i.v. injection would play important role for maximize the drug accumulation. We found that treatment protocol optimization, in addition to the formulation of the liposome, is important for reflecting the advantage of TSL formulation.
While these MDO frameworks introduce important innovations in software design, modular model construction, and user interface design, they treat each discipline analysis as an explicit function evaluation; that is, they assume that each discipline is an explicit mapping between inputs and outputs. This limits the efficiency of the nonlinear solution algorithms that could be used to find a solution to the coupled multidisciplinary system. Furthermore, these MDO frameworks also present the combined multidisciplinary model as an explicit function to the optimizer, which limits the efficiency when computing derivatives for gradient-based optimization of higher-dimensional design spaces. Therefore, while these first framework developments addressed the most pressing issue by significantly lowering the implementation effort for multidisciplinary analysis, they did not provide a means for applying the most efficient MDO techniques.
One can always compute derivatives using finite differences, but analytic derivative methods are much more efficient and accurate. Despite the extensive research into analytic derivatives and their demonstrated benefits, they have not been widely supported in MDO frameworks because their implementation is complex and requires deeper access to the analysis code than can be achieved through an approach that treats all analyses as explicit functions. Therefore, users of MDO frameworks that follow this approach are typically restricted to gradient-free optimization methods, or gradient-based optimization with derivatives computed via finite differences.
The need for frameworks that facilitate the implementation of MDO problems and their solution was identified soon after MDO emerged as a field. Various requirements have been identified over the years. Early on, Salas and Townsend (1998) detailed a large number of requirements that they categorized under software design, problem formulation, problem execution, and data access. Later, Padula and Gillian (2006) more succinctly cited modularity, data handling, parallel processing, and user interface as the most important requirements. While frameworks that fulfill these requirements to various degrees have emerged, the issue of computational efficiency and scalability has not been sufficiently highlighted or addressed.
When solving MDO problems, we have to consider how to organize the discipline analysis models, the problem formulation, and the optimization algorithm in order to obtain the optimum design with the lowest computational cost possible. The combination of the problem formulation and organizational strategy is called the MDO architecture. MDO architectures can be either monolithic (where a single optimization problem is solved) or distributed (where the problem is partitioned into multiple optimization subproblems). Martins and Lambe (2013) describe this classification in more detail and present all known MDO architectures.
The origins of OpenMDAO began in 2008, when Moore et al. (2008) identified the need for a new MDO framework to address aircraft design challenges at NASA. Two years later, Gray et al. (2010) implemented the first version of OpenMDAO (V0.1). An early aircraft design application using OpenMDAO to implement gradient-free efficient global optimization was presented by Heath and Gray (2012). Gray et al. (2013) later presented benchmarking results for various MDO architectures using gradient-based optimization with analytic derivatives in OpenMDAO.
In an effort to unify the theory for the various methods for computing derivatives, Martins and Hwang (2013) derived the unified derivatives equation. This new generalization showed that all the methods for computing derivatives can be derived from a common equation. It also showed that when there are both implicitly and explicitly defined disciplines, the adjoint method and chain rule can be combined in a hybrid approach. Hwang et al. (2014) then realized that this theoretical insight provided a sound and convenient mathematical basis for a new software design paradigm and set of numerical solver algorithms for MDO frameworks. Using a prototype implementation built around the unified derivatives equation (Martins and Hwang 2016), they solved a large-scale satellite optimization problem with 25,000 design variables and over 2 million state variables (Hwang et al. 2014). Later, Gray et al. (2014) developed OpenMDAO V1, a complete rewrite of the OpenMDAO framework based on the prototype work of Hwang et al. with the added ability to exploit sparsity in a coupled multidisciplinary model to further reduce computational cost.
To overcome the serial computing limitation, Hwang and Martins (2018) parallelized the data structures and solver algorithms from their prototype framework, which led to the modular analysis and unified derivatives (MAUD) architecture. Hwang and Martins (2015) used the new MAUD prototype to solve a coupled aircraft allocation-mission-design optimization problem. OpenMDAO V1 was then modified to incorporate the ideas from the MAUD architecture. Gray et al. (2018a) presented an aeropropulsive design optimization problem constructed in OpenMDAO V1 that combined a high-fidelity aerodynamics model with a low-fidelity propulsion model, executed in parallel. One of the central features of the MAUD architecture, enabling the usage of parallel computing and high-fidelity analyses, was the use of hierarchical, matrix-free linear solver design. While advantageous for large parallel models, this feature was inefficient for smaller serial models. The need to support both serial and parallel computing architectures led to the development of OpenMDAO V2, a second rewrite of the framework, which is presented in this paper. 2b1af7f3a8