Maple Global Optimization - Maple Professional Toolbox Series - Maplesoft

# Global Optimization Powered by Optimus

Maple Global Optimization Toolbox
Powered by Optimus®

The Maple Global Optimization Toolbox helps you find the best possible solution to your optimization problems. When faced with non-linear decision models that have a number of local solutions, global optimization techniques allow you to determine the most efficient, optimal solution rather than merely a feasible, sub-optimal one. By implementing the optimal solution, you can produce superior designs and operations, and reduce expenses in terms of reliability, time, money, and other resources.

This toolbox is powered by Optimus technology from Noesis Solutions. Optimus is a platform for simulation process integration and design optimization that includes powerful optimization algorithms.  This same proven optimization technology is available to Maple users as the engine behind the Global Optimization Toolbox. With this toolbox, you can formulate optimization models easily inside the powerful Maple numeric and symbolic system, and then use world-class optimization technology to return the best answer robustly and efficiently.

## Key Features

• Incorporates the following solver modules for nonlinear optimization problems.
• Differential Evolution Algorithm
• Adaptive Stochastic Search Methods
• Global solution further refined using the local optimization solvers in Maple
• Solves models with thousands of variables and constraints.
• Solvers take advantage of Maple arbitrary precision capabilities in their calculations, to greatly reduce numerical instability problems.
• Supports arbitrary objective and constraint functions, including those defined in terms of special functions (for example, Bessel, hypergeometric), derivatives and integrals, and piecewise functions etc. Functions can also be defined in terms of a Maple procedure rather than a formula.
• Interactive Maplet™ assistant for easy problem definition and exploration.
• Built-in model visualization capabilities for viewing one or two-dimensional subspace projections of the objective function, with visualization of the constraints as planes or lines on the objective surface.

## Application Areas

Global optimization problems are prevalent in systems described by highly nonlinear models. These areas include:

• Advanced engineering design
• Econometrics and finance
• Management science
• Medical research and biotechnology
• Chemical and process industries
• Industrial engineering
• Scientific modeling
Integrated Powertrain Control with Maple and MapleSim: Optimal Engine Operating Points

Within the automotive powertrain industry, the engine operating point is an important part of the vehicle’s performance and emissions. The engine operating point, which is determined by the engine speed and torque, impacts fuel consumption, available propulsion power, and emissions. The Brake Specific Fuel Consumption (BSFC) is commonly used as an effective measure of engine performance.

This whitepaper discusses a method of determining an optimal set of operating points for an internal combustion engine based on the BSFC. The described approach is general and may be extended to include additional engine information such as NOx emissions data. Such additional information can be a part of the weighted cost equation used within the optimization process.

Optimization for Engineering Applications with MapleSim and Maple Global Optimization Toolbox

Within the automotive powertrain industry, the engine operating point is an important part of the vehicle’s performance and emissions. The engine operating point, which is determined by the engine speed and torque, impacts fuel consumption, available propulsion power, and emissions. The Brake Specific Fuel Consumption (BSFC) is commonly used as an effective measure of engine performance.

This whitepaper discusses a method of determining an optimal set of operating points for an internal combustion engine based on the BSFC. The described approach is general and may be extended to include additional engine information such as NOx emissions data. Such additional information can be a part of the weighted cost equation used within the optimization process.

## Ready for the next step?

*Evaluations are not available for students or personal edition users.