New release: New solver methods and many more options!
Optimization is the science of finding decisions that satisfy given
constraints, and meet a specific goal at its optimal value. In engineering,
constraints may arise from physical limitations and technical specifications;
in business, constraints are often related to resources, including manpower,
equipment, costs, and time.
The objective of global optimization is to find the "best possible" solution in
nonlinear decision models that frequently have a number of sub-optimal (local)
solutions. Multi-extremal optimization problems can be very difficult. To
obtain a high quality numerical solution, a global "exhaustive" search approach
is necessary. In the absence of global optimization tools, engineers and
researchers are often forced to settle for feasible solutions, often neglecting
the optimum values. In practical terms, this implies inferior designs and
operations, and related expenses in terms of reliability, time, money, and
The Maple Global Optimization 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.
- 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.
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
"The Global Optimization Toolbox for Maple provides a widely
applicable, fully integrated development environment that can support control
engineering applications and help realize the significant potential that global
optimization has as a valuable tool in control system design."
Dr. Didier Henrion
LAAS-CNRS, Toulouse, France