Industrial Optimization

Local Optimization for Linear, Nonlinear, and Queuing Problems

Industrial Optimization is a Mathematica application package designed to solve a wide range of optimization problems. It provides established algorithms for linear and nonlinear optimization as well as modern techniques such as genetic programming. Because the package runs in conjunction with Mathematica, users also have access to the Mathematica programming language and over 1,500 operations that can be used to read, prepare, and analyze data in a single application.

To help novice users begin formulating and solving their problems immediately, Industrial Optimization comes with built-in palettes, detailed explanations, and examples in both electronic and bound formats. Default behaviors have been chosen carefully to be able to handle most situations, and all functions have an extensive assortment of options that allow advanced users to specify the algorithm's behavior and output.

Regardless of the computational tool used, there are instances in which conventional algorithms like Newton's method can't find an optimum or in which convergence is very slow. In these cases, Industrial Optimization provides users with other modern and efficient techniques, such as evolutionary algorithms, to find a solution.

Functions

• Linear optimization routines for solving the following:
  • Linear constrained and unconstrained optimization problems
  • Transportation problems
  • Binary and mixed-integer problems
  • Problems with multiple solutions
  • Simplex diagnostics
• Nonlinear optimization routines for the following methods:
  • Goldstein algorithm
  • Modified Newton method
  • Trust region method
  • Method of reduction
  • Genetic optimization
  • Wolfe-Powell-Fletcher algorithm
  • Quasi-Newton method
  • Method of conjugate gradients
  • Method of active sets
  • Sequential quadratic programming

The user can also create animated graphics of algorithm convergence and calculate the distribution functions and parameters of M/M/s, M/M/1, M/G/1, and Jackson network queuing systems.