Introduction to Optimizer

Using this Guide

This Guide explains how to use the Analytica Optimizer. It provides a Quick Start Tutorial and an introduction to the basic concepts of optimization, including linear, quadratic, and nonlinear programming (NLP), including special topics in NLP. However, it is not a complete textbook on optimization. For more challenging applications, you might find it useful to consult one of the many good textbooks on optimization.

What is the Analytica Optimizer?

The Optimizer enhances Analytica with powerful functions to find optimal decisions and to solve equations. Most Analytica Optimizer models aim to find a decision strategy — values for decision variables — to maximize or minimize a quantified objective subject to a set of equality or inequality constraints. Some models seek a feasible solution that satisfies a set of constraints without regard to an objective.

Types of Optimization

A linear program (LP) require the objective function and constraints to be linear functions of decision variables. LPs are solvable using straightforward algorithms that yield unique (global) maximizing or minimizing solutions. Although LP algorithms are well understood, large-scale optimizations can be computationally complex.

When pairs of decision variables are multiplied together, including squared decision variables, quadratic terms result. A quadratic problem (QP) has quadratic terms in the objective and linear constraints. A generalization of a QP, in which one or more constraints contains quadratic terms, is called a Quadratically Constrained Program (QCP). If the objective and constraint functions satisfy a mathematical property known as convexity, QP solutions are always unique (global). Non-convex formulations can result in “local” solutions that may or may not represent the global optimum.

Nonlinear Programming (NLP) imposes no restrictions on the mathematical properties of objectives and constraints. A wide variety of computational algorithms can be applied to NLPs. Strategies include gradient tracking and genetic algorithms that allow potential solutions to compete within the computation.

With all classes of optimization, Analytica supports variables that are continuous, discrete (integer, Boolean, grouped), or a mixture of continuous and discrete decision variables.

Analytica Optimizer analyzes your objective functions and constraints automatically to discover the type of optimization and select the appropriate solver engine.

Premium Solver Specifications

The standard edition of Analytica Optimizer uses the Premium Solver Platform licensed from Frontline Systems, Inc., the developer of the Optimizer/Solver in Microsoft Excel, and a world leader in spreadsheet optimization.

The Premium Solver is the leading add-on software for spreadsheet optimization, and incorporates state-of-the-art technologies. The LP and QP solver engines that come included with Analytica Optimizer handle up to 8000 variables and 8000 constraints in addition to bounds on the decision variables. Up to 2000 of these variables may be constrained to be integer-valued for Mixed Integer Programing (MIP). Up to 2000 decision variables of any kind are supported when quadratic constraints are present. The NLP solvers offer hybrid methods using classical gradient-search and evolutionary (genetic) algorithms for smooth and discontinuous objective functions with up to 500 decision variables and 250 constraints. Large scale add-on engines that eliminate the limit on variables and constraints entirely are also available at extra cost

If your problems exceed these limits, or you need a solver that is even faster, you can add any of a number of high-end solvers, LP, QP, or NLP, that include some of the most powerful solver engines available anywhere.

Optimizing with Uncertain Values and Intelligent Arrays

The Analytica Optimizer performs optimization under uncertainty to maximize expected values and minimize loss percentiles, as well as other statistical functions of objectives and constraints. Analytica allows users to combine Intelligent arrays with all classes of optimization. Thus, you can easily create arrays of optimizations conditioned on samples from uncertain variables, for parametric analysis of effects of key assumptions, and for each time period in a dynamic model.

Compatibility with Other Analytica Editions

The Analytica Optimizer is an edition of Analytica that includes all the functionalities of the Analytica Enterprise edition. After using Analytica Optimizer to create optimizing models, you can deliver them to end users on the desktop using Analytica Power Player with Optimizer, or via a web browser on a server using the Analytica Web Player (AWP) or Analytica Decision Engine (ADE) with an Optimizer license.