Optimization Characteristics

Introduction

Although the material in this chapter is not specific to Analytica, it should give users a foundation of knowledge sufficient to understand the basic characteristics of an optimization problem and to understand the mathematical characteristics that define different optimization types.

Parts of an optimization problem: General Description

The first step in performing an optimization is to formulate the problem appropriately. An optimization problem is defined by four parts: a set of decision variables, an objective function, bounds on the decision variables, and constraints. The formulation looks like this.

Decision variables

A vector (one-dimensional array) of the variables whose values we can change to find an optimal solution. A solution is a set of values assigned to these decision variables.

Objective

A function of the decision variables that gives a single number evaluating a solution. By default, the Optimizer tries to find the value of the decision variables that minimizes the value of objective. If you set the optional parameter Maximize to True, it instead tries to maximize the objective. For a linear program (LP), the objective is defined by a set of coefficients or weights that apply to the decision variables. For a nonlinear program (NLP), the objective can be any expression or variable that depends on the decision variables.

Bounds

A range on the decision variables, defining what values are allowed. These bounds define the set of possible solutions, called the search space. Each decision variable can have a lower bound and/or an upper bound. If not specified, the lower and upper bounds are -INF and +INF — that is, there are no bounds.

Constraints

The constraints, e.g., , are bounds on functions of the decision variables. They define which solutions are feasible.