Objective Class

An objective function of a mathematical program. It is composed of two parts:
  • a linear mathematical expression, and
  • a direction (minimize or maximize).
The following are some examples of objective functions:
C#
// i, j: nodes
// x[i, j]: arc flow variable
// cost[i, j]: unit flow cost on arc (i,j)
// fixedCost[i]: fixed cost of including node i in the network
Objective minFlowCost = minimize | sum(over(i, j), cost[i, j] * x[i, j]);
Objective minTotalCost = minimize | sum(over(i, j), cost[i, j] * x[i, j]) + sum(over(i), fixedCost[i] * y[i]);

// p: person; t: task
// utility[p, t]: utility of person p when assigned to task t
// fitness[p, t]: fitness of person p's skills to task t
// revenue[t]: revenue of completing task t
// x[p, t]: 1 if person p is assigned to task t; 0 o/w
MathExpr totalUtility = sum(over(p, t), utility[p, t] * x[p, t]);
MathExpr totalFitness = sum(over(p, t), fitness[p, t] * x[p, t]);
MathExpr totalRevenue = sum(over(p, t), revenue[t] * x[p, t]);

double weightUtility = 0.40;
double weightFitness = 0.35;
double weightRevenue = 0.25;

Objective weighted = maximize
                    | weightUtility * totalUtility + weightFitness * totalFitness + weightRevenue * totalRevenue

Definition

Namespace: Orx.MathProg
Assembly: Orx.MathProg (in Orx.MathProg.dll) Version: 1.0.0
C#
public class Objective
Inheritance
Object    Objective

Methods

AsMaximization Returns an objective function with the same expression and with maximize as the direction.
AsMinimization Returns an objective function with the same expression and with minimize as the direction.
CreateForDirection Returns an objective function with the same expression and with the given direction.
Equals
(Inherited from Object)
Finalize
(Inherited from Object)
GetHashCode
(Inherited from Object)
GetType
(Inherited from Object)
LogToConsole Logs the objective function to the console.
MemberwiseClone
(Inherited from Object)
ToString
(Inherited from Object)

Fields

Direction Direction of the objective function: Minimize or Maximize.
Key Text representation of the objective function.
ObjectiveDefinition Definition of the objective function.
ObjectiveKey Key of the objective function.
ObjExpr Objective function expression.

See Also