If no lower bound is provided for a decision variable, Rose assumes that the lower bound for the decision variable is zero, meaning the decision variable is non-negative. If no upper bound is provided for a decision variable, Rose assumes that the upper bound for the decision variable is positive infinity. For details on how to set infinite or infinitesimal bounds on decision variables, refer to the linked article. While many model-building tools typically specify bounds for decision variables by default, Rose provides flexibility in handling large numbers and special cases, such as representing infinity.
If no right-hand side value is provided for a constraint, Rose assumes the right-hand side value to be zero for the constraint.
Continuous decision variables
Continuous decision variables in a mathematical optimization model are variables that can take any real value within a defined range or bounds. Unlike integer variables, continuous variables are not restricted to whole numbers, allowing the model to explore a broader solution space.
Below are the different types of bounds that Rose supports reading in from the .mps file.
- LO = lower bound for continuous decision variable
- UP = upper bound for continuous decision variable
- FR = continuous decision variable that can take on any real value
- FX = decision variable is fixed at the specified value and cannot take on any other value
- MI = lower bound is negative infinity for continuous decision variable
- PL = upper bound is positive infinity for continuous decision variable
An example snippet of the bounds section of an .mps file is provided below. In this example, \(x1\) must be between 10 and 20, inclusive, \(x2\) and \(x4\) can be any real value, positive or negative. \(x3\) must be exactly 80.5, and \(x5\) can be any non-negative real value due to the default lower bound of zero and values 1e20 or larger representing infinity.
BOUNDS
LO BOUND x1 10
UP BOUND x1 20
FR BOUND x2
FX BOUND x3 80.5
MI BOUND x4
PL BOUND x4
UP BOUND x5 1E20
Integer decision variables
Integer decision variables in a mixed-integer programming (MIP) model are variables that are constrained to take on only whole numbers (integers), as opposed to continuous decision variables that can take on any real value, within a specified range. These variables are often used to model decisions that are inherently discrete, such as a counts of items. Integer decision variables make the optimization problem significantly more complex, as they introduce combinatorial elements.
Integer decision variables are subject to the solver tolerance settings, which define how close the variable's value must be to an integer for it to be considered valid. To read more about this tolerance setting, view the following article, Integral tolerance.
Below are the different types of bounds that Rose supports reading in from the .mps file.
- LI = lower bound for integer decision variables
- UI = upper bound for integer decision variables
An example snippet of the bounds section of an .mps file is provided below. In this example, \(x\) must be an integer between 100 and 200, inclusive.
BOUNDS
LI BOUND x 100
UI BOUND x 200
Binary decision variables
Binary decision variables in a mixed-integer programming (MIP) model are a specific type of integer variable that can only take on the values of either 0 or 1. These variables are used to model decisions with two possible outcomes, such as "yes" or "no," "on" or "off," or the selection or exclusion of an option. While they add flexibility and precision to modeling real-world problems, binary variables also increase the complexity of solving MIP models, as the optimization must explore numerous combinations of possible 0-1 configurations to find the optimal solution.
Binary decision variables are subject to the solver tolerance settings, which define how close the variable's value must be to 0 or 1 for it to be considered valid. To read more about this tolerance setting, view the following article, Integral tolerance.
Below are the different types of bounds that Rose supports reading in from the .mps file.
- BV = binary decision variable
An example snippet of the bounds section of an .mps file is provided below. In this example, \(x\) must be a binary decision variable.
BOUNDS
BV BOUND x
Comments
0 comments
Please sign in to leave a comment.