What is the need of integer programming?
Integer programming expresses the optimization of a linear function subject to a set of linear constraints over integer variables.
Will the solution to an optimization problem always consist of integers?
The solution to an linear programming problem “Does not always” consist of integers. The optimal solution of a linear programming model is calculated at a corner point of the feasible region. That corner point will be the intersection point of two or more constraints.
What are integer programming problems?
An integer programming (IP) problem is a linear programming (LP) problem in which the decision variables are further constrained to take integer values. Both the objective function and the constraints must be linear. The most commonly used method for solving an IP is the method of branch-and–bound.
How is the difficulty of a mixed linear integer measured?
A standard answer would be the difficulty is measured by “the quality of the relaxation”, which says a lot without really saying much. The number of integer variables and restrictions does not necessarily imply an increase in the computing burden. In my experience there is no consistent relation between the two.
Can a simplex algorithm be used for integer programming?
Given a starting solution, the Simplex algorithm will systematically find solutions with better values of your goal function. However, it runs using real numbers (or rational numbers). You can use the Simplex algorithm to find a solution for an integer programming problem that is optimal, except that it ignores the need for integer values.
Why is linear programming similar to integer programming?
Linear programming is straightforward because the equations describe an n-dimensional shape and the solution is at one of the vertexes. An algorithm can quickly find the solution by traversing the shape in the direction of the solution. Integer programming is similar, but the solution is at an n-dimensional integer value near one of the vertexes.
Why do you add variables to a bound algorithm?
In many problems, adding variables helps strengthening the linear relaxations and hence, the bounds used at each node of the branch and bound algorithm. In other problems, adding valid inequalities just makes the model bigger and heavier at each node.