Integer programming
Integer programming is a special form of linear programming. Its decision variables can only be integers. The general form is
1. Cutting plane method
There are many types of plane cutting methods, but their basic ideas are the same. Here we take the most classic Gomory plane cutting method as an example. It first solves the linear programming with non-integer constraints, then selects a base variable that is not an integer, defines new constraints and adds the original constraints. The new constraints reduce the feasible range, but retain all integer feasible solutions of the original problem.
2. Branch and Bound
Its basic idea is to continuously divide the feasible region into small sets, and then find the integer optimal solution on the small set. When dividing the feasible region, the integer solution will not be lost.
3. 0–1 planning
It is a special form of integer programming, and the independent variable can only take two values, 0 or 1. Since the value of the independent variable is very limited, the optimal solution can be obtained by the exhaustive method when the number of independent variables is small, and the optimal solution can be obtained by the implicit enumeration method when the number of independent variables is large. Different from the exhaustive method, the implicit enumeration method only checks a part of the value combination of the independent variable. It continuously improves the target value by finding a feasible solution, so it only checks the value combination that is better than the target value. Therefore, in the application of hidden enumeration A feasible solution must be given before the method is presented.