Linear Programming and Integer Programming

Not to mention the purpose of linear planning, pay attention to the linprog functions in matlab and various overloaded forms.

The methods used here mainly involve the problem of optimizing the assignment coefficient matrix obtained by the Hungary method. In addition, pay attention to many problems that can be converted to linear programming problems. Think about how to convert other problems into linear programming problems.

Then there is the linear programming of integers. Obviously this depends on the optimal solution obtained in a non-integer linear programming method. If the optimal solution is an integer, no other work is needed. If there is no solution, no solution is needed. If it is not an integer, some special work is required. There are several methods to obtain the integer optimal solution:

The Branch and restriction method divides the optimal solution of non-shaping into two parts, and then splits the branch, constantly modifies the upper and lower bounds of the target, and finally obtains the integer optimal solution.

Implicit Enumeration is actually an enumeration method.

The 0-1 problem can be computed using the Hungary algorithm or matlab.

Monte Carlo method, this method is based on probability theory, so the obtained optimal solution is only the most likely optimal solution. The 6th power of 10.

The next step is nonlinear planning.