integer programming

A mathematical programming that requires all or part of the variables in the problem to be integers.

It is generally believed that nonlinear integer programming can be divided into linear part and integer part, so integer programming is often regarded as a special part of linear programming. In linear programming problems, some optimal solutions may be fractions or decimals, but for some specific problems, it is often required that the solutions must be integers. For example, the number of machines, the number of people working or the number of cars loaded have all been solved. In order to meet the requirements of integers, at first glance, it seems only necessary to round off the obtained non-integer solution. In fact, the rounded number is not necessarily a feasible solution and an optimal solution, so integer programming should have a special solution. In integer programming, if all variables are limited to integers, it is called pure integer programming. If only some variables are limited to integers, it is called mixed integer programming. A special case of integer programming is 0 1 programming whose variables are limited to 0 or 1.