Leikkaustasomenetelmä

Leikkaustasomenetelmä, known in English as the cutting plane method, is an algorithm used in mathematical optimization to solve linear programming problems. It is particularly effective for problems with a large number of variables but a relatively small number of constraints, where traditional simplex methods might become computationally expensive.

The core idea of the cutting plane method is to iteratively improve a lower bound on the optimal value of an objective function. It starts by solving a relaxed version of the problem, often ignoring certain constraints or treating integer variables as continuous. If the solution to this relaxed problem is feasible for the original problem, it is also the optimal solution. However, if the relaxed solution violates one or more constraints of the original problem, the algorithm generates a new constraint, called a cutting plane. This cutting plane is designed to cut off the current relaxed solution without removing any feasible solutions of the original problem.

The process of adding cutting planes and re-solving the relaxed problem continues until a feasible and optimal solution to the original problem is found. The effectiveness of the cutting plane method depends on the efficiency with which cutting planes can be generated and the number of iterations required to converge to the optimal solution. Various strategies exist for generating cutting planes, each with its own advantages and disadvantages in terms of computational complexity and convergence speed.