kokonaislukumenetelmillä

Kokonaislukumenetelmät, known in English as integer methods or integer programming methods, refer to a class of mathematical optimization techniques used to solve problems where the decision variables must take on integer values. These methods are distinct from continuous optimization methods where variables can be any real number. Integer programming problems are generally more complex to solve than their continuous counterparts, and specialized algorithms are required.

A fundamental concept in kokonaislukumenetelmät is the distinction between pure integer programming, where all variables must be integers, and mixed-integer programming, where some variables can be continuous while others must be integers. Binary integer programming is a special case where variables can only take values of 0 or 1, often used to model yes/no decisions.

Common techniques within kokonaislukumenetelmät include the cutting plane method and branch and bound. The cutting plane method iteratively adds linear constraints (cuts) to the feasible region of the linear programming relaxation of the integer problem, thereby tightening the bounds and eventually leading to an integer optimal solution. Branch and bound systematically explores the solution space by dividing the problem into smaller subproblems and using bounds derived from relaxations to prune branches that cannot contain an optimal integer solution. Other methods include enumeration, dynamic programming, and heuristic algorithms, which may be used for very large or complex problems where exact solutions are computationally infeasible. Kokonaislukumenetelmät have wide applications in areas such as operations research, logistics, finance, and scheduling.