Search results
Results from the WOW.Com Content Network
Integer programming is NP-complete. In particular, the special case of 0–1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. [1] If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. [2]
Integer programming. The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling; Knapsack problem, quadratic knapsack problem, and several variants [2] [3]: MP9 Some problems related to Multiprocessor scheduling
solver for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP). SciPy: BSD general numeric package for Python, with some support for optimization. Uno: MIT Lagrange-Newton solver that unifies nonconvex optimization, implemented in C++. Developed at Argonne National Laboratory and Zuse Institute Berlin. [3]
All computations are performed in exact integer arithmetic using GMP or imath. Many program analysis techniques are based on integer set manipulations. The integers typically represent iterations of a loop nest or elements of an array. isl uses parametric integer programming to obtain an explicit representation in terms of integer divisions.
Efficient solutions to the vehicle routing problem require tools from combinatorial optimization and integer programming.. Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry.
Similarly, an integer program (consisting of a collection of linear constraints and a linear objective function, as in a linear program, but with the additional restriction that the variables must take on only integer values) satisfies both the monotonicity and locality properties of an LP-type problem, with the same general position ...
ML.NET is a free-software machine-learning library for the C# programming language. [4] [5] NAG Library is an extensive software library of highly optimized numerical-analysis routines for various programming environments. O-Matrix is a proprietary licensed matrix programming language for mathematics, engineering, science, and financial analysis.
[1]: sec.5 The problem is parametrized by a positive integer k, and called k-way number partitioning. [2] The input to the problem is a multiset S of numbers (usually integers), whose sum is k*T . The associated decision problem is to decide whether S can be partitioned into k subsets such that the sum of each subset is exactly T .