ILIN: An Implementation of the Integer Labeling Algorithm for Integer Programming (original) (raw)

AN ALGORITHM FOR SOLVING INTEGER LINEAR PROGRAMMING PROBLEMS

The paper describes a method to solve an ILP by describing whether an approximated integer solution to the RLP is an optimal solution to the ILP. If the approximated solution fails to satisfy the optimality condition, then a search will be conducted on the optimal hyperplane to obtain an optimal integer solution using a modified form of Branch and Bound Algorithm.

Integer-Programming-Problem-Formulation

OP Papers, 2011

Integer linear programming is a very important class of problems, both algorithmically and combinatorially.Following are some of the problems in computer Science ,relevant to DRDO, where integer linear Programming can be effectively used to find optimum solutions. * Computer Scientist, Defence R&D Org., Min of Defence, Delhi-110054. email:akdhamija@dipr.drdo.in, dhamija.ak@gmail.com, a k dhamija@yahoo.com.

Contemporary Approaches to the Solution of the Integer Programming Problem

2003

The purpose of this thesis is to provide analysis of the modem development of the methods for solution to the integer linear programming problem. The thesis simultaneously discusses some main approaches that lead to the development of the algorithms for the solution to the integer linear programming problem. Chapter 1 introduces the Generalized Linear Programming Problem alongside with the properties of a solution to the Linear Programming Problem. The simplex procedure presented to solve the Linear Programming Problem by adding slack variables along with the artificial-basis technique. Chapter 2 refers to the primal-dual simplex procedure. The dual simplex algorithm reflects the dual simplex procedure. Chapter 3 discusses the mixed and alternative formulations of the integer programming problem. Chapter 4 considers the optimality conditions with the imposed relaxations to solve the Linear Programming Relaxation Problem. The methods of the Integer Programming are introduced for the ...

Integer Programming: Theory and Practice

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Introduction to Integer Programming

The Kluwer International Series in Engineering and Computer Science, 1992

Introduction to Integer Programming Integer programming models Handouts: Lecture Notes 2 A 2-Variable Integer program maximize 3x + 4y subject to 5x + 8y ≤ 24 x, y ≥ 0 and integer What is the optimal solution? The Feasible Region 0 1 2 3 4 5 Solve LP (ignore integrality) get x=24/5, y=0 and z =14 2/5. Round, get x=5, y=0, infeasible! Truncate, get x=4, y=0, and z =12 Same solution value at x=0, y=3. Optimal is x=3, y=1, and z =13 4 Why integer programs? Advantages of restricting variables to take on integer values-More realistic-More flexibility 7 The game of fiver. Click on a circle, and flip its color and that of adjacent colors. Can you make all of the circles red? 8 The game of fiver.

Modelling Integer Programming with Logic: Language and Implementation

Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2000

The classical algebraic modelling approach for integer programming (IP) is not suitable for some real world IP problems, since the algebraic formulations allow only for the description of mathematical relations, not logical relations. In this paper, we present a language L + for IP, in which we write logical specication of an IP problem. L + is a language based on the predicate logic, but is extended with meta predicates such as at least(m; S), where m is a non-negative integer, meaning that at least m predicates in the set S of formulas hold. The meta predicates facilitate reasoning about a model of an IP problem rigorously and logically. L + is executable in the sense that formulas in L + are mechanically translated into a set of mathematical formulas, called IP formulas, which most of existing IP solvers accept. We give a systematic method for translating formulas in L + to IP formulas. The translation is rigorously dened, veried and implemented in Mathematica 3.0. Our work follows the approach of McKinnon and Williams, and elaborated the language in that (1) it is rigorously dened, (2) transformation to IP formulas is more optimised and veried, and (3) the transformation is completely given in Mathematica 3.0 and is integrated into IP solving environment as a tool for IP.

Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition

INFORMS Journal on Computing, 2000

This paper is about modeling and solving mixed integer programming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically. Fifteen years ago, mainframe computers were required to solve problems with a hundred integer variables. Now it is possible to solve problems with thousands of integer variables on a personal computer and obtain provably good approximate solutions to problems such as set partitioning with millions of binary variables. These advances have been made possible by developments in modeling, algorithms, software, and hardware. This paper focuses on effective modeling, preprocessing, and the methodologies of branch-and-cut and branch-and-price, which are the techniques that make it possible to treat problems with either a very large number of constraints or a very large number of variables. We show how these techniques are useful in important application areas such as network design and crew scheduling. Finally, we discuss the relatively new research areas of parallel integer programming and stochastic integer programming.

Scarf's Procedure for Integer Programming and a Dual Simplex Algorithm

Mathematics of Operations Research, 1985

Scarf has recently introduced an algorithm for integer programs based on the combinatorial concept of primitive set. We show that as the decision variables of the integer program become continuous and the integer program reduces to a linear program, the Scarf algorithm converges to a dual simplex algorithm for the limit linear programming problem. This result is robust in the sense that even before the limit is reached, the dual simplex path is contained in the path of primitive sets generated by the Scarf algorithm.

Constraint Integer Programming: Techniques and Applications

2008

This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This ap- proach is supported by the CIP framework SCIP, which also integrates techniques for solving satisability problems. SCIP is available

A HEURISTIC FOR GENERAL INTEGER PROGRAMMING

Decision Sciences, 1974

When constructing linear programming models one is frequently faced with the restriction that all variables must be integer valued. Integer restrictions are generally required because of the indivisible nature of the items t o be optimized e.g., in hiring it is meaningless to hire fractional people.