Results 1  10
of
17
The Quadratic Assignment Problem: A Survey and Recent Developments
 In Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1994
"... . Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment probl ..."
Abstract

Cited by 96 (16 self)
 Add to MetaCart
. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...
A semidefinite framework for trust region subproblems with applications to large scale minimization
 Math. Programming
, 1997
"... This is an abbreviated revision of the University of Waterloo research report CORR 9432. y ..."
Abstract

Cited by 63 (9 self)
 Add to MetaCart
(Show Context)
This is an abbreviated revision of the University of Waterloo research report CORR 9432. y
Quadratic Optimization
, 1995
"... . Quadratic optimization comprises one of the most important areas of nonlinear programming. Numerous problems in real world applications, including problems in planning and scheduling, economies of scale, and engineering design, and control are naturally expressed as quadratic problems. Moreover, t ..."
Abstract

Cited by 45 (3 self)
 Add to MetaCart
. Quadratic optimization comprises one of the most important areas of nonlinear programming. Numerous problems in real world applications, including problems in planning and scheduling, economies of scale, and engineering design, and control are naturally expressed as quadratic problems. Moreover, the quadratic problem is known to be NPhard, which makes this one of the most interesting and challenging class of optimization problems. In this chapter, we review various properties of the quadratic problem, and discuss different techniques for solving various classes of quadratic problems. Some of the more successful algorithms for solving the special cases of bound constrained and large scale quadratic problems are considered. Examples of various applications of quadratic programming are presented. A summary of the available computational results for the algorithms to solve the various classes of problems is presented. Key words: Quadratic optimization, bilinear programming, concave pro...
A Continuous Approach to Inductive Inference
 Mathematical Programming
, 1992
"... In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g ..."
Abstract

Cited by 39 (2 self)
 Add to MetaCart
In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g using outputs obtained by applying a limited number of random inputs to the hidden function. Given this inputoutput sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used...
An Interior Point Algorithm to Solve Computationally Difficult Set Covering Problems
, 1990
"... ..."
INTERIOR POINT METHODS FOR COMBINATORIAL OPTIMIZATION
, 1995
"... Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivale ..."
Abstract

Cited by 16 (9 self)
 Add to MetaCart
(Show Context)
Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow problems, and methods for solving multicommodity flow problems, including an interior point column generation algorithm.
An Interior Point Approach to Boolean Vector Function Synthesis
 In Proceedings of the 36th MSCAS
, 1993
"... The Boolean vector function synthesis problem can be stated as follows: Given a truth table with n input variables and m output variables, synthesize a Boolean vector function that describes the table. In this paper we describe a new formulation of the Boolean vector function synthesis problem as a ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
(Show Context)
The Boolean vector function synthesis problem can be stated as follows: Given a truth table with n input variables and m output variables, synthesize a Boolean vector function that describes the table. In this paper we describe a new formulation of the Boolean vector function synthesis problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. Preliminary computational results are presented. Introduction The Boolean Vector Function Synthesis Problem has applications in logic, artificial intelligence, machine learning, and digital integrated circuit design. In this paper, we describe a Satisfiability Problem formulation of the Boolean Vector Function Synthesis Problem. This formulation can be approached with a wide range of algorithms. In this paper, preliminary computational results are presented using an interior point algorit...
A Potential Reduction Approach to the Frequency Assignment Problem
, 1995
"... The frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs, or the amount of interference is minimized. We present an algorithm for this problem that is inspired by Karmarkar's interior point potential reduction approac ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
The frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs, or the amount of interference is minimized. We present an algorithm for this problem that is inspired by Karmarkar's interior point potential reduction approach to combinatorial optimization problems. We develop a nonconvex quadratic model of the problem that is very compact as all interference constraints are incorporated in the objective function. Moreover, optimizing this model may result in finding multiple solutions to the problem simultaneously. Several preprocessing techniques are discussed. We report on computational experience with both reallife and randomly generated instances.
Interior point and semidefinite approaches in combinatorial optimization
, 2005
"... Conic programming, especially semidefinite programming (SDP), has been regarded as linear programming for the 21st century. This tremendous excitement was spurred in part by a variety of applications of SDP in integer programming (IP) and combinatorial optimization, and the development of efficient ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
(Show Context)
Conic programming, especially semidefinite programming (SDP), has been regarded as linear programming for the 21st century. This tremendous excitement was spurred in part by a variety of applications of SDP in integer programming (IP) and combinatorial optimization, and the development of efficient primaldual interiorpoint methods (IPMs) and various first order approaches for the solution of large scale SDPs. This survey presents an up to date account of semidefinite and interior point approaches in solving NPhard combinatorial optimization problems to optimality, and also in developing approximation algorithms for some of them. The interior point approaches discussed in the survey have been applied directly to nonconvex formulations of IPs; they appear in a cutting plane framework to solving IPs, and finally as a subroutine to solving SDP relaxations of IPs. The surveyed approaches include nonconvex potential reduction methods, interior point cutting plane methods, primaldual IPMs and firstorder algorithms for solving SDPs, branch and cut approaches based on SDP relaxations of IPs, approximation algorithms based on SDP formulations, and finally methods employing successive convex approximations of the underlying combinatorial optimization problem.
A Potential Reduction Approach to the Radio Link Frequency Assignment Problem
, 1995
"... The frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs and the number of used frequencies is minimized, or the amount of interference is minimized. We present an algorithm for this problem that is based on Karmarkar&apos ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
The frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs and the number of used frequencies is minimized, or the amount of interference is minimized. We present an algorithm for this problem that is based on Karmarkar's interior point potential reduction approach to combinatorial optimization problems. We develop a new quadratic formulation of the problem that reduces the problem size significantly. Several preprocessing techniques are discussed. We report on computational experience with reallife instances, applying Karmarkar's algorithm to the quadratic model. Acknowledgement This report completes my study of Technical Mathematics at the Delft University of Technology. During the period April 1994 to March 1995 I have been working on the development of an interior point potential reduction algorithm for the radio link frequency assignment problem. During these months a number of people were of great help....