qaplib a quadratic assignment problem library abstract after a short introduction into quadratic assignment problems we give a library of problem instances for the quadratic assignment problem the examples are listed y authors in alphabetical order

a heuristic procedure for solving the quadratic assignment problem abstract an heuristic approach to the solution of the quadratic assignment problem is presented a simple procedure is used to get a good feasible starting point then the problem is solved as a nonlinear program ignoring the integrality conditions using minos and lastly the near integer solution is converted into an integer feasible solution using an heuristic procedure the results compare favourably with other procedures in the literature a superior solution to the 19 19 hospital layout problem is found

a semidefinite optimization based approach for global optimization of multi row facility layout abstract this paper is concerned with the multi row facility layout problem given a set of rectangular departments a fixed number of rows and weights for each pair of departments the problem consists of finding an assignment of departments to rows and the positions of the departments in each row so that the total weighted sum of the center to center distances between all pairs of departments is minimized we show how to extend our recent approach for the space free multi row facility layout problem to general multi row facility layout as well as some special cases thereof to the best of our knowledge this is the first global optimization approach for multi row layout that is applicable beyond the double row case a key aspect of our proposed approach is a model for multi row layout that expresses the problem as a discrete optimization problem and thus makes it possible to exploit the underlying combinatorial structure in particular we can explicitly control the number and size of the spaces between departments we construct a semidefinite relaxation of the discrete optimization formulation and present computational results showing that the proposed approach gives promising results for several variants of multi row layout problems on a variety of benchmark instances

optimal block diagonal l_2 scaling of matrices this paper is concerned with optimal one sided and two sided scaling of a matrix with respect to the class of block diagonal matrices optimality conditions are presented a series of lower bounds for the symmetric scaling problems is introduced then for some special cases the solutions are given in a closed form finally differentiability of the best condition number as a function of a symmetric matrix is discussed

a new solution algorithm for improving performance of ant colony optimization this study proposes an improved solution algorithm using ant colony optimization aco for finding global optimum for any given test functions the procedure of the aco algorithms simulates the decision making processes of ant colonies as they forage for food and is similar to other artificial intelligent techniques such as tabu search simulated annealing and genetic algorithms aco algorithms can be used as a tool for optimizing continuous and discrete mathematical functions the proposed algorithm is based on each ant searches only around the best solution of the previous iteration with b the proposed algorithm is called as acorses an abbreviation of aco reduced search space b is proposed for improving aco s solution performance to reach global optimum fairly quickly the acorses is tested on fourteen mathematical test functions taken from literature and encouraging results were obtained the performance of acorses is compared with other optimization methods the results showed that the acorses performs better than other optimization algorithms available in literature in terms of minimum values of objective functions and number of iterations

on the landscape ruggedness of the quadratic assignment problem local search based heuristics have been demonstrated to give very good results to approximately solve the quadratic assignment problem qap in this paper following the works of weinberger and stadler we introduce a parameter called the ruggedness coeffcient which measures the ruggedness of the qap landscape which is the union of a cost function and a neighborhood we give an exact expression and a sharp lower bound for this parameter we are able toderive from it that the landscape of the qap is rather flat and so it gives a theoretical justification of the effectiveness of local search based heuristics for this problem experimental results with simulated annealing are presented which con8rm this conclusion and also the influence of the ruggedness coe5cient on the quality of results obtained

a new lower bound for the quadratic assignment problem we introduce a new lower bound for the quadratic assignment problem based on a sequence of equivalent formulations of the problem we present a procedure for obtaining tight bounds by sequentially applying our approach in conjunction with the a assad and w xu bound and the n christofides and m gerrard bound

optimization of the movements of a component placement machine abstract the efficient operation of an automatic electronic component placement machine panasert rh is considered the machine inserts electronic components into predefined places on a printed circuit board the components are supplied from a set of feeders each containing a sequence of identical components we treat the problem as two different sequencing problems the optimal insertion sequence for a fixed feeder setting is obtained by considering the problem as a three dimensional asymmetric traveling salesman problem the optimal permutation of the components in the feeders for a fixed insertion sequence can be formulated as a quadratic assignment problem the overall problem is solved heuristically and this approach brings suboptimal but in practice good enough component insertion sequences and feeder permutations

the quadratic assignment problem an experimental evaluation of solution strategies since procedures for producing optimal solutions to a quadratic assignment problem are computationally infeasible for any but small problems heuristic techniques for producing approximate solutions must be employed for the solution of real practical problems this paper presents the results of experimentation that demonstrates that a solution procedure which couples a constructive initial placement technique with simple and inexpensive improvement procedures produces good solutions with very reasonable computation requirements the results indicate that such an approach would make the solution of large scale quadratic assignment problems feasible

weighted minimum trace factor analysis in the last decade several authors discussed the so called minimum trace factor analysis mtfa which provides the greatest lower bound g l b to reliability however the mtfa fails to be scale free in this paper we propose to solve the scale problem by maximization of the g l b as the function of weights closely related to the primal problem of the g l b maximization is the dual problem we investigate the primal and dual problems utilizing convex analysis techniques the asymptotic distribution of the maximal g l b is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions finally we outline computational algorithms and consider numerical examples

an exact algorithm for the general quadratic assignment problem abstract we develop an algorithm that is based on the linearization and decomposition of a general quadratic assignment problem of size n into n2 linear assignment problems of size n 1 the solutions to these subproblems are used to calculate a lower bound for the original problem and this bound is then used in an exact branch and bound procedure these subproblems are similar to the minors defined by lawler 16 but permit us to calculate tighter bounds computational experience is given for solution to optimality of general quadratic assignment problems is sizes up to n 10

partition arguments in multiparty communication complexity consider the number in hand multiparty communication complexity model where k players holding inputs x 1 x k 0 1 n communicate to compute the value f x 1 x k of a function f known to all of them the main lower bound technique for the communication complexity of such problems is that of partition arguments partition the k players into two disjoint sets of players and find a lower bound for the induced two party communication complexity problem in this paper we study the power of partition arguments our two main results are very different in nature i for randomized communication complexity we show that partition arguments may yield bounds that are exponentially far from the true communication complexity specifically we prove that there exists a 3 argument function f whose communication complexity is w n while partition arguments can only yield an w logn lower bound the same holds for nondeterministiccommunication complexity ii for deterministic communication complexity we prove that finding significant gaps between the true communication complexity and the best lower bound that can be obtained via partition arguments would imply progress on a generalized version of the log rank conjecture in communication complexity we also observe that in the case of computing relations search problems very large gaps do exist we conclude with two results on the multiparty fooling set technique another method for obtaining communication complexity lower bounds

global optimality conditions and optimization methods for quadratic assignment problems abstract in this paper some global optimality conditions for general quadratic 0 1 programming problems with linear equality constraints are discussed and then some global optimality conditions for quadratic assignment problems qap are presented a local optimization method for qap is derived according to the necessary global optimality conditions a global optimization method for qap is presented by combining the sufficient global optimality conditions the local optimization method and some auxiliary functions some numerical examples are given to illustrate the efficiency of the given optimization methods

on the one dimensional space allocation problem the one dimensional space allocation problem odsap arises when locating rooms along a corridor when setting books on a shelf when allocating information items among the cylinders of a magnetic disk or when storing products in certain warehouses the rooms objects to be located have a known length or width and for each pair of rooms there is a given number of trips between them the problem is to find a sequencing of the rooms which minimizes the total traveled distance this paper deals first with two particular cases in the rooted tree case previous results obtained by adolphson and t c hu for the linear ordering problem are extended and provide efficient solution methods in addition it is shown that most of the assumptions made by adolphson and hu are necessary since relaxing any of them leads to an np complete problem in the case of independent destinations solved by bergmans and pratt when all lengths are equal a unimodality property is shown for an optimum solution but this is not sufficient to lead to a good algorithm and the problem is shown to be np complete for the general problem an exact algorithm using dynamic programming is described and computationally tested

heuristics for biquadratic assignment problems and their computational comparison abstract the biquadratic assignment problem biqap is a generalization of the quadratic assignment problem qap as for any hard optimization problem also for biqap a reasonable effort to cope with the problem is trying to derive heuristics which solve it suboptimally and which possibly yield a good trade off between the solution quality and the time and memory requirements in this paper we describe several heuristics for biqaps in particular pair exchange algorithms improvement methods and variants of simulated annealing and taboo search we implement these heuristics as c codes and analyze their performances

strengthening gilmore s bound for the quadratic assignment problem abstract finding bounds for the quadratic assignment problem is important as part of some procedures for solving this problem in this paper a commonly used bound due to gilmore is extended to a set of possible bounds analytic properties of the functions underlying these bounds are given and computational approaches are suggested which make use of these properties

directional decomposition heuristic for a linear machine cell location problem abstract a machine cell itself can be treated as a machine and the location of such a cell in a linear line configuration reflects an analogy to the machine location problem thus the problem addressed here is a one dimensional equidistant machine cell location problem that considers jobs with sequenced operations and the number of machine cells equals the number of locations that are equally spaced in a linear layout it is always desirable to achieve a cell assignment that minimizes the total inter cell flows and thus the total inter cell flow costs this assignment problem can be formulated as a quadratic assignment problem the optimal solution to which is usually prohibitive since it is a non deterministically polynomial hard problem and a heuristic procedure is justifiably called for in this research many of the investigations involved in seeking an improved location assignment in heuristics are repeated from one search to another each branch of the search requires re computation of all inter cell flows though only some of them have been changed from the previous one such a search mechanism requires considerable computation time thus making the algorithm inefficient this problem can be overcome by directionally decomposing the inter cell flows and incrementally computing them based on the directional decomposition of these flows a directional search is implemented in the heuristic in order to reduce the repetitiveness occurring in the traditional search both the partitioning procedure and the directional decomposition heuristic proposed here are demonstrated through examples and the performance measures indicate the superiority of the heuristic over the existing methods

on the quality of heuristic solutions to a 19 19 quadratic assignment problem abstract recently murtagh et al communicated the best known solution to a 19 19 quadratic assignment problem presented and solved earlier by elshafei their approaches are based on the application of quadratic programming and on the construction of a good initial solution respectively their solutions are confronted with one better solution obtained by lashkari and jaisingh by means of linear assignment approximations and many better solutions obtained by the present author through the application of exchange heuristics the results stress the nonconvex character of the problem and show the rather misleading nature of the concept good initial solution the quality of initial and final solution prove to be rather weakly or even negatively correlated a simple but broad and randomized search results in significantly better solutions while simple statistical aids provide an estimate of the quality of these solutions finally we make remarks concerning some practical issues

an improved annealing scheme for the qap abstract recently there has been some interest in the use of simulated annealing to obtain good solutions to a number of combinatorial problems this paper reports on the use of this method applied to the quadratic assignment problem i e the assignment of inter communicating objects to locations to minimize the total cost of communication between them the result is a much improved annealing scheme for this problem which performs well on a range of examples finding improved solutions for several of the largest problems available in the literature and requiring only modest amounts of computational effort

optimization of the quadratic assignment problem using an ant colony algorithm ant algorithm is a multi agent systems inspired by the behaviors of real ant colonies function to solve optimization problems in this paper an ant colony optimization algorithm is developed to solve the quadratic assignment problem the local search process of the algorithm is simulated annealing in the exploration of the search space the evaluation of pheromones which are laid on the ground by ants is used in this work the algorithm is analyzed by using current problems in the literature and is compared with other metaheuristics

case study on statistically estimating minimum makespan for flow line scheduling problems abstract lower bounds are typically used to evaluate the performance of heuristics for solving combinatorial minimization problems in the absence of tight analytical lower bounds optimal objective function values may be estimated statistically in this paper extreme value theory is used to construct confidence interval estimates of the minimum makespan achievable when scheduling nonsimilar groups of jobs on a two stage flow line experimental results based on randomly sampled solutions to each of 180 randomly generated test problems revealed that i least squares parameter estimators outperformed standard analytical estimators for the weibull approximation to the distribution of the sample minimum makespan ii to evaluate each weibull fit reliably both the anderson darling and kolmogorov smirnov goodness of fit tests should be used and iii applying a local improvement procedure to a large sample of randomly generated initial solutions improved the probability that the resulting weibull fit yielded a confidence interval covering the minimum makespan

lower bounds on communication complexity abstract we prove the following four results on communication complexity 1 for every k 2 the language of encodings of directed graphs of out degree one that contain a path of length k 1 from the first vertex to the last vertex can be recognized by exchanging o k log n 1 bits using a simple k round protocol and requires the exchange of n 1 2 k 4 log 3 n bits by any k 1 round protocol 2 for every k 1 and for infinitely many n 1 there exists a collection of sets lkn 0 1 2n that can be recognized by exchanging o k log n bits using a k round protocol and any k 1 round protocol recognizing lkn requires the exchange of n k bits 3 given a set l 0 1 2n there is a set l 0 1 8n such that any k round protocol recognizing l can be transformed to a k round fixed partition protocol recognizing l with the same communication complexity and vice versa 4 for every integer function f 1 f n n there are languages recognizable by a one round deterministic protocol exchanging f n bits but not by any nondeterministic protocol exchanging f n 1 bits the first two results show in an incomparable way an exponential gap between k 1 round and k round protocols settling a conjecture by papadimitriou and sipser the third result shows that as long as we are interested in existence proofs a fixed partition of the input is not a restriction the fourth result extends a result by papadimitriou and sipser who showed that for every integer function f 1 f n n there is a language accepted by a deterministic protocol exchanging f n bits but not by any deterministic protocol exchanging f n 1 bits

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

convergence of an annealing algorithm the annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems including np hard combinatorial problems such as the travelling salesman steiner trees and others there is an appealing physical analogy for its operation but a more formal model seems desirable in this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1 we also show that there are cases where convergence takes exponentially long that is it is no better than a deterministic method we study how the convergence rate is affected by the form of the problem finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of practical confidence in the solution

a heuristic for quadratic boolean programs with applications to quadratic assignment problems abstract a heuristic for quadratic boolean programs is presented computational tests with quadratic assignment problems qap showed that it finds very good suboptimal solutions in moderate time and behaves computationally stable in the appendix a fortran program for qap is listed which improves an earlier code published by burkard and derigs

multiparty communication complexity and very hard functions a boolean function f x1 xn with xi 0 1 m for each i is hard if its nondeterministic multiparty communication complexity introduced in in proceedings of the 30th ieee focs 1989 p 428 433 c f is at least nm note that c f nm for each f x1 xn with xi 0 1 m for each i a boolean function is very hard if it is hard and its complementary function is also hard in this paper we show that randomly chosen boolean function f x1 xn with xi 0 1 m for each i is very hard with very high probability for n 3 and m large enough in in proceedings of the 12th symposium on theoretical aspects of computer science lncs 900 1995 p 350 360 it has been shown that if f x1 xk xn f1 x1 xk f2 xk 1 xn where c f1 0 and c f2 0 then c f c f1 c f2 we prove here an analogical result if f x1 xk xn f1 x1 xk f2 xk 1 xn then dc f dc f1 dc f2 where dc g denotes the deterministic multiparty communication complexity of the function g and denotes the parity function

a thermodynamically motivated simulation procedure for combinatorial optimization problems abstract exchange algorithms are an important class of heuristics for hard combinatorial optimization problems as e g salesman problems or quadratic assignment problems in kirkpatrick s and cerny s exchange algorithms for the travelling salesman problem and placement problem they propose to perform an exchange not only if the objective function value decreases by this exchange but also in certain cases if the objective function value increases an exchange increasing the objective function value is performed stochastically depending on the size of the increment computational tests with quadratic assignment problems revealed an excellent behaviour in such an approach suboptimal solutions differing 1 2 from the best known solutions are obtained by a simple program in short time by starting this program several times with different starting values all known minimal objective function values were reached thus this approach is well suited also for smaller computers and leads in short time to acceptable solutions

rank reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis one of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries we show in this paper that the set of matrices which can be reduced to rankr has positive lebesgue measure if and only ifr is greater or equal to the ledermann bound in other words the ledermann bound is shown to bealmost surely the greatest lower bound to a reduced rank of the sample covariance matrix afterwards an asymptotic sampling theory of so called minimum trace factor analysis mtfa is proposed the theory is based on continuous and differential properties of functions involved in the mtfa convex analysis techniques are utilized to obtain conditions for differentiability of these functions

heuristic solutions and confidence intervals for the multicovering problem the multicovering problem can be expressed as minimize cx subject to ax b x 0 1 where a is a zero one matrix and b is a vector of positive integers this mathematical model has many applications to scheduling and location problems large examples of such problems arise in industrial commercial and military settings and their size frequently exceeds the limits of computational tractability for this important problem we examine a variety of simple heuristic approaches which can be applied when optimal solutions are not available the approximate solutions thus generated are used to construct confidence intervals for the unknown value of the optimal solution a large scale computational study for randomly generated problmes suggests that these intervals are both very narrow and very likely to contain the optimal solution value a study of 10 very large real world problems further supports the success of our methodology and the quality of the approximate solutions found

some experiments with simulated annealing techniques for packing problems abstract experiments with a variety of combinatorial optimisation problems have shown that the simulated annealing algorithm is an effective local search heuristic method the basic requirements of the algorithm are a neighbourhood structure on the set of feasible solutions and a number of parameters which govern the acceptance or rejection of new solutions generated during the search the quality of the solution is very sensitive to both these factors this paper is concerned with the application of the simulated annealing approach to packing problems and describes a series of experiments carried out to ascertain the effectiveness of the method for such problems and the most appropriate neighbourhood structure to use and the best parameters to apply

optimal two sided diagonal scaling for filter bank frames two sided diagonal scaling for transfer matrices is formulated an efficient algorithm is proposed to compute globally optimal solutions using the iterated bi section and linear matrix inequality lmi solver it is shown that the two sided scaling of filter bank fb frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal and that the frame bound ratio of fb frames can be effectively improved by such scaling explicit formulas are established for both uniform and nonuniform fb frames including detail formulas for discrete weyl heisenberg frames and tree structured fbs discrete wavelets different examples show the effectiveness of the obtained results

optimal block diagonal scaling of block 2 cyclic matrices abstract we describe a class of optimal block diagonal scalings preconditionings of a symmetric positive definite block 2 cyclic matrix generalizing a result of forsythe and strauss 1 for point 2 cyclic matrices

one dimensional machine location problems in a multi product flowline with equidistant locations an assignment of machines to locations along a straight track is required to optimize material flow in many manufacturing systems the assignment of m unique machines to m locations along a linear material handling track with the objective of minimizing the total machine to machine material transportation cost is formulated as a quadratic assignment problem qap the distance matrix in problems involving equally spaced machine locations in one dimension is seen to possess some unique characteristics called amoebic properties since an optimal solution to a problem with large m is computationally intractable the qap is np hard a number of the amoebic properties are exploited to devise heuristics and a lower bound on the optimal solution computational results which demonstrate the performance of the heuristics and the lower bound are presented

optimally scaled matrices necessary and sufficient conditions we shall in this paper consider the problem of determination a row or column scaling of a matrixa which minimizes the condition number ofa this problem was studied by several authors for the cases of the maximum norm and of the sum norm the scale problem was completely solved by bauer 1 and sluis 5 the condition ofa subordinate to the pair of euclidean norms is the ratio where and are the maximal and minimal eigenvalue of a h a 1 2 respectively the euclidean case was considered by forsythe and strauss 3 shapiro 6 proposed some approaches to a numerical solution in this case the main result of this paper is the presentation of necessary and sufficient conditions for optimal scaling in terms of maximizing and minimizing vectors a uniqueness proof for the solution is offered provided some normality assumption is satisfied

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined