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 parallel depth first search branch and bound algorithm for the quadratic assignment problem abstract we propose a new parallel branch and bound algorithm for the quadratic assignment problem which is a combinatorial optimization problem known to be very hard to solve exactly an original method to distribute work to processors using the notion of feeding tree is presented when adequately used it allows to reduce memory contention and load unbalance therefore a linear speed up in the number of processors is reached on a shared memory multiprocessor the cray 2 and the optimality of solutions for famous problems of size less than 20 nugent 16 elshafei 19 scriabin vergin 20 is proved by this program the implementation analysis shows that these results are more than an improvement due to hardware evolution and confirms the usefulness of our parallel branch and bound algorithm for larger quadratic assignment problems

solving lift and project relaxations of binary integer programs we propose a method for optimizing the lift and project relaxations of binary integer programs introduced by lovasz and schrijver in particular we study both linear and semidefinite relaxations the key idea is a restructuring of the relaxations which isolates the complicating constraints and allows for a lagrangian approach we detail an enhanced subgradient method and discuss its efficient implementation computational results illustrate that our algorithm produces tight bounds more quickly than state of the art linear and semidefinite solvers

the quadratic shortest path problem complexity approximability and solution methods we consider the problem of finding a shortest path in a directed graph with a quadratic objective function the qspp we show that the qspp cannot be approximated unless p np for the case of a convex objective function an n approximation algorithm is presented where n is the number of nodes in the graph and apx hardness is shown furthermore we prove that even if only adjacent arcs play a part in the quadratic objective function the problem still cannot be approximated unless p np in order to solve the problem we first propose a mixed integer programming formulation and then devise an efficient exact branch and bound algorithm for the general qspp where lower bounds are computed by considering a reformulation scheme that is solvable through a number of minimum cost flow problems in our computational experiments we solve to optimality different classes of instances with up to 1000 nodes

bounds for the quadratic assignment problem using the bundle method semidefinite programming sdp has recently turned out to be a very powerful tool for approximating some np hard problems the nature of the quadratic assignment problem qap suggests sdp as a way to derive tractable relaxations we recall some sdp relaxations of qap and solve them approximately using a dynamic version of the bundle method the computational results demonstrate the efficiency of the approach our bounds are currently among the strongest ones available for qap we investigate their potential for branch and bound settings by looking also at the bounds in the first levels of the branching tree

convex graph invariant relaxations for graph edit distance the edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions insertions required to transform one graph to another it is np hard to compute in general and a large number of heuristics have been proposed for approximating this quantity with few exceptions these methods generally provide upper bounds on the edit distance between two graphs in this paper we propose a new family of computationally tractable convex relaxations for obtaining lower bounds on graph edit distance these relaxations can be tailored to the structural properties of the particular graphs via convex graph invariants specific examples that we highlight in this paper include constraints on the graph spectrum as well as tractable approximations of the stability number and the maximum cut values of graphs we prove under suitable conditions that our relaxations are tight i e exactly compute the graph edit distance when one of the graphs consists of few eigenvalues we also validate the utility of our framework on synthetic problems as well as real applications involving molecular structure comparison problems in chemistry

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

estimating bounds for quadratic assignment problems associated with hamming and manhattan distance matrices based on semidefinite programming quadratic assignment problems qaps with a hamming distance matrix for a hypercube or a manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems in this paper we consider the issue of how to obtain lower bounds for those two classes of qaps based on semidefinite programming sdp by exploiting the data structure of the distance matrix b we first show that for any permutation matrix x the matrix y alpha e xbx t is positive semidefinite where alpha is a properly chosen parameter depending only on the associated graph in the underlying qap and e ee t is a rank 1 matrix whose elements have value 1 this results in a natural way to approximate the original qaps via sdp relaxation based on the matrix splitting technique our new sdp relaxations have a smaller size compared with other sdp relaxations in the literature and can be solved efficiently by most open source sdp solvers experimental results show that for the underlying qaps of size up to n 200 strong bounds can be obtained effectively

the quadratic three dimensional assignment problem exact and approximate solution methods abstract this paper reports on algorithm development for solving the quadratic three dimensional assignment problem q3ap the q3ap arises for example in the implementation of a hybrid arq automatic repeat request scheme for enriching diversity among multiple packet re transmissions by optimizing the mapping of data bits to modulation symbols typical practical problem sizes would be 8 16 32 and 64 we present an exact solution method based upon a reformulation linearization technique that is one of the best available for solving the quadratic assignment problem qap our current exact algorithm is useful for q3ap instances of size 13 or smaller we also investigate four stochastic local search algorithms that provide optimum or near optimum solutions for large and difficult qap instances and adapt them for solving the q3ap the results of our experiments make it possible to get good solutions to signal mapping problems of size 8 and 16

probabilistic multidimensional scaling complete and incomplete data simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the hefner model this model is a probabilistic multidimensional scaling model which assigns a multivariate normal distribution to each stimulus point it is shown that for such a model standard nonmetric and metric algorithms are not appropriate

implementation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem the efficient implementation of a branch and bound algorithm for the quadratic assignment problem qap incorporating the lower bound based on variance reduction of li pardalos ramakrishnan and resende 1994 is presented a new data structure for efficient implementation of branch and bound algorithms for the qap is introduced computational experiments with the branch and bound algorithm on different classes of qap test problems are reported the branch and bound algorithm using the new lower bounds is compared with the same algorithm utilizing the commonly applied gilmore lawler lower bound both implementations use a greedy randomized adaptive search procedure for obtaining initial upper bounds the algorithms report all optimal permutations optimal solutions for previously unsolved instances from the literature of dimensions n 16 and n 20 have been found with the new algorithm in addition the new algorithm has been tested on a class of large data variance problems requiring the examination of much fewer nodes of the branch and bound tree than the same algorithm using the gilmore lawler lower bound

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

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

solving the quadratic assignment problem with clues from nature this paper describes a new evolutionary approach to solving quadratic assignment problems the proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies es these methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems particularly in continuous optimization the combinatorial variant of es presented here performs very well on the given test problems as compared with the standard 2 opt heuristic and results with simulated annealing and tabu search extensions for practical applications in factory layout are described

lower bounds for the quadratic assignment problem based upon a dual formulation a new bounding procedure for the quadratic assignment problem qap is described which extends the hungarian method for the linear assignment problem lap to qaps operating on the four dimensional cost array of the qap objective function the qap is iteratively transformed in a series of equivalent qaps leading to an increasing sequence of lower bounds for the original problem to this end two classes of operations which transform the four dimensional cost array are defined these have the property that the values of the transformed objective function z are the corresponding values of the old objective function z shifted by some amount c in the case that all entries of the transformed cost array are nonnegative then c is a lower bound for the initial qap if moreover there exists a feasible solution u to the qap such that its value in the transformed problem is zero then c is the optimal value of z and u is an optimal solution for the original qap the transformations are iteratively applied until no significant increase in constant c as above is found resulting in the so called dual procedure dp several strategies are listed for appropriately determining c or equivalently transforming the cost array the goal is the modification of the elements in the cost array to obtain new equivalent problems that bring the qap closer to solution in some cases the qap is actually solved though solution is not guaranteed the close relationship between the dp and the linear programming formulation of adams and johnson is presented the dp attempts to solve adams and johnson s clp a continuous relaxation of a linearization of the qap this explains why the dp produces bounds close to the optimum values for clp calculated by johnson in her dissertation and by resende et al in their interior point algorithm for linear programming the benefit of using dp within a branch and bound algorithm is described then two versions of dp are tested on the nugent test instances from size 5 to size 30 as well as several other test instances from qaplib these compare favorably with earlier bounding methods

a new class of preconditioners for large scale linear systems from interior point methods for linear programming a new class of preconditioners for the iterative solution of the linear systems arising from interior point methods is proposed for many of these methods the linear systems are symmetric and indefinite the system can be reduced to a system of normal equations which is positive definite we show that all preconditioners for the normal equations system have an equivalent for the augmented system while the opposite is not true the new class of preconditioners works better near a solution of the linear programming problem when the matrices are highly ill conditioned the preconditioned system can be reduced to a positive definite one the techniques developed for a competitive implementation are rather sophisticated since the subset of columns is not known a priori the new preconditioner applied to the conjugate gradient method compares favorably with the cholesky factorization approach on large scale problems whose cholesky factorization contains too many nonzero entries

on equivalence of semidefinite relaxations for quadratic matrix programming we analyze two popular semidefinite programming relaxations for quadratically constrained quadratic programs with matrix variables these relaxations are based on vector lifting and on matrix lifting they are of different size and expense we prove under mild assumptions that these two relaxations provide equivalent bounds thus our results provide a theoretical guideline for how to choose a less expensive semidefinite programming relaxation and still obtain a strong bound the main technique used to show the equivalence and that allows for the simplified constraints is the recognition of a class of nonchordal sparse patterns that admit a smaller representation of the positive semidefinite constraint

an optimal tree search method for the manufacturing systems cell formation problem abstract a solution methodology producting exact solutions to the manufacturing systems cell formation problem is presented a distance matrix representing the closeness between pairs of machines with regard to the parts they process is taken into account the proposed approach is an optimal tree search method which empoys two different bounds a classical bound for the quadratic assignment problem and a recently proposed one for the quadratic transportation problem as well as a new heuristic for the cell formation problem a special tree search was designed in order to reduce the size of the tree minimize the computational effort required in time consuming calculations and exploit symmetries of the problem computational results indicate that the proposed algorithm is very efficient in generating optimal solutions at low computational cost

a new bound for the quadratic assignment problem based on convex quadratic programming we describe a new convex quadratic programming bound for the quadratic assignment problem qap the construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for qap the new bound dominates the well known projected eigenvalue bound and appears to be competitive with existing bounds in the trade off between bound quality and computational effort

lower bounds for the quadratic assignment problem via triangle decompositions we consider transformations of the metric quadratic assignment problem qap that exploit the metric structure of a given instance we show in particular how the structural properties of rectangular grids can be used to improve a given lower bound our work is motivated by previous research of palubetskes 1988 and it extends a bounding approach proposed by chakrapani and skorin kapov 1993 our computational results indicate that the present approach is practical it has been applied to problems of dimension up ton 150 moreover the new approach yields by far the best lower bounds on most of the instances of metric qaps that we considered

analog computation through high dimensional physical chaotic neuro dynamics conventional von neumann computers have difficulty in solving complex and ill posed real world problems however living organisms often face such problems in real life and must quickly obtain suitable solutions through physical dynamical and collective computations involving vast assemblies of neurons these highly parallel computations through high dimensional dynamics computation through dynamics are completely different from the numerical computations on von neumann computers computation through algorithms in this paper we explore a novel computational mechanism with high dimensional physical chaotic neuro dynamics we physically constructed two hardware prototypes using analog chaotic neuron integrated circuits these systems combine analog computations with chaotic neuro dynamics and digital computation through algorithms we used quadratic assignment problems qaps as benchmarks the first prototype utilizes an analog chaotic neural network with 800 dimensional dynamics an external algorithm constructs a solution for a qap using the internal dynamics of the network in the second system 300 dimensional analog chaotic neuro dynamics drive a tabu search algorithm we demonstrate experimentally that both systems efficiently solve qaps through physical chaotic dynamics we also qualitatively analyze the underlying mechanism of the highly parallel and collective analog computations by observing global and local dynamics furthermore we introduce spatial and temporal mutual information to quantitatively evaluate the system dynamics the experimental results confirm the validity and efficiency of the proposed computational paradigm with the physical analog chaotic neuro dynamics

investigating the correlation between indicators of predictive diagnostic optimisation and search result quality combinatorially complex problems are often optimised with heuristic solvers which generally provide acceptable results but no indication as to how the quality achieved compares to the best possible in previous work we have introduced predictive diagnostic optimisation pdo a heuristic based on local search that provides information about the search space structure through a set of indicators whilst searching for the optimal solution pdo can collect useful information about the search process such as the variation in the number of steps needed to locally optimise a random solution and the error between the expected and actual qualities of the local optimum known as the prediction error given previous experimental results on the quadratic assignment problem it appears that a high prediction error coincides with lower search quality and vice versa this work confirms this assumption with the help of two additional problems but also shows that the reliability of the prediction error is challenged by structural properties that lead to a homogeneity of the optima basins conversely a high variation in the number of steps that lead to the local optima increases the reliability of the prediction error as an indicator of search quality

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

a branch and bound algorithm for the quadratic assignment problem based on the hungarian method this paper presents a new branch and bound algorithm for solving the quadratic assignment problem qap the algorithm is based on a dual procedure dp similar to the hungarian method for solving the linear assignment problem our dp solves the qap in certain cases i e for some small problems n 7 and for numerous larger problems 7 n 16 that arise as sub problems of a larger qap such as the nugent 20 the dp however does not guarantee a solution it is used in our algorithm to calculate lower bounds on solutions to the qap as a result of a number of recently developed improvements the dp produces lower bounds that are as tight as any which might be useful in a branch and bound algorithm these are produced relatively cheaply especially on larger problems experimental results show that the computational complexity of our algorithm is lower than known methods and that its actual runtime is significantly shorter than the best known algorithms for qaplib test instances of size 16 through 22 our method has the potential for being improved and therefore can be expected to aid in solving even larger problems

matrix lifting semi definite programming for detection in multiple antenna systems this paper presents a computationally efficient decoder for multiple antenna systems the proposed algorithm can be used for any constellation qam or psk and any labeling method the decoder is based on matrix lifting semi definite programming sdp the strength of the proposed method lies in a new relaxation approach applied to the previous work by mobasher this results in a reduction of the number of variables from nk 1 nk 2 2 in the previous work by mobasher to 2n k 2 in the new method where n is twice the number of transmit antennas and k is the number of constellation points in each real dimension it is shown that this reduction in the number of variables results in a significant computational complexity reduction compared to the previous work by mobasher moreover the proposed method offers a better symbol error rate performance as compared to some known and recent sdp based quasi maximum likelihood detection methods reported in the literature

a level 2 reformulation linearization technique bound for the quadratic assignment problem abstract this paper studies polyhedral methods for the quadratic assignment problem bounds on the objective value are obtained using mixed 0 1 linear representations that result from a reformulation linearization technique rlt the rlt provides different levels of representations that give increasing strength prior studies have shown that even the weakest level 1 form yields very tight bounds which in turn lead to improved solution methodologies this paper focuses on implementing level 2 we compare level 2 with level 1 and other bounding mechanisms in terms of both overall strength and ease of computation in so doing we extend earlier work on level 1 by implementing a lagrangian relaxation that exploits block diagonal structure present in the constraints the bounds are embedded within an enumerative algorithm to devise an exact solution strategy our computer results are notable exhibiting a dramatic reduction in nodes examined in the enumerative phase and allowing for the exact solution of large instances

local minima and convergence in low rank semidefinite programming the low rank semidefinite programming problem lrsdpr is a restriction of the semidefinite programming problem sdp in which a bound r is imposed on the rank of x and it is well known that lrsdpr is equivalent to sdp if r is not too small in this paper we classify the local minima of lrsdpr and prove the optimal convergence of a slight variant of the successful yet experimental algorithm of burer and monteiro 5 which handles lrsdpr via the nonconvex change of variables x rrt in addition for particular problem classes we describe a practical technique for obtaining lower bounds on the optimal solution value during the execution of the algorithm computational results are presented on a set of combinatorial optimization relaxations including some of the largest quadratic assignment sdps solved to date

a novel chaotic search for quadratic assignment problems abstract we propose a novel method for solving the quadratic assignment problems first we realize the conventional tabu search on a neural network and modify it to a chaotic version our novel method includes both effects of chaotic dynamics and tabu search we compare the performance of the novel chaotic search with the conventional tabu search and an exponential tabu search whose memory effect for tabu forbidding previous moves decays exponentially we show that the exponential tabu search has higher performance than the conventional tabu search and further that the novel method with a chaotic neural network exhibits the best performance we also propose a controlling method of the chaotic neural network for realizing easy and robust applications of our method then better performance can be realized without manual parameter setting for various problems

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

selective influence through conditional independence let each of several generally interdependent random vectors taken separately be influenced by a particular set of external factors under what kind of the joint dependence of these vectors on the union of these factor sets can one say that each vector is selectively influenced by its own factor set the answer proposed and elaborated in this paper is one can say this if and only if one can find a factor independent random vector given whose value the vectors in question are conditionally independent with their conditional distributions selectively influenced by the corresponding factor sets equivalently the random vectors should be representable as deterministic functions of their factor sets and of some mutually independent and factor independent random variables some of which may be shared by several of the functions

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

a computational study of graph partitioning letg n e be an edge weighted undirected graph the graph partitioning problem is the problem of partitioning the node setn intok disjoint subsets of specified sizes so as to minimize the total weight of the edges connecting nodes in distinct subsets of the partition we present a numerical study on the use of eigenvalue based techniques to find upper and lower bounds for this problem results for bisecting graphs with up to several thousand nodes are given and for small graphs some trisection results are presented we show that the techniques are very robust and consistently produce upper and lower bounds having a relative gap of typically a few percentage points

symmetrization of nonsymmetric quadratic assignment problems and the hoffman wielandt inequality abstract a technique is proposed to transform a nonsymmetric quadratic assignment problem qap into an equivalent one consisting of complex hermitian matrices this technique provides several new hoffman wielandt type eigenvalue inequalities for general matrices and extends the eigenvalue bound for symmetric qaps to the general case

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 low dimensional semidefinite relaxation for the quadratic assignment problem the quadratic assignment problem qap is arguably one of the hardest np hard discrete optimization problems problems of dimension greater than 25 are still considered to be large scale current successful solution techniques use branch and bound methods which rely on obtaining strong and inexpensive bounds in this paper we introduce a new semidefinite programming sdp relaxation for generating bounds for the qap in the trace formulation we apply majorization to obtain a relaxation of the orthogonal similarity set of the quadratic part of the objective function this exploits the matrix structure of qap and results in a relaxation with much smaller dimension than other current sdp relaxations we compare the resulting bounds with several other computationally inexpensive bounds such as the convex quadratic programming relaxation qpb we find that our method provides stronger bounds on average and is adaptable for branch and bound methods

a new lower bound via projection for the quadratic assignment problem new lower bounds for the quadratic assignment problem qap are presented these bounds are based on the orthogonal relaxation of qap the additional improvement is obtained by making efficient use of a tractable representation of orthogonal matrices having constant row and column sums the new bound is easy to implement and often provides high quality bounds under an acceptable computational effort

network based formulations of the quadratic assignment problem abstract we present two formulations of the quadratic assignment problem qap that result in network flow problems with integer variables and side constraints a linearization of the qap is obtained in both cases by considering each facility to consist of two parts a source for all outgoing flows from that facility and a sink for all incoming flows to the facility preliminary computational experience with both approaches is presented

global optimality conditions for quadratic optimization problems with binary constraints we consider nonconvex quadratic optimization problems with binary constraints our main result identifies a class of quadratic problems for which a given feasible point is global optimal we also establish a necessary global optimality condition these conditions are expressed in a simple way in terms of the problem s data we also study the relations between optimal solutions of the nonconvex binary quadratic problem versus the associated relaxed and convex problem defined over the l infty norm our approach uses elementary arguments based on convex duality

computing lower bounds for the quadratic assignment problem with an interior point algorithm for linear programming an example of the quadratic assignment problem qap is the facility location problem in which n facilities are assigned at minimum cost to n sites between each pair of facilities there is a given amount of flow contributing a cost equal to the product of the flow and the distance between sites to which the facilities are assigned proving optimality of qaps has been limited to instances having fewer than 20 facilities largely because known lower bounds are weak we compute lower bounds for a wide range of qaps using a linear programming based lower bound studied by z drezner 1995 on the majority of qaps tested a new best known lower bound is computed on 87 of the instances we produced the best known lower bound on several instances including some having more the 20 facilities the lower bound is tight the linear programs which can be large even for small qaps are solved with an interior point code that uses a preconditioned conjugate gradient algorithm to compute the interior point directions attempts to solve these instances using the cplex primal simplex algorithm as well as the cplex barrier primal dual interior point method were successful only for the smallest instances

solving large quadratic assignment problems on computational grids the quadratic assignment problem qap is among the hardest combinatorial optimization problems some instances of size n 30 have remained unsolved for decades the solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms in this article we describe a novel approach to solve qaps using a state of the art branch and bound algorithm running on a federation of geographically distributed resources known as a computational grid solution of qaps of unprecedented complexity including the nug30 kra30b and tho30 instances is reported

inferences in probability logic abstract we define a particular fuzzy logic able to manage information that is probabilistic in nature in this logic the probabilistic theories are suitable fuzzy sets of formulas that turn out to be lower envelopes while only the complete probabilistic theories coincide with the probabilities

quadratic matrix programming we introduce and study a special class of nonconvex quadratic problems in which the objective and constraint functions have the form f boldmath x tr boldmath x t boldmath a boldmath x 2 tr boldmath b t boldmath x c boldmath x in real r n times r the latter formulation is termed quadratic matrix programming qmp of order r we construct a specially devised semidefinite relaxation sdr and dual for the qmp problem and show that under some mild conditions strong duality holds for qmp problems with at most r constraints using a result on the equivalence of two characterizations of the nonnegativity property of quadratic functions of the above form we are able to compare the constructed sdr and dual problems to other known sdrs and dual formulations of the problem an application to robust least squares problems is discussed

recent advances in the solution of quadratic assignment problems the quadratic assignment problem qap is notoriously difficult for exact solution methods in the past few years a number of long open qaps including those posed by steinberg 1961 nugent et al 1968 and krarup 1972 were solved to optimality for the first time the solution of these problems has utilized both new algorithms and novel computing structures we describe these developments as well as recent work which is likely to result in the solution of even more difficult instances

sequent calculus and data fusion we present a formal method for data fusion based on possibilistic logic the method has been applied to a real world problem of noisy sensor data fusion the position estimation of an autonomous mobile robot navigating in an approximately and partially known office environment using a topological map each place in the map is characterized by a set of logical formulae axiomatizing both symbolic knowledge and uncertain information from the sensors at each time instant during navigation the necessity for each place is calculated using a function generated by a proof system based on sequent calculus several test runs using a real robot have shown the adequacy of the approach in interpreting and disambiguating the information coming from independent perceptual sources in combination with symbolic knowledge

probability like functionals and fuzzy logic abstract the aim of this paper is to show that fuzzy logic is a suitable tool to manage several types of probability like functionals namely we show that the superadditive functions the necessities the upper and lower probabilities and the envelopes can be considered theories of suitable fuzzy logics some general results about the compactness in fuzzy logic are also obtained

random assignment problems abstract analysis of random instances of optimization problems provides valuable insights into the behavior and properties of problem s solutions feasible region and optimal values especially in large scale cases a class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems and many important problems in operations research and computer science can be formulated as assignment problems this paper presents an overview of the recent results and developments in the area of probabilistic assignment problems including the linear and multidimensional assignment problems quadratic assignment problem etc

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

sums of products of functions of x times functions of y we study functions u of the form u x y nk 1ak x bk y mostly by means of two functional determinants wn u and dn u a sample result is that if u has the form on an open subset of a region g on which u is real analytic then u must have this form with possibly different ak and bk on all of g we also study the representability of u x y in the form on a region g in which u is either n times differentiable or is merely continuous the question whether the limit of functions of the form is again of the form is treated moreover we study those functions of the form that are solutions of some classical partial differential equations

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

applications of parametric programming and eigenvalue maximization to the quadratic assignment problem we investigate new bounding strategies based on different relaxations of the quadratic assignment problem in particular we improve the lower bound found by using an eigenvalue decomposition of the quadratic part and by solving a linear program for the linear part the improvement is accomplished by applying a steepest ascent algorithm to the sum of the two bounds