. 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...

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... Knapsack Problems to fix some variables to zero and to separate the rest into two groups those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem with branch and bound. Computational testing, including the set of problems in the OR-library and our own set of difficult problems, shows our approach helps to solve difficult problems in a reasonable amount of time and, in most cases, with a fewer number of nodes in the search tree than leading commercial software. ______________________________________________________________________________________

Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. 1 Introduction and

Abstract—We present a hierarchical solution method to approximately solve the topological network design problem: given positive integers ( 1), minimize the number of arcs required to interconnect nodes, so that the network diameter does not exceed, the maximum node degree does not exceed 1, and the network is single node survivable. The method uses dynamic programming to piece together small networks to create larger networks. The method was used to plan two high-speed packet networks at AT&T. Index Terms—Dynamic programming, hierarchical design, network design, survivability. I. INTRODUCTION AND PROBLEM DEFINITION PLANNING the evolution of a large communications network requires a variety of approximations and estimates. A demand forecast for the various services is required, as well as low-level service planning assumptions (e.g., card redundancy).

Auctions allowing bids for combinations of items are important for (agent mediated) electronic commerce; compared to other auction mechanisms, they often increase the efficiency of the auction, while keeping risks for bidders low. The determination of an optimal winner combination in this type of auctions is a complex computational problem, which has recently attracted some research, and in this paper, we look further into the topic. It is well known that the winner determination problem for a certain class of auctions is equivalent to what in the operations research community is referred to as (weighted) set packing. In this paper we compare some of the recent winner determination algorithms to traditional set packing algorithms, and study how more general auctions can be modeled by use of standard integer programming methods.

It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8]. They also had a good deal to do with shaping my early career and, consequently, much of what followed.

Fulkerson et al. have given two examples of set covering problems that are empirically difficult to solve. They arise from Steiner triple systems and the larger problem, which has a constraint matrix of size 330 × 45 has only recently been solved. In this note, we show that the Steiner triple systems do indeed give rise to a series of problems that are probably hard to solve by implicit enumeration. The main result is that for an n variable problem, branch and bound algorithms using a linear programming relaxation, and/or elimination by dominance require the examination of a super-polynomial number of partial solutions

Tree decomposition and postoptimality