. 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...

In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problem--a difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steady-state genetic algorithm in conjunction with a specialized local search heuristic for solving the set partitioning problem. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steady-state genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty real-world set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, high-quality integer feasible solutions were found for problems with 36,699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints.

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The application of genetic algorithms (GA) to constrained optimization problems has been hindered by the inefficiencies of reproduction and mutation when feasibility of generated solutions is impossible to guarantee and feasible solutions are very difficult to find. Although several authors have suggested the use of both static and dynamic penalty functions for genetic search, this paper presents a general adaptive penalty technique which makes use of feedback obtained during the search along with a dynamic distance metric. The effectiveness of this method is illustrated on two diverse combinatorial applications; (1) the unequalarea, shape-constrained facility layout problem and (2) the series-parallel redundancy allocation problem to maximize system reliability given cost and weight constraints. The adaptive penalty function is shown to be robust with regard to random number seed, parameter settings, number and degree of constraints, and problem instance. 1. Introduction ...

In this paper, we consider solution approaches to a multi-hour combined capacity design and routing problem which arises in the design of dynamically reconfigurable broadband communication networks that uses the virtual path concept. We present a comparative evaluation of four approaches, namely: a genetic algorithm; a Lagrangean relaxation based subgradient optimization method; a generalized proximal point algorithm with subgradient optimization; and finally, a hybrid approach where the subgradient based method is combined with a genetic algorithm. Our computational experience on a set of test problems of varying network sizes shows that the hybrid approach often is the desirable choice in obtaining the minimum cost network while the genetic algorithm based approach has the most difficulty in solving large scale problems. Keywords: Broadband network design, multi-hour network routing and capacity design, combinatorial optimization, genetic algorithm, duality and subgradient optimizati...

this paper, the tness landscapes of several instances of the traveling salesman problem (TSP) are investigated to illustrate why MAs are well-suited for nding near-optimum tours for the TSP. It is shown that recombination{based MAs can exploit the correlation structure of the landscape. A comparison of several recombination operators { including a new generic recombination operator { reveals that when using the sophisticated Lin{Kernighan local search, the performance dierence of the MAs is small. However, the most important property of eective recombination operators is shown to be respectfulness. In experiments it is shown that our MAs with generic recombination are among the best evolutionary algorithms for the TSP. In particular, optimum solutions could be found up to a problem size of 3795, and for large instances up to 85,900 cities, near-optimum solutions could be found in a reasonable amount of time

. In this paper, we review parallel metaheuristics for approximating the global optimal solution of combinatorial optimization problems. Recent developments on parallel implementation of genetic algorithms, simulated annealing, tabu search, variable neighborhood search, and greedy randomized adaptive search procedures (GRASP) are discussed. 1. Introduction Search techniques are fundamental problem-solving methods in computer science and operations research. Search algorithms have been used to solve many classes of problems, including path-finding problems, two-player games, and constraint satisfaction problems. Classical examples of path-finding problems include many combinatorial optimization problems (e.g. integer programming) and puzzles (e.g. Rubic's cube, Eight Puzzle). Chess, backgammon, and Othello belong to the class of two player games, while a classic example of a constraint satisfaction problem is the eight-queens problem. In this paper, we focus on NP-hard combinator...

Genetic algorithms are one example of the use of a random element within an algorithm for combinatorial optimization. We consider the application of the genetic algorithm to a particular problem, the Assembly Line Balancing Problem. A general description of genetic algorithms is given, and their specialized use on our test-bed problems is discussed. We carry out extensive computational testing to find appropriate values for the various parameters associated with this genetic algorithm. These experiments underscore the importance of the correct choice of a scaling parameter and mutation rate to ensure the good performance of a genetic algorithm. We also describe a parallel implementation of the genetic algorithm and give some comparisons between the parallel and serial implementations. Both versions of the algorithm are shown to be effective in producing good solutions for problems of this type (with appropriately chosen parameters). Subject classifications: Programming: combinatorial ...

This paper investigates the power of genetic algorithms at solving the MAX-CLIQUE problem. We measure the performance of a standard genetic algorithm on an elementary set of problem instances consisting of embedded cliques in random graphs. We indicate the need for improvement, and introduce a new genetic algorithm, the multi-phase annealed GA, which exhibits superior performance on the same problem set. As we scale up the problem size and test on "hard" benchmark instances, we notice a degraded performance in the algorithm caused by premature convergence to local minima. To alleviate this problem, a sequence of modifications are implemented ranging from changes in input representation to systematic local search. The most recent version, called union GA, incorporates the features of union cross-over, greedy replacement, and diversity enhancement. It shows a marked speed-up in the number of iterations required to find a given solution, as well as some improvement in the clique size fou...

In this paper, we study the efficacy of genetic algorithms in the context of combinatorial optimization. In particular, we isolate the effects of cross-over, treated as the central component of genetic search. We show that for problems of nontrivial size and difficulty, the contribution of cross-over search is marginal, both synergistically when run in conjunction with mutation and selection, or when run with selection alone, the reference point being the search procedure consisting of just mutation and selection. The latter can be viewed as another manifestation of the Metropolis process. Considering the high computational cost of maintaining a population to facilitate cross-over search, its marginal benefit renders genetic search inferior to its singletonpopulation counterpart, the Metropolis process, and by extension, simulated annealing. This is further compounded by the fact that many problems arising in practice may inherently require a large number of state transitions for a nea...