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19
A Genetic Approach to the Quadratic Assignment Problem
, 1992
"... The Quadratic Assignment Problem (QAP) is a wellknown combinatorial optimization problem with a wide variety of practical applications. Although many heuristics and semienumerative procedures for QAP have been proposed, no dominant algorithm has emerged. In this paper, we describe a Genetic Algori ..."
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Cited by 72 (7 self)
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The Quadratic Assignment Problem (QAP) is a wellknown combinatorial optimization problem with a wide variety of practical applications. Although many heuristics and semienumerative procedures for QAP have been proposed, no dominant algorithm has emerged. In this paper, we describe a Genetic Algorithm (GA) approach to QAP. Genetic algorithms are a class of randomized parallel search heuristics which emulate biological natural selection on a population of feasible solutions. We present computational results which show that this GA approach finds solutions competitive with those of the best previouslyknown heuristics, and argue that genetic algorithms provide a particularly robust method for QAP and its more complex extensions.
Computing globally optimal solutions for singlerow layout problems using semidefinite programming and cutting planes
 INFORMS J. COMPUT
, 2008
"... This paper is concerned with the singlerow facility layout problem (SRFLP). A globally optimal solution to the SRFLP is a linear placement of rectangular facilities with varying lengths that achieves the minimum total cost associated with the (known or projected) interactions between them. We demon ..."
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Cited by 13 (1 self)
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This paper is concerned with the singlerow facility layout problem (SRFLP). A globally optimal solution to the SRFLP is a linear placement of rectangular facilities with varying lengths that achieves the minimum total cost associated with the (known or projected) interactions between them. We demonstrate that the combination of a semidefinite programming relaxation with cutting planes is able to compute globally optimal layouts for large SRFLPs with up to thirty departments. In particular, we report the globally optimal solutions for two sets of SRFLPs previously studied in the literature, some of which have remained unsolved since 1988.
A Genetic Algorithm For Facility Layout Design In Flexible Manufacturing Systems
, 1996
"... The flexible manufacturing system (FMS) facility layout problem (FLP) involves the positioning of cells within a given area so as to minimize the material flow costs between cells. The FLP design includes specifying the spatial coordinates of each cell, the orientation of each cell in either a horiz ..."
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Cited by 13 (0 self)
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The flexible manufacturing system (FMS) facility layout problem (FLP) involves the positioning of cells within a given area so as to minimize the material flow costs between cells. The FLP design includes specifying the spatial coordinates of each cell, the orientation of each cell in either a horizontal or vertical position, and the position of each cell's pickup anddropoff points. The layout design problem is both tactically and strategically important since the layout plays a large role in determining the efficiency and flexibility of the system. The FMS layout problem differs from traditional layout problems in that there are additional constraints on a cell's shape and orientation and the location of the pickup/dropoff points must be determined. A mixed integer programming formulation for the FLP developed byDas (1993) is adapted and heuristically solved in this paper. Because of the NPhard nature of the solution space, a genetic algorithm based decomposition strategy is proposed and computationally tested. A comparison of the computational results with the existing methods indicate that the heuristic is a viable alternative for efficiently and effectively generating layout designs for flexible manufacturing systems.
Comparison of Selection Methods for Evolutionary Optimization
 Evolutionary Optimization
, 2000
"... . Selection is an essential component of evolutionary algorithms, playing an important role especially in solving hard optimization problems. Most previous studies on selection have focused on more or less ideal properties based on asymptotic analysis. In this paper, we address the selection problem ..."
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Cited by 10 (0 self)
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. Selection is an essential component of evolutionary algorithms, playing an important role especially in solving hard optimization problems. Most previous studies on selection have focused on more or less ideal properties based on asymptotic analysis. In this paper, we address the selection problem from a more practical point of view by considering solution quality achievable within acceptable time. The repertoire of methods we compare includes proportional selection, ranking selection, linear ranking, tournament, Genitor selection, simulated annealing, and hillclimbing. All these methods use genetic operators in one form or another to create new search points. Experiments are performed in the context of the machine layout design problem. This problem is a real industrial application having both continuous and discrete optimization characteristics. The experimental results for solving tworow machine layout problems of size ranging from 10 to 50 show strong evidence that ranking and tournament selection are, in general, more effective in both solution quality and convergence time than proportional selection and other methods. We provide a theoretical explanation of the experimental results using a predictive model of evolutionary optimization based on selection differential and response to selection. Keywords: Evolutionary optimization, machine layout design, selection methods, selection differential, response to selection, heritability 1.
Provably NearOptimal Solutions for Very Large SingleRow Facility Layout Problems
, 2009
"... The facility layout problem is a global optimization problem that seeks to arrange a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. This paper is concerned with the singlerow facility layout problem (SRFLP) ..."
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Cited by 5 (0 self)
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The facility layout problem is a global optimization problem that seeks to arrange a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. This paper is concerned with the singlerow facility layout problem (SRFLP), the onedimensional version of facility layout that is also known as the onedimensional space allocation problem. It was recently shown that the combination of a semidefinite programming (SDP) relaxation with cutting planes is able to compute globally optimal layouts for SRFLPs with up to 30 facilities. This paper further explores the application of SDP to this problem. First, we revisit the recently proposed quadratic formulation of this problem that underlies the SDP relaxation and provide an independent proof that the feasible set of the formulation is a precise representation of the set of all permutations on n objects. This fact follows from earlier work of Murata et al., but a proof in terms of the variables and structure of the SDP construction provides interesting insights on our approach. Second, we propose a new matrixbased formulation that yields a new SDP relaxation with fewer linear constraints but still yielding highquality global lower bounds. Using this new relaxation, we are able to compute nearlyoptimal solutions for instances with up to 100 facilities.
A Polyhedral Approach to the Single Row Facility Layout Problem
, 2011
"... The Single Row Facility Layout Problem (SRFLP) is the ..."
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Cited by 5 (1 self)
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The Single Row Facility Layout Problem (SRFLP) is the
Machine utilizations achieved using balanced FMS production ratios in a simulated setting, Working Paper 486, Graduate
, 1986
"... Stecke [21] has developed mathematical programming approaches for determining, from a set of part type requirements, the production ratios (part types to be produced next, and their proportions) which maximize overall machine utilizations by balancing machine workloads in a flexible manufacturing ..."
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Cited by 2 (0 self)
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Stecke [21] has developed mathematical programming approaches for determining, from a set of part type requirements, the production ratios (part types to be produced next, and their proportions) which maximize overall machine utilizations by balancing machine workloads in a flexible manufacturing system (FMS). These mathematical programming (MP) approaches are aggregate in the sense that they do not take into account such things as contention for transportation resources, travel time for workinprocess, contention for machines, finite buffer space, and dispatching rules. In the current study, the sensitivity of machine utilizations to these aggregations i investigated through simulation modeling. For the situation examined, it is found that achieved machine utilizations are a strong function of some of the factors ignored in the MP methodology, ranging from 9.1 % to 22.9% less than those theoretically attainable under the mathematical programming assumptions. The 9.1 % degradation results from modeling with nonzero workinprocess travel times (i.e. 2 minutes per transfer) and using only central workinprocess buffers. Resource levels (e.g. the number of automated guided vehicles; the amount of workinprocess; the number of slack buffers) needed to limit the degradation to 9.1 % correspond to FMS operating conditions which are feasible in practice.
A Polyhedral Study of Triplet Formulation for Single Row Facility Layout Problem
"... The Single Row Facility Layout Problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [Discr ..."
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Cited by 1 (0 self)
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The Single Row Facility Layout Problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [Discrete Applied Mathematics 157(1)(2009)183190]. For any number of departments n, we prove that the dimension of the triplet polytope is n(n−1)(n−2)/3 (this is also true for the projections of this polytope presented by Amaral). We then prove that several valid inequalities presented by Amaral for this polytope are facetdefining. These results provide theoretical support for the fact that the linear program solved over these valid inequalities gives the optimal solution for all instances studied by Amaral.
NorthHolland A distance assignment approach to the facility layout problem
, 1990
"... Abstract: The facility layout problem has generally been formulated as a quadratic assignment problem, where the interacting facilities are assigned to the various ites. In this paper a different approach, based on assigning distances between pairs of sites to pairs of facilities, is taken. A networ ..."
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Abstract: The facility layout problem has generally been formulated as a quadratic assignment problem, where the interacting facilities are assigned to the various ites. In this paper a different approach, based on assigning distances between pairs of sites to pairs of facilities, is taken. A network formulation and analysis of this problem is provided. An algorithm, composed of three phases, is developed. The first phase involves preprocessing of the distance matrix. The second phase involves solving the (generalized assignment) network problem. The third phase employs a heuristic procedure which transforms the solution of the second phase into a feasible assignment of facilities to sites. Finally, computational experience with the new algorithm is provided.
Solving Facility Layout Problem: Threelevel Tabu Search Metaheuristic Approach
"... Abstract — In this paper an improved tabu search (ITS) based approach is proposed for solving facility layout problem (FLP) which is formulated as quadratic assignment problem (QAP). ITS is an improved version of conventional tabu search technique which incorporates three levels viz. intensification ..."
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Abstract — In this paper an improved tabu search (ITS) based approach is proposed for solving facility layout problem (FLP) which is formulated as quadratic assignment problem (QAP). ITS is an improved version of conventional tabu search technique which incorporates three levels viz. intensification, reconstruction, and solution acceptance. To evaluate the efficacy of the proposed ITS, it is tested for benchmark instances taken from published literature. Also, a comparative analysis of ITS with other metaheuristic approach is presented. It is found that ITS based approach provide comparative results. I.