Beasley, J. E.: A Lagrangian heuristic for set covering problems, Naval Res. Logist. 37 (1990), 151--164.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... see [4] Turning to the selection problem we first note that even the plain set covering problem is NP hard, and it is unlikely that there are polynomial algorithms which find approximations within a factor ln n from an optimal solution [25] Lagrangian relaxation approaches for set covering [10] have been investigated for railway problems of similar size to the problems in our test set, see e.g. 14, 15, 17] Hoffman and Padberg [34] apply branch and cut techniques to smaller set partitioning problems with base constraints. Marsten et al. 39] apply the interior point solver of the ....

J. Beasley. A lagrangian heuristic for set-covering problems. Naval Res. Logist., 37(1):151--164, 1990.

....planning, logical data analysis. Interested readers are referred to the survey by Balas [1] and to the annotated bibliography by Ceria, Nobili and Sassano [16] There is also an extensive literature on numerical methods for solving such problems, both exact ( 2] 4] 9] 27] and approximate ([5], 8] 12] 15] 22] 23] 25] An experimental comparison of the main methods is reported in the survey paper by Caprara, Fischetti, and Toth [13] Our objective is to analyse a probabilistic set covering problem, in which the right hand side of (1) is replaced by a binary random vector . ....

J.E. Beasley, A Lagrangian Heuristic for Set Covering Problems. Naval Research Logistics, 37 (1990), 151--164.

.... in practice, but typically do not provide high quality solutions, as reported in Balas and Ho [3] and Balas and Carrera [2] The most effective heuristic approaches to SCP are those based on Lagrangian relaxation following the seminal work by Balas and Ho [3] and then the improvements by Beasley [6], Fisher and Kedia [20] Balas and Carrera [2] Ceria, Nobili and Sassano [15] and Wedelin [31] Lorena and Lopes [27] propose an analogous approach based on surrogate relaxation. Recently, Beasley and Chu [7] and Jacobs and Brusco [25] proposed a genetic and a local search algorithm, ....

J.E. Beasley, "A Lagrangian Heuristic for Set Covering Problems", Naval Research Logistics 37 (1990) 151--164.

....set S typically contains a set R of redundant columns, i.e. columns j such that S nfjg is still a feasible SCP solution. The optimal removal of the redundant columns amounts to solving an SCP defined by the columns in R and the rows in M n ( S j2SnR I j ) The algorithm proposed by Beasley [4] computes, at every iteration of a subgradient optimization procedure, a feasible SCP solution as follows. A set S is initialized with all the columns selected in the solution of the Lagrangian problem. Then, for each row i not covered by S, the column with smallest original cost in J i is added ....

....of removing some columns from the problem. The algorithm by Balas and Carrera [2] is based on the dynamic subgradient procedure described in the previous section. The version producing the best heuristic solutions applies, at every iteration, a greedy heuristic similar to the one used by Beasley [4]. Recall from the previous section that in [2] not all the constraints are relaxed in a Lagrangian way, and that the subgradient procedure works with multiplier vectors which are feasible dual solutions. Accordingly, the solution of the relaxed problem contains all the columns with zero Lagrangian ....

[Article contains additional citation context not shown here]

J.E. Beasley, "A Lagrangian Heuristic for Set Covering Problems", Naval Research Logistics 37 (1990) 151--164.

....that, given the lack of polynomial time optimizing algorithms, there is a need for a computationally effective heuristic algorithm capable of producing good quality (near optimal) solutions with considerably less effort. The so called Lagrangian heuristic algorithm demonstrated by J.E. Beasley [6] looked promising and was reported to outperform the heuristic algorithm of Balas and Ho [3] and two heuristic algorithms of Vasko and Wilson [23] The average deviation from optimal for the Lagrangian heuristic algorithm was reported to be only 0.638 , compared to 7.416 for the Balas and Ho ....

....paper we will describe five Lagrangian heuristic algorithms, all of which begin with the solution to the 5 Lagrangian Heuristics for SCP 4 9 98 Lagrangian relaxation problem, add sets to the cover to gain feasibility if necessary, and remove superfluous sets in the solution. Beasleys algorithm [6] will be referred to as heuristic #1 in this paper for ease of reference. Our other 4 heuristic algorithms are essentially extensions of Beasleys, and, like his algorithm, use not only the solution (perhaps infeasible) of the Lagrangian relaxation. Unlike his algorithm, however, our algorithms ....

[Article contains additional citation context not shown here]

Beasley, J. E., "A Lagrangian Heuristic for Set-Covering Problems", Naval Research Logistics, 37, pp. 151-164 (1990).

....and mentions the need for shape complexityinthe overlap area but does not implement it. Whaite and Ferrie [17] achieve image overlap by a conservativesearch strategy. 2 There are several potential choices for a normalizing value. mS has the advantage of guaranteeing oe kj values in the range [0,1], is reciprocal and is independent of segmentation patch size, object size, rough model sampling density and sensor characteristics. The viewpoint registration graph must beatleast simply connected. Note that the viewpoint registration graph for each patchisa sub graph of the global ....

....such exact methods can be computationally prohibitiveeven for modestly sized IPs. For most medium to large IPs, this leaves a choice of approximate and heuristic algorithms [9] including greedy search (GS) 4] simulated annealing (SN) 13] genetic algorithm (GA) 2] Lagrangian relaxation [1] and neural network [6] methods. Most published performance results [6] 1] deal with random, lowdensity data sets. The VPP falls into the category of a mediumto large IP with non random data and moderate density. A representative size for a measurability matrix generated byouralgorithm will be ....

[Article contains additional citation context not shown here]

J. Beasley. A lagrangian heuristic for set covering problems. Naval Research Logistics, 37:151--164, 1990.

....and mentions the need for shape complexity in the overlap area but does not implement it. Whaite and Ferrie [16] achieve image overlap by a conservative search strategy. 2 There are several potential choices for a normalizing value. mS has the advantage of guaranteeing oe kj values in the range [0,1], is reciprocal and is independent of object or segmentation patch size, rough model sampling density and sensor characteristics. encoding viewpoint connectivity in terms of inter image registration potential. Consequently, we can express the image based registration requirementby stating that ....

....such exact methods can be computationally prohibitiveeven for modestly sized IPs. For most medium to large IPs, this leaves a choice of approximate and heuristic algorithms [9] including greedy search (GS) 5] simulated annealing (SN) 13] genetic algorithms (GA) 2] Lagrangian relaxation [1] and neural network [7] methods. Most published performance results [7] 1] deal with random, lowdensity data sets. The VPP falls into the category of a medium to large IP with nonrandom data and moderate density[12] Finally,we believeaneven more importantareaawaits better theoretical ....

[Article contains additional citation context not shown here]

J. Beasley. A lagrangian heuristic for set covering problems. Naval Research Logistics, 37:151--164, 1990.

....the energy cost of the outgoing aggregate is the minimum weight of the cover plus 1. Approximate algorithms for this problem include greedy heuristics [4, 6] probabilistic methods [17] geneticalgorithms based heuristics [15] neural networks based techniques [9] and Lagrangian heuristics [5]. We chose the greedy heuristic because of its high quality solutions (The worst ratio between the cost of a greedy solution and the optimal solution is ln d 1 where d is the maximum size of any set S i [6, 9] The heuristic of the greedy set covering algorithm is to greedily select the next ....

J.E. Beasley. A lagrangian heuristic for set-covering problems. Naval Research Logistics, 37:151--164, 1990.

....or better than the best manual ones) while using the remaining processing time for improving them by exploring different fixing patterns. For more details of the duty selection mechanism, we refer the reader to [8] Other approaches for solving large set covering problems can be found in [1, 2, 3, 4, 9, 10, 16]. 4.3.3 Output and other functions. The results of a run of the algorithm can be shown by the TURNI system in tabular format, where the successive trips in each duty are listed along with some duty statistics, or in a graphical format in the form of a Gantt chart or a timespace diagram. An ....

J.E. Beasley, "A Lagrangian heuristic for set covering problems," Naval Research Logistics, 31 (1990) 151-164.

....search (Feo et al. 1989) simulated annealing (Johnson, et al. 1989) and neural networks (Aourid and Kaminska, 1994) have also been tried. Unfortunately, there has not been a comparative testing across such methods to determine under what circumstances a specific method might perform best. Beasley (1990) maintains (at http: mscmga.ms.ic.ac.uk info.html) an extensive test set of covering and partitioning problem instances for those who would like to try their hand. We think it safe to say that anything one can think of for approximating the SPP has probably been thought of. In addition, one can ....

....in the description of the procedure. 35 than Z LP . Details can be found in Nemhauser and Wolsey (1988) Needless to say there have been many applications of Lagrangean relaxation to SPP, SPA and SPC and hybrids with exact methods have also been investigated. See Balas and Carrera (1996) and Beasley (1990) for recent examples. 3.4 Column Generation Column generation is a technique for solving linear programs with an exceedingly large number of variables. Each variable gives rise to a column in the constraint matrix, hence the name column generation. A naive implementation of a simplex type ....

J. E. Beasley, "A Lagrangian Heuristic for Set-Covering Problems", Naval Research Logistics, 37, 151--164, 1990.

....instances CFT nds the optimum in a shorter time. The results of the experiments indicate that WSCP is a rather powerful tool for solving large real life airline crew scheduling problems. 3. 2 Experiments on the OR Library SCP Instances We consider the families A D from [4] and the NRE NRH from [5], consisting of randomly generated SCP instances. Each class contains 5 instances. The values of the characteristic parameters of these problem classes, like number of rows and columns, are given in Table 8. We compare experimentally WSCP with the genetic algorithms by Beasley and Chu [6] and by ....

J.E. Beasley. A lagrangian heuristic for set covering problems. Naval Research Logistics, 37:151-164, 1990.

....for SCP, typically based upon tree search procedures, have appeared in the literature (e.g. BH80, Bea87] These algorithms have been used to solve problems with up to 50 rows and 500 columns, albeit at considerable computational cost. The Lagrangian approximation heuristic for SCP of [Bea90a] was tested on problems with up to 500 rows and 5000 columns. The approximation algorithm of [Wed94] was tested on problems generated for airline crew scheduling, involving up to 1600 rows and 105000 columns. Genetic algorithms and simulated annealing algorithms for set covering appear in [Sen93, ....

....mr j value. 3 Methods 3. 1 Random Generated Problems The algorithms were tested on 60 randomly generated problems, see Table 1 for details) which are available electronically [Bea90b] Problem sets 4 6 are from [BH80] problem sets A E are from [Bea87] and problem sets NRE NRF are from [Bea90a] All the problems were randomly produced according to the specified densities, using the scheme of [BH80] namely every column covers at least one row and every row is covered by at least two columns. All these problems were originally generated to test weighted SCP algorithms. In order to use ....

J. E. Beasley. A lagrangian heuristic for set covering problems. Naval Research Logistics, 37:151--164, 1990.

.... in practice, but typically do not provide high quality solutions, as reported in Balas and Ho [3] and Balas and Carrera [2] The most effective heuristic approaches to SCP are those based on Lagrangian relaxation following the seminal work by Balas and Ho [3] and then the improvements by Beasley [7], Fisher and Kedia [31] Balas and Carrera [2] Ceria, Nobili and Sassano [25] and Wedelin [53] We next outline a heuristic which has been designed to attack very large scale instances. The technique outperforms previously published methods: in 92 out of the 94 instances in the literature the ....

J.E. Beasley, "A Lagrangian Heuristic for Set Covering Problems", Naval Research Logistics 37 (1990) 151--164.

....for SCP. More specifically, the following problem instances are considered: ffl Random Problems These are 70 randomly generated problems from the OR library (see Tables 4 and 5) The instances of families 4 6 are from [3] those of families A E are from [4] and those of families NRE NRH are from [5]. As in [14] the original instances have been modified by discarding the costs of the columns, since we are dealing with the unicost SCP. Thus the results obtained are not comparable with those reported in the above mentioned papers (except for the E family, which is also originally produced for ....

J.E. Beasley. A lagrangian heuristic for set covering problems. Naval Research Logistics, 37:151--164, 1990.

....typically do not provide high quality solutions, as reported in Balas and Ho [3] and Balas and Carrera [2] The most effective heuristic approaches to SCP are those based on Lagrangian relaxation. These approaches follow the seminal work by Balas and Ho [3] and then the improvements by Beasley [6], Fisher and Kedia [19] Balas and Carrera [2] Ceria, Nobili and Sassano [15] and Wedelin [30] Lorena and Lopes [26] propose an analogous approach based on surrogate relaxation. Recently, Beasley and Chu [7] and Jacobs and Brusco [24] proposed a genetic and a local search algorithm, ....

J.E. Beasley, "A Lagrangian Heuristic for Set Covering Problems", Naval Research Logistics 37 (1990) 151--164.

....solution we can easily construct a feasible one by deleting customers from all but one route. Unfortunately, SPC as well as SPP is a NP hard problem and so there is little hope to obtain an exact solution in short time. Therefore, we use the Lagrangian heuristic proposed by Beasley [3]. For an introduction to Lagrangian relaxation with applications to the SCP we refer to Beasley [4] 3.4. Building the parallel algorithm A natural way to parallelize the basic algorithm is a master slave approach, in which the master processor holds the pool Omega Gamma The initial solutions S ....

J.E. Beasley, A Lagrangian heuristic for set covering problems, Naval Research Logistic, 37:151--164, 1990. J. Schulze, T. Fahle / A parallel algorithm for the vehicle routing problem 21

....In our work, we study the effects of using different stochastic operators with a penalty based fitness function and a repair heuristic for infeasible solutions on the mscp. More precisely, the traditional one and two point crossover, uniform crossover, and the recently suggested fusion crossover [5] are incorporated in the genetic algorithm GENEsYs. This package is based on Grefenstette s popular software package GENESIS [11] The fitness function uses a graded penalty term to penalize infeasibly bred strings. Unlike other works, such as Beasley et al. 7] that use a tailor made fitness ....

.... short of exhaustive enumeration, that delivers optimum solutions is based on the branch and bound technique (the other being dynamic programming) Approximation algorithms include greedy techniques [9] simulated annealing [22] Lagrangian relaxation and sub gradient optimization techniques [5] and GA based heuristics [17] The interested reader can find more references to the unicost and mscp including more applications in [4] The mscp can be recast by using matrix notation. Elements of E and subsets of F can be represented by an m row, n column, zero one matrix A, with elements a ij ....

J. E. Beasley. A lagrangian heuristic for set-covering problems. Naval Research Logistics, 37:151--164, 1990.

No context found.

Beasley, J. E.: A Lagrangian heuristic for set covering problems, Naval Res. Logist. 37 (1990), 151--164.

No context found.

Beasley, J.E.: A Lagrangian Heuristic for Set Covering Problems, Naval Research Logistics, 37(1):151-164, 1990.

No context found.

Beasley,J.E. 1990. A Lagrangian heuristic for set-covering problems. Naval Research Logistics, 37: 151--164.

No context found.

Beasley,J.E. (1990) A Lagrangian heuristic for set-covering problems. Naval Research Logistics, 37, 151--164.

No context found.

J.E. Beasley, "A Lagrangian Heuristic for Set Covering Problems", Naval Research Logistics 37 (1990) 151--164.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC