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37
A Genetic Algorithm for the Set Covering Problem
 European Journal of Operational Research
, 1996
"... In this paper we present a genetic algorithmbased heuristic for nonunicost set covering problems. We propose several modifications to the basic genetic procedures including a new fitnessbased crossover operator (fusion), a variable mutation rate and a heuristic feasibility operator tailored speci ..."
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Cited by 128 (4 self)
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In this paper we present a genetic algorithmbased heuristic for nonunicost set covering problems. We propose several modifications to the basic genetic procedures including a new fitnessbased crossover operator (fusion), a variable mutation rate and a heuristic feasibility operator tailored specifically for the set covering problem. The performance of our algorithm was evaluated on a large set of randomly generated problems. Computational results showed that the genetic algorithmbased heuristic is capable of producing highquality solutions. Keywords: genetic algorithms; set covering; optimisation. 1 Introduction The set covering problem (SCP) is the problem of covering the rows of a mrow, n column, zeroone matrix (a ij ) by a subset of the columns at minimal cost. Defining x j = 1 if column j (with cost c j ? 0) is in the solution and x j = 0 otherwise, the SCP is Minimise n X j=1 c j x j (1) Subject to n X j=1 a ij x j 1, i = 1; : : : ; m (2) x j 2 f0; 1g, j = 1; ...
A Heuristic Method for the Set Covering Problem
 OPERATIONS RESEARCH
, 1995
"... We present a Lagrangianbased heuristic for the wellknown Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello St ..."
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Cited by 62 (8 self)
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We present a Lagrangianbased heuristic for the wellknown Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello Stato SpA. In 1994 Ferrovie dello Stato SpA, jointly with the Italian Operational Research Society, organized a competition, called FASTER, intended to promote the development of algorithms capable of producing good solutions for these instances, since the classical approaches meet with considerable difficulties in tackling them. The main characteristics of the algorithm we propose are (1) a dynamic pricing scheme for the variables, akin to that used for solving largescale LP's, to be coupled with subgradient optimization and greedy algorithms, and (2) the systematic use of column fixing to obtain improved solutions. Moreover, we propose a number of improvements on the standard way o...
Logical Analysis of Numerical Data
 Mathematical Programming
, 2000
"... The "Logical Analysis of Data" (LAD) is a methodology developed since the late eightees, aimed at discovering hidden structural information in data sets. LAD was originally developed for analyzing binary data by using the theory of partially defined Boolean functions. An extension of LAD for the ana ..."
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Cited by 44 (12 self)
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The "Logical Analysis of Data" (LAD) is a methodology developed since the late eightees, aimed at discovering hidden structural information in data sets. LAD was originally developed for analyzing binary data by using the theory of partially defined Boolean functions. An extension of LAD for the analysis of numerical data sets is achieved through the process of "binarization" consisting in the replacement of each numerical variable by binary "indicator" variables, each showing whether the value of the original variable is above or below a certain level. Binarization was successfully applied to the analysis of a variety of real life data sets. This paper develops the theoretical foundations of the binarization process studying the combinatorial optimization problems related to the minimization of the number of binary variables. To provide an algorithmic framework for the practical solution of such problems, we construct compact linear integer programming formulations of them. We develop...
Computational Experience with Approximation Algorithms for the Set Covering Problem
, 1994
"... The Set Covering problem (SCP) is a well known combinatorial optimization problem, which is NPhard. We conducted a comparative study of eight different approximation algorithms for the SCP, including several greedy variants, fractional relaxations, randomized algorithms and a neural network algorit ..."
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Cited by 42 (2 self)
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The Set Covering problem (SCP) is a well known combinatorial optimization problem, which is NPhard. We conducted a comparative study of eight different approximation algorithms for the SCP, including several greedy variants, fractional relaxations, randomized algorithms and a neural network algorithm. The algorithms were tested on a set of randomgenerated problems with up to 500 rows and 5000 columns, and on two sets of problems originating in combinatorial questions with up to 28160 rows and 11264 columns. On the random problems and on one set of combinatorial problems, the best algorithm among those we tested was the neural network algorithm, with greedy variants very close in second and third place. On the other set of combinatorial problems, the best algorithm was a greedy variant and the neural network performed quite poorly. The other algorithms we tested were always inferior to the ones mentioned above. Theoretical Division and CNLS, MS B213 Los Alamos National Lab, Los Ala...
An Algorithm for Large Scale 01 Integer Programming With Application to Airline Crew Scheduling
, 1995
"... We present an approximation algorithm for solving large 01 integer programming problems where A is 01 and where b is integer. The method can be viewed as a dual coordinate search for solving the LPrelaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working t ..."
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Cited by 33 (5 self)
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We present an approximation algorithm for solving large 01 integer programming problems where A is 01 and where b is integer. The method can be viewed as a dual coordinate search for solving the LPrelaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working together with this method. The approximation scheme works by adjusting the costs as little as possible so that the new problem has an integer solution. The degree of approximation is determined by a parameter, and for different levels of approximation the resulting algorithm can be interpreted in terms of linear programming, dynamic programming, and as a greedy algorithm. The algorithm is used in the CARMEN system for airline crew scheduling used by several major airlines, and we show that the algorithm performs well for large set covering problems, in comparison to the CPLEX system, in terms of both time and quality. We also present results on some well known difficult set covering problems ...
Algorithms for Railway Crew Management
, 1997
"... Crew management is concerned with building the work schedules of crews needed to cover a planned timetable. This is a wellknown problem in Operations Research and has been historically associated with airlines and masstransit companies. More recently, railway applications have also come on the sce ..."
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Cited by 23 (2 self)
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Crew management is concerned with building the work schedules of crews needed to cover a planned timetable. This is a wellknown problem in Operations Research and has been historically associated with airlines and masstransit companies. More recently, railway applications have also come on the scene, especially in Europe. In practice, the overall crew management problem is decomposed into two subproblems, called crew scheduling and crew rostering. In this paper, we give an outline of different ways of modeling the two subproblems and possible solution methods. Two main solution approaches are illustrated for realworld applications. In particular we discuss in some detail the solution techniques currently adopted at the Italian railway company, Ferrovie dello Stato SpA, for solving crew scheduling and rostering problems.
Global Search Methods For Solving Nonlinear Optimization Problems
, 1997
"... ... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the lear ..."
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Cited by 15 (1 self)
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... these new methods, we develop a prototype, called Novel (Nonlinear Optimization Via External Lead), that solves nonlinear constrained and unconstrained problems in a unified framework. We show experimental results in applying Novel to solve nonlinear optimization problems, including (a) the learning of feedforward neural networks, (b) the design of quadraturemirrorfilter digital filter banks, (c) the satisfiability problem, (d) the maximum satisfiability problem, and (e) the design of multiplierless quadraturemirrorfilter digital filter banks. Our method achieves better solutions than existing methods, or achieves solutions of the same quality but at a lower cost.
Set covering approach for reconstruction of sibling relationships
 Optimization Methods and Software
, 2007
"... A new combinatorial approach for modelling and reconstructing sibling relationships in a single generation of individuals without parental information is proposed in this paper. Simple genetic constraints on the fullsibling groups, imposed by the Mendelian inheritance rules, are employed to investi ..."
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Cited by 15 (13 self)
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A new combinatorial approach for modelling and reconstructing sibling relationships in a single generation of individuals without parental information is proposed in this paper. Simple genetic constraints on the fullsibling groups, imposed by the Mendelian inheritance rules, are employed to investigate data from codominant DNA markers. To extract the minimum number of biologically consistent sibling groups, the proposed combinatorial approach is employed to formulate this minimization problem as a set covering problem, which is a wellknown NPhard combinatorial optimization problem. We conducted a simulation study of a relaxed version of the proposed algorithm to demonstrate that our combinatorial approach is reasonably accurate and the exact version of the sibling relationship construction algorithm should be pursued. In addition, the results of this study suggest that the proposed algorithm will pave our way to a new approach in computational population genetics as it does not require any a priori knowledge about allele frequency, population size, mating system or family size distributions to reconstruct sibling relationships.
A 3Flip Neighborhood Local Search for the Set Covering Problem
, 2003
"... The set covering problem (SCP) calls for a minimum cost family of subsets from n given subsets, which together covers the entire ground set. In this paper, we propose a local search algorithm for SCP, which has the following three features. (1) The use of 3flip neighborhood, which is the set of sol ..."
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Cited by 10 (1 self)
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The set covering problem (SCP) calls for a minimum cost family of subsets from n given subsets, which together covers the entire ground set. In this paper, we propose a local search algorithm for SCP, which has the following three features. (1) The use of 3flip neighborhood, which is the set of solutions obtainable from the current solution by exchanging at most three subsets. As the size of 3flip neighborhood is O(n ), the neighborhood search becomes expensive if implemented naively. To overcome this, we propose an e#cient implementation that reduces the number of candidates in the neighborhood without sacrificing the solution quality. (2) We allow the search to visit infeasible region, and incorporate the strategic oscillation technique. (3) The size reduction of the problem by using the information from the Lagrangian relaxation is incorporated, which turned out to be e#ective in solving very large instances. According to computational comparisons on benchmark instances with other existing heuristic algorithms for SCP, our algorithm performs quite e#ectively for various types of problems, especially for very largescale instances.