the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

a tabu search approach to the constraint satisfaction problem as a general problem solver many combinatorial problems including a variety of combinatorial optimization problems can be naturally formulated as a constraint satisfaction problem csp we develop in this paper a tabu search based algorithm for the csp as a foundation for a general problem solver in addition to the basic components of tabu search we develop a number of elaborations such as an automatic control mechanism for the tabu tenure modification of the penalty function to handle objective functions and enlargement of the neighborhood by allowing swap operations computational results with our algorithm are reported for various problems selected from a wide range of applications i e graph coloring generalized assignment set covering timetabling and nurse scheduling our results appear to be competitive with those of existing algorithms specially developed for the respective problem domains

lattice boltzmann model for two dimensional unsteady burgers equation in this paper a special lattice boltzmann model is proposed to simulate two dimensional unsteady burgers equation the maximum principle and the stability are proved the model has been verified by several test examples excellent agreement is obtained between numerical predictions and exact solutions the cases of steep oblique shock waves are solved and compared with the two point compact scheme results the study indicates that lattice boltzmann model is highly stable and efficient even for the problems with severe gradients

improved handling of uncertainty and robustness in set covering problems abstract set covering problems are one of the classical combinatorial optimization problems and part of many different practical applications e g the location of emergency service facilities in many real world problems the required statistical parameters are not precisely known and the obtained solutions may reveal a non adequate performance we introduce a robust formulation of the uncertain probabilistic set covering problem which combines the concepts of robust and probabilistic optimization by introducing robust covering constraints this robust uncertain set covering problem can be stated as a compact mixed integer linear programming model additionally two non compact integer linear model formulations are developed as the strength of these formulations is not known a priori we analyze the performance of these formulations in an extensive computational study a case study for the location of emergency service facilities highlights the benefits of our approach in comparison to a formulation neglecting these uncertainties

enhancing an algorithm for set covering problems abstract in this note we present enhancements to a previously published algorithm for the optimal solution of set covering problems these enhancements relate to the use of a langrangean heuristic feasible solution exclusion constraints gomory f cuts and an improved branching strategy computational results for problems involving up to 400 rows and 4000 columns indicate that the enhanced algorithm gives better computational results than the original algorithm

on the set covering polytope i all the facets with coefficients in 0 1 2 while the set packing polytope through its connection with vertex packing has lent itself to fruitful investigations little is known about the set covering polytope we characterize the class of valid inequalities for the set covering polytope with coefficients equal to 0 1 or 2 and give necessary and sufficient conditions for such an inequality to be minimal and to be facet defining we show that all inequalities in the above class are contained in the elementary closure of the constraint set and that 2 is the largest value ofk such that all valid inequalities for the set covering polytope with integer coefficients no greater thank are contained in the elementary closure we point out a connection between minimal inequalities in the class investigated and certain circulant submatrices of the coefficient matrix finally we discuss conditions for an inequality to cut off a fractional solution to the linear programming relaxation of the set covering problem and to improve the lower bound given by a feasible solution to the dual of the linear programming relaxation

a fast approximation algorithm for solving the complete set packing problem we study the complete set packing problem cspp where the family of feasible subsets may include all possible combinations of objects this setting arises in applications such as combinatorial auctions for selecting optimal bids and cooperative game theory for finding optimal coalition structures although the set packing problem has been well studied in the literature where exact and approximation algorithms can solve very large instances with up to hundreds of objects and thousands of feasible subsets these methods are not extendable to the cspp since the number of feasible subsets is exponentially large formulating the cspp as an milp and solving it directly using cplex for example is impossible for problems with more than 20 objects we propose a new mathematical formulation for the cspp that directly leads to an efficient algorithm for finding feasible set packings upper bounds we also propose a new formulation for finding tighter lower bounds compared to lp relaxation and develop an efficient method for solving the corresponding large scale milp we test the algorithm with the winner determination problem in spectrum auctions the coalition structure generation problem in coalitional skill games and a number of other simulated problems that appear in the literature

a heuristic method for the set covering problem we present a lagrangian based heuristic for the well known set covering problem scp the algorithm was initially designed for solving very large scale scp instances involving up to 5 000 rows an

comparing evolutionary algorithms to the 1 1 ea in this paper we study the conditions in which the random hill climbing algorithm 1 1 ea compares favorably to other evolutionary algorithms eas in terms of fitness function distribution at a given iteration and with respect to the average optimization time our approach is applicable when the reproduction operator of an evolutionary algorithm is dominated by the mutation operator of the 1 1 ea in this case one can extend the lower bounds obtained for the expected optimization time of the 1 1 ea to other eas based on the dominated reproduction operator this method is demonstrated on the sorting problem with ham landscape and the exchange mutation operator we consider several simple examples where the 1 1 ea is the best possible search strategy in the class of the eas

graph theoretic relaxations of set covering and set partitioning problems in this paper we review the graph theoretic relaxations of the set covering problem scp and the set partitioning problem ssp these are a network relaxation which can be solved by the greedy method a matching relaxation and a graph covering relaxation other relaxations such as assignment shortest route and minimum spanning tree are also presented

global optimality conditions for discrete and nonconvex optimizationwith applications to lagrangian heuristics and column generation the well known and established global optimality conditions based on the lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero we develop a set of global optimality conditions that are structurally similar but are consistent for any size of the duality gap this system characterizes a primaldual optimal solution by means of primal and dual feasibility primal lagrangian e optimality and in the presence of inequality constraints a relaxed complementarity condition analogously called complementarity the total size e of those two perturbations equals the size of the duality gap at an optimal solution further the characterization is equivalent to a near saddle point condition which generalizes the classic saddle point characterization of a primaldual optimal solution in convex programming the system developed can be used to explain to a large degree when and why lagrangian heuristics for discrete optimization are successful in reaching near optimal solutions further experiments on a set covering problem illustrate how the new optimality conditions can be utilized as a foundation for the construction of new lagrangian heuristics finally we outline possible uses of the optimality conditions in column generation algorithms and in the construction of core problems

a lagrangian based heuristic for large scale set covering problems we present a new lagrangian based heuristic for solving large scale set covering problems arising from crew scheduling at the italian railways ferrovie dello stato our heuristic obtained impressive results when compared to state of the art codes on a test bed provided by the company which includes instances with sizes ranging from 50 000 variables and 500 constraints to 1 000 000 variables and 5000 constraints 1998 the mathematical programming society inc published by elsevier science b v

von karman howarth equation for three dimensional two fluid plasmas we derive the von karman howarth equation for a full three dimensional incompressible two fluid plasma in the long time limit and for very large reynolds numbers we obtain the equivalent of the hydrodynamic four fifths law this exact law predicts the scaling of the third order two point correlation functions and puts a strong constraint on the plasma turbulent dynamics finally we derive a simple expression for the 4 5 law in terms of third order structure functions which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges

covering problems and core percolations on hypergraphs we introduce two generalizations of core percolation in graphs to hypergraphs related to the minimum hyperedge cover problem and the minimum vertex cover problem on hypergraphs respectively we offer analytical solutions of these two core percolations for uncorrelated random hypergraphs whose vertex degree and hyperedge cardinality distributions are arbitrary but have nondiverging moments we find that for several real world hypergraphs their two cores tend to be much smaller than those of their null models suggesting that covering problems in those real world hypergraphs can actually be solved in polynomial time

edge covering problem under hybrid uncertain environments edge covering problem ecp is to find an edge cover with the minimum weight in a graph by quantifying costs time or opponent s payoffs as weights on edges ecp is employed to model many real life problems in engineering and management since various types of uncertainty always exist in real world this paper considers ecp under hybrid uncertain environments where randomness and fuzziness coexist we propose three decision models and present a hybrid intelligent algorithm to solve the proposed models where genetic algorithm and random fuzzy simulation are embedded numerical experiments are performed to show the robustness of the proposed algorithm

solving large scale maximum expected covering location problems by genetic algorithms a comparative study abstract this paper compares the performance of genetic algorithms gas on large scale maximum expected coverage problems to other heuristic approaches we focus our attention on a particular formulation with a nonlinear objective function to be optimized over a convex set the solutions obtained by the best genetic algorithm are compared to daskin s heuristic and the optimal or best solutions obtained by solving the corresponding integer linear programming ilp problems we show that at least one of the gas yields optimal or near optimal solutions in a reasonable amount of time

an effective and simple heuristic for the set covering problem abstract this paper investigates the development of an effective heuristic to solve the set covering problem scp by applying the meta heuristic meta raps meta heuristic for randomized priority search in meta raps a feasible solution is generated by introducing random factors into a construction method then the feasible solutions can be improved by an improvement heuristic in addition to applying the basic meta raps the heuristic developed herein integrates the elements of randomizing the selection of priority rules penalizing the worst columns when the searching space is highly condensed and defining the core problem to speedup the algorithm this heuristic has been tested on 80 scp instances from the or library the sizes of the problems are up to 1000 rows 10 000 columns for non unicost scp and 28 160 rows 11 264 columns for the unicost scp this heuristic is only one of two known scp heuristics to find all optimal best known solutions for those non unicost instances in addition this heuristic is the best for unicost problems among the heuristics in terms of solution quality furthermore evolving from a simple greedy heuristic it is simple and easy to code this heuristic enriches the options of practitioners in the optimization area

von karman howarth equation for magnetohydrodynamics and its consequences on third order longitudinal structure and correlation functions a derivation in variable dimension of the scaling laws for mixed third order longitudinal structure and correlation functions for incompressible magnetized flows is given for arbitrary correlation between the velocity and magnetic field with full isotropy homogeneity and incompressibility assumed when close to equipartition between kinetic and magnetic energy the scaling relations involve only structure functions in a manner similar to the frac 4 5 law of kolmogorov

a genetic algorithm for the set covering problem abstract in this paper we present a genetic algorithm based heuristic for non unicost set covering problems we propose several modifications to the basic genetic procedures including a new fitness based 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 algorithm based heuristic is capable of producing high quality solutions

an optimal column generation with ranking algorithm for very large scale set partitioning problems in traffic assignment abstract we show in this paper how branch and bound and column generation techniques can be conbined very efficiently to solve to optimality some very large scale set partitioning problems with special structure such as the matrix decomposition problem arising in the context of satellite communication system optimization the main contribution of our approach is the use of column generation during the tree search procedure combined with a ranking procedure which ensures that the exact optimal integer solution is obtained extensive computational experiments are reported for the matrix decomposition problem encountered in the search for optimal schedules in satellite switching systems showing the effectiveness of this approach

minimum weight covering problems in stochastic environments minimum weight covering problems have played an important role in many real applications in this paper two typical minimum weight covering problems namely vertex covering problem and edge covering problem are studied under stochastic environments according to different decision criteria we propose three stochastic programming models the expected minimum weight cover model a minimum weight cover model and the most minimum weight cover model a hybrid intelligent algorithm that integrates stochastic simulation with genetic algorithm is designed to solve the proposed models finally numerical experiments are performed to show the effectiveness and robustness of the proposed algorithm

the probabilistic set covering problem in a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability we analyze the structure of the set of probabilistically efficient points of binary random vectors develop methods for their enumeration and propose specialized branch and bound algorithms for probabilistic set covering problems

a population heuristic for constrained two dimensional non guillotine cutting abstract in this paper we present a heuristic algorithm for the constrained two dimensional non guillotine cutting problem this is the problem of cutting a number of rectangular pieces from a single large rectangle so as to maximise the value of the pieces cut in addition the number of pieces of each type that are cut must lie within prescribed limits our heuristic algorithm is a population heuristic where a population of solutions to the problem are progressively evolved this heuristic is based on a new non linear formulation of the problem computational results are presented for a number of standard test problems taken from the literature and for a number of large randomly generated problems

identifying redundant constraints and implicit equalities in systems of linear constraints redundant constraints are constraints that can be omitted from a system of linear constraints without changing the feasible region implicit equalities are inequality constraints that can be replaced by equalities without changing the feasible region we prove some theorems concerning the identification of both kinds of constraints based on these theorems two methods are developed that allow identification of all redundant constraints and all implicit equalities computational experience on small problems indicates a behavior at least competitive with other methods in this field

lagrangean heuristics for location problems abstract in this paper we present a framework for developing lagrangean heuristics heuristics based upon lagrangean relaxation and subgradient optimisation with respect to location problems computational results are given for four different location problems p median uncapacitated warehouse location capacitated warehouse location and capacitated warehouse location with single source constraints these results indicate that the framework presented in this paper is robust i e it gives good quality solutions for each of these different location problems

a network relaxation based enumeration algorithm for set partitioning abstract hidden network structure in the element set incidence constraint matrix of a set partitioning problem can be identified by using procedures for testing when a binary matrix is transformable to a network the set partitioning problem is thus represented as a network with side constraints this paper reports the development of a new efficient solution procedure for the set partitioning problem facilitated by the new formulation and makes use of lagrangean duality modified subgradients efficient reoptimization and enumeration tree reduction

an efficient local search heuristic with row weighting for the unicost set covering problem abstract the set covering problem scp is np hard we propose a new row weighting local search rwls algorithm for solving the unicost variant of the scp i e uscps where the costs of all sets are identical rwls is a heuristic algorithm that has three major components united in its local search framework 1 a weighting scheme which updates the weights of uncovered elements to prevent convergence to local optima 2 tabu strategies to avoid possible cycles during the search and 3 a timestamp method to break ties when prioritizing sets rwls has been evaluated on a large number of problem instances from the or library and compared with other approaches it is able to find all the best known solutions bks and improve 14 of them although requiring a higher computational effort on several instances rwls is especially effective on the combinatorial or library instances and can improve the best known solution to the hardest instance cyc11 considerably rwls is conceptually simple and has no instance dependent parameters which makes it a practical and easy to use uscp solver

a comparison of lagrangean and surrogate relaxations for the maximal covering location problem abstract we compare heuristics based on lagrangean and surrogate relaxations of the maximal covering location problem mclp the lagrangean relaxation of mclp used in this paper has the integrality property and the surrogate relaxed problem we solve is the lp relaxation of the original 0 1 knapsack problem the heuristics were compared using 331 test problems available in the literature corresponding to networks ranging from 55 to 900 vertices the gaps obtained with both heuristics were very low and did not differ substantially among themselves for the several problem sets used in accordance with theoretical results reviewed in the paper when the initial set of multipliers was determined using a valid bound for mclp the computing times did not differ significantly between the lagrangean and surrogate heuristics

optimal solution of set covering partitioning problems using dual heuristics we present an algorithm for a mixed set covering partitioning model that includes as special cases the well known set covering problem and set partitioning problem the novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm the heuristics are continuous adaptations of the well known greedy and 3 opt methods that have been applied to a variety of combinatorial optimization problems our algorithm has outperformed the current best set covering algorithm of balas and ho 1980 by about a factor of 3 and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude

higher order accurate numerical solution of unsteady burgers equation abstract higher order accurate finite difference schemes for solving the unsteady burgers equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented the unsteady burgers equation belongs to a few nonlinear partial differential equations which has an exact solution and it allows one to compare the numerical solution with the exact one and the properties of different numerical methods we propose an explicit finite difference scheme for a numerical solution of the heat equation with robin boundary conditions it has a sixth order approximation in the space variable and a third order approximation in the time variable as an application we developed numerical schemes for solving a numerical solution of burgers equation using the relationship between the heat and burgers equations this scheme has up to sixth order approximation in the space variables the main advantage of our approach is transition to one dimensional equation which essentially reduces the computation costs compared to other direct methods for solving the unsteady burgers equation the numerical results of test examples are found in good agreement with exact solutions for a wide range of reynolds number and confirm the approximation orders of the schemes proposed

algorithms for railway crew management crew management is concerned with building the work schedules of crews needed to cover a planned timetable this is a well known problem in operations research and has been historically associated with airlines and mass transit 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 real world 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

an efficient mean field approach to the set covering problem a mean field feedback artificial neural network ann algorithm is developed and explored for the set covering problem a convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function an approximate energy minimum is obtained by iterating a set of mean field equations in combination with annealing the approach is numerically tested against a set of publicly available test problems with sizes ranging up to 5 103 rows and 106 columns when comparing the performance with exact results for sizes where these are available the approach yields results within a few percent from the optimal solutions comparisons with other approximate methods also come out well in particular given the very low cpu consumption required typically a few seconds arbitrary problems can be processed using the algorithm via a public domain server 2001 elsevier science b v less

computational experience with approximation algorithms for the set covering problem the set covering problem scp is a well known combinatorial optimization problem which is np hard 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 random generated 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

implications of the monin yaglom relation for rayleigh taylor turbulence the aim of this letter is to assess existing theories for rayleigh taylor small turbulent scales for this purpose we propose to adapt the monin yaglom relation to the rayleigh taylor turbulence context a special emphasis is put on the inhomogeneity of the flow and on the effect of buoyancy forces this relation is then used to show that among existing theories the standard kolmogorov obukhov theory should apply to rayleigh taylor turbulence in the limit of a large reynolds number large times and small scales

a chebyshev spectral collocation method for solving burgers type equations in this paper we elaborated a spectral collocation method based on differentiated chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations the problem is reduced to a system of ordinary differential equations that are solved by runge kutta method of order four numerical results for the nonlinear evolution equations such as 1d burgers kdv burgers coupled burgers 2d burgers and system of 2d burgers equations are obtained the numerical results are found to be in good agreement with the exact solutions numerical computations for a wide range of values of reynolds number show that the present method offers better accuracy in comparison with other previous methods moreover the method can be applied to a wide class of nonlinear partial differential equations

numerical solution of one dimesional burgers equation explicit and exact explicit finite difference methods this paper presents finite difference solution and analytical solution of the finite difference approximations based on the standard explicit method to the one dimensional burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics results obtained by these ways for some modest values of viscosity have been compared with the exact fourier one it is shown that they are in good agreement with each other

a note on a symmetrical set covering problem the lottery problem in a lottery n numbers are drawn from a set of m numbers on a lottery ticket we fill out n numbers consider the following problem what is the minimum number of tickets so that there is at least one ticket with at least p matching numbers we provide a set covering formulation for this problem and characterize its lp solution the existence of many symmetrical alternative solutions makes this a very difficult problem to solve as our computational results indicate

extended self similarity in turbulent flows we report on the existence of a hitherto undetected form of self similarity which we call extended self similarity ess ess holds at high as well as at low reynolds number and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence

measures of intermittency in driven supersonic flows scaling exponents for structure functions of the velocity density and entropy are computed for driven supersonic flows for rms mach numbers of order unity with numerical simulations using the piecewise parabolic method algorithm on grids of up to 512 3 points the driving is made up of either one or three orthogonal shear waves in all cases studied the compressible component of the velocity in the statistically steady regime is weaker than its solenoidal counterpart by roughly a factor of 6 exponents for the longitudinal component of the velocity are comparable to what is found in the incompressible case and appear insensitive to the presence of numerous shocks scaling exponents of the transverse components of the velocity are comparable to those for the longitudinal component density and entropy structure functions display strong departures from linear scaling finally the scaling of structure functions of the energy transfer is also given and compared with the kolmogorov refined similarity hypothesis

a 3 flip neighborhood local search for the set covering problem 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 characteristics 1 the use of 3 flip neighborhood which is the set of solutions obtainable from the current solution by exchanging at most three subsets as the size of 3 flip neighborhood is o n3 the neighborhood search becomes expensive if implemented naively to overcome this we propose an efficient implementation that reduces the number of candidates in the neighborhood without sacrificing the solution quality 2 we allow the search to visit the infeasible region and incorporate the strategic oscillation technique realized by adaptive control of penalty weights 3 the size reduction of the problem by using the information from the lagrangian relaxation is incorporated which is indispensable for solving very large instances according to computational comparisons on benchmark instances with other existing heuristic algorithms for scp our algorithm performs quite effectively for various types of problems especially for very large scale instances

the multicovering problem abstract the multicovering problem is min cx subject to ax b x 0 where a is a matrix whose elements are all zero or one and b is a vector of positive integers this problem has many applications in scheduling location and business areas a variety of industrial commercial and military contexts give rise to large problems of this kind frequently at or beyond the limits of current computational tractability our research goal is the development of a special purpose algorithm capable of solving large problems of this kind conceptual and computational inputs to the algorithm arise from three sources from the generalization of computational tools developed for more specific problems in particular the set covering problem from the adaptation of general integer programming and combinatorial optimization methods and from the development within this paper of special techniques designed to take advantage of the structure of the problem studied following a description of the algorithm we give some computational results for randomly generated problems

a class of high order compact difference schemes for solving the burgers equations abstract in this paper a class of high order compact difference method is introduced for solving the burgers equations firstly a linear high order compact difference scheme is proposed to solve the one dimensional burgers equation the scheme is fourth order accurate in space and second order accurate in time linear stability analysis is conducted to show the scheme is conditionally stable because only three grid points are involved in each time level thomas algorithm can be directly used to solve the tridiagonal linear system then this method is extended to solve the two dimensional and three dimensional coupled burgers equations numerical experiments are carried out to demonstrate the accuracy and dependability of the present method

a graph approach for fuzzy rough feature selection abstract rough sets especially fuzzy rough sets have proven to be a powerful tool for dealing with vagueness and uncertainty in data analysis fuzzy rough feature selection has been shown to be highly useful in data dimensionality reduction however many fuzzy rough feature selection algorithms are still time consuming when dealing with the large scale data sets in this paper the problem of feature selection in fuzzy rough sets is studied in the framework of graph theory we propose a new mechanism for fuzzy rough feature selection it is shown that finding the attribute reduction of a fuzzy decision system can be translated into finding the transversal of a derivative hypergraph based on the graph representation model a novel graph theoretic algorithm for fuzzy rough feature selection is proposed the performance of the proposed method is compared with those of the state of the art methods on various classification tasks experimental results show that the proposed technique outperforms all other known feature selection methods in terms of the computation time especially for the large scale data sets it demonstrates promising performance moreover our proposed method can achieve better classification accuracies with the usage of small number of features

an algorithm for set covering problem in this paper we present an algorithm for the set covering problem that combines problem reduction tests with dual ascent subgradient optimisation and linear programming computational results are presented for problems involving up to 400 rows and 4000 columns

a dynamic subgradient based branch and bound procedure for set covering we discuss a branch and bound algorithm for set covering whose centerpiece is a new integrated upper bounding lower bounding procedure called dynamic subgradient optimization dynsgrad this new procedure applied to a lagrangean dual at every node of the search tree combines the standard subgradient method with primal and dual heuristics that interact to change the lagrange multipliers and tighten the upper and lower bounds fix variables and periodically restate the lagrangean itself extensive computational testing is reported as a stand alone heuristic dynsgrad performs significantly better than other procedures in terms of the quality of solutions obtainable with a certain computational effort when incorporated into a branch and bound algorithm dynsgrad considerably advances the state of the art in solving set covering problems

a space time fully decoupled wavelet galerkin method for solving two dimensional burgers equations abstract a space time fully decoupled formulation for solving two dimensional burgers equations is proposed based on the coiflet type wavelet sampling approximation for a function defined on a bounded interval by applying a wavelet galerkin approach for spatial discretization nonlinear partial differential equations are first transformed into a system of ordinary differential equations in which all matrices are completely independent of time and never need to be updated in the time integration finally the mixed explicit implicit scheme is employed to solve the resulting semi discretization system by numerically studying three widely considered test problems results demonstrate that the proposed method has a much better accuracy and a faster convergence rate than many existing numerical methods most importantly the study also indicates that the present wavelet method is capable of solving the two dimensional burgers equation at high reynolds numbers

a surrogate heuristic for set covering problems abstract the purpose of this paper is to present a new heuristic for set covering problems based upon continuous surrogate relaxations and subgradient optimization the algorithm combines problem reduction tests an adequate step size control and avoid preliminary sorting in solving the continuous surrogate relaxations computational tests for large scale set covering problems up to 1 000 rows and 12 000 columns indicate better quality results than algorithms based on lagrangian relaxations in terms of final solutions and mainly in computer times although the solving of a single surrogate optimization problem is slower than a corresponding lagrangian optimization the overall performance is almost twice as fast this is due to the smaller number of iterations which is a result of faster convergence and less oscillation

a sparse mode spectral method for the simulation of turbulent flows we propose a new algorithm belonging to the family of the sparse mode spectral method to simulate turbulent flows in this method the number of fourier modeskincreases withkmore slowly thankd 1in dimensiond while retaining the advantage of the fast fourier transform examples of applications of the algorithm are given for the one dimensional burgers equation and two dimensional incompressible mhd flows

hierarchical differential evolution for minimal cut sets identification application to nuclear safety systems in this paper we present a hierarchical differential evolution hde algorithm for minimal cut set mcs identification of coherent and non coherent fault trees fts in realistic application of large size systems problems may be encountered in handling a large number of gates and events in this work to avoid any approximation mcs identification is originally transformed into a hierarchical optimization problem stated as the search for the minimum combination of cut sets that can guarantee the best coverage of all the minterms that make the system fail during the first step of the iterative search a multiple population parallel search policy is used to expedite the convergence of the second step of the exploration algorithm the proposed hierarchical method is applied to the reactor protection system rps of a pressurized water reactor pwr and to the the airlock system as of a canadian deuterium uranium candu reactor results are evaluated with respect to the accuracy and computational demand of the solution found

an electromagnetism metaheuristic for the unicost set covering problem in this paper we propose a new heuristic algorithm to solve the unicost version of the well known set covering problem the method is based on the electromagnetism metaheuristic approach which after generating a pool of solutions to create the initial population applies a fixed number of local search and movement iterations based on the electromagnetism theory in addition to some random aspects used in the construction and local search phases we also apply mutation in order to further escape from local optima the proposed algorithm has been tested over 80 instances of the literature on the classical benchmark instances where the number of columns is larger than the number of rows the algorithm by using a fixed set of parameters always found the best known solution and for 12 instances it was able to improve the current best solution by using different parameter settings the algorithm improved 4 additional best known solutions moreover we proved the effectiveness of the electromagnetism metaheuristic approach for the unicost set covering problem by embedding the procedures of the proposed algorithm in a genetic algorithm scheme the worse results obtained by the genetic algorithm show the impact of the electromagnetism metaheuristic approach in conducting the search of the solution space by applying the movements based on the electromagnetism theory finally we report the results obtained by modifying the proposed electromagnetism metaheuristic algorithm for solving the non unicost set covering problem

generation of finite difference formulas on arbitrarily spaced grids on etablit des recurrences simples pour le calcul des poids dans les formules aux differences finies compactes pour les derivees de tous ordres avec une precision d ordre arbitraire sur des grilles a une dimension d espacement arbitraire

the optimal diversity management problem in some industries a certain part can be needed in a very large number of different configurations this is the case e g for the electrical wirings in european car factories a given configuration can be replaced by a more complete therefore more expensive one the diversity management problem consists of choosing an optimal set of some given number k of configurations that will be produced any nonproduced configuration being replaced by the cheapest produced one that is compatible with it we model the problem as an integer linear program our aim is to solve those problems to optimality the large scale instances we are interested in lead to difficult lp relaxations which seem to be intractable by the best direct methods currently available most of this paper deals with the use of lagrangean relaxation to reduce the size of the problem in order to be able subsequently to solve it to optimality via classical integer optimization

simple lagrangian heuristic for the set covering problem abstract in this paper a simple lagrangian heuristic is proposed for the set covering problem it is based on simple and classical ideas lagrangian duality greedy heuristic for the set covering problem subgradient optimization and redundant covers the main interesting point of the paper lies in the fact that the proposed heuristic turns out to be efficient for low density set covering problems with a large number of variables

an adaptation of sh heuristic to the location set covering problem abstract in a recent paper a new surrogate heuristic sh has been proposed for the set covering problem here we present an adaptation of it in order to solve more efficiently the location set covering problem we will show that our new version not only outperforms algorithm sh but that it is more accurate than the pair cma fmc its power is experimentally tested over a set of 65 randomly generated problems

on the 0 1 facets of the set covering polytope in this paper we consider inequalities of the form jxj where j equals 0 or 1 and is a positive integer we give necessary and sufficient conditions for such inequalities to define facets of the set covering polytope associated with a 0 1 constraint matrixa these conditions are in terms of critical edges and critical cutsets defined in the bipartite incidence graph ofa and are in the spirit of the work of balas and zemel on the set packing problem where similar notions were defined in the intersection graph ofa furthermore we give a polynomial characterization of a class of 0 1 facets defined from chorded cycles of the bipartite incidence graph this characterization also yields all the 0 1 liftings of odd hole inequalities for the simple plant location polytope