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

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

a note on the theorems of m g krein and l a sakhnovich on continuous analogs of orthogonal polynomials on the circle abstract continuous analogs of orthogonal polynomials on the circle are solutions of a canonical system of differential equations introduced and studied by krein and recently generalized to matrix systems by sakhnovich we prove that the continuous analogs of the adjoint polynomials converge in the upper half plane in the case of l 2 coefficients but in general the limit can be defined only up to a constant multiple even when the coefficients are in l p for any p 2 the spectral measure is absolutely continuous and the szego kolmogorov krein condition is satisfied thus we point out that krein s and sakhnovich s papers contain an inaccuracy which does not undermine known implications from these results

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

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

a nonquadratic bolza problem and a quasi riccati equation for distributed parameter systems closed loop optimal control of a nonquadratic bolza problem for linear distributed parameter systems and normal solution of an associated quasi riccati operator equation are studied by the approach of a nonlinear integral equation

synthesis of time variant optimal control with nonquadratic criteria abstract under the assumption of convexity of nonquadratic time variant criteria for a linear time variant control system it is proved in this paper that the closed loop synthesis of the optimal control is given by a nonlinear feedback u t r 1 t b t p t x t in which p t x is the normal solution of a quasi riccati operator equation it is also shown that the nonlinear feedback operator p t x can be explicitly expressed by solutions of the associated nonlinear algebraic equation and nonlinear integral equations respectively in three cases corresponding to mayer problems lagrange problems and bolza problems

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

a note on the synthesis of nonquadratic optimal control in a one dimensional linear system the synthesis problem of the optimal control is investigated in a one dimensional linear system with a cost function which is holderian with respect to the control and convex with respect to the final state under some conditions it is proved that the closed loop synthesis is given by a nonlinear state feedback defined in terms of the solution of a bernoulli type operator equation it is also shown that the feedback operator can be explicitly expressed by solutions of associated algebraic equations

on the singular spectrum of schrodinger operators with decaying potential the relation between hausdorff dimension of the singular spectrum of a schrodinger operator and the decay of its potential has been extensively studied in many papers in this work we address similar questions from a different point of view our approach relies on the study of the so called krein systems for schrodinger operators we show that some bounds on the singular spectrum obtained recently by remling and christ kiselev are optimal

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

first kdv integrals and absolutely continuous spectrum for 1 d schrodinger operator we consider 1 d schrodinger operators on l 2 r with slowly decaying potentials under some conditions on the potential related to the first integrals of the kdv equation we prove that the a c spectrum of the operator coincides with the positive semiaxis and the singular spectrum is unstable examples show that for special classes of sparse potentials these results can not be improved

linear nonquadratic optimal control problems with terminal inequality constraints abstract this paper considers a linear nonquadratic optimal control problem subject to nonlinear terminal inequality constraints we approximate it by a series of approximate problems via the penalty method it is shown that the optimal control functions of the approximate problems uniformly converge to the optimal control function of the original terminal constrained problem furthermore the optimal values of the approximate problems also converge to the optimal value of the original problem under some mild conditions

on the coexistence of absolutely continuous and singular continuous components of the spectral measure for some sturm liouville operators with square summable potential abstract we prove that there exist some sturm liouville operators with square summable potentials such that the singular continuous component of the spectral measure lies on the positive half line the hausdorff dimension of the support of this singular measure can be arbitrary number from 0 to 1

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

wkb and spectral analysis of one dimensional schrodinger operators with slowly varying potentials consider a schrodinger operator on l 2 of the line or of a half line with appropriate boundary conditions if the potential tends to zero and is a finite sum of terms each of which has a derivative of some order in l 1 l p for some exponent p 2 then an essential support of the the absolutely continuous spectrum equals almost every generalized eigenfunction is bounded and satisfies certain wkb type asymptotics at infinity if moreover these derivatives belong to l p with respect to a weight x with 0 then the hausdorff dimension of the singular component of the spectral measure is strictly less than one

imbedded singular continuous spectrum for schrodinger operators 1 1 hv v x and some self adjoint boundary condition at zero the operator 1 1 describes a charged particle such as an electron in the electric field v x when v x is decaying quickly one expects the spectral and dynamical properties of hy to remain close to those of the free operator ho recall that with the operator 1 1 one can associate in a canonical way a spectral measure p see for example 6 2 which contains much information about the quantum system the classical result in this direction going back to the beginning of the century is that if v g l1 the spectral measure on the positive semi axis remains purely absolutely continuous in one dimension an absolutely continuous spectrum corresponds to the ballistic rate of propagation of the particle a natural question to ask is what are the critical rates of decay at which some changes in the spectral and dynamical properties of hy may happen as far as v x has any decay at all the essential spectrum coincides with 0 oo but the quality of the spectrum and dynamics may change in 1928 wigner and von neumann 27 showed that there exist potentials v x satisfying v x jsuch that hy has positive imbedded eigenvalue e 1 this is a purely quantum resonance phenomenon since v can be chosen arbitrarily small and the bound state originates from long range correlations in the potential rather than the usual confining effect naboko 17 and simon 25 provided constructions which show that much more drastic changes are possible if the potential decays arbitrarily slower than coulomb namely for any positive function h x which grows at infinity there exist potentials v such that v x yjgand hy has a dense set of positive eigenvalues due to some recent results 3 21 it is known that the absolutely continuous spectrum on the positive semi axis is preserved for v o c l x l 2 e and in fact for v g l2 8 more precisely for such potentials the absolutely continuous part of the spectral measure iac gives positive weight to any subset of 0 oo of positive lebesgue measure therefore the naboko

numerical computation of the nonlinear feedback operators for the nonquadratic time variant optimal control problems in this paper a reliable numerical algorithm for the nonlinear feedback operators for the time variant optimal control with nonquadratic criteria is constructed our approach rests mainly on the modified adomian decomposition method the convergence of the decomposition method as applied to the synthesis equations is investigated the proposed scheme avoids the complexity provided by using other techniques

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

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

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

on the absolutely continuous spectrum of one dimensional schrodinger operators with square summable potentials for continuous and discrete one dimensional schrodinger operators with square summable potentials the absolutely continuous part of the spectrum is essentially supported by 0 and 2 2 respectively this fact is proved by considering a priori estimates for the transmission coefficient

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