on bilevel multi follower decision making general framework and solutions within the framework of any bilevel decision problem a leader s decision is influenced by the reaction of his or her follower when multiple followers who may have had a share in decision variables objectives and constraints are involved in a bilevel decision problem the leader s decision will be affected not only by the reactions of these followers but also by the relationships among these followers this paper firstly identifies nine different kinds of relationships s 1 to s 9 amongst followers by establishing a general framework for bilevel multi follower decision problems for each of the nine a corresponding bilevel multi follower decision model is then developed also this paper particularly proposes related theories focusing on an uncooperative decision problem i e s 1 model as this model is the most basic one for bilevel multi follower decision problems over the nine kinds of relationships moreover this paper extends the kuhn tucker approach for driving an optimal solution from the uncooperative decision model finally a real case study of a road network problem illustrates the application of the uncooperative bilevel decision model and the proposed extended kuhn tucker approach

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

two level linear programming decentralized planning has long been recognized as an important decision making problem many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice multilevel programming models partition control over decision variables among ordered levels within a hierarchical planning structure a planner at one level of the hierarchy may have his objective function and set of feasible decisions determined in part by other levels however his control instruments may allow him to influence the policies at other levels and thereby improve his own objective function this paper examines the special case of the two level linear programming problem geometric characterizations and algorithms are presented with some examples the goal is to demonstrate the tractability of such problems and motivate a wider interest in their study

an extended kuhn tucker approach for linear bilevel programming kuhn tucker approach has been applied with remarkable success in linear bilevel programming blp however it still has some extent unsatisfactory and incomplete one principle challenges is that it could not well handle a linear blp problem when the constraint functions at the upper level are of arbitrary linear form this paper describes theoretical foundation of kuhn tucker approach and proposes an extended kuhn tucker approach to deal with the problem the results have demonstrated that the extended kuhn tucker approach can solve a wider class of linear blp problems can than current capabilities permit

simultaneous column and row generation for large scale linear programs with column dependent rows in this paper we develop a simultaneous column and row generation algorithm that could be applied to a general class of large scale linear programming problems these problems typically arise in the context of linear programming formulations with exponentially many variables the defining property for these formulations is a set of linking constraints which are either too many to be included in the formulation directly or the full set of linking constraints can only be identified if all variables are generated explicitly due to this dependence between columns and rows we refer to this class of linear programs as problems with column dependent rows to solve these problems we need to be able to generate both columns and rows on the fly within an efficient solution approach we emphasize that the generated rows are structural constraints and distinguish our work from the branch and cut and price framework we first characterize the underlying assumptions for the proposed column and row generation algorithm these assumptions are general enough and cover all problems with column dependent rows studied in the literature up until now to the best of our knowledge we then introduce in detail a set of pricing subproblems which are used within the proposed column and row generation algorithm this is followed by a formal discussion on the optimality of the algorithm to illustrate our approach the paper is concluded by applying the proposed framework to the multi stage cutting stock and the quadratic set covering problems

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

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

surrogate constraint normalization for the set covering problem the set covering problem scp is central in a wide variety of practical applications for which finding good feasible solutions quickly often in real time is crucial surrogate constraint normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming this framework remains the core of the most effective constructive heuristics for the solution of the scp chiefly represented by the widely used chvatal method this paper introduces a number of normalization rules and demonstrates their superiority to the classical chvatal rule especially when solving large scale and real world instances directions for new advances on the creation of more elaborate normalization rules for surrogate heuristics are also provided

minimax designs for finite design regions the problem of choosing a design that is representative of a finite candidate set is an important problem in computer experiments the minimax criterion measures the degree of representativeness because it is the maximum distance of a candidate point to the design this article proposes a method for finding minimax designs for finite design regions we establish the relationship between minimax designs and the classical set covering location problem sclp in operations research which is a binary linear program in particular we prove that the set of minimax distances is the set of discontinuities of the function that maps the covering radius to the optimal objective function value we show that solving the sclp at the points of discontinuities which can be determined gives minimax designs these results are employed to design an efficient procedure for finding minimax designs for small sized candidate sets a heuristic procedure is proposed to generate near minimax designs for large candidate sets s

estimation of distribution algorithm for a class of nonlinear bilevel programming problems in this paper a novel evolutionary algorithm called estimation of distribution algorithm eda is proposed for solving a special class of nonlinear bilevel programming problems blpps in which the lower level problem is a convex programming problem for each given upper level decision this special type of blpp is transformed into a equivalent single level constrained optimization problem using the karush kuhn er conditions of the lower level problem then we propose an eda based on the statistical information of the superior candidate solutions to solve the transformed problem we stress that the new population of individuals is sampled from the probabilistic distribution of those superior solutions thus one of the main advantages of eda over most other meta heuristics is its ability to adapt the operators to the structure of the problem although adaptation in eda is usually limited by the initial choice of the probabilistic model in addition two specific rules are established in the initialization procedure to make use of the hierarchical structure of blpps and to handle the constraints moreover without requiring the differentiability of the objective function or the convexity of the search space of the equivalent problem the proposed algorithm can address nonlinear blpps with non differentiable or non convex upper level objective function and upper level constraint functions finally the proposed algorithm has been applied to 16 benchmark problem in five of these problems all of the upper level variables and lower level variables are 10 dimensional the numerical results compared with those of other methods reveal the feasibility and effectiveness of the proposed algorithm

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

optimization of limited network capacity with toll settings a non smooth optimization model is established for determining reserve capacity of a road network with toll settings optimization of limited network capacity with toll settings can be formulated as a mathematical program with equilibrium constraints mpec a quasi newton subgradient projection and contractive method qspc with global convergence is proposed numerical calculations are conducted using an example network where good results are obtained

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

selected topics in column generation dantzig wolfe decomposition and column generation devised for linear programs is a success story in large scale integer programming we outline and relate the approaches and survey mainly recent contributions not yet found in textbooks we emphasize the growing understanding of the dual point of view which has brought considerable progress to the column generation theory and practice it stimulated careful initializations sophisticated solution techniques for the restricted master problem and subproblem as well as better overall performance thus the dual perspective is an ever recurring concept in our selected topics

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

dense lattices in dimensions 27 29 we exhibit integral lattices which are denser than the laminated lattices in dimensions 27 29

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 definition of linear bilevel programming solution linear bilevel programming theory has been studied for many years by a number of researchers from different aspects yet it still remains to some extent unsatisfactory and incomplete the main challenge is how to solve a linear bilevel programming problem when the upper level s constraint functions are of arbitrary linear form this paper proposes a definition for linear bilevel programming solution the performance comparisons have demonstrated that the new model can solve a wider class of problems than current capabilities permit

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

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

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

real time vehicle rerouting problems with time windows this paper introduces and studies real time vehicle rerouting problems with time windows applicable to delivery and or pickup services that undergo service disruptions due to vehicle breakdowns in such problems one or more vehicles need to be rerouted in real time to perform uninitiated services with the objective to minimize a weighted sum of operating service cancellation and route disruption costs a lagrangian relaxation based heuristic is developed which includes an insertion based algorithm to obtain a feasible solution for the primal problem a dynamic programming based algorithm solves heuristically the shortest path problems with resource constraints that result from the lagrangian relaxation computational experiments show that the developed lagrangian heuristic performs very well

universal bound on the performance of lattice codes we present a lower bound on the probability of symbol error for maximum likelihood decoding of lattices and lattice codes on a gaussian channel the bound is tight for error probabilities and signal to noise ratios of practical interest as opposed to most existing bounds that become tight asymptotically for high signal to noise ratios the bound is also universal it provides a limit on the highest possible coding gain that may be achieved at specific symbol error probabilities using any lattice or lattice code in n dimensions in particular it is shown that the effective coding gains of the densest known lattices are much lower than their nominal coding gains the asymptotic as n spl rarr spl infin behavior of the new bound is shown to coincide with the shannon 1948 limit for gaussian channels

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

comparative tests of solution methods for signal controlled road networks in this paper we consider a signal controlled road network with link capacity expansions this network design problem can be formulated as a constrained optimization subject to equilibrium flows a projected quasi newton method is proposed to find good local optimal solutions numerical calculations are conducted using a real data road network and large scale grid networks

constrained 0 1 quadratic programming basic approaches and extensions abstract we describe the simplest technique to tackle 0 1 quadratic programs with linear constraints among those that turn out to be successful in practice this method is due to and familiar to the quadratic assignment experts even if it took some time to realize that most approaches to the problem could be interpreted in these terms whereas it does not appear to be widely known outside this community since the technique is completely general and is by far the most successful one in several other cases such as quadratic knapsack we illustrate it in its full generality pointing out its relationship to lagrangian and linear programming relaxations and discussing further extensions we believe that this method should be in the background of every practitioner in combinatorial optimization

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

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

an approximate programming method based on the simplex method for bilevel programming problem many real problems can be modeled to the problems with a hierarchical structure and bilevel programming is a useful tool to solve the hierarchical optimization problems so the bilevel programming is widely applied and numerous methods have been proposed to solve this programming in this paper we propose an approximate programming algorithm to solve bilevel nonlinear programming problem finally the example illustrates the feasibility of the proposed algorithm

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 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

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

some heuristic methods for solving p median problems with a coverage constraint abstract the aim of this paper is to solve p median problems with an additional coverage constraint these problems arise in location applications when the trade off between distance and coverage is being calculated three kinds of heuristic algorithms are developed first local search procedures are designed both for constructing and improving feasible solutions second a multistart grasp heuristic is developed based on the previous local search methods third by employing lagrangean relaxation methods a very efficient lagrangean heuristic algorithm is designed which extends the well known algorithm of handler and zang for constrained shortest path problems to constrained p median problems finally a comparison of the computational efficiency of the developed methods is made between a variety of problems of different sizes

a bm lambda cut and goal programming based algorithm for fuzzy linear multiple objective bilevel optimization bilevel programming techniques are developed to handle decentralized problems with two level decision makers which are leaders and followers who may have more than one objective to achieve this paper proposes a cut and goal programming based algorithm to solve fuzzy linear multiple objective bilevel flmob decision problems first based on the definition of a distance measure between two fuzzy vectors using cut a fuzzy linear bilevel goal flbg model is formatted and related theorems are proved then using a cut for fuzzy coefficients and a goal programming strategy for multiple objectives a cut and goal programming based algorithm to solve flmob decision problems is presented a case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm finally experiments are carried out to discuss and analyze the performance of this algorithm

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 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

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

modeling and solving the crew rostering problem the crew rostering problem crp aims at determining an optimal sequencing of a given set of duties into rosters satisfying operational constraints deriving from union contract and company regulations previous work on crp addresses mainly urban mass transit systems in which the minimum number of crews to perform the duties can easily be determined and the objective is to evenly distribute the workload among the crews in typical railway applications however the roster construction has to take into account more involved sequencing rules and the main objective is the minimization of the number of crews needed to perform the duties in this paper we propose a basic model for crp and describe a lagrangian lower bound based on the solution of an assignment problem on a suitably defined graph the information obtained through the lower bound computation is used to drive an effective algorithm for finding a tight approximate solution to the problem computational results for real world instances from railway applications involving up to 1 000 duties are presented showing that the proposed approach yields within short computing time lower and upper bound values that are typically very close the code based on the approach we propose won the faro competition organized by the italian railway company ferrovie dello stato spa in 1995

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