adaptive steganalysis of least significant bit replacement in grayscale natural images this paper deals with the detection of hidden bits in the least significant bit lsb plane of a natural image the mean level and the covariance matrix of the image considered as a quantized gaussian random matrix are unknown an adaptive statistical test is designed such that its probability distribution is always independent of the unknown image parameters while ensuring a high probability of hidden bits detection this test is based on the likelihood ratio test except that the unknown parameters are replaced by estimates based on a local linear regression model it is shown that this test maximizes the probability of detection as the image size becomes arbitrarily large and the quantization step vanishes this provides an asymptotic upper bound for the detection of hidden bits based on the lsb replacement mechanism numerical results on real natural images show the relevance of the method and the sharpness of the asymptotic expression for the probability of detection

on the relationship between combinatorial and lp based lower bounds for np hard scheduling problems enumerative approaches to solving optimization problems such as branch and bound require a subroutine that produces a lower bound on the value of the optimal solution in the domain of scheduling problems the requisite lower bound has typically been derived from either the solution to a linear programming lp relaxation of the problem or the solution to a combinatorial relaxation in this paper we investigate from a theoretical perspective the relationship between several lp based lower bounds and combinatorial lower bounds for three scheduling problems in which the goal is to minimize the average weighted completion time of the jobs scheduled we establish a number of facts about the relationship between these different sorts of lower bounds including the equivalence of certain lp based lower bounds for these problems to combinatorial lower bounds used in successful branch and bound algorithms as a result we obtain the first worst case analysis of the quality of the lower bounds delivered by these combinatorial relaxations

aggregation and mixed integer rounding to solve mips in this paper we discuss the use of mixed integer rounding mir inequalities to solve mixed integer programs mir inequalities are essentially gomory mixed integer cuts however as we wish to use problem structure we insist that mir inequalities be generated from constraints or simple aggregations of constraints of the original problem this idea is motivated by the observation that several strong valid inequalities based on specific problem structure can be derived as mir inequalities here we present and test a separation routine for such mir inequalities that includes a heuristic row aggregation procedure to generate a single knapsack plus continuous variables constraint complementation of variables and finally the generation of an mir inequality inserted in a branch and cut system the results suggest that such a routine is a useful additional tool for tackling a variety of mixed integer programming problems

capacitated facility location separation algorithms and computational experience we consider the polyhedral approach to solving the capacitated facility location problem the valid inequalities considered are the knapsack cover flow cover effective capacity single depot and combinatorial inequalities the flow cover effective capacity and single depot inequalities form subfamilies of the general family of submodular inequalities the separation problem based on the family of submodular inequalities is np hard in general for the well known subclass of flow cover inequalities however we show that if the client set is fixed and if all capacities are equal then the separation problem can be solved in polynomial time for the flow cover inequalities based on an arbitrary client set and general capacities and for the effective capacity and single depot inequalities we develop separation heuristics an important part of these heuristics is based on the result that two specific conditions are necessary for the effective cover inequalities to be facet defining the way these results are stated indicates precisely how structures that violate the two conditions can be modified to produce stronger inequalities the family of combinatorial inequalities was originally developed for the uncapacitated facility location problem but is also valid for the capacitated problem no computational experience using the combinatorial inequalities has been reported so far here we suggest how partial output from the heuristic identifying violated submodular inequalities can be used as input to a heuristic identifying violated combinatorial inequalities we report on computational results from solving 60 medium size problems

a multi item production planning model with setup times algorithms reformulations and polyhedral characterizations for a special case we study a special case of a structured mixed integer programming model that arises in production planning for the most general case of the model called pi we have earlier identified families of facet defining valid inequalities l s inequalities introduced for the uncapacitated lot sizing problem by barany van roy and wolsey cover inequalities and reverse cover inequalities pi is hard in this paper we focus on a special case called pic we describe a polynomial algorithm for pic and we use this algorithm to derive an extended formulation of polynomial size for pic projecting from this extended formulation onto the original space of variables we show that l s inequalities cover inequalities and reverse cover inequalities suffice to solve the special case pic by linear programming we also describe fast combinatorial separation algorithms for cover and reverse cover inequalities for pic finally we discuss the relationship between our results for pic and a model studied previously by goemans

a time indexed formulation of non preemptive single machine scheduling problems we consider the formulation of non preemptive single machine scheduling problems using time indexed variables this approach leads to very large models but gives better lower bounds than other mixed integer programming formulations we derive a variety of valid inequalities and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities a cutting plane branch and bound algorithm based on these inequalities has been implemented computational experience on small problems with 20 30 jobs and various constraints and objective functions is presented

on the equivalence of the max min transportation lower bound and the time indexed lower bound for single machine scheduling problems new observations are made about two lower bound schemes for single machine min sum scheduling problems we find that the strongest bound of those provided by transportation problem relaxations can be computed by solving a linear program we show the equivalence of this strongest bound and the bound provided by the lp relaxation of the time indexed integer programming formulation these observations lead to a new lower bound scheme that yields fast approximation of the time indexed bound several techniques are developed to facilitate the effective use of the new lower bound in branch and bound numerical experiments are conducted on 375 benchmark problems of the total weighted tardiness problem from or library results obtained with our new method are spectacular we are able to solve all 125 open problems to optimality

the teacher assignment problem a special case of the fixed charge transportation problem a basic model of the task of assigning classes to professors in such a way that the average number of distinct subjects assigned to each professor is minimized is formulated as a mixed integer program it turns out that the problem is a special case of the fixed charge transportation problem which in some cases corresponds to finding a basic solution of a transportation problem which is as degenerate as possible we present an equivalent alternative formulation of the problem which makes it easy to prove that it is np hard in the strong sense and an exact branch and bound algorithm for its solution based on this alternative formulation is outlined computational experiments with data from a concrete problem concludes the paper

scheduling to minimize average completion time off line and on line approximation algorithms in this paper we introduce two general techniques for the design and analysis of approximation algorithms for np hard scheduling problems in which the objective is to minimize the weighted sum of the job completion times for a variety of scheduling models these techniques yield the first algorithms that are guaranteed to find schedules that have objective function value within a constant factor of the optimum in the first approach we use an optimal solution to a linear programming relaxation in order to guide a simple list scheduling rule consequently we also obtain results about the strength of the relaxation our second approach yields on line algorithms for these problems in this setting we are scheduling jobs that continually arrive to be processed and for each time t we must construct the schedule until time t without any knowledge of the jobs that will arrive afterwards our on line technique yields constant performance guarantees for a variety of scheduling environments and in some cases essentially matches the performance of our off line lp based algorithms

subset coefficient reduction cuts for 0 1 mixed integer programming we describe a method for generating cuts for mixed integer 0 1 programs these cuts are designed to tighten an integer program prior to applying linear programming based branch and bound algorithms the method involves two basic ideas subset selection and coefficient reduction coefficient reduction is a process of reducing the coefficients of the 0 1 variables subset selection is combined with coefficient reduction by applying the coefficient reduction process to the coefficients of a subset of variables from the constraints in the problem formulation the paper exploits these two simple ideas to derive a broad class of cuts for integer programs with both 0 1 and continuous variables it also reports on the use of this methodology in solving a variety of fixed charge problems

separation algorithms for 0 1 knapsack polytopes valid inequalities for 0 1 knapsack polytopes often prove useful when tackling hard 0 1 linear programming problems to generate such inequalities one needs separation algorithms for them i e routines for detecting when they are violated we present new exact and heuristic separation algorithms for several classes of inequalities namely lifted cover extended cover weight and lifted pack inequalities moreover we show how to improve a recent separation algorithm for the 0 1 knapsack polytope itself extensive computational results on miplib and or library instances show the strengths and limitations of the inequalities and algorithms considered

reconstruction from projections based on detection and estimation of objects parts i and ii performance analysis and robustness analysis the problem of reconstructing a multidimensional field from noisy limited projection measurements is approached using an object based stochastic field model objects within a cross section are characterized by a finite dimensional set of parameters which are estimated directly from limited noisy projection measurements using maximum likelihood estimation in part i the computational structure and performance of the ml estimation procedure are investigated for the problem of locating a single object in a deterministic background simulations are also presented in part ii the issue of robustness to modeling errors is addressed

the merchant subtour problem we consider the problem of a travelling merchant who makes money by buying commodities where they are cheap and selling them in other places where he can make a profit the merchant ships commodities of his own choice in a van of fixed capacity given the prices of all the commodities in all of the places and the cost of driving from one place to another the problem the merchant faces each day is to select a subset of the cities that he can visit in a day and to determine the order in which the cities are visited such that the total profit is maximised we call this problem the merchant subtour problem the msp models the pricing problem of a rather complex pickup and delivery problem that was given to us by the dutch logistics company van gend loos we show that a special case of the msp has a totally unimodular constraint matrix this knowledge enables us to develop a tabu search algorithm for finding good feasible solutions to the msp and a branch and price and cut algorithm for solving the msp to optimality the relaxations solved in each node of the branch and bound tree are strengthened by lifted knapsack inequalities lifted cycle inequalities and mod k cuts we present computational results on data sets derived from our main instance of the van gend loos pickup and delivery problem

subdiffusion in a bounded domain with a partially absorbing reflecting boundary the exit time of a subdiffusive process from a bounded domain with a partially absorbing reflecting boundary is considered the short time and long time behaviors of the exit time probability density are investigated by using a spectral decomposition on the basis of the laplace operator eigenfunctions rotation invariant domains are analyzed in depth in order to illustrate the use of theoretical formulas and to compare them to numerical simulations the asymptotic results obtained are relevant for describing subdiffusion inside a living cell with a semipermeable membrane in a chemical reactor filled with catalytic grains of finite reactivity or in mineral or biological samples which are probed by nuclear magnetic resonance measurements subject to surface relaxation

hybrid optimization methods for time dependent sequencing problems abstract in this paper we introduce novel optimization methods for sequencing problems in which the setup times between a pair of tasks depend on the relative position of the tasks in the ordering our proposed methods rely on a hybrid approach where a constraint programming model is enhanced with two distinct relaxations one discrete relaxation based on multivalued decision diagrams and one continuous relaxation based on linear programming both relaxations are used to generate bounds and enhance constraint propagation experiments conducted on three variants of the time dependent traveling salesman problem indicate that our techniques substantially outperform general purpose methods such as mixed integer linear programming and constraint programming models

generating cuts in integer programming with families of special ordered sets abstract this paper describes families of cuts which can be added to integer programming formulations incorporating special ordered sets ways in which the cuts can be used are discussed and some computational experience is presented

survival probability of diffusion with trapping in cellular neurobiology the problem of diffusion with absorption and trapping sites arises in the theory of molecular signaling inside and on the membranes of biological cells in particular this problem arises in the case of spine dendrite communication where the number of calcium ions modeled as random particles is regulated across the spine microstructure by pumps which play the role of killing sites while the end of the dendritic shaft is an absorbing boundary we develop a general mathematical framework for diffusion in the presence of absorption and killing sites and apply it to the computation of the time dependent survival probability of ions we also compute the ratio of the number of absorbed particles at a specific location to the number of killed particles we show that the ratio depends on the distribution of killing sites the biological consequence is that the position of the pumps regulates the fraction of calcium ions that reach the dendrite

the 0 1 knapsack problem with a single continuous variable constraints arising in practice often contain many 0 1 variables and one or a small number of continuous variables existing knapsack separation routines cannot be used on such constraints here we study such constraint sets and derive valid inequalities that can be used as cats for such sets as well for more general mixed 0 1 constraints specifically we investigate the polyhedral structure of the knapsack problem with a single continuous variable called the mixed 0 1 knapsack problem first different classes of facet defining inequalities are derived based on restriction and lifting the order of lifting particularly of the continuous variable plays an important role secondly we show that the flow cover inequalities derived for the single node flow set consisting of are flows into and out of a single node with binary variable lower and upper bounds on each are can be obtained from valid inequalities for the mixed 0 1 knapsack problem thus the separation heuristic we derive for mixed knapsack sets can also be used to derive cuts for more general mixed 0 1 constraints initial computational results on a variety of problems are presented

default risk modeling with position dependent killing abstract diffusion in a linear potential in the presence of position dependent killing is used to mimic a default process different assumptions regarding transport coefficients initial conditions and elasticity of the killing measure lead to diverse models of bankruptcy one stylized fact is fundamental for our consideration empirically default is a rather rare event especially in the investment grade categories of credit ratings hence the action of killing may be considered as a small parameter in a number of special cases we derive closed form expressions for the entire term structure of the cumulative probability of default its hazard rate and intensity comparison with historical data on aggregate global corporate defaults confirms the validity of the perturbation method for estimations of long term probability of default for companies with high credit quality on a single company level we implement the derived formulas to estimate the one year likelihood of default of enron on a daily basis from august 2000 to august 2001 three months before its default and compare the obtained results with forecasts of traditional structural models

o n log n procedures for tightening cover inequalities abstract we present two procedures for tightening cover induced inequalities in 0 1 programs by using knapsack constraints plus some other information from the program the tightening is obtained by solving successive knapsack problems with all 0 1 objective function coefficients and using dominance criteria to avoid the explicit solving of some knapsack problems the new constraints are 0 1 equivalent to and lp tighter than the original ones both procedures have o n log n complexity where n is the number of variables with nonzero coefficients in the knapsack constraint however one of them can strongly reduce the computational effort some computational experience is reported

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

three dimensional reconstruction from projections with incomplete and noisy data by object estimation an estimation approach to three dimensional reconstruction from parallel ray projections with incomplete and very noisy data is described using a stochastic dynamic model for an object of interest in a probed domain of known background density the reconstruction problem is reformulated as a n onlinear state estimation problem an approximate minimum mean square error globally optimal algorithm for the solution of this problem is presented the algorithm which is recursive in a hybrid frequency space domain operates directly on the fourier transformed projection data eliminating altogether the attempt to invert the projection integral equation the simulation example considered in this paper demonstrates that good object estimates may be obtained with as few as five views in a limited sector of 90 and at a signal to noise ratio as low as 0 db

constrained epsilon minimax test for simultaneous detection and classification a constrained epsilon minimax test is proposed to detect and classify nonorthogonal vectors in gaussian noise with a general covariance matrix and in presence of linear interferences this test is epsilon minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability this loss is even more negligible as the signal to noise ratio is large furthermore it is also an epsilon equalizer test since its classification error probabilities are equalized up to a negligible difference when the signal to noise ratio is sufficiently large an asymptotically equivalent test with a very simple form is proposed this equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of euclidean distance numerical experiments on active user identification in a multiuser system confirm the theoretical findings

lot size models with back logging strong reformulations and cutting planes we examine mixed integer programming reformulations of the uncapacitated lot sizing problem with backlogging first we consider the effect of using a standard reformulation technique for fixed charge network flow problems which involves the introduction of new variables leading to a known plant location reformulation and a shortest path reformulation each of these reformulations is strong in the sense that its linear programming relaxation solves the lot sizing problem secondly we attempt to treat the problem in the space of the original variables we give an implicit description of the convex hull of solutions and show how the problem of finding a violated cutting plane can be solved as a linear program we also describe a family of strong valid inequalities which can be generated rapidly by a heuristic and which have proved effective in a cut generation algorithm the efficiency of both the shortest path formulation and the cutting plane algorithm have been tested on a series of multi item capacitated lot sizing problems with backlogging near optimal solutions have been found to problems with 8 periods and up to 100 times

asymptotically uniformly minimax detection and isolation in network monitoring this paper addresses the problem of multiple hypothesis testing detection and isolation of mean vectors in the case of gaussian linear model with nuisance parameters an invariant constrained asymptotically uniformly minimax test is proposed to solve this problem the invariance of the test with respect to the nuisance parameters is obtained by projecting the measurement vector onto a subspace of invariant statistics the proposed test minimizes the maximum probability of false isolation uniformly with respect to the lower bounded projections of the vectors defining the alternative hypotheses this minimization is achieved provided that the signal to noise ratio snr becomes arbitrary large the asymptotic probabilities of false alarm and false isolations and their nonasymptotic bounds are analytically established to illustrate the practical relevance of the proposed test it is applied to the problem of network monitoring it is aimed to detect and isolate volume anomalies in network origin destination od traffic demands from simple link load measurements the ambient traffic i e the od traffic matrix corresponding to the nonanomalous network state is unknown and considered as a nuisance parameter an original linear parsimonious model of the ambient traffic which is indispensable for the proposed asymptotically optimal test is designed the statistical performances of this approach to detect and isolate the anomalies are evaluated by using real data from the abilene network

solving multi item lot sizing problems using strong cutting planes we consider two classes of multi item lot sizing problems the first is a class of single stage problems involving joint machine capacity constraints and or start up costs and the second is a class of multistage problems with general product structure the problems are solved as mixed integer programs based on i an appropriate choice of the initial problem formulation and ii the addition of cuts which are generated automatically by a mathematical programming system mpsarx our results extend and complement those of karmarkar and schrage 1985 afentakis and gavish 1986 eppen and martin 1987 and van roy and wolsey 1987 a major advantage of this approach is its robustness or flexibility by using just a matrix generator and a mathematical programming system with automatic cut generation routines we can formulate and solve model variants without incurring the costs of adapting an algorithm

using lagrangean techniques to solve hierarchical production planning problems this paper proposes and tests a procedure for decomposing a large scale production planning problem modeled as a mixed integer linear program we interpret this decomposition in the context of hax and meal s hierarchical framework for production planning the procedure decomposes the production planning problem into two subproblems which correspond to the aggregate planning subproblem and a disaggregation subproblem in the hax meal framework the linking mechanism for these two subproblems is an inventory consistency relationship which is priced out by a set of lagrange multipliers the best values for the multipliers are found by an iterative procedure which may be interpreted as a feedback mechanism in the hax meal framework at each iteration the procedure finds both a lower bound on the optimal value to the production planning problem and a feasible solution from which an upper bound is obtained our computational tests show that the best feasible solution found from this procedure is very close to o

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

single machine scheduling polyhedra with precedence constraints we consider nonpreemptive single machine scheduling subject to precedence constraints we define feasible schedules by the vector of the job completion times and study the structure of the convex hull of all feasible schedules called the scheduling polyhedron p we derive classes of valid inequalities for p and necessary and sufficient conditions under which they are facet inducing our main result is a complete description of the minimal linear system defining p when the precedence constraints are series parallel moreover this system consists of two classes of facet inducing inequalities associated with series and parallel compositions respectively if the precedence constraints are not series parallel we present another class of facet inducing inequalities for p associated with induced z subgraphs we also show that the convex hull of all preemptive feasible schedules is identical to p if and only if the precedence constraints form an out forest

mixed 0 1 programming by lift and project in a branch and cut framework we investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0 1 programs into a branch and cut framework the cuts we use are of the lift and project variety some of the issues addressed have a theoretical answer but others are of an experimental nature and are settled by comparing alternatives on a set of test problems the resulting code is a robust solver for mixed 0 1 programs we compare it with several existing codes on a wide range of test problems it performs as well as or better than some of the best currently available mixed integer programming codes

valid linear inequalities for fixed charge problems many problems in the operations research management science literature can be formulated with both zero one and continuous variables however the exact optimization of such mixed zero one models remains a computational challenge in this paper we propose to study mixed problems from a mathematical point of view that is similar in spirit to recent research on purely combinatorial problems that has investigated systems of defining linear inequalities or facets of the underlying polytope at least two numerical studies have validated this line of research computationally and the advances in the problem solving capabilities are considerable we expect that similar gains are possible for the mixed zero one problem more precisely we consider the mixed integer programs whose feasible region x is composed of i a simple additive constraint in the continuous variables xj for j 1 2 n and ii constraints 0 xj mjyj defined by binary variables yj for j 1 2 n this type of feasible region arises in a variety of mixed integer problems and particularly in network problems with fixed charges on the arcs we derive two classes of facet defining linear inequalities of the convex hull of x and show that the second of these classes gives a complete description of the convex hull when mj m for all j we also develop methods to detect violated inequalities from these classes so that these facets can be used as cutting planes to strengthen the formulations of certain mixed integer problems

structure of a simple scheduling polyhedron in a one machine nonpreemptive scheduling problem the feasible schedules may be defined by the vector of the corresponding job completion times for given positive processing times the associated simple scheduling polyhedronp is the convex hull of these feasible completion time vectors the main result of this paper is a complete description of the minimal linear system definingp we also give a complete combinatorial description of the face lattice ofp and a simple o n logn separation algorithm this algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems

dynamic knapsack sets and capacitated lot sizing a dynamic knapsack set is a natural generalization of the 0 1 knapsack set with a continuous variable studied recently for dynamic knapsack sets a large family of facet defining inequalities called dynamic knapsack inequalities are derived by fixing variables to one and then lifting surprisingly such inequalities have the simultaneous lifting property and for small instances provide a significant proportion of all the facet defining inequalities we then consider single item capacitated lot sizing problems and propose the joint study of three related sets the first models the discrete lotsizing problem the second the continuous lot sizing problem with wagnerwhitin costs and the third the continuous lot sizing problem with arbitrary costs the first set that arises is precisely a dynamic knapsack set the second an intersection of dynamic knapsack sets and the unrestricted problem can be viewed as both a relaxation and a restriction of the second it follows that the dynamic knapsack inequalities and their generalizations provide strong valid inequalities for all three sets some limited computation results are reported as an initial test of the effectiveness of these inequalities on capacitated lot sizing problems

s3 sets an extension of the beale tomlin special ordered sets in this work an extension of the beale tomlin special ordered sets is introduced that has proved to be efficient for solving certain types of open shop scheduling problems besides their usual characteristics exclusivity constraints in the jobs are allowed more general than tree like precedence structures are considered and semi active schedules that cannot be labeled as non optimal solutions may occur the problem is formulated as a large scale 0 1 model computational experience on some real life problems is reported

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

non bayesian detection and detectability of anomalies from a few noisy tomographic projections the detection of an anomaly from a few noisy tomographic projections is addressed from the statistical point of view an unknown scene is composed of a background considered as a deterministic nuisance parameter with a possibly hidden anomaly because the full pixel by pixel reconstruction is impossible a parametric non bayesian approach is proposed to fill up the gap in the missing data an optimal statistical test which eliminates the background and detects the anomaly is designed the potential advantage of such an approach is its capacity to detect an anomaly target hidden in background designed by an adversary to mask the anomaly a key issue in the non bayesian anomaly detection i e the problem of anomaly detectability is stated and solved in this paper in the case of a bivariate polynomial background defined on an unknown rectangular support the size of detectable anomaly reaches its maximum defined by the number of elementary cells of x ray detector and degree of the polynomial function

agent preferences and the topology of networks in this paper a different framework to study weighed networks is introduced the idea behind this methodology is to consider that each node of the network is an agent that desires to satisfy his her preferences in an economic sense moreover the formation of a link between two agents depends on the benefits and costs associated with this link therefore an edge between two given nodes will arise only if the tradeoff between satisfaction and cost for building it is jointly positive using a computational framework i intend to show that depending on the agents combination of benefits and costs some very well known networks can naturally arise

a polyhedral study of the cardinality constrained knapsack problem a cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive this structure occurs for example in areas such as finance location and scheduling traditionally cardinality constraints are modeled by introducing auxiliary 0 1 variables and additional constraints that relate the continuous and the 0 1 variables we use an alternative approach in which we keep in the model only the continuous variables and we enforce the cardinality constraint through a specialized branching scheme and the use of strong inequalities valid for the convex hull of the feasible set in the space of the continuous variables to derive the valid inequalities we extend the concepts of cover and cover inequality commonly used in 0 1 programming to this class of problems and we show how cover inequalities can be lifted to derive facet defining inequalities we present three families of non trivial facet defining inequalities that are lifted cover inequalities finally we report computational results that demonstrate the effectiveness of lifted cover inequalities and the superiority of the approach of not introducing auxiliary 0 1 variables over the traditional mip approach for this class of problems

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

a multiscale hypothesis testing approach to anomaly detection and localization from noisy tomographic data in this paper we investigate the problems of anomaly detection and localization from noisy tomographic data these are characteristic of a class of problems that cannot be optimally solved because they involve hypothesis testing over hypothesis spaces with extremely large cardinality our multiscale hypothesis testing approach addresses the key issues associated with this class of problems a multiscale hypothesis test is a hierarchical sequence of composite hypothesis tests that discards large portions of the hypothesis space with minimal computational burden and zooms in on the likely true hypothesis for the anomaly detection and localization problems hypothesis zooming corresponds to spatial zooming anomalies are successively localized to finer and finer spatial scales the key challenges we address include how to hierarchically divide a large hypothesis space and how to process the data at each stage of the hierarchy to decide which parts of the hypothesis space deserve more attention for the latter we pose and solve a nonlinear optimization problem for a decision statistic that maximally disambiguates composite hypotheses with no more computational complexity our optimized statistic shows substantial improvement over conventional approaches we provide examples that demonstrate this and quantify how much performance is sacrificed by the use of a suboptimal method as compared to that achievable if the optimal approach were computationally feasible

the ill conditioned nature of the limited angle tomography problem the instability of inverting the limited angle radon transform is studied by constructing the singular value decomposition of this operator connections are established with previously known series expansions and with the discrete prolate spheroidal wave functions mollification methods are shown to delay but not prevent the onset of instability as the angular range of projections is decreased

optimization and universality of brownian search in a basic model of quenched heterogeneous media the kinetics of a variety of transport controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time the so called mean first passage time mfpt problem the occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the mfpt by reducing oversampling of space here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension in a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity the mfpt is analyzed under the constraint of conserved average dynamics that is the spatially averaged diffusivity is kept constant our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the mfpt to the target we prove that the mfpt for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality in contrast to intermittent strategies which are most profitable in low spatial dimensions the spatially inhomogeneous search performs best in higher dimensions discussing our results alongside recent experiments on single particle tracking in living cells we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes

on the polyhedral structure of a multi item production planning model with setup times we present and study a mixed integer programming model that arises as a substructure in many industrial applications this model generalizes a number of structured mip models previously studied and it provides a relaxation of various capacitated production planning problems and other fixed charge network flow problems we analyze the polyhedral structure of the convex hull of this model as well as of a strengthened lp relaxation among other results we present valid inequalities that induce facets of the convex hull under certain conditions we also discuss how to strengthen these inequalities by using known results for lifting valid inequalities for 0 1 continuous knapsack problems

solving mixed integer programming problems using automatic reformulation in this paper we describe computational experience in solving mixed 0 1 programming problems using strong valid inequalities as cutting planes in particular we report on the solution to optimality of 18 medium to large size problems including production planning problems with setup costs and capacity constraints multilevel distribution planning problems drainage and heating system design problems and electricity generator scheduling problems the solution approach uses the theory of strong valid inequalities that we developed in a series of earlier papers here we report specifically on the implementation of an experimental system mpsarx which consists of the sciconic mathematical programming system and an automatic reformulation executor arx that use this theory and on the results obtained with this system

railroad blocking a network design application in this study we formulate the railroad blocking problems as a network design problem with maximum degree and flow constraints on the nodes and propose a heuristic lagrangian relaxation approach to solve the problem the newapproach decomposes the complicated mixed integer programming problem into two simple subproblems so that the storage requirement and computational effort are greatly reduced a set of inequalities are added to one subproblem to tighten the lower bounds and facilitate generating feasible solutions subgradient optimization is used to solve the lagrangian dual an advanced dual feasible solution is generated to speed up the convergence of the subgradient method the model is tested on blocking problems from a major railroad and the results show that the blocking plans generated have the potential to reduce the railroad s operating costs by millions of dollars annually

modeling and solving the two facility capacitated network loading problem this paper studies a topical and economically significant capacitated network design problem that arises in the telecommunications industry in this problem given point to point communication demand in a network must be met by installing loading capacitated facilities on the arcs loading a facility incurs an arc specific and facility dependent cost this paper develops modeling and solution approaches for loading facilities to satisfy the given demand at minimum cost we consider two approaches for solving the underlying mixed integer program a lagrangian relaxation strategy and a cutting plane approach that uses three classes of valid inequalities that we identify for the problem we show that a linear programming formulation that includes these inequalities always approximates the value of the mixed integer program at least as well as the lagrangian relaxation bound our computational results on a set of prototypical telecommunication data show that including these inequalities considerably improves the gap between the integer programming formulation and its linear programming relaxation from an average of 25 to an average of 8 these results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry

using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems we propose an interactive approach for multiple objective integer linear programming moilp problems that combines the use of the tchebycheff metric with cutting plane techniques at each interaction the method computes the nondominated solution for the moilp problem that is closest to a reference point according to the tchebycheff metric the information provided by the decision maker in each dialogue phase is used to adjust the next reference point through a sensitivity analysis stage cutting plane techniques enable the method to take advantage of computations performed at previous iterations to solve the next scalarizing integer program we address both theoretical issues and the computational implementation

different transformations for solving non convex trim loss problems by minlp in the present paper trim loss problems often named the cutting stock problem connected to the paper industry are considered the problem is to cut out a set of product paper rolls from raw paper rolls such that the cost function including the trim loss as well as the costs for the over production is minimized the problem is non convex due to certain bilinear constraints the problem can however be transformed into linear or convex form the resulting transformed problems can thereafter be solved as mixed integer linear programming problems or convex mixed integer non linear programming problems the linear and convex formulations are attractive from a formal point of view since global optimal solutions to the originally non convex problem can be obtained however as the examples considered will show the numerical efficiency of the solutions from the different transformed formulations varies considerably an example based on a trim optimization problem encountered daily at a finnish paper converting mill is finally presented in order to demonstrate differences in the numerical solutions

cutting planes for integer programs with general integer variables we investigate the use of cutting planes for integer programs with general integer variables we show how cutting planes arising from knapsack inequalities can be generated and lifted as in the case of 0 1 variables we also explore the use of gomory s mixed integer cuts we address both theoretical and computational issues and show how to embed these cutting planes in a branch and bound framework we compare results obtained by using our cut generation routines in two existing systems with a commercially available branch and bound code on a range of test problems arising from practical applications 1998 the mathematical programming society inc published by elsevier science b v

effective heuristics for multiproduct partial shipment models motivated by real applications we consider the problem of shipping products to multiple customers from limited inventory after formulating the optimization problems under different restrictions on partial shipments we find that commercially available packages applied directly are unsatisfactory as are simple greedy approaches we develop a scheme of heuristics that enables the user to select a good balance between computation time and effectiveness a detailed computational study of one and two period industrial sized problems indicates that these heuristics are computationally practical and generate solutions that are on average within 34 of the optimum

letter to the editor an efficient linearization technique for mixed 0 1 polynomial problem this paper addresses a new and efficient linearization technique to solve mixed 0 1 polynomial problems to achieve a global optimal solution given a mixed 0 1 polynomial term z c tx 1x 2 x ny where x 1 x 2 x n are binary 0 1 variables and y is a continuous variable also c t can be either a positive or a negative parameter we transform z into a set of auxiliary constraints which are linear and can be solved by exact methods such as branch and bound algorithms for this purpose we will introduce a method in which the number of additional constraints is decreased significantly rather than the previous methods proposed in the literature as is known in any operations research problem decreasing the number of constraints leads to decreasing the mathematical computations extensively thus research on the reducing number of constraints in mathematical problems in complicated situations have high priority for decision makers in this method each n auxiliary constraints proposed in the last method in the literature for the linearization problem will be replaced by only 3 novel constraints in other words previous methods were dependent on the number of 0 1 variables and therefore one auxiliary constraint was considered per 0 1 variable but this method is completely independent of the number of 0 1 variables and this illustrates the high performance of this method in computation considerations the analysis of this method illustrates the efficiency of the proposed algorithm

random distortion testing and optimality of thresholding tests this paper addresses the problem of testing whether the mahalanobis distance between a random signal and a known deterministic model 0 exceeds some given non negative real number or not when has unknown probability distribution and is observed in additive independent gaussian noise with positive definite covariance matrix when is deterministic unknown we prove the existence of thresholding tests on the mahalanobis distance to 0 that have specified level and maximal constant power mcp the mcp property is a new optimality criterion involving wald s notion of tests with uniformly best constant power ubcp on ellipsoids for testing the mean of a normal distribution when the signal is random with unknown distribution constant power maximality extends to maximal constant conditional power mccp and the thresholding tests on the mahalanobis distance to 0 still verify this novel optimality property our results apply to the detection of signals in independent and additive gaussian noise in particular for a large class of possible model mismatches mccp tests can guarantee a specified false alarm probability in contrast to standard neyman pearson tests that may not respect this constraint

fixed charge transportation problem facets of the projection polyhedron in this paper we consider the well known fixed charge transportation problem to send any flow from source si to destination tj we incur a unit variable shipping cost of cij and a fixed cost fij here we study the structure of the projection polyhedron of this problem in the space of 0 1 variables associated with fixed charges and we develop several classes of valid inequalities and derive conditions under which they are facet defining in some cases if the conditions are not satisfied we show how they can be lifted to define facets several heuristics for generating and adding these facets are presented using these results we develop a computationally effective algorithm for solving the problem the computational results clearly indicate the usefulness of this approach

valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems multicommodity extended formulations of single source uncapacitated fixed charge network flow problems have significantly sharper linear programming relaxations than the standard flow formulations however the tradeoff is the introduction of many new constraints and variables to accomodate a sink oriented flow disaggregation in this paper we introduce a new family of dicut collection inequalities and show that they completely describe the projection of the multicommodity formulation onto the original variables a simple subclass is seen to include a variety of known inequalities for particular models and combinatorial separation is examined for some special cases

a lagrangean relax and cut approach for the two stage capacitated facility location problem abstract the two stage capacitated facility location problem is to find the optimal locations of depots to serve customers with a given demand the optimal assignment of customers to depots and the optimal product flow from plants to depots in order to solve this problem a lagrangean heuristic is proposed which is based on the relaxation of the capacity constraints the resulting lagrangean subproblem is an uncapacitated facility location problem with an aggregate capacity constraint and can be solved efficiently by branch and bound methods the best bound available from this relaxation is computed by means of a weighted dantzig wolfe decomposition approach feasible solutions are constructed from those of the lagrangean subproblems by applying simple reassignment procedures furthermore the relaxation is strengthened by adding and dualizing valid inequalities which are violated by the fractional primal solution of the dual master program computational results and comparisons with some other bounds and heuristics for this problem are presented

progressive interval heuristics for multi item capacitated lot sizing problems we consider a family of n items that are produced in or obtained from the same production facility demands are deterministic for each item and each period within a given horizon of t periods if in a given period an order is placed setup costs are incurred the aggregate order size is constrained by a capacity limit the objective is to find a lot sizing strategy that satisfies the demands for all items over the entire horizon without backlogging and that minimizes the sum of inventory carrying costs fixed order costs and variable order costs all demands cost parameters and capacity limits may be time dependent in the basic joint setup cost js model the setup cost of an order does not depend on the composition of the order the joint and item dependent setup cost jis model allows for item dependent setup costs in addition to the joint setup costs we develop and analyze a class of so called progressive interval heuristics a progessive interval heuristic solves a js or jis problem over a progressively larger time interval always starting with period 1 but fixing the setup variables of a progressively larger number of periods at their optimal values in earlier iterations different variants in this class of heuristics allow for different degrees of flexibility in adjusting continuous variables determined in earlier iterations of the algorithm for the js model and the two basic implementations of the progressive interval heuristics we show under some mild parameter conditions that the heuristics can be designed to be e optimal for any desired value of e 0 with a running time that is polynomially bounded in the size of the problem they can also be designed to be simultaneously asymptotically optimal and polynomially bounded a numerical study covering both the js and jis models shows that a progressive interval heuristic generates close to optimal solutions with modest computational effort and that it can be effectively used to solve large scale problems

lifted flow cover inequalities for mixed 0 1 integer programs we investigate strong inequalities for mixed 0 1 integer programs derived from flow cover inequalities flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities however because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients lifting of flow cover inequalities is computationally very demanding we present a computationally efficient way to lift flow cover inequalities based on sequence independent lifting techniques and give computational results that show the effectiveness of our lifting procedures

the relation of time indexed formulations of single machine scheduling problems to the node packing problem the relation of time indexed formulations of nonpreemptive single machine scheduling problems to the node packing problem is established and then used to provide simple and intuitive alternate proofs of validity and maximality for previously known results on the facial structure of the scheduling problem previous work on the facial structure has focused on describing the convex hull of the set of feasible partial schedules schedules in which not all jobs have to be started the equivalence between the characteristic vectors of this set and those of the set of feasible node packings in a graph whose structure is determined by the parameters of the scheduling problem is established the main contribution of this paper is to show that the facet inducing inequalities for the convex hull of the set of feasible partial schedules that have integral coefficients and right hand side 1 or 2 are the maximal clique inequalities and the maximally and sequentially lifted 5 hole inequalities of the convex hull of the set of feasible node packings in this graph respectively

strong formulations for mixed integer programming a survey we attempt to motivate and survey recent research on the use of strong valid inequalities and reformulation to solve mixed integer programming problems

fixed charge transportation on a path optimization lp formulations and separation in the fixed charge transportation problem the goal is to optimally transport goods from depots to clients when there is a fixed cost associated to transportation or equivalently to opening an arc in the underlying bipartite graph we further motivate its study by showing that it is both a special case and a strong relaxation of the big bucket multi item lot sizing problem and a generalization of a simple variant of the single node flow set this paper is essentially a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path we give a mathcal o n 3 time optimization algorithm and a mathcal o n 2 size linear programming extended formulation we describe a new class of inequalities that we call path modular inequalities we give two distinct proofs of their validity the first one is direct and crucially relies on sub and super modularity of an associated set function the second proof is by showing that the projection of the extended linear programming formulations onto the original variable space yields exactly the polyhedron described by the path modular inequalities thus we also show that these inequalities suffice to describe the convex hull of the set of feasible solutions

a polyhedral approach to single machine scheduling problems we report new results for a time indexed formulation of nonpreemptive single machine scheduling problems we give complete characterizations of all facet inducing inequalities with integral coefficients and right hand side 1 or 2 for the convex hull of the set of feasible partial schedules i e schedules in which not all jobs have to be started furthermore we identify conditions under which these facet inducing inequalities are also facet inducing for the original polytope which is the convex hull of the set of feasible complete schedules i e schedules in which all jobs have to be started to obtain insight in the effectiveness of these classes of facet inducing inequalities we develop a branch and cut algorithm based on them we evaluate its performance on the strongly np hard single machine scheduling problem of minimizing the weighted sum of the job completion times subject to release dates

on the 0 1 knapsack polytope this paper deals with the 0 1 knapsack polytope in particular we introduce the class ofweight inequalities this class of inequalities is needed to describe the knapsack polyhedron when the weights of the items lie in certain intervals a generalization of weight inequalities yields the so called weight reduction principle and the class of extended weight inequalities the latter class of inequalities includes minimal cover and l k configuration inequalities the properties of lifted minimal cover inequalities are extended to this general class of inequalities

first exit times of harmonically trapped particles a didactic review we revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by a one or multidimensional ornstein uhlenbeck process we start by recalling the main derivation steps of a propagator using langevin and fokker planck equations the mean exit time the moment generating function and the survival probability are then expressed through confluent hypergeometric functions and thoroughly analyzed we also present a rapidly converging series representation of confluent hypergeometric functions that is particularly well suited for numerical computation of eigenvalues and eigenfunctions of the governing fokker planck operator we discuss several applications of first exit times such as the detection of time intervals during which motor proteins exert a constant force onto a tracer in optical tweezers single particle tracking experiments adhesion bond dissociation under mechanical stress characterization of active periods of trend following and mean reverting strategies in algorithmic trading on stock markets relation to the distribution of first crossing times of a moving boundary by brownian motion some extensions are described including diffusion under quadratic double well potential and anomalous diffusion

reformulation of the multiperiod milp model for capacity expansion of chemical processes the problem of selecting processes and capacity expansion policies for a chemical complex consisting of continuous chemical processes can be formulated as a multiperiod mixed integer linear programming milp problem based on a variable disaggregation technique which exploits lot sizing substructures we propose two reformulations of the conventional milp model the first one is an nlp reformulation which very quickly yields good suboptimal solutions the second is an milp reformulation for exact solutions which leads to up to an order of magnitude faster computational results for large problems due to its tighter linear programming relaxation

varepsilon optimal non bayesian anomaly detection for parametric tomography the non bayesian detection of an anomaly from a single or a few noisy tomographic projections is considered as a statistical hypotheses testing problem it is supposed that a radiography is composed of an imaged nonanomalous background medium considered as a deterministic nuisance parameter with a possibly hidden anomaly because the full voxel by voxel reconstruction is impossible an original tomographic method based on the parametric models of the nonanomalous background medium and radiographic process is proposed to fill up the gap in the missing data exploiting this ldquoparametric tomography rdquo a new detection scheme with a limited loss of optimality is proposed as an alternative to the nonlinear generalized likelihood ratio test which is untractable in the context of nondestructive testing for the objects with uncertainties in their physical geometrical properties the theoretical results are illustrated by the processing of real radiographies for the nuclear fuel rod inspection

capacitated facility location valid inequalities and facets we examine the polyhedral structure of the convex hull of feasible solutions of the capacitated facility location problem in particular we derive necessary and sufficient conditions for a family of effective capacity inequalities to be facet defining and further results on a more general family called submodular inequalities