design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

tradeoff based decomposition and decision making in multiobjective programming to facilitate the evaluation of tradeoffs and the articulation of preferences in multiple criteria decision making a multiobjective decomposition scheme is proposed that restructures the original problem as a collection of smaller sized subproblems with only subsets of the original criteria a priori preferences on objective tradeoffs are integrated into this process by modifying the ordinary pareto order by more general domination cones and decision makers are supported by an interactive decision making procedure to coordinate any remaining tradeoffs using concepts of approximate efficiency a theoretical foundation for this method is provided and an illustrative application to multiobjective portfolio optimization is described in detail

a simple augmented constraint method for multi objective mathematical integer programming problems abstract a simple augmented constraint saugmecon method is put forward to generate all non dominated solutions of multi objective integer programming moip problems the saugmecon method is a variant of the augmented constraint augmecon method proposed in 2009 and improved in 2013 by mavrotas et al however with the saugmecon method all non dominated solutions can be found much more efficiently thanks to our innovations to algorithm acceleration these innovative acceleration mechanisms include 1 an extension to the acceleration algorithm with early exit and 2 an addition of an acceleration algorithm with bouncing steps the same numerical example in lokman and koksalan 2012 is used to illustrate workings of the method then comparisons of computational performance among the method proposed by ozlen and azizog lu 2009 ozlen et al 2013 the method developed by lokman and koksalan 2012 and the saugmecon method are made by solving randomly generated general moip problem instances as well as special moip problem instances such as the mokp and mosp problem instances presented in table 4 in lokman and koksalan 2012 the experimental results show that the saugmecon method performs the best among these methods more importantly the advantage of the saugmecon method over the method proposed by lokman and koksalan 2012 turns out to be increasingly more prominent as the number of objectives increases

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

interactive algorithms for multiple criteria nonlinear programming problems abstract in this paper several interactive procedures for solving multiple criteria nonlinear programming problems have been developed these are based on the generalized reduced gradient method for solving single objective nonlinear programming problems they can handle maximization problems with nonlinear concave objectives nonlinear convex constraints and an implicit quasi concave preference function of the decision maker the interactive procedures work with information of varying degrees of accuracy from the decision maker thereby extending and strengthening a number of existing methods

preference structure representation using convex cones in multicriteria integer programming a new efficient system of representing the decision maker s preference structure in solving multicriteria integer programming problems is developed the problem is solved by an interactive branch and bound method that employs the procedure of zionts and wallenius zionts s j wallenius 1983 an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions management sci 295 for multicriteria linear programming the decision maker s underlying utility function is assumed to be pseudoconcave and his pairwise comparisons of decision alternatives are used to determine his preference structure in terms of certain convex cones in the objective function space and constraints on the weights on the objectives in the weight space the two forms of preference structure representation are interrelated and their underlying theory is developed the primary objective of a representation scheme is exactness and in this respect it is shown that the constraints on the weights are not adequate for representing nonlinear utility functions on the other hand the convex cones exactly represent any quasiconcave utility function and clearly avoid the approximations and inaccuracies in other utility assessment systems accordingly an efficient ordered representation using convex cones is developed an algorithmic framework for multicriteria integer programming that integrates the representation using convex cones with the branch and bound solution procedure is developed computational experience with bicriteria problems having up to 80 variables and 40 constraints is presented

some issues in measuring and reporting solution quality of interactive multiple objective programming procedures issues in measuring and reporting solution quality are examined when value functions are used in computational experiments of interactive multiple objective programming procedures they include value functions used weights assigned to the objective functions in the value functions the size of the efficient set and the number of objective functions the feasibility and existence of the ideal and nadir points are also discussed detailed examples are presented to demonstrate these issues neither the users nor in fact the researchers may discern these issues even though they have strong impacts on the reported solution qualities common practices in the computational experiments of interactive multiple objective programming procedures are reviewed

a class of interaction round a face models and its equivalence with an ice type model a new model called the temperley lieb interactions model is introduced in two dimensional lattice statistics on a square lattice the temperley lieb equivalence of this model to the six vertex self dual potts critical hard hexagons and critical nonintersecting string models is established a graphical equivalence of this model to the six vertex model generalizes this equivalence to noncritical cases of the above models the order parameters of a specialization of this model are studied

solving multiple criteria problems by interactive decomposition an interactive decomposition method is developed for solving the multiple criteria mc problem based on nonlinear programming duality theory the mc problem is decomposed into a series of subproblems and relaxed master problems each subproblem is a bicriterion problem and each relaxed master problem is a standard linear program the prime objective of the decomposition is to simplify and facilitate the process of making preference assessments and tradeoffs across many conflicting objectives therefore the decision maker s preference function is not assumed to be known explicitly rather the decision maker is required to make only limited local preference assessments in the context of feasible and nondominated alternatives also the preference assessments are of the form of ordinal paired comparisons and in most of them only two criteria are allowed to change their values simultaneously while the remaining l 2 criteria are held fixed at certain levels

on the design of ldpc code ensembles for biawgn channels existing design methods for irregular low density parity check ldpc codes over the additive white gaussian noise channel are based on using asymptotic analysis tools such as density evolution in an optimization process such a process is computationally expensive particularly when a large number of constituent variable node degrees are involved in the design in this paper we propose a systematic approach for the design of irregular ldpc codes the proposed method which is based on a pre computed upper bound on the fraction of edges connected to variable nodes of degree 3 is considerably less complex than the conventional optimization approach through a number of examples we demonstrate that using our method ensembles with performance very close to those devised based on optimization can be designed in addition to having very good performance the number of constituent variable node degrees in the designed ensembles is only three or four this in some cases is much smaller than the corresponding number for optimization based designs with similar performance

ldpc codes based on latin squares cycle structure stopping set and trapping set analysis it is well known that certain combinatorial structures in the tanner graph of a low density parity check ldpc code exhibit a strong influence on its performance under iterative decoding these structures include cycles stopping trapping sets and parameters such as the diameter of the code in general it is very hard to find a complete characterization of such configurations in an arbitrary code and even harder to understand the intricate relationships that exist between these entities it is therefore of interest to identify a simple setting in which all the described combinatorial structures can be enumerated and studied within a joint framework one such setting is developed in this paper for the purpose of analyzing the distribution of short cycles and the structure of stopping and trapping sets in tanner graphs of ldpc codes based on idempotent and symmetric latin squares the parity check matrices of ldpc codes based on latin squares have a special form that allows for connecting combinatorial parameters of the codes with the number of certain subrectangles in the latin squares subrectangles of interest can be easily identified and in certain instances completely enumerated this study can be extended in several different directions one of which is concerned with modifying the code design process in order to eliminate or reduce the number of configurations bearing a negative influence on the performance of the code another application of the results includes determining to which extent a configuration governs the behavior of the bit error rate curve in the waterfall and error floor regions

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

identical capacity channel decomposition for design of universal ldpc codes design of low density parity check ldpc codes suitable for all channels which exhibit a given capacity c is investigated such codes are referred to as universal ldpc codes first based on numerous observations a conjecture is put forth that a code working on n equal capacity channels also works on any convex combination of these n channels as a supporting evidence we prove that a code satisfying the stability condition on n channels also satisfies the stability condition on the convex hull of these n channels then a channel decomposition method is suggested which spans any given channel with capacity c in terms of a number of identical capacity basis channels we expect codes that work on the basis channels to be suitable for any convex combination of the bases i e all channels with capacity c such codes are found over a wide range of rates an upper bound on the achievable rate of universal ldpc codes is suggested through examples it is shown that our codes achieve rates extremely close to this upper bound in comparison with existing ldpc codes designed for a given channel significant performance gain is reported when codes are used over various channels of equal capacity

universality in sandpile models a classification of sandpile models into universality classes is presented on the basis of extensive numerical simulations in which we measure an extended set of exponents the manna two state model s s manna j phys a 24 l363 1991 is found to belong to a universality class of random neighbor models which is distinct from the universality class of the original model of bak tang and wiesenfeld p bak c tang and k wiesenfeld phys rev lett 59 381 1987 directed models are found to belong to a universality class which includes the directed model introduced and solved by dhar and ramaswamy d dhar and r ramaswamy phys rev lett 63 1659 1989

interactive stability cutting plane algorithm for multiobjective nonlinear programming problems abstract in this paper we introduce an interactive stability cutting plane algorithm for determining a best compromise solution to a multiobjective nonlinear programming problems in situations with an implicitly defined utility function the method is called interactive stability cutting plane compromise programming iscpcp the cutting planes which i am going to derive are based on suitable pairwise trade offs between the objective functions as prescribed by the decision maker dm at each iterate generated by the algorithm this algorithm requires no line searches and generates iterates that are all contained in the efficient frontier this feature facilitates the preference judgment of the decision maker and permits an analyst to terminate short of optimality with an efficient near optimal solution also we investigate the stability of its efficient solutions which are obtained by using this algorithm an illustrating example is presented to clarify this algorithm

the quantum symmetric xxz chain at delta 1 2 alternating sign matrices and plane partitions we consider the ground state wavefunction of the quantum symmetric antiferromagnetic xxz chain with open and twisted boundary conditions at along with the ground state wavefunction of the corresponding o n loop model at n 1 based on exact results for finite size systems sums involving the wavefunction components and in some cases the largest component itself are conjectured to be directly related to the total number of alternating sign matrices and plane partitions in certain symmetry classes

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

an algorithm for the multiple objective integer linear programming problem abstract a technique is presented for solving the multiple objective integer linear programming problem the technique can be used to identify some or all efficient solutions while the technique is applicable with any integer programming algorithm it is well suited for implementation using integer postoptimality techniques such an implementation based on balas additive algorithm is described for problems with zero one variables

nonlinear multiple objective optimization an algorithm and some theory this paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using zionts wallenius type of interaction the zionts wallenius method as extended in this paper can be used for solving multiple criteria problems with concave objective and implicit value functions and convex feasible regions modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed

tree structured expectation propagation for ldpc decoding over bms channels in this paper we put forward the tree structured expectation propagation tep algorithm for decoding block and convolutional low density parity check codes over any binary channel we have already shown that tep improves belief propagation bp over the binary erasure channel bec by imposing marginal constraints over a set of pairs of variables that form a tree or a forest the tep decoder is a message passing algorithm that sequentially builds a tree forest of erased variables to capture additional information disregarded by the standard bp decoder which leads to a noticeable reduction of the error rate for finite length codes in this paper we show how the tep can be extended to any channel specifically to binary memoryless symmetric bms channels we particularly focus on how the tep algorithm can be adapted for any channel model and more importantly how to choose the tree forest to keep the gains observed for block and convolutional ldpc codes over the bec

direction specific gradient scaling for interactive multicriterion optimization using an abstract mass concept in the method of abstract forces for the direction finding or tradeoff cut subproblems of interactive multicriterion optimization it is necessary to scale criterion gradients previously an ad hoc analyst assisted but nevertheless effective scaling method was used this paper introduces a concept of abstract mass it is shown that the previous ad hoc scaling method may be considered an approximation to the present direction specific approach also the abstract mass approach provides a strengthening of the original newton s second law of motion analogy motivation for the method of abstract forces a method for automatic and direction specific scaling is proposed which depends on the solution of a continuous piecewise polynomial system of equations the method is illustrated on an example with three criterion functions in this example newton s method for solving simultaneous nonlinear systems converges to a solution more generally restart homotopy methods may be required

tree expectation propagation for ml decoding of ldpc codes over the bec we propose a decoding algorithm for ldpc codes that achieves the maximum likelihood ml solution over the binary erasure channel bec in this channel the tree structured expectation propagation tep decoder improves the peeling decoder pd by processing check nodes of degree one and two however it does not achieve the ml solution as the tree structure of the tep allows only for approximate inference in this paper we provide the procedure to construct the structure needed for exact inference this algorithm denoted as generalized tree structured expectation propagation gtep modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph the gtep decoder upon completion either provides the unique ml solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ml solution we also explain the algorithm as a gaussian elimination method relating the gtep to other ml solutions compared to previous approaches it presents an equivalent complexity it exhibits a simpler graphical message passing procedure and most interesting the algorithm can be generalized to other channels

interactive multiobjective complex search abstract an interactive procedure based on box s complex search is used to solve the vector maximization problem this method has the advantage that the decision maker s underlying value function need not be explicitly specified also the problem may have nonlinear objective functions and nonlinear constraints several example problems are presented

an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions this paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties the method is an extension of our earlier method published in this journal zionts s wallenius j 1976 an interactive programming method for solving the multiple criteria problem management sci 22 6 652 663 various technical problems present in predecessor versions have been resolved in addition to presenting the supporting theory and algorithm we discuss certain options in implementation and summarize our practical experience with several versions of the method

temperley lieb stochastic processes we discuss one dimensional stochastic processes defined through the temperley lieb algebra related to the q 1 potts model for various boundary conditions we formulate a conjecture relating the probability distribution which describes the stationary state to the enumeration of a symmetry class of alternating sign matrices objects that have received much attention in combinatorics

on decoding of low density parity check codes over the binary erasure channel this paper investigates decoding of low density parity check ldpc codes over the binary erasure channel bec we study the iterative and maximum likelihood ml decoding of ldpc codes on this channel we derive bounds on the ml decoding of ldpc codes on the bec we then present an improved decoding algorithm the proposed algorithm has almost the same complexity as the standard iterative decoding however it has better performance simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm we also provide some graph theoretic properties of different decoding algorithms of ldpc codes over the bec which we think are useful to better understand the ldpc decoding methods in particular for finite length codes

interactive multidimensional programming models for locational decisions abstract the paper is devoted to an extension of traditional location theory in two directions first the usual assumption of a single cost function will be abandoned by introducing multiple objectives this gives rise to a multidimensional programming framework for the traditional location models the paper provides a solution algorithm for the latter problem next the assumption of a uniform space will be tackled by taking account of discrete candidate locations this problem can be solved by means of an adjusted multiciteria analysis the solution algorithms for both extensions are based on an interactive strategy so that the decision maker may identify the most favourable location in a finite number of steps

a branch and bound algorithm for mixed zero one multiple objective linear programming abstract in this paper a branch and bound algorithm for the generation of the efficient set in mixed zero one multiple objective linear programming problems is presented the algorithm is developed as to take account of the multiple objectives in the node fathoming procedure in order to extend the algorithm s applicability to large sized problems from real life an interactive procedure is introduced which systematically reduces the number of efficient points and thus saves considerable computational effort without losing essential information the algorithm is tested in randomly generated problems along with a case study conceming the power generation sector

solving the biobjective zero one knapsack problem by an efficient lp based heuristic abstract in this paper we propose a simple and useful method the core of which is an efficient lp based heuristic for solving biobjective 0 1 knapsack problems extensive computational experiments show that the proposed method is able to generate a good approximation to the nondominated set very efficiently we also suggest three qualitative criteria to evaluate such an approximation in addition the method can be extended to other problems having properties similar to the knapsack problem

an interactive branch and bound algorithm for multiple criteria optimization we present a new interactive algorithm for multiple criteria optimization the algorithm is of the branch and bound type and differs from previous interactive algorithms in several ways first the field of application is wider because it applies to two important classes of multiple criteria decision problems those for which the feasible set is convex and those for which the feasible set is discrete secondly the algorithm does not require a great deal from the decision maker he is merely required to indicate his preference between two vectors whenever the algorithm so demands

tree structure expectation propagation for ldpc decoding over the bec we present the tree structure expectation propagation tree ep algorithm to decode low density parity check ldpc codes over discrete memoryless channels dmcs expectation propagation generalizes belief propagation bp in two ways first it can be used with any exponential family distribution over the cliques in the graph second it can impose additional constraints on the marginal distributions we use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the ldpc code s tanner graph thanks to these additional constraints the tree ep marginal estimates for each variable in the graph are more accurate than those provided by bp we also reformulate the tree ep algorithm for the binary erasure channel bec as a peeling type algorithm tep and we show that the algorithm has the same computational complexity as bp and it decodes a higher fraction of errors we describe the tep decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters the solution of these equations is used to predict the tep decoder performance in both the asymptotic regime and the finite length regimes over the bec while the asymptotic threshold of the tep decoder is the same as the bp decoder for regular and optimized codes we propose a scaling law for finite length ldpc codes which accurately approximates the tep improved performance and facilitates its optimization

an overview of techniques for solving multiobjective mathematical programs multiobjective mathematical programming has been one of the fastest growing areas of or ms during the last 15 years this paper presents some reasons for the rapidly growing increase in interest in multiobjective mathematical programming a discussion of the advantages and disadvantages of the three general approaches articulation of the decision maker s preference structure over the multiple objectives prior to during or after the optimization towards multiobjective mathematical programming a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming and a discussion of important areas for further research the overview concentrates on those techniques which require an articulation of the decision maker s preference structure either during or after the optimization since these are the areas where most of the recent research has been conducted it differs from previous overviews in that in addition to the timing of the elicited preference informa

a comparative study of interactive tradeoff cutting plane methods for momp abstract in this paper four interactive cutting plane methods developed for multiple objective mathematical programming problems are compared to one another using randomly selected problems tradeoff cutting plane methods converge to the best compromise solution by iteratively reducing the objective space by cutting planes the cutting planes are constructed using partial preference information obtained from the decision maker the performance of the four methods is evaluated and compared to one another by solving the test problems under i four classes of preference functions in addition to the original preference functions to simulate the nonexisting decision maker ii different precision levels in the decision maker s comparative accuracy iii decision space expanded or contracted and iv inconsistent responses by the decision maker based on the comparative study some guidelines for performing a comparative study of multicriteria interactive methods are presented

direct variance design a multiobjective control theory a theory for designing linear state feedback controllers to directly accommodate variance constraints imposed on the system states is offered such controllers guarantee an average closed loop response to gaussian input disturbances the method provides a mechanism for directly assigning all variance values the diagonal elements of the covariance matrix to the closed loop system the theory may be viewed as offering direct access to a new set of design variables the state variances

low floor decoders for ldpc codes one of the most significant impediments to the use of ldpc codes in many communication and storage systems is the error rate floor phenomenon associated with their iterative decoders the error floor has been attributed to certain subgraphs of an ldpc code s tanner graph induced by so called trapping sets we show in this paper that once we identify the trapping sets of an ldpc code of interest a sum product algorithm spa decoder can be custom designed to yield floors that are orders of magnitude lower than floors of the the conventional spa decoder we present three classes of such decoders 1 a bi mode decoder 2 a bit pinning decoder which utilizes one or more outer algebraic codes and 3 three generalized ldpc decoders we demonstrate the effectiveness of these decoders for two codes the rate 1 2 2640 1320 margulis code which is notorious for its floors and a rate 0 3 640 192 quasi cyclic code which has been devised for this study although the paper focuses on these two codes the decoder design techniques presented are fully generalizable to any ldpc code

efficient maximum likelihood decoding of ldpc codes over the binary erasure channel we propose an efficient maximum likelihood ml decoding algorithm for decoding low density parity check ldpc codes over the binary erasure channel bec we also analyze the computational complexity of the proposed algorithm

multicriteria integer programming a hybrid dynamic programming recursive approach dynamic programming recursive equations are used to develop a procedure to obtain the set of efficient solutions to the multicriteria integer linear programming problem an alternate method is produced by combining this procedure with branch and bound rules computational results are reported

symmetry classes of alternating sign matrices under one roof in a previous article math co 9712207 we derived the alternating sign matrix asm theorem from the izergin korepin determinant for a partition function for square ice with domain wall boundary here we show that the same argument enumerates three other symmetry classes of alternating sign matrices vsasms vertically symmetric asms even htsasms half turn symmetric asms and even qtsasms quarter turn symmetric asms the vsasm enumeration was conjectured by mills the others by robbins math co 0008045 we introduce several new types of asms uasms asms with a u turn side uuasms two u turn sides osasms off diagonally symmetric asms oosasms off diagonally off antidiagonally symmetric and uosasms off diagonally symmetric with u turn sides uasms generalize vsasms while uuasms generalize vhsasms vertically and horizontally symmetric asms and another new class vhpasms vertically and horizontally perverse osasms oosasms and uosasms are related to the remaining symmetry classes of asms namely dsasms diagonally symmetric dasasms diagonally anti diagonally symmetric and tsasms totally symmetric asms we enumerate several of these new classes and we provide several 2 enumerations and 3 enumerations our main technical tool is a set of multi parameter determinant and pfaffian formulas generalizing the izergin korepin determinant for asms and the tsuchiya determinant for uasms solv int 9804010 we evaluate specializations of the determinants and pfaffians using the factor exhaustion method

an interactive dynamic programming approach to multicriteria discrete programming abstract several interactive schemes for solving multicriteria discrete programming problems are developed under a dynamic programming framework it is assumed that the decision maker s preference structure satisfies the conditions of transitivity monotonicity and nonsatiation hybrid procedures are also structured by including branch and bound ideas into the recursions initial computational results are offered

interactive relaxation method for a broad class of integer and continuous nonlinear multiple criteria problems an interactive decomposition algorithm for solving a broad class of multiple criteria mc problems is presented in this paper on the one hand the method is designed to solve a broad class of mc problems including complex ones i e problems with nonlinear objective functions and nonlinear constraints with continuous and or integer valued decision variables and with an unknown underlying nonlinear preference function on the other hand the method is intended to reduce the assessment burden on the decision maker dm by simplifying and facilitating the task of making preference assessments and tradeoffs the method is efficient from a computational standpoint since the only program that needs to be solved at each iteration is linear in the decision variables also the algorithm is capable of producing lower and upper bounds lb and ub on the optimal objective value of the mc problem at each iteration although the dm s preference function is not assumed to be known explicitly lb and ub can be used to terminate the search prematurely at a satisfactory good enough solution and consequently to reduce the computational time as well as the number of preference assessments that the dm must make finally all the tradeoffs that the dm is required to make are of the form of ordinal paired comparisons most of which are particularly simple since they involve changes in only two criteria at a time also all the preference assessments are made in the context of feasible solutions only

how self organized criticality works a unified mean field picture we present a unified dynamical mean field theory based on the single site approximation to the master equation for stochastic self organized critical models in particular we analyze in detail the properties of sandpile and forest fire ff models in analogy with other nonequilibrium critical phenomena we identify an order parameter with the density of active sites and control parameters with the driving rates depending on the values of the control parameters the system is shown to reach a subcritical absorbing or supercritical active stationary state criticality is analyzed in terms of the singularities of the zero field susceptibility in the limit of vanishing control parameters the stationary state displays scaling characteristics of self organized criticality soc we show that this limit corresponds to the breakdown of space time locality in the dynamical rules of the models we define a complete set of critical exponents describing the scaling of order parameter response functions susceptibility and correlation length in the subcritical and supercritical states in the subcritical state the response of the system to small perturbations takes place in avalanches we analyze their scaling behavior in relation with branching processes in sandpile models because of conservation laws a critical exponents subset displays mean field values ensuremath nu frac 1 2 and ensuremath gamma 1 in any dimensions we treat bulk and boundary dissipation and introduce a critical exponent relating dissipation and finite size effects we present numerical simulations that confirm our results in the case of the forest fire model our approach can distinguish between different regimes soc ff and deterministic ff studied in the literature and determine the full spectrum of critical exponents

a review of interactive methods for multiobjective integer and mixed integer programming this paper makes a review of interactive methods devoted to multiobjective integer and mixed integer programming moip momip problems the basic concepts concerning the characterization of the non dominated solution set are first introduced followed by a remark about non interactive methods vs interactive methods then we focus on interactive moip momip methods including their characterization according to the type of preference information required from the decision maker the computing process used to determine non dominated solutions and the interactive protocol used to communicate with the decision maker we try to draw out some contrasts and similarities of the different types of methods

estimating aspiration levels from discrete choices computational techniques and experiences abstract this paper discusses the problem of estimating aspiration or reference levels in criteria space from choices between alternatives characterized by multiple criteria several methods for such estimations are developed and compared taking into account both solution quality and computational efficiency methods based on mixed integer linear programming which provide optimal solutions require unacceptable computing times for application in interactive systems an alternative method based on a direct search algorithm is shown to be an effective way of generating high quality estimates with small computational effort

gradient projection and local region search for multiobjective optimisation this paper presents a new method for multiobjective optimisation based on gradient projection and local region search the gradient projection is conducted through the identification of normal vectors of an efficient frontier the projection of the gradient of a nonlinear utility function onto the tangent plane of the efficient frontier at a given efficient solution leads to the definition of a feasible local region in a neighbourhood of the solution within this local region a better efficient solution may be sought to implement such a gradient based local region search scheme a new auxiliary problem is developed if the utility function is given explicitly this search scheme results in an iterative optimisation algorithm capable of general nonseparable multiobjective optimisation otherwise an interactive decision making algorithm is developed where the decision maker dm is expected to provide local preference information in order to determine trade off directions and step sizes optimality conditions for the algorithms are established and the convergence of the algorithms is proven a multiobjective linear programming molp problem is taken for example to demonstrate this method both graphically and analytically a nonlinear multiobjective water quality management problem is finally examined to show the potential application of the method to real world decision problems

critical behaviour in a non local interface model the raise and peel model is a recently proposed one dimensional statistical model describing a fluctuating interface the evolution of the model follows from the competition between adsorption and desorption processes the model is non local due to the possible occurrence of avalanches at a special ratio of the adsorption desorption rates the model is integrable and many rigorous results are known off the critical point the phase diagram and scaling properties are not known in this paper we search for indications of phase transition studying the gap in the spectrum of the non hermitian generator of the stochastic interface evolution we present results for the gap obtained from exact diagonalization and from monte carlo estimates derived from temporal correlations of various observables

a dual differentiable exact penalty function a new penalty function is associated with an inequality constrained nonlinear programming problem via its dual this penalty function is globally differentiable if the functions defining the original problem are twice globally differentiable in addition the penalty parameter remains finite this approach reduces the original problem to a simple problem of maximizing a globally differentiable function on the product space of a euclidean space and the nonnegative orthant of another euclidean space many efficient algorithms exist for solving this problem for the case of quadratic programming the penalty function problem can be solved effectively by successive overrelaxation sor methods which can handle huge problems while preserving sparsity features

the raise and peel model of a fluctuating interface we propose a one dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter the adsorption rate at a special value of this parameter the model has some interesting features for example the spectrum is given by conformal field theory and the stationary non equilibrium probability distribution is given by the two dimensional equilibrium distribution of the ice model with domain wall type boundary conditions this connection is used to find exact analytic expressions for several quantities of the stochastic model vice versa some understanding of the ice model with domain wall type boundary conditions can be obtained by the study of the stochastic model at the special point we study several properties of the model such as the height fluctuations as well as cluster and avalanche distributions the latter has a long tail which shows that the model exhibits self organized criticality we also find in the stationary state a special surface phase transition without enhancement and with a crossover exponent 2 3 furthermore we study the phase diagram of the model as a function of the adsorption rate and find two massive phases and a scale invariant phase where conformal invariance is broken

maxwell construction the hidden bridge between iterative and maximum a posteriori decoding there is a fundamental relationship between belief propagation and maximum a posteriori decoding a decoding algorithm which is called the maxwell decoder is introduced and provides a constructive description of this relationship both the algorithm itself and the analysis of the new decoder are reminiscent of the maxwell construction in thermodynamics this paper investigates in detail the case of transmission over the binary erasure channel while the extension to general binary memoryless channels is discussed in a companion paper

a class of practical interactive branch and bound algorithms for multicriteria integer programming abstract a practical interactive solution approach to multicriteria integer programming problems is developed the problem is solved by a branch and bound method that employs the zionts and wallenius procedure 23 for solving the multicriteria linear programming problem the development of algorithms for multicriteria decision problems itself is a multicriteria problem which involves the simultaneous minimization of the number of questions asked of the decision maker and the solution time two branch and bound algorithms that follow different search strategies to meet different levels of these criteria have been developed further two families of hybrid algorithms that incorporate a combination of the strategies of the two algorithms have also been developed strategies for the exploration of the decision maker s preference structure are discussed computational experience with the algorithms is presented the class of algorithms represents a collection of viable solution strategies applicable to a variety of decision making styles

stochastic processes and conformal invariance we discuss a one dimensional model of a fluctuating interface with a dynamic exponent z 1 the events that occur are adsorption which is local and desorption which is nonlocal and may take place over regions of the order of the system size in the thermodynamic limit the time dependence of the system is given by characters of the c 0 logarithmic conformal field theory of percolation this implies in a rigorous way a connection between logarithmic conformal field theory and stochastic processes the finite size scaling behavior of the average height interface width and other observables are obtained the avalanches produced during desorption are analyzed and we show that the probability distribution of the avalanche sizes obeys finite size scaling with new critical exponents

a convergent interactive cutting plane algorithm for multiobjective optimization this paper presents an interactive cutting plane algorithm for determining a best compromise solution to a multiobjective optimization problem in situations with an implicitly defined utility function we derive cutting planes that are based on suitable pairwise trade offs between the objective functions as prescribed by the decision maker at each iterate generated by the algorithm the proposed algorithm requires no line searches and generates iterates that are all contained in the efficient frontier this feature facilitates the preference judgment of the decision maker and permits an analyst to terminate short of optimality with an efficient near optimal solution a convergence analysis establishes that any accumulation point generated by the algorithm is a best compromise solution we also conduct an error analysis to point out the effect of inconsistencies in trade off information provided by the decision maker the algorithm may be extended to situations involving nonconvex feasible regions as well as nonconcave for a max problem objective functions we offer remarks for such cases and describe an application to an urban runoff control design problem

finding efficient solutions for rectilinear distance location problems efficiently abstract given n planar existing facility locations a planar new facility location x is called efficient if there is no other location y for which the rectilinear distance between y and each existing facility is at least as small as between x and each existing facility and strictly less for at least one existing facility rectilinear distances are typically used to measure travel distances between points via rectilinear aisles or street networks we first present a simple arrow algorithm based entirely on geometrical analysis that constructs all efficient locations we then present a row algorithm which is of order n log n that constructs all efficient locations and establish that no alternative algorithm can be of a lower order

using dea to obtain efficient solutions for multi objective 0 1 linear programs abstract this paper concerns the problem of a service oriented public sector entity to allocate limited resources to different activities while keeping conflicting objectives in mind the multi objective resource allocation problem mrap is to select activities to be performed the authors formulate the problem as a multi objective 0 1 linear problem the authors implement data envelopment analysis dea with the banker charnes and cooper s bcc model to measure the decision making unit s dmu efficiency in this study the production function is a mathematical statement relating the technological relationship between the objectives and resources of mrap each dmu presents a technological relationship i e dmu presents a relationship between resources and objectives this relationship gives information about the use of resources and satisfactoriness of objectives the inputs and outputs respectively outline resources and objectives the production possibility set represents feasible solutions for mrap moreover due to the multiple objectives of problems the method derives a solution set instead of an optimal solution in single objective ones this solution set a well known efficient solutions set forms the decision set of problems each dmu results from an alternative a combination of activities the production possibility set presents all the candidates of dmu the set of alternatives resulting in efficient dmus is efficient solutions of mrap the authors developed a two stage algorithm to generate and evaluate dmus the first stage generates a dmu with the maximum of the distance function the second stage is then used to evaluate the efficiency of the generated dmu

new closedness results for efficient sets in multiple objective mathematical programming abstract there are various theoretical algorithmic and practical reasons for developing necessary and sufficient conditions for the efficient set of a multiple objective mathematical programming problem p to be closed yet only a small number of results of this type limited to special cases of problem p have been developed in this article we present a necessary condition and several sufficient conditions for the closedness of the efficient sets of more general cases of problem p than have heretofore been studied our approach relies in part upon generalizing the concepts of quasi concavity and strict quasi concavity for real valued functions to vector valued functions our approach also relies upon some new characterizations of an efficient solution for problem p that we develop in the article

multi criteria branch and bound a vector maximization algorithm for mixed 0 1 multiple objective linear programming the paper describes the multi criteria branch and bound mcbb algorithm a vector maximization algorithm capable of deriving all efficient extreme points for small and medium sized mixed 0 1 multiple objective linear programming mixed 0 1 molp particular emphasis is given to computational aspects aiming principally at accelerating the solution procedure for facilitating the decision maker s search toward the most preferred efficient solution the notion of efficient combinations of the binary variables is further exploited it is also shown that the mcbb algorithm can be used in single objective problems mixed integer lp problems in order to determine all alternative optima as well as in mixed integer molp problems and pure 0 1 molp problems that frequently arise in practice a computational experiment is included in the paper in order to illustrate the performance of the algorithm

a genetic algorithm approach to single and multiobjective structural optimization with discrete continuous variables a search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems this procedure known as a genetic algorithm ga utilizes a blending of the principles of natural genetics and natural selection a lack of dependence on the gradient information makes gas less susceptible to pitfalls of convergence to a local optimum to model the multiple objective functions in the problem formulation a co operative game theoretic approach is proposed examples dealing with single and multiobjective geometrical design of structures with discrete continuous design variables and using artificial genetic search are presented simulation results indicate that gas converge to optimum solutions by searching only a small fraction of the solution space the optimum solutions obtained using gas compare favourably with optimum solutions obtained using gradient based search techniques the results indicate that the efficiency and power of gas can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency