formulating the mixed integer fractional posynomial programming the mixed integer fractional posynomial programming mifpp problem arises from the summation minimization of several quotient terms appearing in the objective function subject to given constraints all decision variables of the problem could be binary integer and or continuous with without absolute value functions this paper addresses the problem of providing an optimization approach which could certainly obtain a solution as close as possible to a global optimum in order to solve the complex mifpp problem several strategies are used including linear programming relaxation modified goal programming logarithmic piecewise function lpf and so on in addition the proposed model solves the undefined problem of the logarithm of zero or negative in the lpf this significantly improved the utility of lpf in real applications finally an illustrative example is included to demonstrate the solution procedure of the proposed model

gibbs like ensembles and the inference of pure states abstract arguments of the jaynes maximum entropy sort have proved to be surprisingly successful in providing one with approximate descriptions of pure states in a variety of scenarios entirely bypassing any consideration of schrodinger s equation thus far however the concomitant algorithm was unable to incorporate input information concerning expectation values of complementary observables we discuss here how to overcome this difficulty by taking recourse to ideas borrowed from gibbs ones concerning statistical ensembles the ensuing approach is able to yield starting from a reduced set of expectation values approximate wave functions of a rather good quality as illustrated by simple examples

the maximum entropy inference of solutions to pdes we use the maximum entropy variational technique to infer solutions to second order partial differential equations we restrict ourselves to problems with dirichlet boundary conditions first we construct a basis of moment functions in terms of which we set up the constraints for a maximum entropy inversion for the inference of solutions to elliptic equations then we extend the scheme to the inference of time dependence in evolution equations this extension is done by solving a small system of first order initial value differential equations for the moments of the solution vector

an approximate approach of global optimization for polynomial programming problems abstract many methods for solving polynomial programming problems can only find locally optimal solutions this paper proposes a method for finding the approximately globally optimal solutions of polynomial programs representing a bounded continuous variable x i as the addition of a discrete variable d i and a small variable i a polynomial term x i x i can be expanded as the sum of d i x j d j i and i j a procedure is then developed to fully linearize d i x j and d j e i and to approximately linearize i j with an error below a pre specified tolerance this linearization procedure can also be extended to higher order polynomial programs several polynomial programming examples in the literature are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a pre specified error

diffusion in deterministic fractals a model for polymer electrolytes abstract we present simulation results for random walks on a family of sierpinski carpets under a periodically varying bias the diffusivity obtained from these results shows a power law variation of the bias with frequency the exponent depends on details of the carpet generator we discuss applicability of these results to real materials with fractal structure such as polymer electrolytes with different salt concentrations

scaling exponents for random walks on sierpinski carpets and number of distinct sites visited a new algorithm for infinite fractal lattices the scaling exponent for the mean square distance covered in a random walk dw and the average number of distinct sites visited dn are determined for a family of sierpinski carpet patterns we suggest a new random walk algorithm to generate walks on an effectively infinite deterministic fractal lattice the algorithm is applied to several sierpinski carpet patterns with the same hausdorff dimension we show that the systems have a quite different scaling exponent dw and further that the generally accepted result dn ds does not hold for all of these where ds is the spectral dimension

a complete algorithm for linear fractional programs abstract the linear fractional programming lfp algorithms attempt to optimize a quotient of two linear functions subject to a set of linear constraints the existing lfp algorithms are problem dependent and none is superior to others in all cases these algorithms explicitly require i the denominator of the objective function does not vanish in the feasible region ii the denominator of the objective function is positive iii the feasible region is bounded moreover some of these algorithms fail whenever iv some constraints are redundant we present a simplex type algorithm which is compact and efficiently detects conditions i iii and relaxes assumption iv the proposed algorithm is evolutionary in the sense that it builds up in a systematic manner to solve any lfp type problems numerical examples illustrate the algorithm

solving differential equations by a maximum entropy minimum norm method with applications to fokker planck equations the method of maximum entropy minimum norm is utilized to produce a general method of solving differential equations the technique is a generalization and extension of previous work performed by baker jarvis j math phys 30 302 1989 it is found that introducing an additional constraint on the norm of the solution vector produces a probability distribution that is integrable over the entire real axis a number of simplifications occur in this extended method the lagrange multipliers and solution vector can be solved for explicitly thus eliminating the necessity of solving systems of nonlinear equations for the lagrange multipliers as was required in the previous approach it is shown that the solution obtained is equivalent to a minimum norm approximation the maximum entropy solution of differential equations with fourier moments is shown to be identical to a fourier series solution additionally the new method is applied to solving the random walk and fokker planck equations

the pore structure of sierpinski carpets in this paper a new method is developed to investigate the pore structure of finitely and even infinitely ramified sierpinski carpets the holes in every iteration stage of the carpet are described by a hole counting polynomial this polynomial can be computed iteratively for all carpet stages and contains information about the distribution of holes with different areas and perimeters from which dimensions governing the scaling of these quantities can be determined whereas the hole area is known to be two dimensional the dimension of the hole perimeter may be related to the random walk dimension

approximate solution of fredholm integral equations by the maximum entropy method an approximate means of solving fredholm integral equations by the maximum entropy method is developed the fredholm integral equation is converted to a generalized moment problem whose approximate solution by maximum entropy methods has been successfully implemented in a previous paper by mead and papanicolaou l r mead and n papanicolaou j math phys 25 2404 1984 several explicit examples are given of approximate maximum entropy solutions of fredholm integral equations of the first and second kinds and of the wiener hopf type both the weaknesses and strengths of the method are discussed

quantal euclidean mappings abstract given a set of non commuting operators o 1 o n and the assumed knowledge of the expectation values of a subset containing just m of them we discuss in quite general terms what can be predicted about the behaviour of the expectation values of the remaining operators when the concomitant wave functions are not available not even in principle because the pertinent hamiltonian is unknown an r m r n m mapping ensues information theoretical tools are employed and some simple examples examined

optimization of functions with rank two variation over a box abstract this paper deals with optimization of functions that depend on large scale data via a linear transformation of rank two an algorithm is presented which under mild assumptions finds the global solution with polynomial time complexity in the worst case provided the critical points of the objective can be controlled with the same effort moreover for important subclasses of objectives including the linear fractional and the quadratic case we arrive at a linear time algorithm for both cases small simulation studies are provided to illustrate the average case runtime behaviour as a possible application sensitivity of cost assessment in communication networks is addressed where the problems may have tens of thousands of variables

the role of information measures in the determination of the maximum entropy minimum norm solution of the generalized inverse problem we discuss here the role of different information measures vis a vis the maximum entropy minimum norm method of baker jarvis et al bj for dealing with under determined inverse linear transforms it is shown that the structure of the approximate solutions provided by the bj approach does not depend upon the functional form of the information measure

how to select and how to rank projects the promethee method abstract in this paper we present the promethee methods a new class of outranking methods in multicriteria analysis their main features are simplicity clearness and stability the notion of generalized criterion is used to construct a valued outranking relation all the parameters to be defined have an economic signification so that the decision maker can easily fix them two ways of treatment are proposed it is possible to obtain either a partial preorder promethee i or a complete one promethee ii both on a finite set of feasible actions a comparison is made with the electre iii method the stability of the results given by the two methods is analysed numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed

algorithms for generalized fractional programming a generalized fractional programming problem is specified as a nonlinear program where a nonlinear function defined as the maximum over several ratios of functions is to be minimized on a feasible domain of n the purpose of this paper is to outline basic approaches and basic types of algorithms available to deal with this problem and to review their convergence analysis the conclusion includes results and comments on the numerical efficiency of these algorithms

the equitable dispersion problem most optimization problems focus on efficiency based objectives given the increasing awareness of system inequity resulting from solely pursuing efficiency we conceptualize a number of new element based equity oriented measures in the dispersion context we propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter element distances given the proposed optimization framework we develop corresponding mathematical programming formulations as well as their mixed integer linear reformulations we also discuss computational complexity issues related graph theoretic interpretations and provide some preliminary computational results

maximum entropy approach with higher moments for solving fokker planck equation abstract the maximum entropy method with higher number of moments is used to solve the fokker planck equation an adopted newton method is used to iterate the maximum entropy set of equations the method is used to calculate the probability density function of the fokker planck equation the calculations are carried out for three examples 1 the bistable systems of double well potential that is used in many problems related to the fluctuation and relaxation processes in far from equilibrium systems 2 the malthus verhulst model which is used to study the evolution of the number of individuals of an ecological species and the evolution of the intensity of the laser light 3 the black scholes equation used in financial market option pricing although the maximum entropy approach has several advantages it is not convergent at large times and so cannot be used to calculate the steady state solution

a note on scale transformations in the promethee v method abstract as already noted by mavrotas et al 2006 the promethee v method for multi attribute analysis of portfolio problems will fail to include an item in a portfolio if it has a negative net flow with respect to other items although adding such an item might actually improve the entire portfolio however the model formulated by mavrotas et al introduces a bias in favor of large portfolios because the promethee v method is sensitive to scale transformations the present paper analyzes this effect and proposes a method to correct it

quantum inference as an under determined linear problem and the collective of accessible states abstract a detailed mathematical analysis of the collective of accessible micro states compatible with a given set of a priori fixed expectation values generalized ensemble is undertaken to such an effect the problem of quantum inference is framed as an under determined linear problem the analysis is based upon the splitting of the pertinent statistical distribution the density matrix one is trying to infer into two orthogonal components one of the components happens to coincide with the minimum norm solution of the linear problem posed by the fulfillment of the a priori conditions on the given expectation values the remaining component belongs to the null space of the expectation values transformation

low density expansion for a two state random walk in a random environment a nearest neighbor random walk on z2 is considered where points of the lattice are labeled good or bad a particle takes a vertical step with probability ag or ab and a horizontal step with probability 1 ag or 1 ab depending on whether its present site is good or bad steps of size 1 are as probable as steps of size 1 if the good and bad sites are placed randomly with density of bad sites it is known that there exists an a such that for almost every placement of sites the random walk in the long run behaves like a homogeneous walk with vertical probability a and horizontal probability 1 a here the problem of estimating a as a function of is considered in particular when ag 1 2 ab fixed the first two terms of the expansion of a at 0 are rigorously derived

note a preference ranking organisation method the promethee method for multiple criteria decision making principles for a new family of outranking methods are given the main aim of the proposed promethee approach is to be as easily understood as possible by the decision maker it is based on extensions of the notion of criterion six possible extensions are considered these extensions can easily be identified by the decision maker because the parameters to be defined at most 2 have an economic significance a valued outranking graph is constructed by using a preference index two possibilities are considered to solve the ranking problem by using this valued graph promethee i provides a partial preorder and promethee ii a total preorder on the set of the possible actions

on the posynomial fractional programming problems abstract the posynomial fractional programming pfp problem arises from the summation minimization of several quotient terms which are composed of posynomial terms appearing in the objective function subject to given posynomial constraints this paper proposes an approximate approach to solving a pfp problem a linear programming relaxation is derived for the problem based on piecewise linearization techniques which first convert a posynomial term into the sum of absolute terms these absolute terms are then linearized by some linearization techniques the proposed approach could reach a solution as close as possible to a global optimum

properties of maximum entropy approximate solutions to fredholm integral equations the properties of the maximum entropy approximate solutions to fredholm integral equations of the second kind are discussed it is proved that the approximate solutions exist and converge to the exact one for a wider class of problems than previously determined the correspondence between the maximum entropy technique and the galerkin method is established and on its basis an upper a posterior bound for a solution is found

a parametric method for solving the linear fractional programming problem this paper describes an approach for determining the optimal solution of the linear fractional programming problem this approach is based mainly on a parametric analysis of a related linear substitution problem whereas existing algorithms for linear fractional programs concentrate solely on determining the optimal solution the approach described in this paper provides the decision maker with additional insights and valuable information on the underlying decision problem when the usual algorithms are applied this additional information which is gained by the parametric analysis of the substitution problem can be obtained only by further computational effort

project prioritization under policy restrictions a combination of mcda with 0 1 programming abstract multiple criteria decision aid methods are increasingly used in financial decision making in order to capture the multifaceted character of modern enterprises activated in a complex and versatile market environment this paper presents a multiple criteria approach for the selection of firms applying for financial support from public funds besides the budget constraint the specific decision situation imposes the consideration of additional policy constraints that prevent from directly exploiting rankings provided by a multiple criteria method in such a case the problem solution is to find a set of alternatives satisfying the constraints and at the same time maximizing a measure of global performance the proposed procedure relies on the promethee v method which belongs to the well known promethee family of multiple criteria outranking methods and is combined with an integer programming formulation capable to effectively deal with the problem s combinatorial character this method is modified in order to avoid any bias in the selection of the optimal set that may arrive because of the apparent contradiction between the rate of resources consumption and the coefficients of the alternatives in the additive objective function

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

maximum entropy minimum norm method for the determination of level densities abstract a new simple maximum entropy minimum norm inversion method is devised for obtaining the energy density of states from some limited information about the partition function an improvement upon the saddle point approximation can be obtained with the present method at low temperatures where the saddle point approach is less accurate

solution to boundary value problems using the method of maximum entropy the method of maximum entropy is used to solve a class of linear boundary value problems the method is based on using various moments of the differential equation as constraints when maximizing the entropy various examples are presented and compared to exact solutions for varying numbers of moments it is found that the maximum entropy approximation is in many cases better than a fourier series solution for a given number of expansion terms and moments the method is very general and will find applications in many areas of physics a comparison of the amount of work necessary for the maximum entropy solution versus finite difference techniques is presented and it is found that the maximum entropy technique shows promise as an alternative solution technique

on the q 1 2 non extensive maximum entropy distribution abstract a detailed mathematical analysis on the q 1 2 non extensive maximum entropy distribution of tsallis is undertaken the analysis is based upon the splitting of such a distribution into two orthogonal components one of the components corresponds to the minimum norm solution of the problem posed by the fulfillment of the a priori conditions on the given expectation values the remaining component takes care of the normalization constraint and is the projection of a constant onto the null space of the expectation values transformation

a simple method for obtaining weakly efficient points in multiobjective linear fractional programming problems abstract the properties of linear fractional functions facilitate the usage of a well known scalar optimization problem that gives weakly efficient points separately the weak efficiency can be detected with another scalar optimization test based on the same properties the numerical estimation of the nadir vector is considered as a possible application

selection among ranked projects under segmentation policy and logical constraints abstract the paper proposes a method for project selection under a specific decision situation where a final selection is guided by two aspects 1 satisfaction of certain segmentation policy and or logical constraints and 2 assurance that the individual evaluation of the projects is respected to the maximum degree this approach is somewhat different than the usual portfolio optimization where combinations of projects are compared without special concern on respecting the project s ranking the entire process is implemented in two phases the projects are first ranked usually through a multicriteria approach the obtained complete preorder of the projects is then used in an integer programming module in order to effectively drive the final selection that satisfies the segmentation and or logical constraints the innovative part of the proposed approach is the way it overcomes the well known bias towards low cost projects which is caused by the knapsack formulation commonly used in the integer programming phase actually this is the main source of divergence between the final selection and the initial complete preorder of the projects the proposed method improves an agreement between the final selection of projects obtained from the integer programming model and the ranking obtained from the multicriteria approach

fractional programming applications and algorithms abstract the paper deals with decision problems that give rise to the optimization of ratios subject to constraints these so called fractional programs have been treated in a considerable number of papers it is attempted to survey applications as well as solution methods in linear quadratic and concave convex fractional programming in the first part we give a detailed outline on the major areas of applications of fractional programming following a brief review on some basic theoretical results like duality relations in the second part we then discuss different algorithmic approaches a primal a dual and a parametric solution method is considered here we try to determine for each method the kind of fractional programs that are solved by it suitably

a maximum entropy method for solving the boundary value problem of second order ordinary differential equations we propose a new method to solve the boundary value problem for a class of second order linear ordinary differential equations which has a non negative solution the method applies the maximum entropy principle to approximating the solution numerically the theoretical analysis and numerical examples show that our method is convergent we propose a new method to solve the boundary value problem for a class of second order linear ordinary differential equations which has a non negative solution the method applies the maximum entropy principle to approximating the solution numerically the theoretical analysis and numerical examples show that our method is convergent

an efficient linearization approach for mixed integer problems abstract oral and kettani previously developed a linearization technique published in management science in 1990 and in operational research in 1992 for solving quadratic and cubic mixed integer problems for a quadratic problem with n 0 1 variables their method would introduce n additional continuous variables and n auxiliary constraints for a cubic problem with n 0 1 variables their method would introduce 3n additional continuous variables and 3n auxiliary constraints this linearization approach of oral and kettani has been accepted as the most efficient linearization technique published requiring the least number of additional continuous variables and auxiliary constraints however their method is difficult to extend for linearizing higher order polynomial terms that appear in mixed integer problems and in addition all constraints should be kept as linear this note proposes a new general model for linearizing various orders of mixed integer problems which cannot be solved by oral and kettani s model when the order is higher than three some computational results show that the proposed model is more efficient than oral kettani s method because it uses less additional variables and auxiliary constraints to linearize the same size of mixed integer problems in addition the proposed model can be easily applied to polynomial mixed integer terms that appear in the objective function and or constraints

identifying large robust network clusters via new compact formulations of maximum k club problems abstract network robustness issues are crucial in a variety of application areas in many situations one of the key robustness requirements is the connectivity between each pair of nodes through a path that is short enough which makes a network cluster more robust with respect to potential network component disruptions a k club which by definition is a subgraph of a diameter of at most k is a structure that addresses this requirement assuming that k is small enough with respect to the size of the original network we develop a new compact linear 0 1 programming formulation for finding maximum k clubs that has substantially fewer entities compared to the previously known formulation o kn 2 instead of o n k 1 which is important in the general case of k 2 and is rather tight despite its compactness moreover we introduce a new related concept referred to as an r robust k club or k r club which naturally arises from the developed k club formulations and extends the standard definition of a k club by explicitly requiring that there must be at least r distinct paths of length at most k between all pairs of nodes a compact formulation for the maximum r robust k club problem is also developed and error and attack tolerance properties of the important special case of r robust 2 clubs are investigated computational results are presented for multiple types of random graph instances

maximum entropy in the problem of moments the maximum entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem in important special cases such as the hausdorff moment problem we establish necessary and sufficient conditions for the existence of a maximum entropy solution and examine the convergence of the resulting sequence of approximations a number of explicit illustrations are presented in addition to some elementary examples we analyze the maximum entropy reconstruction of the density of states in harmonic solids and of dynamic correlation functions in quantum spin systems we also briefly indicate possible applications to the lee yang theory of ising models to the summation of divergent series and so on the general conclusion is that maximum entropy provides a valuable approximation scheme a serious competitor of traditional pade like procedures

a global approach for general 0 1 fractional programming abstract current methods of general 0 1 fractional programming g fp can only find the local optimum this paper proposes a new method of solving g fp problems by a mixed 0 1 linear program to obtain a global optimum given a mixed 0 1 polynomial term xy where x is a 0 1 variable and 0 y 1 we develop a theorem to transfer the xy term into a set of mixed 0 1 linear inequalities based on this theorem a g fp problem can be solved by a branch and bound method to obtain the global solution

an approximate approach for fractional programming with absolute value functions this paper considers the following fractional programming with absolute value functions fp a email protected email protected j 1 nc j x j email protected j 1 nd j x j n x d x subjecttoax b where x email protected r n is unrestricted b email protected r m a and b are the scalars a is an m n matrix c js and d js are unconstrained in sign in some cases when some of c js are positive and others are negative adjacent extreme point simplex type methods oper res 19 1 1971 120 eur j oper res 141 2002 233 oper res 13 6 1965 1029 fractional programming heldermann verlag berlin 1988 cannot be used to solve the problem fp a in view of this this paper proposes an approximate approach to reaching as close as possible an optimal solution of the problem fp a first the problem fp a is converted into an equivalent non linear quadratic mixed integer programming with absolute value then the model is linearized using piecewise logarithmic program with some linearization techniques the whole problem is then solvable using the branch and bound method the numerical example demonstrates that the proposed model can easily be applied to problem fp a

a note on a global approach for general 0 1 fractional programming abstract based on an approach recently proposed for obtaining global optimal solution of general 0 1 fractional programming g fp problem a theorem is presented in this research through this theorem the nonlinear terms appearing in the formulation transformed from g fp can be directly replaced by a set of linear inequalities the g fp problem can hence be easily and more efficiently solved as a mixed integer program

bi asymptotic fractals fractals between lower and upper bounds extending the idea of rigaut s asymptotic fractals issuing a turnover from a constant to a power law behaviour towards smaller scales we extend this idea to asymptotic fractals with both lower and upper turnover points i e the fractal region is terminated towards larger scales by another constant value this behaviour is typical for natural fractals such biological cell boundaries here we present a new analytic function describing this bi asymptotic behaviour the introduced parameters can be directly interpreted we show the advantage of this function in fitting processed images of natural and mathematical fractals in comparison with standard procedures the determined dimension is significantly more accurate a program package with this new function is available

mixed integer programming for the 0 1 maximum probability model abstract in this paper we study the 0 1 maximum probability model that consists in maximizing the probability that a certain quantity ctx is greater than a prescribed constant t where c and x are n vectors c1 cn are mutually independent and normally distributed random variables and x is a vector of n binary variables such that ax b where b is an m vector and a is an m n matrix it is known that this problem can be formulated as a nonlinear fractional program we show how to solve it exactly using mixed integer programming the advantage of the approach is that it requires only standard commercially available software the computational results which we present show that this technique makes it possible to treat instances with up to 100 random variables in a few seconds of cpu time

application of the non outranked sorting genetic algorithm to public project portfolio selection this paper proposes the application of multi criteria analysis to the problem of allocating public funds to competing programs projects or policies with a subjective approach applied to define the concept of highest portfolio social return this portfolio corresponds to an attainable non strictly outranked state of the social object under consideration its existence requires a decision maker dm to establish a relational preference system of minimal consistency as the number of feasible portfolios increases exponentially the dm s asymmetric preference relation should be computable to perform an exploration of the portfolio space the complexity of many real situations requires evolutionary algorithms but in presence of many objectives evolutionary algorithms are inefficient we overcome this problem by using the extended non outranked sorting genetic algorithm nosga ii which handles multi criteria preferences through a robust model based on a binary fuzzy outranking relation expressing the truth value of the predicate portfolio x is at least as good as portfolio y the dm is assumed to be capable of assigning the parameters for constructing the outranking relation in case of collective decision making we first assume that the possible differing values of the group members are not strongly conflicting so that a consensus can be achieved on the model s parameters otherwise we propose a method in which each member of the heterogeneous group gets his her own best portfolio these individual solutions are then aggregated in a group s best acceptable portfolio which maximizes a measure of group satisfaction and minimizes regret the proposal is examined through two real size problems in which good solutions are reached the first example is useful to illustrate the case of social action program selection the second illustrates the case of basic research project portfolios

approximate time dependent solutions of partial differential equations the maxent minimum norm approach a new approach to inverse problems with incomplete data the maxent minimum norm scheme was recently introduced by baker jarvis bj this method is based on the application of jaynes s maxent principle to a probability distribution defined on the functional space of all the possible solutions of the problem in the present work we consider the application of these ideas to non equilibrium time dependent systems in the spirit of jaynes s information theory approach to statistical mechanics we focus on the behaviour of a small number of physically relevant mean values by recourse to the bj procedure the equations of motion of those mean values are closed and an approximate description of the system s evolution is obtained it is also shown that the bj method is closely related to curado s case i e q 2 and standard mean values of tsallis nonextensive thermostatistics

solving special nonlinear fractional programming problems via parametric linear programming abstract a new procedure is developed to solve a generalized linear fractional programming problem we find the optimal solutions in two steps first we solve a parametric linear programming problem using the results of this step we then define a simple optimization problem in the second step this yields an optimal value which together with the results of the parametric analysis provides the optimal solutions of the considered fractional programming problem

project selection with discounted returns and multiple constraints abstract this paper considers the problem of selecting a subset of n projects subject to multiple resource constraints the objective is to maximize the net present value of the total return where the return from each project depends on its completion time and the previously implemented projects it is observed that the optimal order sequence of projects does not depend on the particular subset of selected projects and hence the overall problem reduces to a multiconstraint nonlinear integer 0 1 problem this problem can be solved optimally in pseudo polynomial time using a dynamic programming method but the method is impractical except when the number of constraints k is very small we therefore propose two heuristic methods which require o n 3 k and o n 4 k computations respectively and evaluate them computationally on 640 problems with up to 100 projects and up to 8 constraints the results show that the best heuristic is on the average within 0 08 of the optimum for the single constraint case and within 2 61 of the optimum for the multiconstraint case

on the polynomial mixed 0 1 fractional programming problems abstract this paper proposes a new method of solving polynomial mixed 0 1 fractional programming p01fp problems to obtain a global optimum given a polynomial 0 1 term x 1 x 2 x n y where x i is a 0 1 variable and y is a continuous variable we develop a linearization technique to transfer the x 1 x 2 x n y term into a set of mixed 0 1 linear inequalities based on this technique the p01fp can then be solved by a branch and bound method to obtain the global solution

a column generation algorithm for choice based network revenue management during the past few years there has been a trend to enrich traditional revenue management models built upon the independent demand paradigm by accounting for customer choice behavior this extension involves both modeling and computational challenges one way to describe choice behavior is to assume that each customer belongs to a segment which is characterized by a consideration set i e a subset of the products provided by the firm that a customer views as options customers choose a particular product according to a multinomial logit criterion a model widely used in the marketing literature in this paper we consider the choice based deterministic linear programming model cdlp of gallego et al 2004 gallego g g iyengar r phillips a dubey 2004 managing flexible products on a network technical report corc tr 2004 01 department of industrial engineering and operations research columbia university new york and the follow up dynamic programming decomposition heuristic of van ryzin and liu 2008 van ryzin g j q liu 2008 on the choice based linear programming model for network revenue management manufacturing service oper management10 2 288 310 we focus on the more general version of these models where customers belong to overlapping segments to solve the cdlp for real size networks we need to develop a column generation algorithm we prove that the associated column generation subproblem is indeed np hard and propose a simple greedy heuristic to overcome the complexity of an exact algorithm our computational results show that the heuristic is quite effective and that the overall approach leads to high quality practical solutions

anomalous diffusion on random fractal composites stochastic fractals generated from combinations of deterministic fractals have the advantage of being tractable to some extent but also being closer to real materials since they are partially disordered in the present work we focus our attention on the remarkable nonlinear mixing behavior exhibited by fractals generated as random combinations of two different sierpinski carpet generators when patterns with different anomalous diffusion exponents and the same or different fractal dimensions are combined together the effective diffusion exponent cannot in general be expressed as a linear weighted average of the diffusion exponents of the constituents the effective exponent may show a maximum or minimum for certain compositions an explanation of this interesting phenomenon is offered on the basis of details of the carpet generator particularly on the number and position of connection points which determine the connectivity of the fractal composite

modelling porous structures by repeated sierpinski carpets abstract porous materials such as sedimentary rocks often show a fractal character at certain length scales deterministic fractal generators iterated upto several stages and then repeated periodically provide a realistic model for such systems on the fractal diffusion is anomalous and obeys the law r 2 t 2 d w where r 2 is the mean square distance covered in time t and d w 2 is the random walk dimension the question is how is the macroscopic diffusivity related to the characteristics of the small scale fractal structure which is hidden in the large scale homogeneous material in particular do structures with same d w necessarily lead to the same diffusion coefficient at the same iteration stage the present paper tries to shed some light on these questions

error bounds in maximum entropy approximations a useful technique in underdetermined inverse problems is that of maximum entropy a simple error bound for averages over a distribution approximated by the maximum entropy method in the case of the undetermined hausdorff moment problem was devised under the conditions specified the error bound for averages over such an approximate distribution can be very tight numerical examples to illustrate are presented

the attractive traveling salesman problem in the attractive traveling salesman problem the vertex set is partitioned into facility vertices and customer vertices a maximum profit tour must be constructed on a subset of the facility vertices profit is computed through an attraction function every visited facility vertex attracts a portion of the profit from the customer vertices based on the distance between the facility and customer vertices and the attractiveness of the facility vertex a gravity model is used for computing the profit attraction the problem is formulated as an integer non linear program a linearization is proposed and strengthened through the introduction of valid inequalities and a branch and cut algorithm is developed a tabu search algorithm is also implemented computational results are reported

application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media we consider the application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media it is found that answers to interesting physics questions can be expressed in terms of several new fractal dimensions in addition to the fractal dimensiond f 1 d the fractal dimension of the backbone arises in connection with electric current flow 2 d red the fractal dimension of the singly connected bonds in the backbone arises in connection with its equivalence to the thermal scaling power 3 d e the fractal dimension of the of the elastic backbone 4 d u the fractal dimension of the unscreened perimeter arises in connection with the viscosity singularity at the gelation threshold 5 d min the fractal dimension of the minimum path or chemical distance between two sites arises in co nnection with the aharony stauffer conjecture 6 dw the fractal dimension of a random walk 7 d g the fractal dimension of growth sites that arise as a random walk creates a cluster relations among these fractal dimensions are discussed some of which can be proved and others of which are conjectures whose validity has been established only in certain limiting cases

budgeting with bounded multiple choice constraints abstract we consider a budgeting problem where a specified number of projects from some disjoint classes has to be selected such that the overall gain is largest possible and such that the costs of the chosen projects do not exceed a fixed upper limit the problem has several application in government budgeting planning and as relaxation from other combinatorial problems it is demonstrated that the problem can be transformed to an equivalent multiple choice knapsack problem through dynamic programming a naive transformation however leads to a drastic increase in the number of variables thus we propose an algorithm for the continuous problem based on dantzig wolfe decomposition a master problem solves a continuous multiple choice knapsack problem knowing only some extreme points in each of the transformed classes the individual subproblems find extreme points for each given direction using a median search algorithm an integer optimal solution is then derived by using the dynamic programming transformation to a multiple choice knapsack problem for an expanding core the individual classes are considered in an order given by their gradients and the transformation to a multiple choice knapsack problem is performed when needed in this way only a dozen of classes need to be transformed for standard instances from the literature computational experiments are presented showing that the developed algorithm is orders of magnitude faster than a general lp mip algorithm