vector valued variational principle in fuzzy metric space and its applications a vector valued ekeland s variational principle and its equivalents in fuzzy metric space are presented in this paper our result unifies and extends some of the previous results about single valued and vector valued ekeland s variational principle as an application we obtain a fixed point theorem in fuzzy metric space under a new contractive condition which is a new generalization of well known banach contraction principle all of our results are also new even in usual metric spaces

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

the maximum covering shortest path problem a multiobjective network design and routing formulation abstract in this paper the authors introduce the maximum covering shortest path problem and the maximum population shortest path problem a special case of the former model both models are formulated as two objective integer programs a summary of the results of a sample problem for the latter formulation is given possible modifications to and extensions and applications of both models are also presented with these formulations the authors extend the concept of coverage from facility location analysis to network design and routing analysis

function variational principles and coercivity abstract the function type extension of ekeland s variational principle j math anal appl 47 1974 324 353 due to zhong nonlinear anal 29 1997 1421 1431 is deductible in a simplified manner and in a larger functional context this is also true for his normed coercivity result based on palais smale techniques

a quadratic petrov galerkin solution for kinematic wave overland flow a petrov galerkin pg finite element method was developed to solve the kinematic wave formulation of the overland flow equations the resultant model uses quadratic basis functions and test functions that are modified by polynomials of cubic and quartic order yielding a formulation that includes four ph parameters the pg model was found to reduce the mean sum of square error of the solution compared to a conventional bubnov galerkin finite element solution by about a factor of 3 as the courant number cr approached one good results were also achieved with the pg method for problems that resulted in shock formation which are typical of many applied problems of concern pg parameters were found to depend strongly upon the courant number and weakly upon the number of nodes in the system polynomial expressions were derived to approximate the pg parameters over the range 0 cr 1 as the number of nodes in the system increased a single parameter version of the model yielded solutions approaching the accuracy of the four parameter model

a reference direction approach to multiple objective integer linear programming abstract we propose the use of a reference direction reference point approach to solving multiple objective integer linear programming problems the reference direction reference point is determined by the aspiration levels for the criteria that the decision maker wants to improve within this framework two methods are developed viz a pure integer method that operates entirely with integer solutions and a continuous integer method that works with continuous solutions and finds an integer solution closest to the continuous solution in terms of the achievement scalarizing function obviously the pure integer method is time consuming we therefore propose a decision support system that combines the two methods this way the adbantages of each method can be used to their fullest extent we illustrate the proposed decision support system with a numerical example

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

an interactive reference point approach for multiobjective mixed integer programming using branch and bound abstract we propose an interactive reference point approach for multiple objective mixed integer linear programming problems that exploits the use of branch and bound techniques for solving the scalarizing programs at each dialogue phase the decision maker must specify a criterion reference point or just choose an objective function he she wants to improve in respect to the previous efficient nondominated solution in the latter case a directional search is performed adjusting automatically the reference point used at each stage tchebycheff mixed integer scalarizing programs are successively solved by branch and bound postoptimality techniques have been developed enabling the algorithm to profit from previous computations to solve the next scalarizing programs the previous branch and bound tree is used as a starting point and operations of simplification and branching are then performed to obtain a new efficient solution computational results have shown that this approach is effective for carrying out directional or local searches for efficient solutions

multiobjective solution of the uncapacitated plant location problem abstract in this paper we consider the discrete multiobjective uncapacitated plant location problem we present an exact and an approximate approach to obtain the set of non dominated solutions the two approaches resort to dynamic programming to generate in an efficient way the non dominated solution sets the solution methods that solve the problems associated with the generated states are based on the decomposition of the problem on two nested subproblems we define lower and upper bound sets that lead to elimination tests that have shown to have a high performance computational experiments on a set of test problems show the good performance of the proposal

a method for finding well dispersed subsets of non dominated vectors for multiple objective mixed integer linear programs abstract we present an algorithm for generating a subset of non dominated vectors of multiple objective mixed integer linear programming starting from an initial non dominated vector the procedure finds at each iteration a new one that maximizes the infinity norm distance from the set dominated by the previously found solutions when all variables are integer it can generate the whole set of non dominated vectors

a branch and bound algorithm for a class of biobjective mixed integer programs most real world optimization problems are multiobjective by nature involving noncomparable objectives many of these problems can be formulated in terms of a set of linear objective functions that should be simultaneously optimized over a class of linear constraints often there is the complicating factor that some of the variables are required to be integral the resulting class of problems is named multiobjective mixed integer programming momip problems solving these kinds of optimization problems exactly requires a method that can generate the whole set of nondominated points the pareto optimal front in this paper we first give a survey of the newly developed branch and bound methods for solving momip problems after that we propose a new branch and bound method for solving a subclass of momip problems where only two objectives are allowed the integer variables are binary and one of the two objectives has only integer variables the proposed method is able to find the full set of nondominat

the multiobjective discrete optimization problem a weighted min max two stage optimization approach and a bicriteria algorithm we study the multiple objective discrete optimization modo problem and propose two stage optimization problems as subproblems to be solved to obtain efficient solutions the mathematical structure of the first level subproblem has similarities to both tchebycheff type of approaches and a generalization of the lexicographic max ordering problem that are applicable to multiple objective optimization we present some results that enable us to develop an algorithm to solve the bicriteria discrete optimization problem for the entire efficient set we also propose a modification of the algorithm that generates a sample of efficient solutions that satisfies a prespecified quality guarantee we apply the algorithm to solve the bicriteria knapsack problem our computational results on this particular problem demonstrate that our algorithm performs significantly better than an equivalent tchebycheff counterpart moreover the computational behavior of the sampling version is quite promising

an algorithm of internal feasible directions for linear integer programming abstract an approximate algorithm for solving pure integer problems is examined the algorithm belongs to the class of component algorithms using feasible integer directions the basic characteristics of the algorithm are analyzed testing on an ibm pc at personal computer is carried out the proposed algorithm is compared with other well known approximate algorithms

an interactive procedure for multiple objective integer linear programming problems abstract there are many practical problems where the objective functions and the constraints can be represented by linear functions but the decision variables are restricted to only integer values our objective is to present an interactive procedure for the multiple objective integer linear programming problem that is fast does not place too many demands on the decision maker and can be implemented without requiring any special software we illustrate the proposed procedure with a numerical example and report some computational experience

a method for finding the set of non dominated vectors for multiple objective integer linear programs abstract an algorithm for enumerating all non dominated vectors of multiple objective integer linear programs is presented using a straightforward theoretical approach the problem is solved using a sequence of progressively more constrained integer linear programs generating a new solution at each step the algorithm can also give subsets of efficient solutions that can be useful for designing interactive procedures for large real life problems

exact algorithm for bi objective 0 1 knapsack problem in this paper we propose a new procedure based on linear mathematical programming formulation to find all efficient solutions of bi objective 0 1 knapsack problem we solve a limited number of single objective problems to find efficient solutions of bi objective 0 1 knapsack problem we show that the proposed method is able to generate efficient solutions with less constraints and variables than the general linear program found in the literature an example is presented to illustrate the steps of the procedure

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

a multiple criteria method for choosing among discrete alternatives abstract an interactive method is presented for solving a discrete alternative multiple criteria problem under certainty the method is based on the approach of zionts and wallenius a computer program embodying the method has been written and the results to date have been favorable extensions to the case in which some of the criteria are not readily quantifiable are also considered

a streamline upwind full galerkin method for space time convection dominated transport problems an original space time finite element approach for the solution of the diffusion convection equation is proposed in this paper a slight manipulation of the differential equation suggests that transient transport problems may in fact be seen as steady state space time transport problems accurately and easily soluble by the standard galerkin technique however concerning convective transport involving sharp fronts or coarse discretization it is shown that implementation of dissipation along space time trajectories significantly improves the solutions classical comparative test problems are run to establish the performances of this method and to show the limits of the more sophisticated petrov and taylor galerkin schemes evocation of a possible space time anisotropy generated by usual finite difference time stepping procedures as well as comparative analysis of amplification matrices help to understand the accuracy and the robustness of the proposed approach

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

cut a multicriteria approach for concavifiable preferences we consider the problem of helping a decision maker dm choose from a set of multiattributed objects when her preferences are concavifiable i e representable by a concave value function we establish conditions under which preferences or preference intensities are concavifiable we also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the dm this can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure we report on the practical use of this procedure with several dms for a flat choice problem and its computational performance on a set of project portfolio selection problem instances the use of preference intensities is found to provide significant improvements to the performance of the procedure

on some nonlinear problems induced by an abstract maximal element principle abstract in this paper by applying an abstract maximal element principle on quasi ordered sets established by lin and du we obtain a generalized brezis browder principle system vectorial versions of ekeland s variational principle and maximal element principle and a vectorial version of takahashi s nonconvex minimization theorem moreover we investigate the equivalence between scalar versions and vectorial versions of these results

zero one programming with multiple criteria abstract the study of multiple criteria problems is not new but during the last seventeen years more and more study has been done in this area the study of 0 1 multiple criteria problems started much later than the study of continuous multiple criteria problems some of the earliest works on 0 1 problems with multiple criteria was first presented in 1973 quite a few solution methods have been developed since then especially during the last seven years in this paper most of these methods and some applications will be treated

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

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

non diffusive n 2 degree petrov galerkin methods for two dimensional transient transport computations a new non diffusive petrov galerkin type finite element method which uses test functions two polynomial degrees higher than the trial functions is developed for the transient convection dominated transport equation in two dimensions the scheme uses bilinear quadrilateral finite elements for the spatial discretization and crank nicolson finite differencing for the time integration the standard product extension of very successful one dimensional n 2 degree upwinding functions to two dimensions is ineffective for general 2 d flow problems especially at higher courant numbers where cross derivative truncation terms become important therefore effective n 2 degree test functions are developed through an analysis by which the truncation error terms in the discrete nodal equation are eliminated up to fifth order the new scheme is very effective for general 2 d flows over a wide courant number range and eliminates the troublesome cross derivative truncation terms the scheme is simple and robust in that the upwinding coefficients are readily defined and only dependent on courant number numerical examples illustrate the excellent behaviour of the new scheme

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

a method for generating all efficient solutions of 0 1 multi objective linear programming problem in this paper a method is proposed to find all efficient solutions of 0 1 multi objective linear programming molp problem these solutions are specified without generating all feasible solutions corresponding to a feasible solution of 0 1 molp problem a vector is constructed which its components are the values of objective functions the method consists of a one stage algorithm in each iteration of this algorithm for obtaining some efficient solutions of 0 1 molp problem a 0 1 single objective linear programming problem is solved

preference convex unanimity in multiple criteria decision making the approach which results in the definition of stochastic dominance orders for risky decision making can also be applied to the nonrisky case that is one may postulate that alternative x dominates alternative y if x is preferred to y by every possible decision maker with specified preference characteristics one such unanimity order is the standard componentwise vector order of multiple objective optimization in this paper a unanimity order is constructed based upon characteristics of preference convexity in conjunction with finitely many elicited preference responses since the new order properly includes the vector order the corresponding efficient frontier may be smaller

a multiple objective interactive lagrangean relaxation approach abstract this paper extends the lagrangean relaxation ideas for integer scalar optimisation problems to integer vector optimisation problems and incorporates an interactive branch and bound routine

a fuzzy programming approach to multiobjective multidimensional 0 1 knapsack problems abstract the objective of this paper is to present an interactive procedure for the multiobjective multidimensional 0 1 knapsack problem that takes into consideration the incorporation of fuzzy goals of the decision maker that is easy to use since it requires from the decision maker to handle only one parameter namely the aspiration level of each objective and that is fast and can treat our problem as a usual 0 1 knapsack problem using already available software namely the primal effective gradient method used primarily to solve the large scale cases to get some statistics on the behavior of the algorithm a number of randomly generated simulation of problems is solved from our numerical experience it is possible to conclude that our proposed method is a worthwhile alternative to existing methods from a practical point of view

an enhanced conversion scheme for lexicographic multiobjective integer programs abstract a number of approaches have been proposed and several implemented for the solution of lexicographic multiobjective programming problems these approaches may be divided into two classes the first encompasses the development of algorithms specifically designed to deal directly with the initial model while the second attempts to transform efficiently the lexicographic multiobjective model into an equivalent single objective programming problem this second approach would appear particularly attractive since it permits the use of conventional readily available mathematical programming software in this paper we address a particular form of the lexicographic multiobjective model specifically one in which all functions are linear and all variables integer it is then shown how a recently developed scheme for the transformation of this model may be substantially improved as a result lexicographic multiobjective integer linear programs may be easily converted into conventional linear integer programs wherein the magnitude of the objective function coefficients are minimized

accurate petrov galerkin methods for transient convective diffusion problems the petrov galerkin method is applied to transient convective diffusion problems with convection dominance weighting functions are used which differ from the shape functions by both symmetric and non symmetric modifications it is proved that the symmetric modifications largely influence the accuracy by a one dimensional and a two dimensional example it is shown how to choose this modification to maximize accuracy

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

multi objective branch and bound abstract branch and bound is a well known generic method for computing an optimal solution of a single objective optimization problem based on the idea divide to conquer it consists in an implicit enumeration principle viewed as a tree search although the branch and bound was first suggested by land and doig 1960 the first complete algorithm introduced as a multi objective branch and bound that we identified was proposed by kiziltan and yucaoglu 1983 rather few multi objective branch and bound algorithms have been proposed this situation is not surprising as the contributions on the extensions of the components of branch and bound for multi objective optimization are recent for example the concept of bound sets which extends the classic notion of bounds has been mentioned by villarreal and karwan 1981 but it was only developed for the first time in 2001 by ehrgott and gandibleux and fully defined in 2007 this paper describes a state of the art of multi objective branch and bound which reviews concepts components and published algorithms it mainly focuses on the contributions belonging to the class of optimization problems who has received the most of attention in this context from 1983 until 2015 the linear optimization problems with zero one variables and mixed 0 1 continuous variables only papers aiming to compute a complete set of efficient solutions are discussed

reducibility of minimax to minisum 0 1 programming problems abstract we consider 0 1 programming problems with a minimax objective function and any set of constraints upon appropriate transformations of its cost coefficients such a minimax problem can be reduced to a linear minisum problem with the same set of feasible solutions such that an optimal solution to the latter will also solve the original minimax problem although this reducibility applies for any 0 1 programming problem it is of particular interest for certain locational decision models among the obvious implications are that an algorithm for solving a p median minisum problem in a network will also solve a corresponding p center minimax problem it should be emphasized that the results presented will in general only hold for 0 1 problems due to intrinsic properties of the minimax criterion

an algorithm for multiobjective zero one linear programming a branch and bound algorithm is presented which is based on the extension of implicit enumeration techniques to multiobjective zero one linear programming and which appears to be computationally quite efficient domination tests aiming at identifying paths of the enumeration tree that lead to dominated solutions as high up the tree as possible are developed some computational results are also given

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

an interactive algorithm for solving multiple objective integer linear programming problems abstract we propose a reference direction based interactive algorithm to solve multiple objective integer linear programming moilp problems at each iteration of the solution procedure the algorithm finds weak nondominated solutions to the relaxed moilp problem only at certain iterations if the dm so desires an additional mixed integer programming problem is solved to find an integer weak nondominated solution which is close to the current continuous weak nondominated solution to the relaxed moilp problem in the proposed algorithm dm has to provide only the reference point at each iteration no special software is required to implement the proposed algorithm the algorithm is illustrated with an example

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

least squares finite elements for first order hyperbolic systems application de la methode des moindres carres a elements finis a l approximation des systemes hyperboliques du premier ordre analyse de la stabilite exemples

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

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

time accurate solution of advection diffusion problems by finite elements abstract the taylor galerkin method recently proposed for the spatial and temporal discretization of hyperbolic equations is employed to derive accurate and efficient numerical schemes for the solution of time dependent advection diffusion problems two distinct numerical strategies are discussed the first is suitable for evolutionary problems while the second is appropriate for situations in which a steady state is eventually reached for purely evolutionary problems the taylor galerkin method is applied to the complete advection diffusion equation and through modifications of the standard mass matrix is shown to generate an incremental form of the crank nicolson time stepping method such an incremental form also lends itself to the derivation of computationally simple but accurate explicit algorithms to deal with transient situations which evolve towards a highly convective steady state the global taylor galerkin method is found to be ineffective since it reduces to the standard galerkin formulation as the temporal term vanishes for such cases we suggest the use of a splitting up method in which advection and diffusion are treated separately by appropriate taylor galerkin methods the proposed methods are illustrated first for linear constant coefficient equations they are successively extended to deal with nonlinear and multi dimensional problems numerical applications indicate their effectiveness

bicriteria network location bnl problems with criteria dependent lengths and minisum objectives abstract we present a new location model which is a generalization of the bicritera median problem we introduce two sum objectives and criteria dependent edge lengths for this np complete problem a solution method finding all the efficient solutions is presented the method is a two phases approach which can easily be applied as an interactive method in phase 1 the supported solutions are found and in phase 2 the unsupported solutions are found this method can be thought of as a general approach to bi objective combinatorial optimization boco problems

an approach for solving nonlinear multi objective separable discrete optimization problem with one constraint we propose an exact solution approach for solving nonlinear multi objective optimization problems with separable discrete variables and a single constraint the approach converts the multi objective problem into a single objective problem by using surrogate multipliers from which we find all the solutions with objective values within a given range we call this the surrogate target problem which is solved by using an algorithm based on the modular approach computational experiments demonstrate the effectiveness of this approach in solving large scale problems a simple example is presented to illustrate an interactive decision making process

solving zero one multiple objective programs through implicit enumeration abstract research on algorithms designed to solve zero one multiple objective linear programs has been rather limited this paper presents a solution procedure for these problems based on the concept of implicit enumeration computational experience is reported and analyzed advantages disadvantages and extensions of the algorithm are discussed

an algorithm for the bi criterion integer programming problem abstract we specify a variation of the weighting method for multi criterion optimization which determines nondominated solutions to the bi criterion integer programming problem the technique makes use of imposed constraints based on nondominated points for the bi criterion case we develop an algorithm which finds all nondominated points by solving a sequence of single criterion integer programming problems we present computational results for the linear 0 1 case and discuss the extension of our algorithm to the general multi criterion integer programming problem

equivalent weights for lexicographic multi objective programs characterizations and computations abstract a recent paper 19 demonstrated the existence of a set of equivalent weights for which the optimal solution set of a preemptive priority multi objective program is precisely equal to the set of optimal solutions to the resulting nonpreemptive program with the objective function given as a linear weighting of the multiple objectives this paper addresses two further issues firstly for some important special cases or applications it is demonstrated that not only is the computation of a set of equivalent weights feasible but it is also highly desirable two algorithms are presented to compute a set of equivalent weights one method is a direct specialization of the approach adopted in 19 whereas the second approach is an alternative technique the latter method is shown to yield weights of uniformly smaller values than the former method while being of the same computational complexity and is hence preferable secondly as opposed to constructing one vector of equivalent weights a characterization is provided for the entire set of equivalent weights

an interactive procedure using domination cones for bicriterion shortest path problems abstract in this paper an interactive procedure is developed for the bicriterion shortest path problem it is assumed that the decision maker s inherant utility function is quasi concave and non increasing and that the network consists of non negative integer valued arc lengths the proposed procedure uses the concept of domination cones which it develops from pairwise comparisons of alternatives these domination cones are used to fathom a large number of pareto optimal solutions extensive computational testing was performed on large grid networks simulating the decision maker s response using polynomial utility functions the results indicate that our proposed procedure is able to converge to the optimal solution in a reasonably small number of pairwise comparisons even for those problems with a large number of pareto optimal solutions

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

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

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

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

petrov galerkin method for multidimensional time dependent convective diffusion equations a petrov galerkin finite element method for two and three dimensional time dependent convection diffusion equations is presented in the context of two space dimensions the method involves perturbed weighting functions in the weighted residuals formulation that are bilinear in space and quadratic in time and depend on two parameters which are calculated according to a local analysis for the one dimensional case the perturbations to the weighting functions can be interpreted as an added local anisotropic balancing diffusion and an added dispersion in the direction of the convective motion the effectiveness of the method is shown through several examples involving the convective and diffusive transport of scalar distributions in known velocity fields

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