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

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

feedforward control is dual to deconvolution a duality is demonstrated between optimal feedforward control and optimal deconvolution or input estimation these two problems are normally discussed separately in the literature but have close similarities duality between them can be demonstrated if and only if one uses general problem formulations with frequency shaped weighting in the criteria from one of the problems the dual problem can then be obtained immediately from the block diagram by reversing the directions of arrows interchanging summation points and node points and transposing all transfer function matrices this result applies for continuous and discrete time problems as well as for minimization of j g for any transfer function norms for which gt g a derivation of a polynomial solution to the frequency weighted discrete time mimo lqg feedforward control problem illustrates the use of the duality

solving multiobjective multiconstraint knapsack problems using mathematical programming and evolutionary algorithms abstract in this paper we solve instances of the multiobjective multiconstraint or multidimensional knapsack problem momckp from the literature with three objective functions and three constraints we use exact as well as approximate algorithms the exact algorithm is a properly modified version of the multicriteria branch and bound mcbb algorithm which is further customized by suitable heuristics three branching heuristics and a more general purpose composite branching and construction heuristic are devised comparison is made to the published results from another exact algorithm the adaptive e constraint method laumanns m thiele l zitzler e 2006 an efficient adaptive parameter variation scheme for metaheuristics based on the epsilon constraint method european journal of operational research 169 932 942 using the same data sets furthermore the same problems are solved using standard multiobjective evolutionary algorithms moea namely the spea2 and the nsgaii the results from the exact case show that the branching heuristics greatly improve the performance of the mcbb algorithm which becomes faster than the adaptive e constraint regarding the performance of the moea algorithms in the specific problems spea2 outperforms nsgaii in the degree of approximation of the pareto front as measured by the coverage metric especially for the largest instance

a novel derivation methodology for polynomial lq controller design a simple derivation method for optimization of linear quadratic lq controllers is presented in the discrete time polynomial systems framework a control law variation regarded as a potential feedforward from the innovations is used orthogonality is evaluated in the frequency domain by collectively cancelling unstable poles by zeros the suggested method summarized as a three step scheme is exemplified on a disturbance measurement feedforward and an output feedback problem it is a simple more direct alternative to the completing the squares approach

a weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program abstract various computational difficulties arise in using decision set based vector maximization methods to solve multiple objective linear programming problems as a result several researchers have begun to explore the possibility of solving these problems by examining subsets of their outcome sets rather than of their decision sets in this article we present and validate a basic weight set decomposition approach for generating the set of all efficient extreme points in the outcome set of a multiple objective linear program based upon this approach we then develop an algorithm called the weight set decomposition algorithm for generating this set a sample problem is solved using this algorithm and the main potential computational and practical advantages of the algorithm are indicated

polynomial solution of the standard multivariable spl hscr sub 2 optimal control problem in this work the authors solve the standard multivariable spl hscr sup 2 optimal control problem using polynomial matrix techniques

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

some properties of location problems with block and round norms the point objective problem and the weber problem are two well known formulations for locating a new facility with respect to a set of fixed facilities when locations are represented as points on a plane the point objective problem is a multiple objective formulation of minimizing the distance from a variable point to each of the fixed points similarly the weber problem is a single objective formulation of minimizing the sum of transportation costs between the variable point and the fixed points where transportation cost is a function of distance generalizing solution properties for these problems from distance measures given by the euclidean rectilinear ip and one infinity norms this paper develops solution properties under the broad classes of distance measures given by block and round norms for the point objective problem we show that i the efficient set for all round norms is the convex hull of the set of fixed points and ii the efficient set under a block norm tends to the convex hull for a sequence of block norms approaching a round norm for the weber problem we prove that i an optimal location for any block norm may be found in a finite set of intersection points belonging to the convex hull and ii this set tends to the convex hull for a sequence of block norms approaching a round norm finally we use these results to propose a synthesis of some of the main properties in continuous and network location theory

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

paper efficient algorithm for matrix spectral factorization an algorithm is presented for the spectral factorization of polynomial or rational matrices arising in optimal control and filtering theory as well as in network theory there are two versions of the algorithm one applicable to continuous time problems the other to discrete time ones both versions are based on newton s method feature quadratic convergence and provide a significant improvement in efficiency over the existing methods

two machine flow shop scheduling with two criteria maximum earliness and makespan abstract in this study we address the problem of minimizing makespan and maximum earliness simultaneously in a two machine flow shop environment we develop a branch and bound procedure that generates all efficient solutions with respect to two criteria we propose several lower and upper bounding schemes to enhance the efficiency of the algorithm we also propose a heuristic procedure that generates approximate efficient solutions our computational results reveal that the branch and bound procedure is capable of solving problems with up to 25 jobs and the heuristic procedure produces approximate efficient solutions that are very close to exact efficient solutions in very small computation times

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

use of reference points for solving monlp problems abstract the paper discusses a scalar problem that uses a reference point for solving the multiobjective nonlinear programming monlp problem some properties of the solution of this scalar problem are described in order to improve the achieved value of one criterion only the corresponding component of the reference point has to be changed

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

general polynomial solution to the optimal feedback feedforward stochastic tracking problem a general solution to the optimal stochastic tracking problem in the presence of both measurable and immeasurable disturbances is obtained using polynomial techniques the plant under consideration includes a coloured measurement noise signal in addition all disturbance and reference sub systems may be unstable the problem formulation involves a cost function which has dynamic weighting elements a feedforward compensator is incorporated in the optimization procedure for the rejection of the measurable disturbance

on pareto optima the fermat weber problem and polyhedral gauges this paper deals with multiobjective programming in which the objective functions are nonsymmetric distances derived from different gauges to the points of a fixed finite subset of n it emphasizes the case in which the gauges are polyhedral in this framework the following result is known if the gauges are polyhedral then each pareto optimum is the solution to a fermat weber problem with strictly positive coefficients we give a new proof of this result and we show that it is useful in finding the whole set of efficient points of a location problem with polyhedral gauges also we characterize polyhedral gauges in terms of a property of their subdifferential

hull properties in location problems abstract some properties of the solution set for single and multifacility continuous location problems with l p distances are given a set reduction algorithm is developed for problems in k dimensional space having rectangular distances

the compromise hypersphere for multiobjective linear programming abstract for a linear programming problem with q 2 objective functions that is a multiobjective linear programming problem we propose a method for ranking the full set or a subset of efficient extreme point solutions the idea is to enclose the given efficient solutions as represented by q dimensional points in objective space within an annulus of minimum width where the width is determined by a hypersphere that minimizes the maximum deviation of the points from the surface of the hypersphere we argue that the hypersphere represents a surface of compromise and that the point closest to its surface should be considered as the best compromise efficient solution also given a ranked sub set of efficient solutions a procedure is given that associates to each efficient solution a set of q positive weights that causes the efficient solution to be optimal with respect to the given set of efficient solutions

coupled polynomial equations for lq control synthesis and an algorithm for solution the polynomial equation approach can be used to solve a variety of important control problems the approach leads to the requirement to solve linear polynomial equations we present a new algorithm for the numerical solution of a general coupled pair of linear polynomial equations the algorithm is based upon the method of polynomial reductions theoretically solving the coupled equations together enhances the numerical robustness of the equation solution the algorithm finds a specific and unique minimal degree solution of the equations the general couple of equations studied is representative of a number of problems in linear control theory and the minimal degree solution usually corresponds to an optimizing solution of the control problem

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

an interactive multiobjective nonlinear programming procedure abstract this paper develops a method for interactive multiobjective nonlinear programming procedure monlp it provides a detailed description of an efficient algorithm and reports on promising computational results it also discusses several alternative strategies for implementing grg code generalized reduced gradient which is known as one of the best methods for solving nonlinear optimization problems abadie 1978 the method relies on three steps 1 generation of a subset of feasible efficient solutions 2 interactive definition by decision maker dm of his preference structure according to desired outcome 3 determination of a compromise solution using nonlinear optimization a global analysis based on reference point search procedure is performed in the criteria space following this methodology it is possible for the dm to find his final solution a microcomputer version for medium problems of the method is available

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

newton s method for multiobjective optimization we propose an extension of newton s method for unconstrained multiobjective optimization multicriteria optimization this method does not use a priori chosen weighting factors or any other form of a priori ranking or ordering information for the different objective functions newton s direction at each iterate is obtained by minimizing the max ordering scalarization of the variations on the quadratic approximations of the objective functions the objective functions are assumed to be twice continuously differentiable and locally strongly convex under these hypotheses the method as in the classical case is locally superlinear convergent to optimal points again as in the scalar case if the second derivatives are lipschitz continuous the rate of convergence is quadratic our convergence analysis uses a kantorovich like technique as a byproduct existence of optima is obtained under semilocal assumptions

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 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

optimal multivariable regulation with disturbance measurement feedforward abstract the problem of optimal stochastic regulation based on output feedback and disturbance measurement feedforward for multivariable systems is solved using the polynomial equation approach two independent couples of polynomial matrix equations are derived which yield the feedback and the feedforward parts of the regulator

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

diffusion in superconducting percolation networks number of sites visited two models of diffusion in superconducting percolation networks are studied on a one dimensional system the authors use chains of 5 105 sites and study the scaling properties of the mean squared displacement of termites which execute random walks on the network mean number of distinct sites visited and mean number of visits to the origin they find that although these quantities can be described by well defined scaling laws the values of the critical exponents appear to depend on the time interval in which the walks are studied they observe at least four different scaling regimes the implications of these results for higher dimensional systems are discussed

multi objective optimization over convex disjunctive feasible sets using reference points abstract in this paper we consider the multiple objective optimization problem moop where concave functions are to be maximized over a feasible set represented as a union of compact convex sets to solve this problem we consider two auxiliary scalar optimization problems which use reference points the first one contains only continuous variables it has higher dimensionality however it is convex the second scalar problem is a mixed integer programming problem the solutions of both scalar problems determine nondominated points some other properties of these problems are also discussed

meaning and validity of interactive procedures as tools for decision making this papers examines procedures based on answers to questions an entity q asks an actor d in accordance with a protocol p the aim is either to select an alternative a considered by d to be the optimal choice among a set of alternatives a or to formulate a utility function u considered relevant by d for comparing alternatives in a what gives meaning to the final result of this type of interactive procedure on which criteria can its validity be assessed in analysing three questions of a parlor game we can produce evidence that the answers to such questions do not depend on p alone but that the way in which d produces his answers plays just a central role threee different hypotheses concerning this points led us to a new approach to this type of question an approach which point out the illusive nature of certain types of answers

multi objective integer programming a general approach for generating all non dominated solutions in this paper we develop a general approach to generate all non dominated solutions of the multi objective integer programming moip problem our approach which is based on the identification of objective efficiency ranges is an improvement over classical e constraint method objective efficiency ranges are identified by solving simpler moip problems with fewer objectives we first provide the classical e constraint method on the bi objective integer programming problem for the sake of completeness and comment on its efficiency then present our method on tri objective integer programming problem and then extend it to the general moip problem with k objectives a numerical example considering tri objective assignment problem is also provided

a steepest descent method for vector optimization in this work we propose a cauchy like method for solving smooth unconstrained vector optimization problems when the partial order under consideration is the one induced by the nonnegative orthant we regain the steepest descent method for multicriteria optimization recently proposed by fliege and svaiter we prove that every accumulation point of the generated sequence satisfies a certain first order necessary condition for optimality which extends to the vector case the well known gradient equal zero condition for real valued minimization finally under some reasonable additional hypotheses we prove global convergence to a weak unconstrained minimizer as a by product we show that the problem of finding a weak constrained minimizer can be viewed as a particular case of the so called abstract equilibrium problem

a rounding algorithm for approximating minimum manhattan networks for a set t of n points terminals in the plane a manhattan network on t is a network n t v e with the property that its edges are horizontal or vertical segments connecting points in email protected t and for every pair of terminals the network n t contains a shortest l 1 path between them a minimum manhattan network on t is a manhattan network of minimum possible length the problem of finding minimum manhattan networks has been introduced by gudmundsson levcopoulos and narasimhan j gudmundsson c levcopoulos g narasimhan approximating a minimum manhattan network nordic journal of computing 8 2001 219 232 proc approx 99 1999 pp 28 37 and its complexity status is unknown several approximation algorithms with factors 8 4 and 3 have been proposed recently kato imai and asano r kato k imai t asano an improved algorithm for the minimum manhattan network problem isaac 02 in lncs vol 2518 2002 pp 344 356 have given a factor 2 approximation algorithm however their correctness proof is incomplete in this paper we propose a rounding 2 approximation algorithm based on an lp formulation of the minimum manhattan network problem

use of reference points for molp problems analysis abstract two scalar problems intended for analysis of multiple objective linear programming molp problems are considered in the paper these problems use reference points and it is shown how to change the reference point in order to improve the attained value of one criterion

a bi reference procedure for interactive multiple criteria programming the paper presents an interactive procedure to search the set of nondominated outcomes of a multiple criteria linear programming problem the procedure requires the decision maker to specify the worst outcome then the ideal outcome is identified and the improvement direction from the worst to ideal outcomes is constructed a trial solution is found by moving from a current solution along the improvement direction while maximizing the step size for a trial solution the decision maker is requested to partition the set of objective functions into three categories those to be improved those which may remain unchanged those which may be relaxed based on this partition the procedure displaces the worst and ideal outcomes calculates the new improvement direction and the entire process is repeated the method terminates when two successive trial solutions are reasonably similar

multicriteria planar location problems abstract given q different objective functions three types of single facility problems are considered lexicographic pareto and max ordering problems after discussing the interrelation between the problem types a complete characterization of lexicographic locations and some instances of pareto and max ordering locations is given the characterizations result in efficient solution algorithms for finding these locations the paper relies heavily on the theory of restricted locations developed by the same authors and can be further extended for instance to multi facility problems with several objectives the proposed approach is more general than previously published results on multicriteria planar location problems and is particularly suited for modelling real world problems

finding a weights restricted efficient extreme point and using it for solving molp problems this paper deals with solving a multiple objective linear programming problem a preferred weights vector from a restricted set of weights incorporating the case that the weighted problem may have unbounded solution is used for generating a preferred efficient extreme point the final solution can be found by changing interactively weights restrictions or comparing weights restricted efficient extreme points also the results can be used in vector maximum and interactive methods

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

efficient computation of the search region in multi objective optimization multi objective optimization procedures usually proceed by iteratively producing new solutions for this purpose a key issue is to determine and efficiently update the search region which corresponds to the part of the objective space where new nondominated points could lie in this paper we elaborate a specific neighborhood structure among local upper bounds thanks to this structure the update of the search region with respect to a new point can be performed more efficiently compared to existing approaches moreover the neighborhood structure provides new insight into the search region and the location of nondominated points

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

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

polynomial optimization of stochastic discrete time control for unstable plants the matrix polynomial method of optimization of linear multivariable discrete time control for unstable plants with stationary stochastic inputs is derived in a constructive manner new sufficient conditions are obtained and kucera s second diophantine equation is found directly from the requirement that the system be stable although the second equation must be satisfied it is proved that it need not be used in the optimization when a certain coprimeness exists

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

optimizing a linear function over an integer efficient set in this paper a method for optimizing a linear function over the integer pareto optimal set without having to determine all integer efficient solutions is presented the proposed algorithm is based on a simple selection technique that improves the linear objective value at each iteration two types of cuts are performed successively until the optimal value is obtained and the current truncated region contains no integer feasible solution

bicriteria network flow problems integer case abstract we consider a bicriteria network flow problem with flow variables restricted to integer values the set of efficient solutions to the problem can be obtained by adopting a bicriteria integer programming technique the purpose of this paper is to present a new technique which capitalizes on the network structure and the unimodular property of the incidence matrix the procedure uses efficient solutions to the continuous version of the bicriteria network flow problem and parametric programming in order to generate the efficient solutions to the bicriteria integer network flow problem the performance of the algorithm is also discussed

optimal parallel model solutions using the polynomial approach solutions to the optimal filtering and open loop control problems using a generalized parallel model scheme are presented the solutions are based on the algebra of polynomial matrices different c

implied polynomial matrix equations in multivariable stochastic optimal control abstract this paper reports recent work in the theoretical development of the polynomial equation approach to the optimization of multivariable control systems the algebraic properties of the polynomial matrix equations which define the optimal controller are investigated and new results concerned with the numerical solvability of the equations are derived

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

first exit time of termites and random super normal conductor networks the resistance of a random super normal conductor network is calculated through the diffusion of a termite which performs a random walk on the normal bonds and has the same probability to exist from any point on a cluster of superconducting bonds the first time t that the termite exits at a distance r from the origin averaged over many configurations and runs is found to behave as t approximately r2k for r xi pc p s describes the divergence of the conductivity as p to pc p being the concentration of the superconductor scaling arguments are used to show that k 1 s 2 theta where 2 theta is the fractal dimension of random walks on single clusters at pc numerical simulations at two dimensions d 2 yields s 1 34 or 0 10 and k 1 34 or 0 03 in agreement with scaling the authors also show that the probability of return to the origin at time t behaves as t dk2 preliminary results at d 1 and other calculations methods are also discussed

transport in a two component randomly composite material scaling theory and computer simulations of termite diffusion near the superconducting limit the question of transport in a random two component mixture is addressed to this end two models are precisely formulated that effectively extend to two component mixtures the de gennes ant model of one component systems we develop and test a scaling theory and we solve some of the problems associated with the limit where one of the components is superconducting our work provides the first practical realisation of the termite model of a random superconducting network which performs a normal walk in the normal regions of the material but performs a new and unique form of random walk in the superconducting regions we find that the divergence of the electrical conductivity at the percolation threshold can be described by this random walk and that the critical exponent s is given by s 1 3 f 0 1 in d 2 if we perturb away from the pure superconduct ing limit we find that the electrical properties can still be described by the random walk model with a crossover exponent i 0 4 d 2 moreover we find that the diffusion constant in this region is described by a scaling form so that data can be made to collapse upon a single curve whose form is governed by the exponents s and i

a polynomial approach to the mimo lq servo and disturbance rejection problems abstract a novel matrix fraction solution to the discrete time lq stochastic tracking and servo problems is extended to the disturbance rejection problem unlike recent contributions here the resulting control law at time t is given in terms of an expectation conditioned to the accessible disturbance given up to time t k if k is positive and large enough the optimal feedforward input can be tightly approximated without requiring any stochastic model for the disturbance if the latter is known also for recurrent or predictable disturbance the optimal feedforward input is obtained by solving a single bilateral diophatine equation

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

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

on the asymptotic properties of the lqg feedforward self tuner in this paper we investigate the stability and convergence of the indirect adaptive lqg feedforward controller designed in order to precompensate the effect of the measurable disturbances for a general s1so non minimum phase stable plant we study the equilibrium set of the associated ode and obtain a necessary condition and some sufficient conditions on the parameters of the original plant structure such that the limit set contains only the true parameter vector as shown by some examples the limit set in general contains points which do not correspond to the true parameter vector nor yield an optimal controller design simulation results show that in certain cases when no extra excitation is present the parameter estimates can indeed converge to such limit points meaning that the adaptive system is not self tuning finally the global stability and convergence of the adaptive controller based on the stochastic gradient algorithm are established and it is shown that if the exogenous input is

the random normal superconductor mixture in one dimension two models for random two conductor mixtures by diffusion processes are considered in the one dimensional case it is shown that the two models are not in the same universality class this is seen to be an artefact of systems with pc 1 however a scaling theory proposed earlier is tested for this simple one dimensional case and confirmed

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

an improved version of the augmented e constraint method augmecon2 for finding the exact pareto set in multi objective integer programming problems generation or a posteriori methods in multi objective mathematical programming momp is the most computationally demanding category among the momp approaches due to the dramatic increase in computational speed and the improvement of mathematical programming algorithms the generation methods become all the more attractive among today s decision makers in the current paper we present the generation method augmecon2 which is an improvement of our development augmecon although augmecon2 is a general purpose method we will demonstrate that augmecon2 is especially suitable for multi objective integer programming moip problems specifically augmecon2 is capable of producing the exact pareto set in moip problems by appropriately tuning its running parameters in this context we compare the previous and the new version in a series of new and old benchmarks found in the literature we also compare augmecon2 s performance in the generation of the exact pareto sets with established methods and algorithms based on specific moip problems knapsack set packing and on published results except from other mathematical programming methods augmecon2 is found to be competitive also with multi objective meta heuristics momh in producing adequate approximations of the pareto set in multi objective combinatorial optimization moco problems

optimal multivariable lqg control using a single diophantine equation the general solution of the optimal lqg problem using the polynomial equation approach involves the solution of a couple of two sided matrix polynomial equations the conditions under which a single one sided equation which is related to the original two the implied diophantine equation yields the unique optimal controller are derived in this paper the result has considerable relevance to aspects such as computation and self tuning control applications

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

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

cutting plane method for multiple objective stochastic integer linear programming abstract this paper grapples with the problem of incorporating integer variables in the constraints of a multiple objective stochastic linear program moslp after representing uncertain aspirations of the decision maker by converting the original problem into a deterministic multiple objective integer linear program moilp a cutting plane technique may be used to compute all the efficient solutions of the last model leaving the decision maker to choose a solution according to his preferences a numerical example is also included for illustration

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

theory and methodology a bicriteria approach to the two machine flow shop scheduling problem in this paper we address the problem of minimizing makespan and sum of completion times simultaneously in a two machine flow shop environment we formulate the problem as a bicriteria scheduling problem and develop a branch and bound procedure that iteratively solves restricted single objective scheduling problems until the set of efficient solutions is completely enumerated we report computational results and explore certain properties of the set of efficient solutions we then discuss their implications for the decision maker

a non interactive elicitation method for non linear multiattribute utility functions theory and application to agricultural economics practical implementation of multiattribute utility theory is limited partly for the lack of operative methods to elicit the parameters of the multiattribute utility function particularly when this function is not linear as a consequence most studies are restricted to linear specifications which are easier to estimate and to interpret we propose an indirect method to elicit the parameters of a non linear utility function to be compatible with the observed behaviour of decision makers rather than with their answers to direct surveys the idea rests on approaching the parameter estimation problem as a dual of the decision problem by making the observed decisions to be compatible with a rational decision making process

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

polynomial optimization of stochastic feedback control for unstable plants abstract the role of kucera s two diophantine equations is explored in the optimization of a discrete time feedback controller for a multivariate unstable plant subject to stochastic reference and disturbance but it is usually only necessary to solve one of the equations however with an unstable plant an extra diophantine equation must be solved when there is output measurement noise

termite and ant diffusions in the d dimensional lattice trapping model the coherent medium approximation of odagaki and lax 1981 is generalised to the trapping model the frequency dependent diffusion constant in the d dimensional hypercubic lattice is studied when the jump rate obeys a bimodal distribution the coherent medium approximation gives the correct static diffusion constant the imaginary part of the ac part of the diffusion constant vanishes linearly in frequency omega when d 2 as omega ln omega when d 2 and as omega d 2 when d 4 as omega 2 ln omega when d 4 and as omega d 2 when d 4 the termite limit is studied by taking the limit that one of the two jump rates probability p becomes infinite in the termite diffusion the static diffusion constant is critical at p 1 and the critical exponents are the same as those for the termite diffusion in the hopping model the ant or ant lion limit is defined by the limit of one jump rate being zero the imaginary and real parts of the ac diffusion constant vanish linearly and quadratically in frequency respectively the critical exponent of the leading real part of the diffusion constant is one less than the corresponding exponent for the ant diffusion in the hopping model below the percolation threshold while the leading imaginary part has the same critical exponent as those in the hopping model

a new algorithm for solving planar multiobjective location problems involving the manhattan norm abstract this paper is devoted to the study of unconstrained planar multiobjective location problems where distances between points are defined by means of the manhattan norm we characterize the nonessential objectives and by eliminating them we develop an effective algorithm for generating the whole set of efficient solutions as the union of a special family of rectangles and line segments we prove the correctness of this algorithm analyze its complexity and present illustrative computational results obtained by a matlab based implementation

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

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

an algorithm for optimizing a linear function over an integer efficient set optimizing a linear function over the efficient set of a multiobjective integer linear programming moilp problem is a topic of unquestionable practical as well as mathematical interest within the field of multiple criteria decision making as known those problems are particularly difficult to deal with due to the discrete nature of the efficient set which is not explicitly known nor a suitable implicit description is available in this work an exact algorithm is presented to optimize a linear function over the efficient set of a moilp the approach here proposed defines a sequence of progressively more constrained single objective integer problems that successively eliminates undesirable points from further consideration the algorithm has been coded in c sharp using cplex solver and computational experiments have been undertaken in order to analyze performance properties of the algorithm over different problem instances randomly generated

hopping conduction in insulator conductor superconductor mixtures the coherent medium approximation is applied to study the frequency dependent diffusion constant in two and three dimensional ant termite like mixtures where three types of jump rates normal metallic superconducting and insulating are distributed randomly the dc diffusion constant vanishes when p r pc where p and r are the probabilities that a given bond is metallic and superconducting respectively and z is the coordination number of the lattice pc rc identical to 2 z in the low frequency limit the real and imaginary parts of the ac diffusion constant go as a z d p r f omega and b z d p r g omega respectively a behaviour similar to the pure ant limit the behaviour of f omega and g omega is examined below at and above the percolation thresholds in both two and three dimensions the coefficients a and b of these leading terms diverge as r to rc superconducting region percolates indicating enhancement in the dielectric constant