goal programming for decision making an overview of the current state of the art there have been significant advances in the theory of goal programming gp in recent years particularly in the area of intelligent modelling and solution analysis the intention of this paper is to provide an overview of these developments to detail and assess the current state of the art in the subject and to highlight areas which seem promising for future research modelling techniques such as detection and restoration of pareto efficiency normalisation redundancy checking and non standard utility function modelling are overviewed the connection between gp and other multi objective programming techniques as well as a utility interpretation of gp are examined the rationality of ranking multi criteria decision making techniques and of placing gp in such a ranking is discussed

non linear oscillations of a rotor in active magnetic bearings abstract the non linear response of a rotor supported by active magnetic bearings is investigated and both primary and internal resonances are considered the method of multiple scales is used to obtain four first order ordinary differential equations that describe the modulation of the amplitudes and phases of vibrations in the horizontal and vertical directions the steady state response and the stability of the solutions are determined numerically from the reduced system it is shown that the steady state solutions lose their stability by either saddle node bifurcation or hopf bifurcation in the regime of multiple coexisting solutions two stable solutions are found the effect of imbalance eccentricity as well as the effect of the proportional and derivative gains of the controller on the non linear response of the system are studied finally numerical simulations are performed to verify the analytical predictions

reference points and approximation algorithms in multicriteria discrete optimization abstract mathematical research on multicriteria optimization problems predominantly revolves around the set of pareto optimal solutions in practice on the other hand methods that output a single solution are more widespread reference point methods are a successful example of this approach and are widely used in real world multicriteria optimization a reference point solution is the solution closest to a given reference point in the objective space we study the connection between reference point methods and approximation algorithms for multicriteria optimization problems over discrete sets in particular we establish that in terms of computational complexity computing approximate reference point solutions is polynomially equivalent to approximating the pareto set complementing these results we show for a number of general algorithmic techniques in single criteria optimization how they can be lifted to reference point optimization in particular we lift the link between dynamic programming and fptas as well as certain lp rounding techniques the latter applies e g to set cover and several machine scheduling problems

meta goal programming abstract in most of the goal programming gp applications reported in the literature the election of the gp variant is made in a mechanistic way by the analyst however each variant implies a different preference structure and thus it should be chosen by the decision maker moreover the final solution of the problem depends critically on the variant chosen in this paper it is assumed that the use of a combination of gp variants may reflect in many cases more precisely the actual preferences of the decision maker in this way a sensitivity analysis of the solution obtained as well as of the own model structure can be very helpful to let the decision maker clarify his her knowledge about the reality analysed this type of problem requires a more general approach that leads to a gp formulation of the initial gp model this type of meta gp approach is presented in this paper

a classification model based on goal programming with non standard preference functions with application to the prediction of cinema going behaviour this paper presents a goal programming model that allows for the flexible handling of the two group classification problem the goal programming model is based around the concepts of non standard preference functions and penalty function modelling an extension to a generalised distance metric case is given the inclusion of multiple levels of classification based upon different levels of certainty is incorporated into the model the model is tested on a real life data set pertaining to cinema going attendance and conclusions are drawn both in the context of the methodology and of the application

evolution equation of phenotype distribution general formulation and application to error catastrophe an equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics the equation is solved by using the singular perturbation method and assuming that the number of bases in the genetic sequence is large applying the equation to the mutation selection model by eigen provides the critical mutation rate for the error catastrophe phenotypic fluctuation of clones individuals sharing the same gene is introduced into this evolution equation with this formalism it is found that the critical mutation rate is sometimes increased by the phenotypic fluctuations i e noise can enhance robustness of a fitted state to mutation our formalism is systematic and general while approximations to derive more tractable evolution equations are also discussed

combining equity and utilitarianism in a mathematical programming model we discuss the problem of combining the conflicting objectives of equity and utilitarianism for social policy making in a single mathematical programming model the definition of equity we use is the rawlsian one of maximizing the minimum utility over individuals or classes of individuals however when the disparity of utility becomes too great the objective becomes progressively utilitarian such a model is particularly applicable not only to health provision but to other areas as well building a mixed integer linear programming milp formulation of the problem raises technical issues because the objective function is nonconvex and the hypograph is not milp representable in its initial form we present a succinct formulation and show that it is sharp in the sense that its linear programming relaxation describes the convex hull of the feasible set before extra resource allocation or policy constraints are added we apply the formulation to a healthcare planning problem and show that instances of realistic size are easily solved by standard milp software this paper was accepted by dimitris bertsimas optimization

bifurcation behavior of a rotor supported by active magnetic bearings abstract the non linear dynamics of a rigid rotor levitated by active magnetic bearings is investigated the vibrations in the horizontal and vertical directions are analyzed on the center manifold near the double zero degenerate point by using normal form method the resulting normal forms in the horizontal and vertical directions are different due to the effect of rotor weight it is shown that the vibratory behavior in the vertical direction can be reduced on the center manifold to the bogdanov takens form for the autonomous case there exist saddle node bifurcation and hopf bifurcation for local analysis and a saddle connection bifurcation for global analysis for non autonomous case the melnikov technique is used to determine the critical parameter at which the homoclinic orbits intersect transversally for the vibrations in the horizontal direction the essential non linear terms of the truncated normal form are third order the behaviors of zero solutions are given finally numerical simulations are performed to verify the analytical predictions

stability and bifurcation in a neural network model with two delays abstract a simple neural network model with two delays is considered linear stability of the model is investigated by analyzing the associated characteristic transcendental equation for the case without self connection it is found that the hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem an example is given and numerical simulations are performed to illustrate the obtained results

delay induced instabilities in nonlinear feedback systems extending general methods developed in synergetics to construct order parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems it will be shown that in the vicinity of an instability the dynamical behavior of the infinite dimensional delay system is approximately governed by a low dimensional set of order parameter equations which turn out to be of the form of ordinary differential equations i e they no longer contain memory terms the general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase locked loop where the finite propagation time of the signal in the feedback loop is taken into account

quasispecies theory for multiple peak fitness landscapes we use a path integral representation to solve the eigen and crow kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions in the general case we find that the solution to these molecular evolution models can be written as the optimum of a fitness function with constraints enforced by lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space the results for the eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system

compromise programming non interactive calibration of utility based metrics utility functions have been used widely to support multi objective decision making expansion of a general additive utility function around the ideal results in a composite linear quadratic metric of a compromise programming problem determining the unknown parameters of the composite linear quadratic metric requires substantial interaction with the decision maker who might not always be available or capable to participate in such a process we propose a non interactive method that uses information on observed attribute levels to obtain the unknown parameters of the composite linear quadratic metric and enables forecasting and scenario analysis the method is illustrated with a small scale numerical example

quasispecies model of evolution with migration we consider the model of asexual evolution with migration which was proposed by waclaw et al phys rev lett 105 268101 2010 prltao0031 900710 1103 physrevlett 105 268101 this model setting is based on the standard mutation scheme from the quasispecies theory but with replicators moving from one habitat to another the primary goal is to solve exactly the infinite population genome length version of the model for the independent random distribution of fitnesses considered in the original paper moreover we propose the analytical solution for the single peak and the symmetric fitness landscape our analytical solution is exact at the limit of large n we found two phases the correlated phase with the identical distributions of mutations in both habitats and the uncorrelated phase where the second habitat is choosing another peak of distribution in sequence space compared to the peak in the first habitat

solvable biological evolution model with a parallel mutation selection scheme based on the connection between a quantum spin model and an asexual biological evolution model with a single peak fitness function in parallel mutation selection scheme we solve exactly both static and dynamics of the evolution model we find that relaxation in such a parallel scheme is faster than that in a connected scheme of eigen model our method can also be extended to other fitness functions

stability and hopf bifurcation of a magnetic bearing system with time delays the effect of time delays occurring in the feedback control loop on the linear stability of a simple magnetic bearing system is investigated by analyzing the associated characteristic transcendental equation it is found that a hopf bifurcation can take place when time delays pass certain values the direction and stability of the hopf bifurcation are determined by constructing a center manifold and by applying the normal form method it is also found that a codimension two bifurcation can occur through a hopf and a steady state bifurcation interaction finally numerical simulations are performed to verify the analytical predictions

a practical weight sensitivity algorithm for goal and multiple objective programming this paper presents a weight sensitivity algorithm that can be used to investigate a portion of weight space of interest to the decision maker in a goal or multiple objective programme the preferential information required from the decision maker is an initial estimate of their starting solution with an equal weights solution being used as a default if this is not available and preference information that will define the portion of weight space on which the sensitivity analysis is to be conducted the different types of preferential information and how they are incorporated by the algorithm are discussed the output of the algorithm is a set of distinct solutions that characterise the portion of weight space searched the possible different output requirements of decision makers are detailed in the context of the algorithm the methodology is demonstrated on two examples one hypothetical and the other relating to predicting cinema going behaviour conclusions and avenues for future research are given

schwinger boson formulation and solution of the crow kimura and eigen models of quasispecies theory we express the crow kimura and eigen models of quasispecies theory in a functional integral representation we formulate the spin coherent state functional integrals using the schwinger boson method in this formulation we are able to deduce the long time behavior of these models for arbitrary replication and degradation functions we discuss the phase transitions that occur in these models as a function of mutation rate we derive for these models the leading order corrections to the infinite genome length limit

error threshold in simple landscapes we consider the quasispecies description of a population evolving in both the master sequence landscape where a single sequence is evolutionarily preferred over all others and the rem landscape where the fitness of different sequences is an independent identically distributed random variable we show that in both cases the error threshold is analogous to a first order thermodynamical transition where the overlap between the average genotype and the optimal one drops discontinuously to zero

stability and bifurcation of rotor motion in a magnetic bearing abstract the equations of motion of a two degrees of freedom mass in a magnetic bearing are non linear in displacement with geometric coupling of the magnetic bearing coupling the horizontal and vertical components of rotor motion the non linear forced response is studied in two ways 1 using imbalance force 2 using non imbalance harmonic force in the forced response only periodic motion is investigated here stable periodic motion is obtained by numerical integration and by the approximate method of trigonometric collocation where unstable motion coexists with stable motion after a bifurcation of periodic motion the unstable motion is obtained by the collocation method the periodic motions local stability and bifurcation behavior are obtained by floquet theory the parameters i e rotor speed imbalance eccentricity forcing amplitude rotor weight and geometric coupling are investigated to find regimes of non linear behavior such as jumps and subharmonic motion

a general structure of achievement function for a goal programming model abstract a key element of a goal programming model is the achievement function that is the function that measures the degree of minimisation of the unwanted deviation variables of the goals considered in the model the three oldest and still most widely used forms of achievement functions are the following archimedean lexicographic and minmax while they are the most common other newer versions can offer theoretical and practical advantages these newer forms will be analytically described and interpreted in utility terms throughout this paper the presentation will end with a very general structure which encompasses as particular cases basically all the achievement functions proposed in the literature

multi choice goal programming with utility functions abstract goal programming gp has been and still is the most widely used technique for solving multiple criteria decision problems and multiple objective decision problems by finding a set of satisfying solutions however the major limitation of goal programming is that can only use aspiration levels with scalar value for solving multiple objective problems in order to solve this problem multi choice goal programming mcgp was proposed by chang 2007a following the idea of mcgp this study proposes a new concept of level achieving in the utility functions to replace the aspiration level with scalar value in classical gp and mcgp for multiple objective problems according to this idea it is possible to use the skill of mcgp with utility functions to solve multi objective problems the major contribution of using the utility functions of mcgp is that they can be used as measuring instruments to help decision makers make the best appropriate policy corresponding to their goals with the highest level of utility achieved in addition the above properties can improve the practical utility of mcgp in solving more real world decision management problems

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

evolution models with lethal mutations on symmetric or random fitness landscapes we calculate the mean fitness for evolution models when the fitness is a function of the hamming distance from a reference sequence and there is a probability that this fitness is nullified eigen model case or tends to the negative infinity crow kimura model case we calculate the mean fitness of these models the mean fitness is calculated also for the random fitnesses with logarithmic normal distribution reasonably describing sometimes the situation with rna viruses

selecting the cp metric a risk aversion approach abstract through a linkage between arrow s risk theory and compromise programming we obtain a reliable specification of the metric defining the compromise distance from a point to the ideal point in the n attribute space

dynamics of the eigen and the crow kimura models for molecular evolution we introduce an alternative way to study molecular evolution within well established hamilton jacobi formalism showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the 1n accuracy where n is the genome length for a smooth and monotonic fitness function this approach gives two dynamical phases smooth dynamics and discontinuous dynamics the latter phase arises naturally with no explicite singular fitness function counterintuitively the hamilton jacobi method yields straightforward analytical results for the models that utilize fitness as a function of hamming distance from a reference genome sequence we also show the way in which this method gives dynamical phase structure for multipeak fitness

compromise programming a utility based linear quadratic composite metric from the trade off between achievement and balanced non corner solutions abstract in this paper compromise programming cp is viewed as the maximization of the decision maker s additive utility function whose arguments are the criteria under consideration subject to an efficient frontier of criteria and the non negativity constraints in a deterministic context this is equivalent to minimizing the difference distance between utility at the ideal point and utility at a frontier point on the criteria map a meaningful statement as minimizing distances to the utopia is the ethos of compromise programming by taylor expansion of utility around the ideal point the distance to the utopia becomes the weighted sum of linear and quadratic cp distances which gives us the composite metric while the linear terms pursue achievement the quadratic ones pursue balanced non corner solutions because some decision makers fear imbalance while others prefer large achievements even to the detriment of balance the paper defines an aversion to imbalance ratio so that the composite linear quadratic metric should conform to this ratio depending on the decision maker s preferences and attitudes as the problem of selecting an appropriate metric is an ongoing issue in cp the paper is a contribution to theory and practice for the sole purpose of suggesting industrial applications an example is developed

frustration stability and delay induced oscillations in a neural network model the effect of time delays on the linear stability of equilibria in an artificial neural network of hopfield type is analyzed the possibility of delay induced oscillations occurring is characterized in terms of properties of the not necessarily symmetric connection matrix of the network such oscillations are possible exactly when the network is frustrated equivalently when the signed digraph of the matrix does not require the perron property nonlinear analysis centre manifold computation of a three unit frustrated network is presented giving the nature of the bifurcations taking place a supercritical hopf bifurcation is shown to occur and a codimension two bifurcation is unfolded

experimental bifurcations and chaos in a modified self sustained macro electromechanical system abstract a class of self sustained macro electromechanical maems systems is made up of a rayleigh duffing oscillator actuating a mechanical arm through a magnetic coupling in this paper to avoid experimental constraints an audio amplifier is added to the device quenching phenomenon bifurcation and chaos are predicted and shown to occur in a device of this class of maems especially by using linear stability analysis the condition for the quenching phenomenon is derived chaos and bifurcation are predicted using lyapunov exponent and bifurcation diagram a prototype of device is designed and fabricated experimental results for this device that are consistent with results from theoretical investigations are presented and convincingly show quenching phenomenon bifurcation and chaos

incorporating additional meta objectives into the extended lexicographic goal programming framework this paper introduces two new meta objectives into the extended goal programming framework the first meta objective is the number of unmet goals and the second is a measure of closeness to the pairwise comparisons given by the decision maker these complement the original two meta objectives of the weighted sum of deviations and the maximal weighted deviation to provide a flexible four meta objective framework lexicographic and non lexicographic representations of the framework are developed an example relating to transportation is solved in both the lexicographic and non lexicographic forms weight sensitivity analysis is applied to the meta weight parameters for the non lexicographic case in order to find a range of available distinct solutions

a new method for the solution of models of biological evolution derivation of exact steady state distributions we investigate well known models of biological evolution and address the open problem of how construct a correct continuous analog of mutations in discrete sequence space we deal with models where the fitness is a function of a hamming distance from the reference sequence the mutation selection master equation in the discrete sequence space is replaced by a hamilton jacobi equation for the logarithm of relative frequencies of different sequences the steady state distribution mean fitness and the variance of fitness are derived all our results are asymptotic in the large genome limit a variety of important biological and biochemical models can be solved by this new approach

nonresonant hopf bifurcations of a controlled van der pol duffing oscillator abstract the trivial equilibrium of a van der pol duffing oscillator with a nonlinear feedback control may lose its stability via hopf bifurcations when the time delay involved in the feedback control reaches certain values nonresonant hopf hopf interactions may occur in the controlled van der pol duffing oscillator when the corresponding characteristic equation has two pairs of purely imaginary roots with the aid of normal form theory and centre manifold theorem as well as a perturbation method the dynamic behaviour of the nonresonant co dimension two bifurcation is investigated by studying the possible solutions and their stability of the four dimensional ordinary differential equations on the centre manifold in the vicinity of the nonresonant hopf bifurcation the oscillator may exhibit the initial equilibrium solution two periodic solutions as well as a quasi periodic solution on a two dimensional torus depending on the dummy unfolding parameters and nonlinear terms the analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation