two level linear programming decentralized planning has long been recognized as an important decision making problem many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice multilevel programming models partition control over decision variables among ordered levels within a hierarchical planning structure a planner at one level of the hierarchy may have his objective function and set of feasible decisions determined in part by other levels however his control instruments may allow him to influence the policies at other levels and thereby improve his own objective function this paper examines the special case of the two level linear programming problem geometric characterizations and algorithms are presented with some examples the goal is to demonstrate the tractability of such problems and motivate a wider interest in their study

delay dependent exponential stability of stochastic systems with time varying delay nonlinearity and markovian switching the problem of delay dependent stability in the mean square sense for stochastic systems with time varying delays markovian switching and nonlinearities is investigated both the slowly time varying delays and fast time varying delays are considered based on a linear matrix inequality approach delay dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature

production planning problem with sequence dependent setups as a bilevel programming problem abstract each of n products is to be processed on two machines in order to satisfy known demands in each of t periods only one product can be processed on each machine at any given time each switch from one item to another requires sequence dependent setup time the objective is to minimize the total setup time and the sum of the costs of production storage and setup we consider the problem as a bilevel mixed 0 1 integer programming problem the objective of the leader is to assign the products to the machines in order to minimize the total sequence dependent setup time while the objective of the follower is to minimize the production storage and setup cost of the machine we develop a heuristics based on tabu search for solving the problem at the end some computational results are presented

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

the mixed integer linear bilevel programming problem a two person noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem in this paper we examine the case where each player tries to maximize the individual objective function over a jointly constrained polyhedron the decision variables are variously partitioned into continuous and discrete sets the leader goes first and through his choice may influence but not control the responses available to the follower for two reasons the resultant problem is extremely difficult to solve even by complete enumeration first it is not possible to obtain tight upper bounds from the natural relaxation and second two of the three standard fathoming rules common to branch and bound cannot be applied fully in light of these limitations we develop a basic implicit enumeration scheme that finds good feasible solutions within relatively few iterations a series of heuristics are then proposed in an effort to strike a balance between accuracy and speed the computational results suggest that some compromise is needed when the problem contains more than a modest number of integer variables

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

super efficiency in vector optimization we introduce a new concept of efficiency in vector optimization this concept super efficiency is shown to have many desirable properties in particular we show that in reasonable settings the super efficient points of a set are norm dense in the efficient frontier we also provide a chebyshev characterization of super efficient points for nonconvex sets and a scalarization theory when the underlying set is convex

exact solution approaches for bilevel lot sizing abstract in this paper we propose exact solution methods for a bilevel uncapacitated lot sizing problem with backlogs this is an extension of the classical uncapacitated lot sizing problem with backlogs in which two autonomous and self interested decision makers constitute a two echelon supply chain the leader buys items from the follower in order to meet external demand at lowest cost the follower also tries to minimize its costs both parties may backlog we study the leader s problem i e how to determine supply requests over time to minimize its costs in view of the possible actions of the follower we develop two mixed integer linear programming reformulations as well as cutting planes to cut off feasible but suboptimal solutions we compare the reformulations on a series of benchmark instances

sliding mode output feedback controller design using linear matrix inequalities considers a sliding mode controller which requires only output information and is static in nature the novelty of the approach is in the rationale and method used to synthesize the linear control component which involves a linear matrix inequality optimization the so called reachability condition used in sliding mode controller analysis is not required to be satisfied globally instead sliding is only expected to take place within a subset of the state space referred to as the sliding patch

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

isolated minimizers and proper efficiency for c0 1 constrained vector optimization problems abstract we consider the vector optimization problem min c f x g x k where f r n r m and g r n r p are c 0 1 i e locally lipschitz functions and c r m and k r p are closed convex cones we give several notions of solution efficiency concepts among them the notion of properly efficient point p minimizer of order k and the notion of isolated minimizer of order k we show that each isolated minimizer of order k 1 is a p minimizer of order k the possible reversal of this statement in the case k 1 is studied through first order necessary and sufficient conditions in terms of dini derivatives observing that the optimality conditions for the constrained problem coincide with those for a suitable unconstrained problem we introduce sense i solutions those of the initial constrained problem and sense ii solutions those of the unconstrained problem further we obtain relations between sense i and sense ii isolated minimizers and p minimizers

computational difficulties of bilevel linear programming we show using small examples that two algorithms previously published for the bilevel linear programming problem blp may fail to find the optimal solution and thus must be considered to be heuristics a proof is given that solving blp problems is np hard which makes it unlikely that there is a good exact algorithm

finite time stability and stabilization of nonlinear stochastic hybrid systems this paper deals with the problem of finite time stability and stabilization of nonlinear markovian switching stochastic systems which exist impulses at the switching instants using multiple lyapunov function theory a sufficient condition is established for finite time stability of the underlying systems furthermore based on the state partition of continuous parts of systems a feedback controller is designed such that the corresponding impulsive stochastic closed loop systems are finite time stochastically stable a numerical example is presented to illustrate the effectiveness of the proposed method

computation of the optimal tolls on the traffic network abstract the present paper is devoted to the computation of optimal tolls on a traffic network that is described as fuzzy bilevel optimization problem as a fuzzy bilevel optimization problem we consider bilinear optimization problem with crisp upper level and fuzzy lower level an effective algorithm for computation optimal tolls for the upper level decision maker is developed under assumption that the lower level decision maker chooses the optimal solution as well the algorithm is based on the membership function approach this algorithm provides us with a global optimal solution of the fuzzy bilevel optimization problem

fuzzy programming approach to multi level programming problems multi level programming is characterized as mathematical programming to solve decentralized planning problems we have considered a multi level linear programming problem and applied fuzzy mathematical programming fmp approach to obtain the solution of the system we have suggested fmp method for the minimization of the objectives using linear membership functions fmp is a supervised search procedure supervised by the higher level decision maker dm the higher level dm provides the preferred values of decision variables under his control to enable the lower level dm to search for his optimum in a wider feasible space and the bounds of his objective function to direct the lower level dm to search for his solutions in the right direction

relaxations for two level multi item lot sizing problems we consider several variants of the two level lot sizing problem with one item at the upper level facing dependent demand and multiple items or clients at the lower level facing independent demands we first show that under a natural cost assumption it is sufficient to optimize over a stock dominant relaxation we further study the polyhedral structure of a strong relaxation of this problem involving only initial inventory variables and setup variables we consider several variants uncapacitated at both levels with or without start up costs uncapacitated at the upper level and constant capacity at the lower level constant capacity at both levels we finally demonstrate how the strong formulations described improve our ability to solve instances with up to several dozens of periods and a few hundred products

robust h_ infty control for nonlinear stochastic systems a sliding mode approach this paper considers the sliding mode control for nonlinear stochastic systems modeled by ito stochastic differential equations it is noted that there exist state and exogenous disturbance dependent noise in the controlled systems by utilizing h infin disturbance attenuation technique a novel sliding mode control method is proposed such that the resultant system is asymptotically stable in probability with a prescribed h infin performance sufficient conditions for the solvability of these problems are derived via nonlinear hamilton jacobi hj type inequalities moreover it is shown that for a class of special nonlinear stochastic systems the h infin sliding mode control design can be obtained by solving linear matrix inequalities lmis finally a numerical simulation example is given

a single item economic lot sizing problem with a non uniform resource approximation we study a generalization of the classical single item capacitated economic lot sizing problem to the case of a non uniform resource usage for production the general problem and several special cases are shown to be non approximable with any polynomially computable relative error in polynomial time an optimal dynamic programming algorithm and its approximate modification are presented for the general problem fully polynomial time approximation schemes are developed for two np hard special cases 1 cost functions of total production are separable and holding and backlogging cost functions are linear with polynomially related slopes and 2 all holding costs are equal to zero

robust sliding mode control of uncertain time delay systems a robust sliding mode control design methodology is presented in this paper for a class of uncertain time delay systems the systems are assumed to have structured unmatched and time varying parameter uncertainties as well as matched and bounded external disturbances delay independent sufficient conditions for the design of a stable sliding manifold are given first in terms of an are and then via the schur complement as linear matrix inequalities lmis a controller guaranteeing convergence of the state trajectory to the sliding manifold is then developed and then generalized to account for uncertainties in the delay a technique for the adaptation of controller gains is also presented a lyapunov method underlies both sliding manifold and controller design a numerical example with simulation results illustrates the effectiveness of the methodology

robust stability criterion for uncertain stochastic systems with time varying delay via sliding mode control abstract this paper is focused on sliding mode control smc for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and stochastic perturbations may appear in the controlled system a new integral type switching surface function is first constructed then a sufficient condition for the existence of sliding surface is established in terms of linear matrix inequalities lmis by employing some free weighting matrices which guarantees the robustly stochastically stable of the sliding mode dynamic system with time varying delay for all admissible uncertainties moreover a smc law is synthesized to drive the system state trajectories onto the predefined switching surface in a finite time finally a simulation example is provided to illustrate the effectiveness of the proposed theory

computational complexity of the capacitated lot size problem in this paper we study the computational complexity of the capacitated lot size problem with a particular cost structure that is likely to be used in practical settings for the single item case new properties are introduced classes of problems solvable by polynomial time algorithms are identified and efficient solution procedures are given we show that special classes are np hard and that the problem with two items and independent setups is np hard under conditions similar to those where the single item problem is easy topics for further research are discussed in the last section

application of particle swarm optimization algorithm for solving bi level linear programming problem bi level linear programming is a technique for modeling decentralized decision it consists of the upper level and lower level objectives this paper attempts to develop an efficient method based on particle swarm optimization pso algorithm with swarm intelligence the performance of the proposed method is ascertained by comparing the results with genetic algorithm ga using four problems in the literature and an example of supply chain model the results illustrate that the pso algorithm outperforms ga in accuracy

strict efficiency in vector optimization the notion of strict minimum of order m for real optimization problems is extended to vector optimization its properties and characterization are studied in the case of finite dimensional spaces multiobjective problems also the notion of super strict efficiency is introduced for multiobjective problems and it is proved that in the scalar case all of them coincide necessary conditions for strict minimality and for super strict minimality of order m are provided for multiobjective problems with an arbitrary feasible set when the objective function is frechet differentiable necessary and sufficient conditions are established for the case m 1 resulting in the situation that the strict efficiency and super strict efficiency notions coincide

a new heuristic method for the flow shop sequencing problem abstract a new heuristic method is presented for solving the m machine n job flow shop scheduling problem this method named spirit is composed of two phases the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques the results of the heuristic are compared with those from other well known methods

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

geoffrion type characterization of higher order properly efficient points in vector optimization abstract we consider the constrained vector optimization problem min c f x x a where x and y are normed spaces a x 0 x are given sets c y c y is a closed convex cone and f x 0 y is a given function we recall the notion of a properly efficient point p minimizer for the considered problem and in terms of the so called oriented distance we define also the notion of a properly efficient point of order n p minimizers of order n we show that the p minimizers of higher order generalize the usual notion of a properly efficient point the main result is the characterization of the p minimizers of higher order in terms of trade offs in such a way we generalize the result of a m geoffrion a m geoffrion proper efficiency and the theory of vector maximization j math anal appl 22 3 1968 618 630 in two directions namely for properly efficient points of higher order in infinite dimensional spaces and for arbitrary closed convex ordering cones

degrees of efficiency and degrees of minimality in this work we characterize different types of solutions of a vector optimization problem by means of a scalarization procedure usually different scalarizing functions are used in order to obtain the various solutions of the vector problem here we consider different kinds of solutions of the same scalarized problem our results allow us to establish a parallelism between the solutions of the scalarized problem and the various efficient frontiers stronger solution concepts of the scalar problem correspond to more restrictive notions of efficiency besides the usual notions of weakly efficient and efficient points which are characterized as global and strict global solutions of the scalarized problem we also consider some restricted notions of efficiency such as strict and proper efficiency which are characterized as tikhonov well posed minima and sharp minima for the scalarized problem

designing robust coverage networks to hedge against worst case facility losses in order to design a coverage type service network that is robust to the worst instances of long term facility loss we develop a facility location interdiction model that maximizes a combination of initial coverage by p facilities and the minimum coverage level following the loss of the most critical r facilities the problem is formulated both as a mixed integer program and as a bilevel mixed integer program to solve the bilevel program optimally a decomposition algorithm is presented whereby the original bilevel program is decoupled into an upper level master problem and a lower level subproblem after sequentially solving these problems supervalid inequalities can be generated and appended to the upper level master in an attempt to force it away from clearly dominated solutions computational results show that when solved to optimality the bilevel decomposition algorithm is up to several orders of magnitude faster than performing branch and bound on the mixed integer program

a new approach for solving linear bilevel problems using genetic algorithms bilevel programming involves two optimization problems where the constraint region of the first level problem is implicitly determined by another optimization problem this paper develops a genetic algorithm for the linear bilevel problem in which both objective functions are linear and the common constraint region is a polyhedron taking into account the existence of an extreme point of the polyhedron which solves the problem the algorithm aims to combine classical extreme point enumeration techniques with genetic search methods by associating chromosomes with extreme points of the polyhedron the numerical results show the efficiency of the proposed algorithm in addition this genetic algorithm can also be used for solving quasiconcave bilevel problems provided that the second level objective function is linear

sliding mode control for stochastic systems subject to packet losses this paper investigates the problem of sliding mode control for stochastic system under the effect of packet dropout in this work a new sliding function dependent on the probability of packet dropout is constructed by means of a lyapunov function involved in sliding mode variable and system state both the reachabiltiy and the stability are analyzed simultaneously and the sufficient condition is derived via linear matrix inequalities finally numerical simulation results are given

strict efficiency in set valued optimization in this paper we develop the notion of a phi minimizer or strict efficiency for a set valued map its properties and relations with other similar notions are studied in special circumstances under suitable conditions we prove that a point is a phi minimizer of a vector function if and only if it is a phi minimizer of a certain family of linear scalarizations we also establish a characterization of strict efficiency through a nonlinear scalarization which is a generalization of the gerstewitz function defined on the power set of the image space the final part is focused on minimizers of order one and we provide several necessary or sufficient conditions without convexity assumptions through different kinds of derivatives as contingent radial among others various illustrative examples showing the applicability of our results are also presented

a simple tabu search method to solve the mixed integer linear bilevel programming problem abstract multilevel programming is characterized as mathematical programming to solve decentralized planning problems the models partition control over decision variables among ordered levels within a hierarchical planning structure of which the linear bilevel form is a special case of a multilevel programming problem in a system with such a hierarchical structure the high level decision making situations generally require inclusion of zero one variables representing yes no decisions we provide a mixed integer linear bilevel programming formulation in which zero one decision variables are controlled by a high level decision maker and real value decision variables are controlled by a low level decision maker an algorithm based on the short term memory component of tabu search called simple tabu search is developed to solve the problem and two supplementary procedures are proposed that provide variations of the algorithm computational results disclose that our approach is effective in terms of both solution quality and efficiency

razumikhin type theorems on stability of neutral stochastic functional differential equations recently mao 1995 initiated the study of exponential stability of neutral stochastic functional differential equations nsfdes and employed the razumikhin techniques to investigated the stability problem of nsfdes however the importance of general asymptotic stability has not been considered this paper studies razumikhin type theorems on general pth moment asymptotic stability of nsfdes the theorems established in this paper work for some cases to which the existing results cannot be applied

brief paper smc design for robust h control of uncertain stochastic delay systems recently sliding mode control method has been extended to accommodate stochastic systems however the existing results employ an assumption that may be too restrictive for many stochastic systems this paper aims to remove this assumption and present in terms of lmis a sliding mode control design method for stochastic systems with state delay in some cases the proposed method provides a control scheme for finite time stabilization of stochastic delay systems

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

solving bi level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm bi level linear programming consisting of upper level and lower level objectives is a technique for modeling decentralized decision this study presents a hybrid of immune genetic algorithm and vector controlled particle swarm optimization igvpso to solve the bi level linear programming problem blpp it is applied to a supply chain model that is a blpp using four problems from the literature and the supply chain distribution models the computational results indicate that the proposed method is superior to some algorithms

stabilization of uncertain nonholonomic systems via time varying sliding mode control this note addresses the robust stabilization problem for a general class of nonholonomic systems in the presence of drift uncertainties the control approach developed is based on the combined applications of the sliding mode control technique and nonlinear time varying systems theory first some properties of nonlinear time varying systems are introduced for the purpose of designing sliding mode controller an explicit time varying feedback form is provided to guarantee the existence and uniqueness of periodic time varying solution for the corresponding linear periodic partial differential equation second an explicit discontinuous feedback control law is presented to guarantee the existence of sliding mode the first integrals obtained by the previous periodic partial differential equation are then directly used to determine the switching function the uniform asymptotic stability of the closed loop system is proved via the invariance principle of nonlinear time varying systems finally an example is given to illustrate the proposed approach

robust control of delay systems a sliding mode control design via lmi this paper considers the sliding mode control of uncertain systems with single or multiple constant or time varying state delays submitted to additive perturbations the sliding surface is designed so to maximize the calculable set of admissible delays the conditions for the existence of the sliding regime are studied by using lyapunov krasovskii functionals and lyapunov razumikhin functions lmis are used for the optimization procedure two examples illustrate the proposed method

lmi based sliding surface design for integral sliding mode control of mismatched uncertain systems we propose a linear matrix inequality lmi based sliding surface design method for integral sliding mode control of mismatched uncertain systems the uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix as well as the input matrix we give a sufficient condition for the existence of a sliding surface guaranteeing asymptotic stability of the full order sliding mode dynamics we also give an lmi characterization of the sliding surface together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time additionally we give an lmi condition of sliding surfaces guaranteeing the alpha stability constraint finally we give a simulation result to show the effectiveness of our method

necessary and sufficient conditions for isolated local minima of nonsmooth functions we consider the mathematical programming problem find inf f x mid x in c where f is an arbitrary extended real valued function and c a subset of a finite dimensional space we give necessary and sufficient optimality conditions for this problem generalizing previous results of a auslendex this journal 22 1984 pp 239 254

an algorithm for solving the general bilevel programming problem the conflict that naturally arises in a hierarchical system can often be modeled as a multistage optimization problem this paper considers the sequential uncooperative problem in which two decision makers wish to maximize their own objective functions over a feasible region defined by interactive strategy sets the resultant problem is known as the bilevel program such programs are inherently nonconvex and resistant to standard nonlinear programming solution techniques such as piecewise linearization and convex underestimating envelopes alternatively a grid search algorithm is offered which exhibits the desirable property of monotonicity the algorithm is based on two sets of necessary conditions previously developed and combined here to provide an operational check for stationarity and local optimality potential solutions are obtained from a parameterized master program whose feasible region approximates that of the original problem as the one dimensional parameter is varied over the unit interval

robust covariance control for perturbed stochastic multivariable system via variable structure control based on the concept of variable structure control this paper investigates the steady state covariance assignment problem for perturbed stochastic multivariable systems by using the invariance property of variable structure systems the matched perturbation of the system disappears on the sliding mode with the aid of ito formula the controller u t is proposed combining the sliding phase and hitting phase of the system design the control feedback gain matrix g is derived to satisfy the steady state covariance assignment