on a mutualism model with feedback controls we propose and study a mutualism model with feedback controls by applying a new differential inequality we show that the conditions which ensure the permanence of the system are the same as that of the model without feedback controls which means that the feedback control variables have no influence on the persistent property of the system our results not only improve but also complement some existing ones

on the periodic solutions of periodic multi species kolmogorov type competitive system with delays and feedback controls abstract in this paper we consider a periodic multi species kolmogorov type competitive system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive periodic solution of the system are obtained as application the existence of the positive periodic solution of a kind of nonlinear competitive model with delays and feedback controls is discussed

a multi objective programming approach to 1 5 dimensional assortment problem in this paper we study a 1 5 dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations we propose a new multi objective mixed integer linear programming milp model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders an equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes have also been considered a new method called the conic scalarization is proposed for scalarizing non convex multi objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches

a hybrid genetic algorithm for the two dimensional single large object placement problem in the two dimensional single large object placement problem we are given a rectangular master surface which has to be cut into a set of smaller rectangular items with the aim of maximizing the total value of the pieces cut we consider the special case in which the items cannot be rotated and must be cut with their edges always parallel to the edges of the surface we present new greedy algorithms and a hybrid genetic approach with elitist theory immigration rate heuristics on line and tailored crossover operators extensive computational results for a large number of small and large benchmark test problems are presented the results show that our approach outperforms existing heuristic algorithms

positive periodic solutions of a single species model with feedback regulation and distributed time delay in this paper by using the continuation theorem of coincidence degree theory a criterion of the existence of positive periodic solutions is obtained for a single species model with feedback regulation and distributed time delay

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

global asymptotic stability in n species non autonomous lotka volterra competitive systems with infinite delays and feedback control abstract a non autonomous lotka volterra competition system with infinite delays and feedback control and without dominating instantaneous negative feedback is investigated by means of a suitable lyapunov functional sufficient conditions are derived for the global asymptotic stability of the system some new results are obtained

an exact two dimensional non guillotine cutting tree search procedure we consider the two dimensional cutting problem of cutting a number of rectangular pieces from a single large rectangle so as to maximize the value of the pieces cut we develop a lagrangean relaxation of a zero one integer programming formulation of the problem and use it as a bound in a tree search procedure subgradient optimization is used to optimize the bound derived from the lagrangean relaxation problem reduction tests derived from both the original problem and the lagrangean relaxation are given incorporating the bound and the reduction tests into a tree search procedure enables moderately sized problems to be solved

a reduction approach for solving the rectangle packing area minimization problem abstract in the rectangle packing area minimization problem rpamp we are given a set of rectangles with known dimensions we have to determine an arrangement of all rectangles without overlapping inside an enveloping rectangle of minimum area the paper presents a generic approach for solving the rpamp that is based on two algorithms one for the 2d knapsack problem kp and the other for the 2d strip packing problem spp in this way solving an instance of the rpamp is reduced to solving multiple spp and kp instances a fast constructive heuristic is used as spp algorithm while the kp algorithm is instantiated by a tree search method and a genetic algorithm alternatively all these spp and kp methods have been published previously finally the best variants of the resulting rpamp heuristics are combined within one procedure the guillotine cutting condition is always observed as an additional constraint the approach was tested on 15 well known rpamp instances above all mcnc and gsrc instances and new best solutions were obtained for 10 instances the computational effort remains acceptable moreover 24 new benchmark instances are introduced and promising results are reported

global stability of a single species model with feedback control and distributed time delay in this paper by constructing a suitable lyapunov functional a criterion is obtained for the global stability of a single species model with feedback control and distributed time delay

the bottomn left bin packing heuristic an efficient implementation we study implementations of the bottom left heuristic for two dimensional bin packing to pack n rectangles into an infinite vertical strip of fixed width the strategy considered here places each rectangle in turn as low as possible in the strip in a left justified position for reasons of simplicity and good performance the bottom left heuristic has long been a favorite in practical applications however the best implementations found so far require a number of steps o n3 in this paper we present an implementation of the bottom left heuristic which requires linear space and quadratic time the algorithm is fairly practical and we believe that even for relatively small values of n it gives the most efficient implementation of the heuristic to date it proceeds by first determining all the possible locations where the next rectangle can fit then selecting the lowest of them it is optimal among all the algorithms based on this exhaustive strategy and its generality makes it adaptable to different packing heuristics

a tabu search algorithm for a two dimensional non guillotine cutting problem in this paper we study a two dimensional non guillotine cutting problem the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut the problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet we propose a tabu search algorithm several moves based on reducing and inserting blocks of pieces have been defined intensification and diversification procedures based on long term memory have been included the computational results on large sets of test instances show that the algorithm is very efficient for a wide range of packing and cutting problems

an effective quasi human based heuristic for solving the rectangle packing problem abstract in this paper we introduce an effective deterministic heuristic less flexibility first for solving the classical np complete rectangle packing problem many effective heuristics implemented for this problem are cpu intensive and non deterministic in nature others including the polynomial approximation methodology j assoc comput mach 32 1 1985 130 are too laborious for practical problem sizes the technique we propose is inspired and developed by enhancing some rule of thumb guidelines resulting from the generation long work experience of human professionals in ancient days although the less flexibility first heuristic is a deterministic algorithm the results are very encouraging this algorithm can consistently produce packing densities of around 99 on most randomly generated large examples as compared with the recent results of a well known simulated annealing based rectangle packing rp algorithm ieee trans computer aided design integrated circuits systems 17 1 1998 60 the results are much better both in less dead space 2 4 vs 6 7 and much less cpu time 9 57 vs 331 78 seconds experimenting our heuristics on a public rectangle packing data set covering instances of 16 97 rectangles the average unpack ratio is quite satisfactory 0 92 for bounding boxes limited to be optimum and 2 68 for the completed packing while most cases spend only a few minutes in cpu time

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

the dynamic behavior of n species cooperation system with continuous time delays and feedback controls in this paper we consider a n species cooperation system with continuous time delays and feedback controls for general nonautonomous case by using differential inequality theory and constructing a suitable lyapunov functional we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system for the periodic case we obtain sufficient conditions which guarantee the existence uniqueness and stability of a positive periodic solution for the almost periodic case by using the razumikhin type theorem we obtain the sufficient conditions which guarantee the existence of a positive almost periodic solution of the system

permanence of a discrete nonlinear n species cooperation system with time delays and feedback controls a discrete nonlinear n species cooperation system with time delays and feedback controls is considered in this paper sufficient conditions which ensure the permanence of the system are obtained it is shown that these conditions are weaker than those of chen f d chen permanence of a discrete n species cooperation system with time delays and feedback controls appl math comput 186 2007 23 29 that is our investigation shows that the additional condition in chen s paper is not necessary

permanence in nonautonomous multi species predator prey system with feedback controls a nonautonomous multi species predator prey system with feedback controls is proposed in this paper where the competition among the predator species and among the prey species is considered also some important factors such as the effect of toxins and the age structure are also considered average conditions are obtained for permanence and global attractivity in the system the results obtained here generalized the main results of zhao and jiang j d zhao j f jiang permanence in nonautonomous lotka volterra system with predator prey appl math computat 152 2004 99 109

a genetic algorithm for the set covering problem abstract in this paper we present a genetic algorithm based heuristic for non unicost set covering problems we propose several modifications to the basic genetic procedures including a new fitness based crossover operator fusion a variable mutation rate and a heuristic feasibility operator tailored specifically for the set covering problem the performance of our algorithm was evaluated on a large set of randomly generated problems computational results showed that the genetic algorithm based heuristic is capable of producing high quality solutions

a bidirectional building approach for the 2d constrained guillotine knapsack packing problem abstract this paper investigates the 2d guillotine knapsack packing problem in which the objective is to select and cut a set of rectangles from a sheet with fixed size and maximize the total profit of the selected rectangles the orientation of the rectangles is fixed and the guillotine cut in which the cut must be parallel to the sides of the sheet to divide it into two completely separated sheets is required two well known methods namely the top down and bottom up approaches are combined into a coherent algorithm to address this problem computational experiments on benchmark test sets show that the approach finds the optimal solution for almost all moderately sized instances and outperforms all existing approaches for larger instances

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

a population heuristic for constrained two dimensional non guillotine cutting abstract in this paper we present a heuristic algorithm for the constrained two dimensional non guillotine cutting problem this is the problem of cutting a number of rectangular pieces from a single large rectangle so as to maximise the value of the pieces cut in addition the number of pieces of each type that are cut must lie within prescribed limits our heuristic algorithm is a population heuristic where a population of solutions to the problem are progressively evolved this heuristic is based on a new non linear formulation of the problem computational results are presented for a number of standard test problems taken from the literature and for a number of large randomly generated problems

a hybrid heuristic algorithm for the 2d variable sized bin packing problem in this paper we consider the two dimensional variable sized bin packing problem 2dvsbpp with guillotine constraint 2dvsbpp is a well known np hard optimization problem which has several real applications a mixed bin packing algorithm mixpacking which combines a heuristic packing algorithm with the best fit algorithm is proposed to solve the single bin problem and then a backtracking algorithm which embeds mixpacking is developed to solve the 2dvsbpp a hybrid heuristic algorithm based on iterative simulated annealing and binary search named hha is then developed to further improve the results of our backtracking algorithm computational experiments on the benchmark instances for 2dvsbpp show that hha has achieved good results and outperforms existing algorithms

stability of a random diffusion with linear drift we consider a linear system with markovian switching which is perturbed by gaussian type noise if the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable we also show that under certain conditions the linear system with markovian switching can be stabilized by such noisy perturbation

improved lmi representations for the analysis and the design of continuous time systems with polytopic type uncertainty simple modifications to the representation of the bounded real lemma brl in the linear continuous time invariant case are introduced these modifications reduce the overdesign that occurs in the analysis and the design of systems with polytopic type uncertainties a different lyapunov function accompanies each of the vertices of the uncertainty polytope thus eliminating the need for quadratic stability or stabilizability the advantages of these new representations are demonstrated by way of two examples

positive almost periodic solutions of a class of lotka volterra type competitive system with delays and feedback controls abstract in this paper we study the positive almost periodic solutions for a class of almost periodic lotka volterra type system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive almost periodic solution of the system is obtained our new criterion which improves and generalizes some well known results can be easily checked

stability and stabilization of continuous time switched linear systems this paper addresses two strategies for the stabilization of continuous time switched linear systems the first one is of open loop nature trajectory independent and is based on the determination of a minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function to be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition including chattering is expressed being nonconvex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

positive periodic solutions for a neutral differential system with feedback control applying a fixed point theorem of strict set contractions some new criteria are established for the existence of positive periodic solutions of the following neutral differential system with feedback controldx t dt x t r t a 0 t x t a 1 t x email protected 1 t a 2 t x email protected 2 t email protected t u email protected 1 t du t dt a t u t b t x email protected 2 t

dynamic output feedback control of switched linear systems this paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete time domains a particular class of matrix inequalities the so called lyapunov metzler inequalities provides conditions for open loop stability analysis and closed loop switching control using state and output feedback switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the hamilton jacobi bellman inequality an upper bound on the optimal cost associated with a closed loop stabilizing switching strategy is provided as well the solution of the output feedback problem is based on the construction of a full order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule throughout the theoretical results are illustrated by means of academic examples a realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

cutting stock problems and solution procedures this paper discusses some of the basic formulation issues and solution procedures for solving one and two dimensional cutting stock problems linear programming sequential heuristic and hybrid solution procedures are described for two dimensional cutting stock problems with rectangular shapes we also propose an approach for solving large problems with limits on the number of times an ordered size may appear in a pattern

an exact algorithm for general orthogonal two dimensional knapsack problems abstract we present a new exact tree search procedure for solving two dimensional knapsack problems in which a number of small rectangular pieces each of a given size and value are required to be cut from a large rectangular stock plate the objective is to maximise the value of pieces cut or minimise the wastage we consider the case where there is a maximum number of times that a piece may be used in a cutting pattern the algorithm limits the size of the tree search by using a bound derived from a langrangean relaxation of a 0 1 integer programming formulaton of the problem subgradient optimisation is used to optimise this bound reduction tests derived from both the original problem and the lagrangean relaxation produce substantial computational gains the computational performance of the algorithm indicates that it is an effective procedure capable of solving optimally practical two dimensional cutting problems of medium size

characterization and modelling of guillotine constraints this paper focuses on guillotine cuts which often arise in real life cutting stock problems in order to construct a solution verifying guillotine constraints the first step is to know how to determine whether a given cutting pattern is a guillotine pattern for this purpose we first characterize guillotine patterns by proving a necessary and sufficient condition then we propose a polynomial algorithm to check this condition based on this mathematical characterization of guillotine patterns we then show that guillotine constraints can be formulated into linear inequalities the performance of the algorithm to check guillotine cutting patterns is evaluated by means of computational results

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

robust output feedback h control of uncertain markovian jump systems with mode dependent time delays this paper describes the synthesis of robust output feedback h control for a class of uncertain markovian jump linear systems with time delays which are time varying and depend on the system modes of operation under the assumption of known bounds of system uncertainties and the control system gain variations we present sufficient conditions on the existence of robust stochastic stability and disturbance h attenuation through the changes of variables and schur complements these sufficient conditions can be rewritten in a set of coupled linear matrix inequalities with which robust control can be easily constructed as an added advantage the control design depends only on the measured parameter of markovian jumping at time t which might be corrupted by measurement noises numerical examples are provided to demonstrate the effectiveness of the proposed approach

stabilization of markovian systems via probability rate synthesis and output feedback this technical note is concerned with the stabilization problem of markovian jump linear systems via designing switching probability rate matrices and static output feedback gains a novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of markovian jump linear systems based on this a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices extensions to the polytopic uncertain case are also provided all the conditions are formulated in terms of linear matrix inequalities with some equality constraints which can be solved by two modified cone complementarity linearization algorithms examples are given to show the effectiveness of the proposed method

permanence of a discrete n species cooperation system with time delays and feedback controls in this paper a discrete n species cooperation system with time delays and feedback controls is proposed by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

permanence and existence of periodic solutions for a generalized system with feedback control sufficient conditions are obtained for the permanence and the existence of positive periodic solutions of the delay differential system with feedback control 0 1 dxdt x t f t x email protected 1 t x email protected n t c t u email protected t email protected t u t a t x email protected t the method involves the application of estimation for uniform upper and lower bounds of solutions when these results are applied to some special population models with multiple delays some new results are obtained and some known results are generalized especially our conclusions generalize and complement the results in chen et al f d chen j h yang l j chen x d xie on a mutualism model with feedback controls appl math comput 214 2009 581 587 and huo and li h f huo w t li positive periodic solutions of a class of delay differential system with feedback control appl math comput 148 2004 35 46

an and or graph approach to the solution of two dimensional non guillotine cutting problems this work is concerned with unconstrained two dimensional non guillotine cutting problems where a rectangular plate is cut into a number of rectangular pieces in such a way as to optimize an objective function we reduce the state space of the problem by considering non guillotine cutting patterns which are combinations of guillotine and simple non guillotine cuts these cutting patterns are represented as complete paths in an and or graph and a branch and bound method is described we provide rules and heuristics that reduce the graph search and present computational results from randomly generated examples as well as from the literature

a genetic algorithm for the two dimensional strip packing problem with rectangular pieces given a set of rectangular pieces and a container of fixed width and variable length the two dimensional strip packing problem 2d spp consists of orthogonally placing all the pieces within the container without overlapping such that the overall length of the layout is minimised until now mainly heuristics for example genetic algorithms ga were proposed for the 2d spp which use encoded solutions that are manipulated by standard operators in this paper a ga for the 2d spp is suggested that works without any encoding of solutions rather fully defined layouts are manipulated as such by means of specific genetic operators two additional constraints namely the orientation constraint and the guillotine constraint can be taken into account the ga is subjected to a comprehensive test using benchmark instances with up to 5000 pieces compared to eleven competing methods from the literature the ga performs best

brief continuous time state feedback h2 control of markovian jump linear systems via convex analysis continuous time h 2 control problem for the class of linear systems with markovian jumps mjls using convex analysis is considered in this paper the definition of the h 2 norm for continuous time mjls is presented and related to the appropriate observability and controllability gramians a convex programming formulation for the h 2 control problem of mjls is developed that enables us to tackle the optimization problem of mjls under the assumption that the transition rate matrix p p i j for the markov chain may not be exactly known but belongs to an appropriate convex set an equivalence between the convex formulation when p is exactly known and the usual dynamic programming approach of quadratic optimal control of mjls is established it is shown that there exists a solution for the convex programming problem if and only if there exists the mean square stabilizing solution for a set of coupled algebraic riccati equations these results are compared with other related works in the current literature

almost periodic solution for n species lotka volterra competitive system with delay and feedback controls abstract in this paper a n species lotka volterra competition system with delay and feedback controls is investigated by means of the theory of comparison theorem and suitable lyapunov functional some sufficient conditions for the existence and uniqueness of almost positive periodic solutions of this system is obtained