time dependent differential inclusions cocycle attractors and fuzzy differential equations traditional formulations of fuzzy differential equations do not reproduce the rich and varied behavior of crisp differential equations des a recent interpretation in terms of differential inclusions expressed level setwise overcomes this deficiency and opens up for profitable investigation such properties as stability attraction periodicity and the like this is especially important for investigating continuous systems which are uncertain or incompletely specified this paper studies attractors of fuzzy des in terms of cocycles and encompasses both the time dependent and autonomous cases

adaptive configuration of evolutionary algorithms for constrained optimization in the literature many different evolutionary algorithms eas with different search operators have been reported for solving optimization problems however no single algorithm is consistently able to solve all types of problems to overcome this problem the recent trend is to use a mix of operators within a single algorithm there are also cases where multiple methodologies each with a single search operator have been used under one approach these approaches outperformed the single operator based single algorithm approaches in this paper we propose a new algorithm framework that uses multiple methodologies where each methodology uses multiple search operators we introduce it as the ea with adaptive configuration where the first level is to decide the methodologies and the second level is to decide the search operators in this approach all operators and population sizes are updated adaptively although the framework may sound complex one can gain significant benefits from it in solving optimization problems the proposed framework has been tested by solving two sets of specialized benchmark problems the results showed a competitive if not better performance when it was compared to the state of the art algorithms moreover the proposed algorithm significantly reduces the computational time in comparison to both single and multi operator based algorithms

random attractors for stochastic 2d navier stokes equations in some unbounded domains abstract we show that the stochastic flow generated by the 2 dimensional stochastic navier stokes equations with rough noise on a poincare like domain has a unique random attractor one of the technical problems associated with the rough noise is overcomed by the use of the corresponding cameron martin or reproducing kernel hilbert space our results complement the result by brze niak and li 2006 10 who showed that the corresponding flow is asymptotically compact and also generalize caraballo et al 2006 12 who proved existence of a unique attractor for the time dependent deterministic navier stokes equations

finite fractal dimension of pullback attractors for non autonomous 2d navier stokes equations in some unbounded domains abstract we study the asymptotic behaviour of non autonomous 2d navier stokes equations in unbounded domains for which a poincare inequality holds in particular we give sufficient conditions for their pullback attractor to have finite fractal dimension the existence of pullback attractors in this framework comes from the existence of bounded absorbing sets of pullback asymptotically compact processes t caraballo g ukaszewicz j real pullback attractors for asymptotically compact nonautonomous dynamical systems nonlinear anal 64 3 2006 484 498 we show that under suitable conditions the method of lyapunov exponents in p constantin c foias r temam attractors representing turbulent flows mem amer math soc 53 1984 5 for the dimension of attractors can be developed in this new context

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

disturbed exploitation compact differential evolution for limited memory optimization problems this paper proposes a novel and unconventional memetic computing approach for solving continuous optimization problems characterized by memory limitations the proposed algorithm unlike employing an explorative evolutionary framework and a set of local search algorithms employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators the proposed memetic computing approach is based on a populationless compact evolutionary framework which instead of processing a population of solutions handles its statistical model this evolutionary framework is based on a differential evolution which cooperatively employs two exploitative search operators the first is based on a standard differential evolution mutation and exponential crossover and the second is the trigonometric mutation these two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions the action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population which has the role of disturbing the excessively exploitative action of the framework and thus inhibits its premature convergence the proposed algorithm namely disturbed exploitation compact differential evolution is a simple and memory wise cheap structure that makes use of the memetic computing paradigm in order to solve complex optimization problems the proposed approach has been tested on a set of various test problems and compared with state of the art compact algorithms and with some modern population based meta heuristics numerical results show that disturbed exploitation compact differential evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms including some memetic approaches and complex modern differential evolution based algorithms in order to show the potential of the proposed approach in real world applications disturbed exploitation compact differential evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro controller numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature

on the dynamics of nonautonomous periodic general dynamical systems and differential inclusions abstract we establish the existence and stability results for periodic nonautonomous uniform forward attractors of periodic general dynamical systems set valued dynamical systems we also investigate the dynamical behavior of nonautonomous periodic differential inclusion x t f t x t on r m with only upper semi continuous right hand side by applying the abstract results firstly we show that if the system has a compact uniformly attracting set then it has a periodic nonautonomous uniform forward attractor a secondly we prove that a is robust with respect to both internal and external perturbations finally we apply the robustness result to discuss the effects of small time delays to asymptotic stability of the system

robust event triggered mpc with guaranteed asymptotic bound and average sampling rate we propose a robust event triggered model predictive control mpc scheme for linear time invariant discrete time systems subject to bounded additive stochastic disturbances and hard constraints on the input and state for given probability distributions of the disturbances acting on the system we design event conditions such that the average frequency of communication between the controller and the actuator in the closed loop system attains a given value we employ tube mpc methods to guarantee robust constraint satisfaction and a robust asymptotic bound on the system state moreover we show that instead of a given periodically updated tube mpc scheme an appropriate event triggered mpc scheme can be applied with the same guarantees on constraints and region of attraction but with a reduced number of average communications

the spectrum of prime ideals in tensor triangulated categories we define the spectrum of a tensor triangulated category k as the set of so called prime ideals endowed with a suitable topology in this very generality the spectrum is the universal space in which one can define supports for objects of k this construction is functorial with respect to all tensor triangulated functors several elementary properties of schemes hold for such spaces e g the existence of generic points or some quasi compactness locally trivial morphisms are proved to be nilpotent we establish in complete generality a classification of thick ideal subcategories in terms of arbitrary unions of closed subsets with quasi compact complements thomason s theorem for schemes mutatis mutandis we also equip this spectrum with a sheaf of rings turning it into a locally ringed space we compute examples and show that our spectrum unifies the schemes of algebraic geometry and the support varieties of modular representation theory

teaching learning based optimization with dynamic group strategy for global optimization abstract global optimization remains one of the most challenging tasks for evolutionary computation and swarm intelligence in recent years there have been some significant developments in these areas regarding the solution of global optimization problems in this paper we propose an improved teaching learning based optimization tlbo algorithm with dynamic group strategy dgs for global optimization problems different to the original tlbo algorithm dgstlbo enables each learner to learn from the mean of his corresponding group rather than the mean of the class in the teacher phase furthermore each learner employs the random learning strategy or the quantum behaved learning strategy in his corresponding group in the learner phase regrouping occurs dynamically after a certain number of generations helping to maintain the diversity of the population and discourage premature convergence to verify the feasibility and effectiveness of the proposed algorithm experiments are conducted on 18 numerical benchmark functions in 10 30 and 50 dimensions the results show that the proposed dgstlbo algorithm is an effective method for global optimization problems

pullback attractors for asymptotically compact non autonomous dynamical systems abstract first we introduce the concept of pullback asymptotically compact non autonomous dynamical system as an extension of the similar concept in the autonomous framework our definition is different from that of asymptotic compactness already used in the theory of random and non autonomous dynamical systems as developed by crauel flandoli kloeden schmalfuss amongst others which means the existence of a random or time dependent family of compact attracting sets next we prove a result ensuring the existence of a pullback attractor for a non autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets this attractor is minimal and in most practical applications it is unique finally we illustrate the theory with a 2d navier stokes model in an unbounded domain

an efficient composite heuristic for the symmetric generalized traveling salesman problem the main purpose of this paper is to introduce a new composite heuristic for solving the generalized traveling salesman problem the proposed heuristic is composed of three phases the construction of an initial partial solution the insertion of a node from each non visited node subset and a solution improvement phase we show that the heuristic performs very well on 36 tsplib problems which have been solved to optimality by other researchers we also propose some simple heuristics that can be used as basic blocks to construct more efficient composite heuristics

the stability of attractors for non autonomous perturbations of gradient like systems abstract we study the stability of attractors under non autonomous perturbations that are uniformly small in time while in general the pullback attractors for the non autonomous problems converge towards the autonomous attractor only in the hausdorff semi distance upper semicontinuity the assumption that the autonomous attractor has a gradient like structure the union of the unstable manifolds of a finite number of hyperbolic equilibria implies convergence i e also lower semicontinuity provided that the local unstable manifolds perturb continuously we go further when the underlying autonomous system is itself gradient like and show that all trajectories converge to one of the hyperbolic trajectories as t in finite dimensional systems in which we can reverse time and apply similar arguments to deduce that all bounded orbits converge to a hyperbolic trajectory as t this implies that the gradient like structure of the attractor is also preserved under small non autonomous perturbations the pullback attractor is given as the union of the unstable manifolds of a finite number of hyperbolic trajectories

composite systems with uncertain couplings of fixed structure scaled riccati equations and the problem of quadratic stability we consider large scale systems consisting of a finite number of separate uncertain subsystems which interact via uncertain couplings of arbitrarily prescribed structure the couplings are viewed as structured perturbations of the block diagonal system representing the collection of the separate nominal subsystems the nominal system we define spectral value sets and stability radii for these time invariant structured perturbations and derive formulas for their computation scaled riccati equations are introduced to obtain explicit formulas for the stability radii with respect to time varying and possibly nonlinear perturbations of the given structure from these we derive necessary and sufficient conditions under which the stability radii with respect to time invariant and time varying perturbations are equal these results are obtained by constructing joint quadratic liapunov functions of optimal robustness with their help we prove necessary and sufficient conditions for quadratic stability and sufficient conditions for the validity of a generalized aizerman conjecture

a metaheuristic algorithm to solve satellite broadcast scheduling problem in this paper a new effective and scalable differential evolution algorithm is proposed for optimizing the satellite broadcast s scheduling problem sbs the satellite broadcast s scheduling optimization problem is known to be an np complete problem in which the aim is to find a valid broadcasting pattern to earth stationed terminals which maximizes the number of timeslots utilized for broadcasting under certain constraints the algorithm proposed sd bde is a binary version of differential evolution hybridized with ideas extracted from stochastic diffusion search on top of that a repair heuristic mechanism is added to resolve constraint violations preliminary analysis shows that the repair heuristic is very effective as compared to other versions which include other heuristics further the performance of the proposed algorithm is tested thoroughly against published work toward solving sbs problem as well as state of the art existing binary coded population based similar algorithms in this paper we used along with instances reported in the literature for such problem randomly generated benchmark s instances of varying sizes for the sake of creating a unified large scale set to compare different algorithm against experimental results show that the proposed algorithm outperformed the existing algorithms by finding better or optimal solutions for almost all tested benchmarks

a self adaptive combined strategies algorithm for constrained optimization using differential evolution there are a huge number of differential evolution variants that have been proposed in the literature for solving constrained problems however none of them was considered as being a well accepted approach for solving a broad range of problems with different mathematical properties therefore in this paper for a better coverage of the problem characteristics a self adaptive differential evolution algorithm is introduced to do that it uses multiple search operators in conjunction with multiple constraint handling techniques the need for such an approach is justified by experimental analysis on a well known set of problems the results show that the proposed algorithm is superior to other state of the art algorithms

support theory via actions of tensor triangulated categories we give a definition of the action of a tensor triangulated category t on a triangulated category k in the case that t is rigidly compactly generated and k is compactly generated we show this gives rise to a notion of supports which categorifies work of benson iyengar and krause and extends work of balmer and favi we prove that a suitable version of the local to global principle holds very generally a relative version of the telescope conjecture is formulated and we give a sufficient condition for it to hold

lin kernighan heuristic adaptations for the generalized traveling salesman problem abstract the lin kernighan heuristic is known to be one of the most successful heuristics for the traveling salesman problem tsp it has also proven its efficiency in application to some other problems in this paper we discuss possible adaptations of tsp heuristics for the generalized traveling salesman problem gtsp and focus on the case of the lin kernighan algorithm at first we provide an easy to understand description of the original lin kernighan heuristic then we propose several adaptations both trivial and complicated finally we conduct a fair competition between all the variations of the lin kernighan adaptation and some other gtsp heuristics it appears that our adaptation of the lin kernighan algorithm for the gtsp reproduces the success of the original heuristic different variations of our adaptation outperform all other heuristics in a wide range of trade offs between solution quality and running time making lin kernighan the state of the art gtsp local search

pullback attractors for a nonautonomous nonclassical diffusion equation with variable delay we present the existence of pullback attractors in ch01 and ch2 h01 for the processes associated with the nonautonomous nonclassical diffusion equations with delays new methods for checking the asymptotical compactness of the solutions are used

pullback attractors of a multi valued process generated by parabolic differential equations with unbounded delays abstract the theory of nonautonomous multi valued dynamical systems and a method of asymptotic compactness based on the concept of the kuratowski measure of the noncompactness of a bounded set are used to prove the existence of pullback attractors in the weighted space c v for the multi valued process associated with the nonautonomous parabolic differential equation with infinite delay for which the uniqueness of solutions need not hold

pullback permanence in a non autonomous competitive lotka volterra model abstract the goal of this work is to study in some detail the asymptotic behaviour of a non autonomous lotka volterra model both in the conventional sense as t and in the pullback sense starting a fixed initial condition further and further back in time the non autonomous terms in our model are chosen such that one species will eventually die out ruling out any conventional type of permanence in contrast we introduce the notion of pullback permanence and show that this property is enjoyed by our model this is not just a mathematical artifice but rather shows that if we come across an ecology that has been evolving for a very long time we still expect that both species are represented and their numbers are bounded below even if the final fate of one of them is less happy the main tools in the paper are the theory of attractors for non autonomous differential equations the sub supersolution method and the spectral theory for linear elliptic equations

dynamics for a stochastic reaction diffusion equation with additive noise abstract in this paper we present a new scheme to study the dynamics of a stochastic reaction diffusion equation with the nonlinearity satisfying a dissipative condition with polynomial growth of arbitrary order p 2 firstly we use this scheme to establish some new estimates higher order integrability of the difference of the solutions near the initial time instead of using the usual estimates about higher regularities and higher order integrability of solutions secondly we verify that the attraction in the usual l 2 q l 2 q d pullback random attractor indeed can be l 2 norm for any 0 and the solutions of the equation are continuous in h 0 1 q with respect to initial data thirdly we obtain the existence of pullback random attractor in h 0 1 q as an application of the continuity even for the corresponding deterministic cases the results and methods introduced in this paper are new

kernel induced fuzzy clustering of image pixels with an improved differential evolution algorithm a modified differential evolution de algorithm is presented for clustering the pixels of an image in the gray scale intensity space the algorithm requires no prior information about the number of naturally occurring clusters in the image it uses a kernel induced similarity measure instead of the conventional sum of squares distance use of the kernel function makes it possible to partition data that is linearly non separable and non hyper spherical in the original input space into homogeneous groups in a transformed high dimensional feature space a novel search variable representation scheme is adopted for selecting the optimal number of clusters from several possible choices extensive performance comparison over a test suite of 10 gray scale images and objective comparison with manually segmented ground truth indicates that the proposed algorithm has an edge over a few state of the art algorithms for automatic multi class image segmentation

pullback attractors for reaction diffusion delay equations on unbounded domains with non autonomous deterministic and stochastic forcing terms the existence of a pullback attractor in a space of higher regularity is established for the non autonomous non compact dynamical system associated with the reaction diffusion delay equation with both non autonomous deterministic and stochastic forcing terms defined on all n dimensional space the asymptotical compactness of the solutions is demonstrated by using the uniform estimates for far field values of solutions and a new method

a selected pullback attractor abstract we introduce a new class of multivalued processes generated by generalized processes and a new concept of pullback attractor named a selected pullback attractor and we establish suitable conditions for the existence of such a selected pullback attractor finally we give and application to nonautonomous problems with dynamic boundary conditions

a decentralized quantum inspired particle swarm optimization algorithm with cellular structured population this paper proposes a decentralized form of quantum inspired particle swarm optimization qpso with cellular structured population called cqpso for keeping the population diversity and balancing the global and local search the cqpso is further improved by re designing the local attractor in the sub population called cqpso lbest in order to accelerate the diffusion of the best solution and thus enhance the performance of cqpso the particles in cqpso and cqpso lbest are distributed in a two dimensional 2d grid and only allowed to interact with their neighbors according to the specified neighborhood which plays a role in exploiting the search space inside the neighborhood the overlapping particles work for delivering the information among the nearest neighborhoods acting as exploring the search space with diffusion of solutions during the evolutionary process theoretical studies are made to analyze the global convergence of cpso and cqpso lbest based on the theory of probabilistic metric space we systematically investigate the performance of cqpso lbest on 42 benchmark functions with different properties including unimodal multimodal separated shifted rotated noisy and mis scaled and compare with a set of pso variants with different topologies and swarm based evolutionary algorithms eas the experimental results demonstrate the better performance of cqpso lbest moreover two real world problems which are two dimensional 2d iir digital filter design and economic dispatch ed problem from power systems area are used to evaluate cqpso lbest and the experimental results verified the advantages of cqpso lbest

a random key genetic algorithm for the generalized traveling salesman problem the generalized traveling salesman problem is a variation of the well known traveling salesman problem in which the set of nodes is divided into clusters the objective is to find a minimum cost tour passing through one node from each cluster we present an effective heuristic for this problem the method combines a genetic algorithm ga with a local tour improvement heuristic solutions are encoded using random keys which circumvent the feasibility problems encountered when using traditional ga encodings on a set of 41 standard test problems with symmetric distances and up to 442 nodes the heuristic found solutions that were optimal in most cases and were within 1 of optimality in all but the largest problems with computation times generally within 10 seconds the heuristic is competitive with other heuristics published to date in both solution quality and computation time

smashing subcategories and the telescope conjecture an algebraic approach we prove a modified version of ravenel s telescope conjecture it is shown that every smashing subcategory of the stable homotopy category is generated by a set of maps between finite spectra this result is based on a new characterization of smashing subcategories which leads in addition to a classification of these subcategories in terms of the category of finite spectra the approach presented here is purely algebraic it is based on an analysis of pure injective objects in a compactly generated triangulated category and covers therefore also situations arising in algebraic geometry and representation theory

effective search for pittsburgh learning classifier systems via estimation of distribution algorithms pittsburgh style learning classifier systems lcss in which an entire candidate solution is represented as a set of variable number of rules combine supervised learning with genetic algorithms gas to evolve rule based classification models it has been shown that standard crossover operators in gas do not guarantee an effective evolutionary search in many sophisticated problems that contain strong interactions between features in this paper we propose a pittsburgh style learning classifier system based on the bayesian optimization algorithm with the aim of improving the effectiveness and efficiency of the rule structure exploration in the proposed method classifiers are generated and recombined at two levels at the lower level single rules contained in classifiers are produced by sampling bayesian networks which characterize the global statistical information extracted from the current promising rules in the search space at the higher level classifiers are recombined by rule wise uniform crossover operators to keep the semantics of rules in each classifier experimental studies on both artificial and real world binary classification problems show that the proposed method converges faster while achieving solutions with the same or even higher accuracy compared with the original pittsburgh style lcss

non autonomous perturbation of autonomous semilinear differential equations continuity of local stable and unstable manifolds abstract in this paper we prove a result on lower semicontinuity of pullback attractors for dynamical systems given by semilinear differential equations in a banach space the situation considered is such that the perturbed dynamical system is non autonomous whereas the limiting dynamical system is autonomous and has an attractor given as union of unstable manifold of hyperbolic equilibrium points starting with a semilinear autonomous equation with a hyperbolic equilibrium solution and introducing a very small non autonomous perturbation we prove the existence of a hyperbolic global solution for the perturbed equation near this equilibrium then we prove that the local unstable and stable manifolds associated to them are given as graphs roughness of dichotomy plays a fundamental role here moreover we prove the continuity of this local unstable and stable manifolds with respect to the perturbation with that result we conclude the lower semicontinuity of pullback attractors

robust minkowski lyapunov functions abstract a necessary and sufficient condition for solvability of the lyapunov inequality for polytopic linear inclusions over the space of minkowski functions of nonempty compact and convex sets that contain the origin as an interior point is derived it is demonstrated that the introduced framework results in a nonconservative stability analysis of polytopic linear inclusions

a lagrange duality characterisation for stability under arbitrary switching in switched positive linear systems abstractthe present communication is concerned with uniform exponential stability under arbitrary switching in discrete time switched positive linear systems lagrange duality is used in order to obtain a new characterisation for uniform exponential stability which is in terms of sets of inequalities involving each of the matrices that represent the modes of the system these sets of inequalities are shown to generalise the classical linear lyapunov inequality that characterises in positive matrices the property of being schur each solution to these sets of inequalities is shown to provide a representation in terms of a number of linear functionals for a common lyapunov function for the switched positive linear system a result is further presented which conveys to a conservative upper bound on the minimum required number of linear functionals in the above mentioned representation and also to a method for computing them our proof for the aforementioned characterisation is based on another equ

an ensemble of discrete differential evolution algorithms for solving the generalized traveling salesman problem in this paper an ensemble of discrete differential evolution algorithms with parallel populations is presented in a single populated discrete differential evolution dde algorithm the destruction and construction dc procedure is employed to generate the mutant population whereas the trial population is obtained through a crossover operator the performance of the dde algorithm is substantially affected by the parameters of dc procedure as well as the choice of crossover operator in order to enable the dde algorithm to make use of different parameter values and crossover operators simultaneously we propose an ensemble of dde edde algorithms where each parameter set and crossover operator is assigned to one of the parallel populations each parallel parent population does not only compete with offspring population generated by its own population but also the offspring populations generated by all other parallel populations which use different parameter settings and crossover operators as an application area the well known generalized traveling salesman problem gtsp is chosen where the set of nodes is divided into clusters so that the objective is to find a tour with minimum cost passing through exactly one node from each cluster the experimental results show that none of the single populated variants was effective in solving all the gtsp instances whereas the edde performed substantially better than the single populated variants on a set of problem instances furthermore through the experimental analysis of results the performance of the edde algorithm is also compared against the best performing algorithms from the literature ultimately all of the best known averaged solutions for larger instances are further improved by the edde algorithm

graph lyapunov function for switching stabilization and distributed computation abstract this paper studies stabilization of discrete time switched linear systems slss using the notion of graph control lyapunov functions gclfs a gclf is a set of lyapunov functions defined on a weighted digraph where each lyapunov function is represented by a node in the digraph and there is a lyapunov inequality associated with each subgraph consisting of a node and its out neighbors the weight of a directed edge indicates the decay or growth rate of the lyapunov functions it is proved that an sls is switching stabilizable if and only if there exists a gclf the main benefits of gclfs are reduced computational cost and conservatism for stabilizability tests besides we show that the proposed gclf framework unifies several control lyapunov functions and the related stabilization theorems moreover we propose a distributed algorithm to evaluate the stabilizability with reduced computational costs by taking benefits of the graph structure of gclfs several examples are given to demonstrate the efficiency of the algorithm

a real coded genetic algorithm with a direction based crossover operator in this paper we develop a parallel structured real coded genetic algorithm rcga named the rga rdd for numerical optimization technically the proposed rga rdd integrates three specially designed evolutionary operators the ranking selection rs direction based crossover dbx and the dynamic random mutation drm as a whole to mimic a specific evolutionary process unlike the conventional rcgas that perform evolutionary operators in a series framework the rga rdd embeds a coordinator in the inner parallel loop to organize the operations of the dbx and drm so that a higher possibility of locating the global optimum is ensured besides based on the results of a systematic parametric analysis we provide a parameter selection guideline for the settings of the proposed rga rdd furthermore a data driven optimization scheme which incorporates the uniform design for design of experiments and a shape tunable neural network for auxiliary decision support is applied to search for an optimal set of the algorithm parameters the effectiveness and applicability of the proposed rga rdd are demonstrated through a variety of benchmarked optimization problems followed by comprehensive comparisons with some existing state of the art evolutionary algorithms extensive simulation results reveal that the performance of the proposed rga rdd is superior to comparative methods in locating the global optimum for real parameter optimization problems especially for unsolved multimodal and high dimensional hybrid functions

the bousfield lattice of a triangulated category and stratification for a tensor triangulated category which is well generated in the sense of neeman it is shown that the collection of bousfield classes forms a set this set has a natural structure of a complete lattice which is then studied using the notions of stratification and support

a framework for stabilization of nonlinear sampled data systems based on their approximate discrete time models a unified framework for design of stabilizing controllers for sampled data differential inclusions via their approximate discrete time models is presented both fixed and fast sampling are considered in each case sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete time plant models also stabilizes the exact discrete time plant model for sufficiently small integration and or sampling periods previous results in the literature are extended to cover 1 continuous time plants modeled as differential inclusions 2 general approximate discrete time plant models 3 dynamical discontinuous controllers modeled as difference inclusions and 4 stability with respect to closed arbitrary not necessarily compact sets

pullback attractors for multi valued non compact random dynamical systems generated by reaction diffusion equations on an unbounded domain in this paper we study pullback attractors of reaction diffusion equations on an unbounded domain with non autonomous deterministic as well as stochastic forcing terms for which the uniqueness of solutions need not hold we first present the existence and structure of pullback attractors of multi valued non compact random dynamical systems then we prove the existence of pullback attractors in l2 rn lp rn and h1 rn for multi valued non compact random dynamical systems associated with the reaction diffusion equations on rn and the identical relation of pullback attractors in different spaces is also provided in particular the measurability of pullback attractors is established for reaction diffusion equations on rn

ensemble strategies with adaptive evolutionary programming mutation operators such as gaussian levy and cauchy have been used with evolutionary programming ep according to the no free lunch theorem it is impossible for ep with a single mutation operator to outperform always for example classical ep cep with gaussian mutation is better at searching in a local neighborhood while the fast ep fep with the cauchy mutation performs better over a larger neighborhood motivated by these observations we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call this approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process in addition the recently proposed adaptive ep aep using gaussian acep and cauchy afep mutations is also evaluated in the aep the strategy parameter values are adapted based on the search performance in the previous few generations the performance of ensemble is compared with a mixed mutation strategy which integrates several mutation operators into a single algorithm as well as against the aep with a single mutation operator improved performance of the ensemble over the single mutation based algorithms and mixed mutation algorithm is verified using statistical tests

on the lyapunov stability of discrete time processes modeled by difference inclusions abstract the subject of this note is the stability in the sense of lyapunov of difference inclusions connection with the convergence of algorithms is also discussed

a simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem over the last decade many metaheuristics have been applied to the flowshop scheduling problem ranging from simulated annealing or tabu search to complex hybrid techniques some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated in fact several published methods require substantial implementation efforts exploit problem specific speed up techniques that cannot be applied to slight variations of the original problem and often re implementations of these methods by other researchers produce results that are quite different from the original ones in this work we present a new iterated greedy algorithm that applies two phases iteratively named destruction were some jobs are eliminated from the incumbent solution and construction where the eliminated jobs are reinserted into the sequence using the well known neh construction heuristic optionally a local search can be applied after the construction phase our iterated greedy algorithm is both very simple to implement and as shown by experimental results highly effective when compared to state of the art methods

pullback attractors for a non autonomous incompressible non newtonian fluid this paper studies the pullback asymptotic behavior of solutions for a non autonomous incompressible non newtonian fluid in two dimensional 2d bounded domains we first prove the existence of pullback attractors av in space v has h2 regularity see notation in section 2 and ah in space h has l2 regularity for the cocycle corresponding to the solutions of the fluid then we verify the regularity of the pullback attractors by showing av ah which implies the pullback asymptotic smoothing effect of the fluid in the sense that the solutions become eventually more regular than the initial data

a hybrid coevolutionary algorithm for designing fuzzy classifiers rule learning is one of the most common tasks in knowledge discovery in this paper we investigate the induction of fuzzy classification rules for data mining purposes and propose a hybrid genetic algorithm for learning approximate fuzzy rules a novel niching method is employed to promote coevolution within the population which enables the algorithm to discover multiple rules by means of a coevolutionary scheme in a single run in order to improve the quality of the learned rules a local search method was devised to perform fine tuning on the offspring generated by genetic operators in each generation after the ga terminates a fuzzy classifier is built by extracting a rule set from the final population the proposed algorithm was tested on datasets from the uci repository and the experimental results verify its validity in learning rule sets and comparative advantage over conventional methods

hochster duality in derived categories and point free reconstruction of schemes for a commutative ring r we exploit localization techniques and point free topology to give an explicit realization of both the zariski frame of r the frame of radical ideals in r and its hochster dual frame as lattices in the poset of localizing subcategories of the unbounded derived category d r this yields new conceptual proofs of the classical theorems of hopkinsneeman and thomason next we revisit and simplify balmer s theory of spectra and supports for tensor triangulated categories from the viewpoint of frames and hochster duality finally we exploit our results to show how a coherent scheme x ox can be reconstructed from the tensor triangulated structure of its derived category of perfect complexes

parallel memetic structures memetic computing mc structures are algorithms composed of heterogeneous operators memes for solving optimization problems in order to address these problems this study investigates and proposes a simple yet extremely efficient structure namely parallel memetic structure pms pms is a single solution optimization algorithm composed of tree operators the first one being a stochastic global search which explores the entire decision space searching for promising regions in analogy with electrical networks downstream of the global search component there is a parallel of two alternative elements i e two local search algorithms with different features in terms of search logic whose purpose is to refine the search in the regions detected by the upstream element the first local search explores the space along the axes while the second performs diagonal movements in the direction of the estimated gradient the pms algorithm despite its simplicity displays a respectable performance compared to that of popular meta heuristics and modern optimization algorithms representing the state of the art in the field thanks to its simple structure pms appears to be a very flexible algorithm for various problem features and dimensionality values unlike modern complex algorithm that are specialized for some benchmarks and some dimensionality values pms achieves solutions with a high quality in various and diverse contexts for example both on low dimensional and large scale problems an application example in the field of magnetic sensors further proves the potentials of the proposed approach this study confirms the validity of the ockham s razor in mc efficiently designed simple structures can perform as well as if not better than complex algorithms composed of many parts

numerical approximations to the stationary solutions of stochastic differential equations in this paper we investigate the possibility of approximating the stationary solution of a stochastic differential equation sde we start with the random dynamical system generated by the sde with the multiplicative noise we prove that the pullback flow has a stationary point however the stationary point is not constructible explicitly therefore we look at the numerical approximation we prove that the discrete time random dynamical system also has a stationary point finally we prove mean square convergence of the approximate stationary solution to the exact stationary solution as the time step diminishes as well as almost surely convergence when the time step is rational

efficient local search algorithms for known and new neighborhoods for the generalized traveling salesman problem abstract the generalized traveling salesman problem gtsp is a well known combinatorial optimization problem with a host of applications it is an extension of the traveling salesman problem tsp where the set of cities is partitioned into so called clusters and the salesman has to visit every cluster exactly once while the gtsp is a very important combinatorial optimization problem and is well studied in many aspects the local search algorithms used in the literature are mostly basic adaptations of simple tsp heuristics hence a thorough and deep research of the neighborhoods and local search algorithms specific to the gtsp is required we formalize the procedure of adaptation of a tsp neighborhood for the gtsp and classify all other existing and some new gtsp neighborhoods for every neighborhood we provide efficient exploration algorithms that are often significantly faster than the ones known from the literature finally we compare different local search implementations empirically

pullback d attractors for nonautonomous sine gordon equations abstract in this paper we consider the pullback d attractor for the nonautonomous sine gordon wave equation we will show the existence of the pullback d attractor in v h and in d a v to this end some abstract results are established we use the methods provided by q f ma s h wang c k zhong necessary and sufficient conditions for the existence of global attractors for semigroups and applications j indiana univ math 51 6 2002 to establish some sufficient conditions for the existence of the pullback d attractor of an infinite dimensional dynamical system

pullback attractors of non autonomous reaction diffusion equations in h01 abstract using a method based on the concept of the kuratowski measure of noncompactness of a bounded set as well as some new estimates of the solutions we prove the existence of a unique minimal pullback attractor in h 0 1 for the process associated with non autonomous reaction diffusion equation without any restriction on the growing order of nonlinear terms p 2 is arbitrary in addition the external forces g t satisfy only the weaker integrability condition than in the earlier similar research of song and wu 2007 25 and li et al 2009 18

generalized tensor idempotents and the telescope conjecture we transpose rickard s construction of idempotent representations to the general context of tensor triangulated categories we connect our construction to the telescope conjecture and prove that the latter is of local nature as an illustration we extend the affine telescope theorem of neeman to arbitrary noetherian schemes we also develop supports for non compact objects

a lagrangian based approach for the asymmetric generalized traveling salesman problem this paper presents an optimal approach for the asymmetric generalized traveling salesman problem gtsp the gtsp is defined on a directed graph in which the nodes are grouped into m predefined mutually exclusive and exhaustive sets with the arc set containing no intraset arcs the problem is to find a minimum cost m arc directed cycle which includes exactly one node from each set our approach employs a lagrangian relaxation to compute a lower bound on the total cost of an optimal solution the lower bound and a heuristically determined upper bound are used to identify and remove arcs and nodes which are guaranteed not to be in an optimal solution finally we use an efficient branch and bound procedure which exploits the multiple choice structure of the node sets we present computational results for the optimal approach tested on a series of randomly generated problems the results show success on a range of problems with up to 104 nodes

pullback attractors and extremal complete trajectories for non autonomous reaction diffusion problems abstract we analyse the dynamics of the non autonomous nonlinear reaction diffusion equation u t u f t x u subject to appropriate boundary conditions proving the existence of two bounding complete trajectories one maximal and one minimal our main assumption is that the nonlinear term satisfies a bound of the form f t x u u c t x u 2 d t x u where the linear evolution operator associated with c t x is exponentially stable as an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the non autonomous linear problem u t u c t x u between different l p spaces

stratifying modular representations of finite groups we classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple or equiv alently all modules one application is a proof of the telescope conjecture in this context others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups along the way we establish similar classifications for differential graded modules over graded polynomial rings and over graded exterior algebras

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

backtracking search optimization algorithm for numerical optimization problems this paper introduces the backtracking search optimization algorithm bsa a new evolutionary algorithm ea for solving real valued numerical optimization problems eas are popular stochastic search algorithms that are widely used to solve non linear non differentiable and complex numerical optimization problems current research aims at mitigating the effects of problems that are frequently encountered in eas such as excessive sensitivity to control parameters premature convergence and slow computation in this vein development of bsa was motivated by studies that attempt to develop simpler and more effective search algorithms unlike many search algorithms bsa has a single control parameter moreover bsa s problem solving performance is not over sensitive to the initial value of this parameter bsa has a simple structure that is effective fast and capable of solving multimodal problems and that enables it to easily adapt to different numerical optimization problems bsa s strategy for generating a trial population includes two new crossover and mutation operators bsa s strategies for generating trial populations and controlling the amplitude of the search direction matrix and search space boundaries give it very powerful exploration and exploitation capabilities in particular bsa possesses a memory in which it stores a population from a randomly chosen previous generation for use in generating the search direction matrix thus bsa s memory allows it to take advantage of experiences gained from previous generations when it generates a trial preparation this paper uses the wilcoxon signed rank test to statistically compare bsa s effectiveness in solving numerical optimization problems with the performances of six widely used ea algorithms pso cmaes abc jde clpso and sade the comparison which uses 75 boundary constrained benchmark problems and three constrained real world benchmark problems shows that in general bsa can solve the benchmark problems more successfully than the comparison algorithms

ensemble of niching algorithms although niching algorithms have been investigated for almost four decades as effective procedures to obtain several good and diverse solutions of an optimization problem no effort has been reported on combining different niching algorithms to form an effective ensemble of niching algorithms in this paper we propose an ensemble of niching algorithms ena and illustrate the concept by an instantiation which is realized using four different parallel populations the offspring of each population is considered by all parallel populations the instantiation is tested on a set of 16 real and binary problems and compared against the single niching methods with respect to searching ability and computation time results confirm that ena method is as good as or better than the best single method in it on every test problem moreover comparison with other state of the art niching algorithms demonstrates the competitiveness of our proposed ena

a niche hybrid genetic algorithm for global optimization of continuous multimodal functions a niche hybrid genetic algorithm nhga is proposed in this paper to solve continuous multimodal optimization problems more efficiently accurately and reliably it provides a new architecture of hybrid algorithms which organically merges the niche techniques and nelder mead s simplex method into gas in the new architecture the simplex search is first performed in the potential niches which likely contain a global optimum to locate the promising zones within search space quickly and reliably then another simplex search is used to quickly discover the global optimum in the located promising zones the proposed method not only makes the exploration capabilities of gas stronger through niche techniques but also has more powerful exploitation capabilities by using simplex search so it effectively alleviates premature convergence and improves weak exploitation capacities of gas a set of benchmark functions is used to demonstrate the validity of nhga and the role of every component of nhga numerical experiments show that the nhga may efficiently and reliably obtain a more accurate global optimum for the complex and high dimension multimodal optimization problems it also demonstrates that the new hybrid architecture is potential and can be used to generate more potential hybrid algorithms

common lyapunov functions and gradient algorithms this note is concerned with the problem of finding a quadratic common lyapunov function for a large family of stable linear systems we present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families

eigenclassifiers for combining correlated classifiers in practice classifiers in an ensemble are not independent this paper is the continuation of our previous work on ensemble subset selection a ulas m semerci o t yildiz e alpaydin incremental construction of classifier and discriminant ensembles information sciences 179 9 2009 1298 1318 and has two parts first we investigate the effect of four factors on correlation i algorithms used for training ii hyperparameters of the algorithms iii resampled training sets iv input feature subsets simulations using 14 classifiers on 38 data sets indicate that hyperparameters and overlapping training sets have higher effect on positive correlation than features and algorithms second we propose postprocessing before fusing using principal component analysis pca to form uncorrelated eigenclassifiers from a set of correlated experts combining the information from all classifiers may be better than subset selection where some base classifiers are pruned before combination because using all allows redundancy

unconventional initialization methods for differential evolution the crucial role played by the initial population in a population based heuristic optimization cannot be neglected it not only affects the search for several iterations but often also has an influence on the final solution if the initial population itself has some knowledge about the potential regions of the search domain then it is quite likely to accelerate the rate of convergence of the optimization algorithm in the present study we propose two schemes for generating the initial population of differential evolution de algorithm these schemes are based on quadratic interpolation qi and nonlinear simplex method nsm in conjugation with computer generated random numbers the idea is to construct a population that is biased towards the optimum solution right from the very beginning of the algorithm the corresponding algorithms named as qide using quadratic interpolation and nsde using non linear simplex method are tested on a set of 20 traditional benchmark problems with box constraints and 7 shifted non traditional functions taken from literature comparison of numerical results with traditional de and opposition based de ode show that the proposed schemes considered by us for generating the random numbers significantly improves the performance of de in terms of convergence rate and average cpu time

evolutionary multimodal optimization using the principle of locality the principle of locality is one of the most widely used concepts in designing computing systems to explore the principle in evolutionary computation crowding differential evolution is incorporated with locality for multimodal optimization instead of generating trial vectors randomly the first method proposed takes advantage of spatial locality to generate trial vectors temporal locality is also adopted to help generate offspring in the second method proposed temporal and spatial locality are then applied together in the third method proposed numerical experiments are conducted to compare the proposed methods with the state of the art methods on benchmark functions experimental analysis is undertaken to observe the effect of locality and the synergy between temporal locality and spatial locality further experiments are also conducted on two application problems one is the varied line spacing holographic grating design problem while the other is the protein structure prediction problem the numerical results demonstrate the effectiveness of the methods proposed

generating functions of switched linear systems analysis computation and stability applications in this paper a unified framework is proposed to study the exponential stability of discrete time switched linear systems and more generally the exponential growth rates of their trajectories under three types of switching rules arbitrary switching optimal switching and random switching it is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong the weak and the mean generating functions respectively in particular necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence various properties of the generating functions are established and their relations are discussed algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples

multithreaded parallel dual population genetic algorithm mpdpga for unconstrained function optimizations on multi core system various problems viz population diversity problem premature convergence problem and curse of dimensionality problem are associated with genetic algorithm ga dual population ga dpga helps to provide additional population diversity to the main population by means of crossbreeding between the main population and reserve population this helps to solve the problem of premature convergence and helps in early convergence of the algorithm the binary encoded multithreaded parallel dpga mpdpga is proposed in this paper to solve the problems of population diversity and premature convergence the experimental results show that the performance mean standard deviation and standard error of mean student t test mean function evaluation and success rate of mpdpga is better than serial dpga sdpga and simple ga sga

pullback attractors for nonautonomous wave equations with critical exponent abstract in this paper we prove the existence of a pullback attractor for a nonautonomous wave equation with critical exponent to do this we first use the concept of pullback d asymptotic compactness given in t caraballo g ukaszewicz j real pullback attractors for asymptotically compact nonautonomous dynamical systems nonlinear anal 64 2006 484 498 to show the existence of pullback attractor of nonautonomous dynamical systems and then we give a new method for verifying the pullback d asymptotic compactness

bousfield localization on formal schemes let x ox be a noetherian formal scheme and consider dqct x its derived category of sheaves with quasi coherent torsion homology we show that there is a bijection between the set of rigid i e ideals localizing subcategories of dqct x and subsets in x generalizing previous work by neeman if moreover x is separated the associated localization and acyclization functors are described in certain cases when z x is a stable for specialization subset its associated acyclization is r z when x is a scheme the corresponding localizing subcategories are generated by perfect complexes and we recover thomason s classification of thick subcategories on the other hand if y x is generically stable we show that the associated localization functor is hom x r x yo x g

multi objective evolutionary algorithms based on the summation of normalized objectives and diversified selection most multi objective evolutionary algorithms moeas use the concept of dominance in the search process to select the top solutions as parents in an elitist manner however as moeas are probabilistic search methods some useful information may be wasted if the dominated solutions are completely disregarded in addition the diversity may be lost during the early stages of the search process leading to a locally optimal or partial pareto front beside this the non domination sorting process is complex and time consuming to overcome these problems this paper proposes multi objective evolutionary algorithms based on summation of normalized objective values and diversified selection snov ds the performance of this algorithm is tested on a set of benchmark problems using both multi objective evolutionary programming moep and multi objective differential evolution mode with the proposed method the performance metric has improved significantly and the speed of the parent selection process has also increased when compared with the non domination sorting in addition the proposed algorithm also outperforms ten other algorithms

pullback asymptotic behavior of solutions for a non autonomous non newtonian fluid on two dimensional unbounded domains this paper studies the pullback asymptotic behavior of solutions for a non autonomous non newtonian fluid on r l l for some l 0 we first use the technique of truncation functions together with the decomposition of spatial domain to prove the existence of a pullback attractor in then we discuss the upper semicontinuity of the pullback attractors when the spatial domains vary from m to where m m 1 is an expanding sequence of simply connected bounded and smooth subdomains of such that m 1 m let a a r and am am r be the pullback attractors corresponding to and m respectively we establish for each r that for any neighborhood o a of a am enters o a if m is large enough

difference methods for differential inclusions a survey the main objective of this survey is to study convergence properties of difference methods applied to differential inclusions it presents in a unified way a number of results scattered in the li

asymptotic behaviour of nonautonomous difference inclusions abstract nonautonomous difference inclusions are formulated as difference inclusion cocycles which generalize set valued semigroups corresponding to autonomous difference inclusions and the existence of a difference inclusion cocycle attractor is established under the assumption of upper semi continuity of the cocycle mappings if the difference inclusion cocycle has an absorbing set several illustrative examples are provided

a particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem abstract in this paper a particle swarm optimization algorithm pso is presented to solve the permutation flowshop sequencing problem pfsp with the objectives of minimizing makespan and the total flowtime of jobs for this purpose a heuristic rule called the smallest position value spv borrowed from the random key representation of bean j c bean genetic algorithm and random keys for sequencing and optimization orsa journal of computing 6 2 1994 154 160 was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems in addition a very efficient local search called variable neighborhood search vns was embedded in the pso algorithm to solve the well known benchmark suites in the literature the pso algorithm was applied to both the 90 benchmark instances provided by taillard e taillard benchmarks for basic scheduling problems european journal of operational research 64 1993 278 285 and the 14 000 random narrow random and structured benchmark instances provided by watson et al j p watson l barbulescu l d whitley a e howe contrasting structured and random permutation flowshop scheduling problems search space topology and algorithm performance orsa journal of computing 14 2 2002 98 123 for makespan criterion the solution quality was evaluated according to the best known solutions provided either by taillard or watson et al the total flowtime criterion was evaluated with the best known solutions provided by liu and reeves j liu c r reeves constructive and composite heuristic solutions to the p ci scheduling problem european journal of operational research 132 2001 439 452 and rajendran and ziegler c rajendran h ziegler ant colony algorithms for permutation flowshop scheduling to minimize makespan total flowtime of jobs european journal of operational research 155 2 2004 426 438 for the total flowtime criterion 57 out of the 90 best known solutions reported by liu and reeves and rajendran and ziegler were improved whereas for the makespan criterion 195 out of the 800 best known solutions for the random and narrow random problems reported by watson et al were improved by the vns version of the pso algorithm

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

a branch and cut algorithm for the symmetric generalized traveling salesman problem we consider a variant of the classical symmetric traveling salesman problem in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster this np hard problem is known in the literature as the symmetric generalized traveling salesman problem gtsp and finds practical applications in routing scheduling and location routing in a companion paper fischetti et al fischetti m j j salazar p toth 1995 the symmetric generalized traveling salesman polytope networks 26 113 123 we modeled gtsp as an integer linear program and studied the facial structure of two polytopes associated with the problem here we propose exact and heuristic separation procedures for some classes of facet defining inequalities which are used within a branch and cut algorithm for the exact solution of gtsp heuristic procedures are also described extensive computational results for instances taken from the literature and involving up to 442 nodes are reported

niching particle swarm optimization with local search for multi modal optimization multimodal optimization is still one of the most challenging tasks for evolutionary computation in recent years many evolutionary multi modal optimization algorithms have been developed all these algorithms must tackle two issues in order to successfully solve a multi modal problem how to identify multiple global local optima and how to maintain the identified optima till the end of the search for most of the multi modal optimization algorithms the fine local search capabilities are not effective if the required accuracy is high these algorithms fail to find the desired optima even after converging near them to overcome this problem this paper integrates a novel local search technique with some existing pso based multimodal optimization algorithms to enhance their local search ability the algorithms are tested on 14 commonly used multi modal optimization problems and the experimental results suggest that the proposed technique not only increases the probability of finding both global and local optima but also reduces the average number of function evaluations

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method