a theoretical and empirical study on unbiased boundary extended crossover for real valued representation we present a new crossover operator for real coded genetic algorithms employing a novel methodology to remove the inherent bias of pre existing crossover operators this is done by transforming the topology of the hyper rectangular real space by gluing opposite boundaries and designing a boundary extension method for making the fitness function smooth at the glued boundary we show the advantages of the proposed crossover by comparing its performance with those of existing ones on test functions that are commonly used in the literature and a nonlinear regression on a real world dataset

a novel selection evolutionary strategy for constrained optimization the existence of infeasible solutions makes it very difficult to handle constrained optimization problems cops in a way that ensures efficient optimal and constraint satisfying convergence although further optimization from feasible solutions will typically lead in a direction that generates further feasible solutions certain infeasible solutions can also provide useful information about the optimal direction of improvement for the objective function how well an algorithm makes use of these two solutions determines its performance on cops this paper proposes a novel selection evolutionary strategy nses for constrained optimization a self adaptive selection method is introduced to exploit both informative infeasible and feasible solutions from a perspective of combining feasibility with multi objective problem mop techniques since the global optimal solution of a cop is a feasible non dominated solution both non dominated solutions with low constraint violation and feasible ones with low objective values are beneficial to an evolution process thus the exploration and exploitation of both of these two kinds of solutions are preferred during the selection procedure several theorems and properties are given to prove the above assertion furthermore the performance of our method is evaluated using 22 well known benchmark functions experimental results show that the proposed method outperforms state of the art algorithms in terms of the speed of finding feasible solutions and the stability of converging to global optimal solutions in particular when dealing with problems that have zero feasibility ratios and more than one active constraint our method provides feasible solutions within fewer fitness evaluations fes and converges to the optimal solutions more reliably than other popular methods from the literature

nonzero bound on fiedler eigenvalue causes exponential growth of h infinity norm of vehicular platoon we consider platoons composed of identical vehicles and controlled in a distributed way that is each vehicle has its own onboard controller the regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller which thus implements an asymmetric bidirectional control scheme the weights can vary along the platoon we prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph laplacian matrix the fiedler eigenvalue furthermore it is shown that existence of this bound always signals undesirable scaling properties of the platoon namely the h infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used hence the benefits of a uniform gap in the spectrum of a laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows

stability of boolean networks the joint effects of topology and update rules we study the stability of orbits in large boolean networks we treat the case in which the network has a given complex topology and we do not assume a specific form for the update rules which may be correlated with local topological properties of the network while recent past work has addressed the separate effects of complex network topology and certain classes of update rules on stability only crude results exist about how these effects interact we present a widely applicable solution to this problem numerical simulations confirm our theory and show that local correlations between topology and update rules can have profound effects on the qualitative behavior of these systems

minimal controllability of conjunctive boolean networks is np complete abstract given a conjunctive boolean network cbn with n state variables we consider the problem of finding a minimal set of state variables to directly affect with an input so that the resulting conjunctive boolean control network cbcn is controllable we give a necessary and sufficient condition for controllability of a cbcn an o n 2 time algorithm for testing controllability and prove that nonetheless the minimal controllability problem for cbns is np hard

mistuning based control design to improve closed loop stability margin of vehicular platoons we consider a decentralized bidirectional control of a platoon of n identical vehicles moving in a straight line the control objective is for each vehicle to maintain a constant velocity and inter vehicular separation using only the local information from itself and its two nearest neighbors each vehicle is modeled as a double integrator to aid the analysis we use continuous approximation to derive a partial differential equation pde approximation of the discrete platoon dynamics the pde model is used to explain the progressive loss of closed loop stability with increasing number of vehicles and to devise ways to combat this loss of stability if every vehicle uses the same controller we show that the least stable closed loop eigenvalue approaches zero as o 1 n2 in the limit of a large number n of vehicles we then show how to ameliorate this loss of stability by small amounts of mistuning i e changing the controller gains from their nominal values we prove that with arbitrary small amounts of mistuning the asymptotic behavior of the least stable closed loop eigenvalue can be improved to o 1 n all the conclusions drawn from analysis of the pde model are corroborated via numerical calculations of the state space platoon model

an effective co evolutionary differential evolution for constrained optimization many practical problems can be formulated as constrained optimization problems due to the simple concept and easy implementation the penalty function method has been one of the most common techniques to handle constraints however the performance of this technique greatly relies on the setting of penalty factors which are usually determined by manual trial and error and the suitable penalty factors are often problem dependent and difficult to set in this paper a differential evolution approach based on a co evolution mechanism named cde is proposed to solve the constrained problems first a special penalty function is designed to handle the constraints second a co evolution model is presented and differential evolution de is employed to perform evolutionary search in spaces of both solutions and penalty factors thus the solutions and penalty factors evolve interactively and self adaptively and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously simulation results based on several benchmark functions and three well known constrained design problems as well as comparisons with some existed methods demonstrate the effectiveness efficiency and robustness of the proposed method

parabolic pde based multi agent formation control on a cylindrical surface abstractthis paper considers the modelling and control design of the multi agent systems in the 3 d space the communication graph of the agents is a mesh grid 2 d cylindrical surface different from most existing literatures where the agents are modelled by ordinary differential equations odes we treat the agents as a continuum in this paper more specifically we model the collective dynamics of the agents by two reaction advection diffusion 2 d partial differential equations pdes the pde states represent the agent positions and the equilibria correspond to possible formation manifolds these pdes can be open loop unstable and the boundary stabilisation problem of the pdes on the cylindrical surface is solved using the backstepping method an all explicit observer based output control scheme is constructed which is distributed in the sense that each agent only needs local information closed loop exponential stability in the l2 h1 and h2 spaces is proved for the controller designs numerical

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

discrimination of singleton and periodic attractors in boolean networks abstract determining the minimum number of sensor nodes to observe the internal state of the whole system is important in analysis of complex networks however existing studies suggest that a large number of sensor nodes are needed to know the whole internal state in this paper we focus on identification of a small set of sensor nodes to discriminate statically and periodically steady states using the boolean network model where steady states are often considered to correspond to cell types in other words we seek a minimum set of nodes to discriminate singleton and periodic attractors we prove that one node is not necessarily enough but two nodes are always enough to discriminate two periodic attractors by using the chinese remainder theorem based on this we present an algorithm to determine the minimum number of nodes to discriminate all given attractors we also present a much more efficient algorithm to discriminate singleton attractors the results of computational experiments suggest that attractors in realistic boolean networks can be discriminated by observing the states of only a small number of nodes

reconstruction of kauffman networks applying trees abstract according to kauffman s theory s kauffman the origins of order self organization and selection in evolution oxford university press new york 1993 enzymes in living organisms form a dynamic network which governs their activity for each enzyme the network contains a collection of enzymes affecting the enzyme and a boolean function prescribing next activity of the enzyme as a function of the present activity of the affecting enzymes kauffman s original pure random structure of the connections was criticized by barabasi and albert a l barabasi r albert emergence of scaling in random networks science 286 1999 509 512 their model was unified with kauffman s network by aldana and cluzel m aldana p cluzel a natural class of robust networks proc natl acad sci usa 100 2003 8710 8714 kauffman postulated that the dynamic character of the network determines the fitness of the organism if the network is either convergent or chaotic the chance of survival is lessened if however the network is stable and critical the organism will proliferate kauffman originally proposed a special type of boolean functions to promote stability which he called the property canalyzing this property was extended by shmulevich et al i shmulevich h lahdesmaki e r dougherty j astola w zhang the role of certain post classes in boolean network models of genetic networks proc natl acad sci usa 100 2003 10734 10739 using post classes following their ideas we propose decision tree functions for enzymatic interactions the model is fitted to microarray data of cogburn et al l a cogburn w wang w carre l rejt t e porter s e aggrey j simon system wide chicken dna microarrays gene expression profiling and discovery of functional genes poult sci assoc 82 2003 939 951 l a cogburn x wang w carre l rejt s e aggrey m j duclos j simon t e porter functional genomics in chickens development of integrated systems microarrays for transcriptional profiling and discovery of regulatory pathways comp funct genom 5 2004 253 261 in microarray measurements the activity of clones is measured the problem here is the reconstruction of the structure of enzymatic interactions of the living organism using microarray data the task resembles summing up the whole story of a film from unordered and perhaps incomplete collections of its pieces two basic ingredients will be used in tackling the problem in our earlier works l rejt g tusnady evolution of random boolean nk models in tierra environment in i berkes e csaki m csorg eds limit theorems in probability an statistics budapest vol ii 2002 pp 499 526 we used an evolutionary strategy called tierra which was proposed by ray t s ray evolution complexity entropy and artificial reality physica d 75 1994 239 263 for investigating complex systems here we apply this method together with the tree structure of clones found in our earlier statistical analysis of microarray measurements l rejt g tusnady clustering methods in microarrays period math hungar 50 2005 199 221

nested canalyzing unate cascade and polynomial functions this paper focuses on the study of certain classes of boolean functions that have appeared in several different contexts nested canalyzing functions have been studied recently in the context of boolean network models of gene regulatory networks in the same context polynomial functions over finite fields have been used to develop network inference methods for gene regulatory networks finally unate cascade functions have been studied in the design of logic circuits and binary decision diagrams this paper shows that the class of nested canalyzing functions is equal to that of unate cascade functions furthermore it provides a description of nested canalyzing functions as a certain type of boolean polynomial function using the polynomial framework one can show that the class of nested canalyzing functions or equivalently the class of unate cascade functions forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and computational algebra as a corollary of the functional equivalence derived here a formula in the literature for the number of unate cascade functions provides such a formula for the number of nested canalyzing functions

c psa constrained pareto simulated annealing for constrained multi objective optimization in recent years evolutionary algorithms eas have been extensively developed and utilized to solve multi objective optimization problems however some previous studies have shown that for certain problems an approach which allows for non greedy or uphill moves unlike eas can be more beneficial one such approach is simulated annealing sa sa is a proven heuristic for solving numerical optimization problems but owing to its point to point nature of search limited efforts has been made to explore its potential for solving multi objective problems the focus of the presented work is to develop a simulated annealing algorithm for constrained multi objective problems the performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems a comparison with other established multi objective optimization algorithms such as infeasibility driven evolutionary algorithm idea non dominated sorting genetic algorithm ii nsga ii and multi objective scatter search ii moss ii has been included to highlight the benefits of the proposed approach

genetic networks with canalyzing boolean rules are always stable we determine stability and attractor properties of random boolean genetic network models with canalyzing rules for a variety of architectures for all power law exponential and flat in degree distributions we find that the networks are dynamically stable furthermore for architectures with few inputs per node the dynamics of the networks is close to critical in addition the fraction of genes that are active decreases with the number of inputs per node these results are based upon investigating ensembles of networks using analytical methods also for different in degree distributions the numbers of fixed points and cycles are calculated with results intuitively consistent with stability analysis fewer inputs per node implies more cycles and vice versa there are hints that genetic networks acquire broader degree distributions with evolution and hence our results indicate that for single cells the dynamics should become more stable with evolution however such an effect is very likely compensated for by multicellular dynamics because one expects less stability when interactions among cells are included we verify this by simulations of a simple model for interactions among cells

passivity based control for multi vehicle systems subject to string constraints in this paper we show how heterogeneous bidirectional vehicle strings can be modelled as port hamiltonian systems analysis of stability and string stability within this framework is straightforward and leads to a better understanding of the underlying problem nonlinear local control and additional integral action is introduced to design a suitable control law guaranteeing l 2 string stability of the system with respect to bounded disturbances

differential evolution with dynamic stochastic selection for constrained optimization how much attention should be paid to the promising infeasible solutions during the evolution process is investigated in this paper stochastic ranking has been demonstrated as an effective technique for constrained optimization in stochastic ranking the comparison probability will affect the position of feasible solution after ranking and the quality of the final solutions in this paper the dynamic stochastic selection dss is put forward within the framework of multimember differential evolution firstly a simple version named dss mde is given where the comparison probability decreases linearly the algorithm dss mde has been compared with two state of the art evolution strategies and three competitive differential evolution algorithms for constrained optimization on 13 common benchmark functions dss mde is also evaluated on four well studied engineering design examples and the experimental results are significantly better than current available results secondly other dynamic settings of the comparison probability for dss mde are also designed and tested from the experimental results dss mde is effective for constrained optimization finally dss mde with a square root adjusted comparison probability is evaluated on the 22 benchmark functions in cec 06 and the experimental results on most functions are competitive

entropy based efficiency enhancement techniques for evolutionary algorithms this paper introduces the notion of an entropy measurement for populations of candidate solutions in evolutionary algorithms developing both conditional and joint entropy based algorithms we describe the inherent characteristics of the entropy measurement and how these affect the search process following these discussions we develop a recognition mechanism through which promising candidate solutions can be identified without the need of invoking costly evaluation functions this on demand evaluation strategy odes is able to perform decision making tasks regardless of whether the actual fitness evaluation is necessary or not making it an ideal efficiency enhancement technique for accelerating the computational process of evolutionary algorithms two different evolutionary algorithms a traditional genetic algorithm and a multivariate estimation of distribution algorithm are employed as example targets for the application of our on demand evaluation strategy ultimately experimental results confirm that our method is able to broadly improve the performance of various population based global searchers

commentscomments on canalizing boolean functions maximize mutual information in their recent paper canalizing boolean functions maximize mutual information klotz et al argued that canalizing boolean functions maximize certain mutual informations by an argument involving fourier analysis on the hypercube this note supplies short new proofs of their results based on a coupling argument and also clarifies a point on the necessity of considering randomized functions

deviation bounds in multi agent systems described by undirected graphs the theory of port hamiltonian systems is used to derive upper bounds for the state deviations in multi agent systems described by undirected graphs pinned to a reference signal the upper bounds for the deviations in networks of first or second order agents respectively depend on the minimal eigenvalue of the extended laplacian of the system in networks of first order agents the deviations decay exponentially with a rate depending on the same minimal eigenvalue in case networks of second order systems meet specific design properties it can be shown that the deviations also decay exponentially with half the rate compared to first order systems

on achieving size independent stability margin of vehicular lattice formations with distributed control we study the stability margin of a vehicular formation with distributed control in which the control at each vehicle only depends on the information from its neighbors in an information graph we consider a d dimensional lattice as information graph of which the 1 d platoon is a special case the stability margin is measured by the real part of the least stable eigenvalue of the closed loop state matrix which quantifies the rate of decay of initial errors in 1 it was shown that with symmetric control in which two neighbors put equal weight on information received from each other the stability margin of a 1 d vehicular platoon decays to 0 as 0 1 n2 where n is the number of vehicles moreover a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains the stability margin scaling can be improved to 0 1 n in this technical note we show that with judicious choice of nonvanishing asymmetry in control the stability margin of the closed loop can be bounded away from zero uniformly in n asymmetry in control gains thus makes the control architecture highly scalable the results are also generalized to d dimensional lattice information graphs that were studied in 2 and the correspondingly stronger conclusions than those derived in 2 are obtained in addition we show that the size independent stability margin can be achieved with relative position and relative velocity rprv feedback as well as relative position and absolute velocity rpav feedback while the analysis in 1 2 was only for the rpav case

broad edge of chaos in strongly heterogeneous boolean networks the dynamic stability of the boolean networks representing a model for the gene transcriptional regulation kauffman model is studied by calculating analytically and numerically the hamming distance between two evolving configurations this turns out to behave in a universal way close to the phase boundary only for in degree distributions with a finite second moment in degree distributions of the form pd k k with 2 3 thus having a diverging second moment lead to a slower increase of the hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite n with decreasing we conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms

periodic attractors of random truncator maps this paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system we represent the symbolic dynamics generated by this system as a non commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure a stochastic model is constructed on these endomorphisms which leads to the classification of the distribution of periodic orbits for random truncator maps this framework is applied to investigate the periodic transitions of bornholdt s spin market model

order or chaos in boolean gene networks depends on the mean fraction of canalizing functions we explore the connection between order chaos in boolean networks and the naturally occurring fraction of canalizing functions in such systems this fraction turns out to give a very clear indicati

cultured differential evolution for constrained optimization a cultural algorithm with a differential evolution population is proposed in this paper this cultural algorithm uses different knowledge sources to influence the variation operator of the differential evolution algorithm in order to reduce the number of fitness function evaluations required to obtain competitive results comparisons are provided with respect to three techniques that are representative of the state of the art in the area the results obtained by our algorithm are similar in quality to those obtained by the other approaches with respect to which it was compared however our approach requires a lower number of fitness function evaluations than the others

multi agent deployment in 3 d via pde control this paper introduces a methodology for modelling analysis and control design of a large scale system of agents deployed in 3 d space the agents communication graph is a mesh grid disk 2 d topology in polar coordinates treating the agents as a continuum we model the agents collective dynamics by complex valued reaction diffusion 2 d partial differential equations pdes in polar coordinates whose states represent the position coordinates of the agents due to the reaction term in the pdes the agents can achieve a rich family of 2 d deployment manifolds in 3 d space which correspond to the pdes equilibrium as determined by the boundary conditions unfortunately many of these deployment surfaces are open loop unstable to stabilize them a heretofore open and challenging problem of pde stabilization by boundary control on a disk has been solved in this paper using a new class of explicit backstepping kernels that involve the poisson kernel a dual observer which is also explicit allows to estimate the positions of all the agents as needed in the leaders feedback by only measuring the position of their closest neighbors hence an all explicit control scheme is found which is distributed in the sense that each agent only needs local information closed loop exponential stability in the l 2 h 1 and h 2 spaces is proved for both full state and output feedback designs numerical simulations illustrate the proposed approach for 3 d deployment of discrete agents

brief paper finite time multi agent deployment a nonlinear pde motion planning approach the systematic flatness based motion planning using formal power series and suitable summability methods is considered for the finite time deployment of multi agent systems into planar formation profiles along predefined spatial temporal paths thereby a distributed parameter setting is proposed where the collective leader follower agent dynamics is modeled by two boundary controlled nonlinear time varying pdes governing the motion of an agent continuum in the plane the discretization of the pde model directly induces a decentralized communication and interconnection structure for the multi agent system which is required to achieve the desired spatial temporal paths and deployment formations

coherence in large scale networks dimension dependent limitations of local feedback we consider distributed consensus and vehicular formation control problems specifically we address the question of whether local feedback is sufficient to maintain coherence in large scale networks subject to stochastic disturbances we define macroscopic performance measures which are global quantities that capture the notion of coherence a notion of global order that quantifies how closely the formation resembles a solid object we consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1 2 and higher dimensions with vehicular platoons corresponding to the 1 d case a common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions in particular we show that it is impossible to have large coherent 1 d vehicular platoons with only local feedback we analyze these effects in terms of the underlying energetic modes of motion showing that they take the form of large temporal and spatial scales resulting in an accordion like motion of formations a conclusion can be drawn that in low spatial dimensions local feedback is unable to regulate large scale disturbances but it can in higher spatial dimensions this phenomenon is distinct from and unrelated to string instability issues which are commonly encountered in control problems for automated highways

boolean dynamics of networks with scale free topology the dynamics of boolean networks with scale free topology are studied the existence of a phase transition from ordered to chaotic dynamics governed by the value of the scale free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories the phase diagram shows that the phase transition occurs for values of the scale free exponent in the open interval 2 2 5 since the boolean networks under study are directed graphs the scale free topology of the input connections and that of the output connections are studied separately ultimately these two topologies are shown to be equivalent a numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scale free topologies and networks with homogeneous random topologies however an important result of this work is that the fine tuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scale free finally based on the results presented in this work it is hypothesized that the scale free topology favors the evolution and adaptation of network functioning from a biological perspective

stratification and enumeration of boolean functions by canalizing depth abstract boolean network models have gained popularity in computational systems biology over the last dozen years many of these networks use canalizing boolean functions which has led to increased interest in the study of these functions the canalizing depth of a function describes how many canalizing variables can be recursively picked off until a non canalizing function remains in this paper we show how every boolean function has a unique algebraic form involving extended monomial layers and a well defined core polynomial this generalizes recent work on the algebraic structure of nested canalizing functions and it yields a stratification of all boolean functions by their canalizing depth as a result we obtain closed formulas for the number of n variable boolean functions with depth k which simultaneously generalizes enumeration formulas for canalizing and nested canalizing functions

a modification to moea d de for multiobjective optimization problems with complicated pareto sets this paper presents an algorithm named the uniform design multiobjective differential algorithm based on decomposition umode d for optimizing multiobjective problems the algorithm is a modification to the new version of moea d based on differential evolution de i e moea d de proposed by li and zhang 2009 20 its distinguishing features include 1 the uniform design method is applied to generate the aggregation coefficient vectors so that the decomposed scalar optimization subproblems are uniformly distributed and therefore the algorithm could explore uniformly the region of interest from the initial iteration 2 the simplified quadratic approximation with three best points is employed to improve the local search ability and the accuracy of the minimum scalar aggregation function value umode d is compared with the original moea d de and nsga ii by solving a wide set of problems with complicated pareto set shapes in this paper experimental results indicate that umode d significantly outperforms moea d de and nsga ii on these test problems two sets of experiments are carried out to illustrate the efficiency of the uniform design method and the simplified quadratic approximation separately in addition umode d is tested on cec 2009 problems and combinatorial knapsack problems experimental results show that the proposed algorithm performs better than the further improved moea d for almost all the cec 2009 problems and the results obtained are very competitive when comparing umode d with some other algorithms on these multiobjective knapsack problems

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

leader enabled deployment onto planar curves a pde based approach we introduce an approach for stable deployment of agents onto families of planar curves namely 1 d formations in 2 d space the agents collective dynamics are modeled by the reaction advection diffusion class of partial differential equations pdes which is a broader class than the standard heat equation and generates a rich geometric family of deployment curves the pde models whose state is the position of the agents incorporate the agents feedback laws which are designed based on a spatial internal model principle namely the agents feedback laws allow the agents to deploy to a family of geometric curves that correspond to the model s equilibrium curves parameterized by the continuous agent identity 0 1 however many of these curves are open loop unstable stable deployment is ensured by leader feedback designed in a manner similar to the boundary control of pdes by discretizing the pde model with respect to we impose a fixed communication topology specifically a chain graph on the agents and obtain control laws that require communication with only an agent s nearest neighbors on the graph a pde based approach is also used to design observers to estimate the positions of all the agents which are needed in the leader s feedback by measuring only the position of the leader s nearest neighbor hence the leader uses only local information when employing output feedback

constrained optimization based on modified differential evolution algorithm this paper presents a novel constrained optimization based on modified differential evolution algorithm comde in the new algorithm a new directed mutation rule based on the weighted difference vector between the best and the worst individuals at a particular generation is introduced the new directed mutation rule is combined with the modified basic mutation strategy de rand 1 bin where only one of the two mutation rules is applied with the probability of 0 5 the proposed mutation rule is shown to enhance the local search ability of the basic differential evolution de and to get a better trade off between convergence rate and robustness two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction additionally a dynamic non linear increased crossover probability is utilized to balance the global exploration and local exploitation comde also includes a modified constraint handling technique based on feasibility and the sum of constraints violations a new dynamic tolerance technique to handle equality constraints is also adopted the effectiveness and benefits of the new directed mutation strategy and modified basic strategy used in comde has been experimentally investigated the effect of the parameters of the crossover probability function and the parameters of the dynamic tolerance equation on the performance of comde have been analyzed and evaluated by different experiments numerical experiments on 13 well known benchmark test functions and five engineering design problems have shown that the new approach is efficient effective and robust the comparison results between the comde and the other 28 state of the art evolutionary algorithms indicate that the proposed comde algorithm is competitive with and in some cases superior to other existing algorithms in terms of the quality efficiency convergence rate and robustness of the final solution

difference equation for tracking perturbations in systems of boolean nested canalyzing functions this paper studies the spread of perturbations through networks composed of boolean functions with special canalyzing properties canalyzing functions have the property that at least for one value of one of the inputs the output is fixed irrespective of the values of the other inputs in this paper the focus is on partially nested canalyzing functions in which multiple but not all inputs have this property in a cascading fashion they naturally describe many relationships in real networks for example in a gene regulatory network the statement if gene a is expressed then gene b is not expressed regardless of the states of other genes implies that a is canalyzing on the other hand the additional statement if gene a is not expressed and gene c is expressed then gene b is automatically expressed otherwise gene b s state is determined by some other type of rule implies that gene b is expressed by a partially nested canalyzing function with more than two variables but with two canalyzing variables in this paper a difference equation model of the probability that a network node s value is affected by an initial perturbation over time is developed analyzed and validated numerically it is shown that the effect of a perturbation decreases towards zero over time if the boolean functions are canalyzing in sufficiently many variables the maximum dynamical impact of a perturbation is shown to be comparable to the average impact for a wide range of values of the average sensitivity of the network percolation limits are also explored these are parameter values which generate a transition of the expected perturbation effect to zero as other parameters are varied so that the initial perturbation does not scale up with the parameters once the percolation limits are reached

a novel differential search algorithm and applications for structure design differential search method is recently proposed to solve box constrained global optimization problems in this paper we will further extend this method to solve generalized constrained optimization problems particularly for structure design optimization problems to handle the constraints we first propose a novel dynamic s type soft threshold penalty method then the original constrained optimization problem is transformed into a sequence of unconstrained optimization problems the proposed method is mainly comprised of two steps parameter iteration and solution iteration the parameter iteration is to update the dynamic penalty parameter through a soft threshold scheme and the solution iteration is to implement differential search algorithm to solve an unconstrained optimization problem two benchmark sets cec2006 and cec2010 and four engineering structure design optimization problems are solved by our proposed algorithm as well as many other swarm based algorithms proposed in recent literatures numerical results show that our method can achieve better performance but with fewer function evaluations comparing with the existing algorithms

handling equality constraints in evolutionary optimization abstract over the last few decades several methods have been proposed for handling functional constraints while solving optimization problems using evolutionary algorithms eas however the presence of equality constraints makes the feasible space very small compared to the entire search space as a consequence the handling of equality constraints has long been a difficult issue for evolutionary optimization methods this paper presents a hybrid evolutionary algorithm hea for solving optimization problems with both equality and inequality constraints in hea we propose a new local search technique with special emphasis on equality constraints the basic concept of the new technique is to reach a point on the equality constraint from the current position of an individual solution and then explore on the constraint landscape we believe this new concept will influence the future research direction for constrained optimization using population based algorithms the proposed algorithm is tested on a set of standard benchmark problems the results show that the proposed technique works very well on those benchmark problems

information flow and its relation to stability of the motion of vehicles in a rigid formation in this note we consider the effect of information flow on the propagation of errors in spacing in a collection of vehicles trying to maintain a rigid formation during translational maneuvers the motion of each vehicle is described using a linear time invariant lti system we consider undirected and connected information flow graphs and assume that each vehicle can communicate with a maximum of q vehicles where q may vary with the size n of the collection we consider translational maneuver of a reference vehicle where its steady state velocity is different from its initial velocity in the absence of any disturbing forces acting on the vehicles during the maneuver it is desired that the collection be controlled in such a way that its motion asymptotically resembles that of a rigid body in the presence of bounded disturbing forces acting on the vehicles it is desired that the maximum deviation of the motion of the collection from that of a rigid body be bounded and be independent of the size of the collection we consider a decentralized feedback control scheme where the controller of each vehicle takes into account the aggregate errors in position and velocity from the vehicles with which it is in direct communication we assume that all vehicles start at their respective desired positions and velocities since the displacement of every vehicle at the end of the maneuver of the reference vehicle must be the same we show that the loop transfer function must have at least two poles at the origin we then show that if the loop transfer function has three or more poles at the origin then the motion of the collection is unstable that is its deviation from the rigid body motion is arbitrarily large if the size of the formation is sufficiently large if l is the number of poles of the transfer function relating the position of a vehicle with its control input we show that if q n n rarr0 as nrarrinfin then there is a low frequency sinusoidal disturbance of at most unit amplitude acting on each vehicle such that the maximum errors in spacing response increase at least as omega radicn q n l 1 a function p n is omega q n if there exists a nonzero constant c 0 and a n such that p n gesc q n for all n n a consequence of the results presented in this note is that the maximum errors in spacing and velocity of any vehicle can be made insensitive to the size of the collection only if there is at least one vehicle in the collection that communicates with at least omega n other vehicles in the collection

the number of multistate nested canalyzing functions abstract identifying features of molecular regulatory networks is an important problem in systems biology it has been shown that the combinatorial logic of such networks can be captured in many cases by special functions called nested canalyzing in the context of discrete dynamic network models it was also shown that the dynamics of networks constructed from such functions has very special properties that are consistent with what is known about molecular networks and that simplify analysis it is important to know how restrictive this class of functions is for instance for the purpose of network reverse engineering this paper contains a formula for the number of such functions and a comparison to the class of all functions in particular it is shown that as the number of variables becomes large the ratio of the number of nested canalyzing functions to the number of all functions converges to zero this shows that the class of nested canalyzing functions is indeed very restrictive the principal tool used for this investigation is a description of these functions as polynomials and a parametrization of the class of all such polynomials in terms of relations on their coefficients this parametrization can also be used for the purpose of network reverse engineering using only nested canalyzing functions

improving the performance of weighted lagrange multiplier methods for nonlinear constrained optimization abstract nonlinear constrained optimization problems in discrete and continuous spaces are an important class of problems studied extensively in artificial intelligence and operations research these problems can be solved by a lagrange multiplier method in continuous space and by an extended discrete lagrange multiplier method in discrete space when constraints are satisfied these methods rely on gradient descents in the objective space to find high quality solutions on the other hand when constraints are violated these methods rely on gradient ascents in the lagrange multiplier space in order to increase the penalties on unsatisfied constraints and to force the constraints into satisfaction the balance between gradient descents and gradient ascents depends on the relative weights between the objective function and the constraints which indirectly control the convergence speed and solution quality of the lagrangian method to improve convergence speed without degrading solution quality we propose an algorithm to dynamically control the relative weights between the objective and the constraints starting from an initial weight the algorithm automatically adjusts the weights based on the behavior of the search progress with this strategy we are able to eliminate divergence reduce oscillation and speed up convergence we show improved convergence behavior of our proposed algorithm on both nonlinear continuous and discrete problems

string stability of interconnected systems introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems intuitively string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded it is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input output stable the authors derive sufficient weak coupling conditions which guarantee the asymptotic string stability of a class of interconnected systems under the same weak coupling conditions string stable interconnected systems remain string stable in the presence of small structural singular perturbations in the presence of parameter mismatch these weak coupling conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient based parameter adaptation law is used and that the states of all the systems go to zero asymptotically

the stability of boolean network with transmission sensitivity abstract boolean network has been widely used in modeling biological systems and one of the key problems is its stability in response to small perturbations based on the hypothesis that the states of all nodes are homogenously updated great progress has been made in previous works in real biological networks however the updates of genes typically show much heterogeneity to address such conditions we introduce transmission sensitivity into boolean network model by the method of semi annealed approximation we illustrate that in a homogenous network the critical condition of stability has no connection with its transmission sensitivity as for heterogeneous networks it reveals that correlations between network topology and transmission sensitivity can have profound effects on the its stability this result shows a new mechanism that affects the stability of boolean network which could be used to control the dynamics in real biological systems

approximation error in pde based modelling of vehicular platoons we study the problem of how much error is introduced in approximating the dynamics of a large vehicular platoon by using a partial differential equation as was done in barooah mehta and hespanha barooah p mehta p g and hespanha j p 2009 mistuning based decentralised control of vehicular platoons for improved closed loop stability ieee transactions on automatic control 54 2100 2113 hao barooah and mehta hao h barooah p and mehta p g 2011 stability margin scaling laws of distributed formation control as a function of network structure ieee transactions on automatic control 56 923 929 in particular we examine the difference between the stability margins of the coupled ordinary differential equations ode model and its partial differential equation pde approximation which we call the approximation error the stability margin is defined as the absolute value of the real part of the least stable pole the pde model has proved useful in the design of distributed control schemes barooah et al 2009 hao et al 2011 it provides insight into the effect of gains of local controllers on the closed loop stability margin that is lacking in the coupled ode model here we show that the ratio of the approximation error to the stability margin is o 1 n where n is the number of vehicles thus the pde model is an accurate approximation of the coupled ode model when n is large numerical computations are provided to corroborate the analysis

transients of platoons with asymmetric and different laplacians abstract we consider an asymmetric control of platoons of identical vehicles with nearest neighbor interaction recent results show that if the vehicle uses different asymmetries for position and velocity errors the platoon has a short transient and low overshoots in this paper we investigate the properties of vehicles with friction to achieve consensus an integral part is added to the controller making the vehicle a third order system we show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities simulations suggest that our system has a better performance than other nearest neighbor scenarios moreover an optimization based procedure is used to find the controller properties

the influence of canalization on the robustness of boolean networks abstract time and state discrete dynamical systems are frequently used to model molecular networks this paper provides a collection of mathematical and computational tools for the study of robustness in boolean network models the focus is on networks governed by k canalizing functions a recently introduced class of boolean functions that contains the well studied class of nested canalizing functions the variable activities and sensitivity of a function quantify the impact of input changes on the function output this paper generalizes the latter concept to c sensitivity and provides formulas for the activities and c sensitivity of general k canalizing functions as well as canalizing functions with more precisely defined structure a popular measure for the robustness of a network the derrida value can be expressed as a weighted sum of the c sensitivities of the governing canalizing functions and can also be calculated for a stochastic extension of boolean networks these findings provide a computationally efficient way to obtain derrida values of boolean networks deterministic or stochastic that does not involve simulation

canalizing boolean functions maximize mutual information information processing in biologically motivated boolean networks is of interest in recent information theoretic research one measure to quantify this ability is the well known mutual information using fourier analysis we show that canalizing functions maximize mutual information between a single input variable and the outcome of a function with fixed expectation a similar result can be obtained for the mutual information between a set of input variables and the output further if the expectation of the function is not fixed we obtain that the mutual information is maximized by a function only dependent on this single variable i e the dictatorship function we prove our findings for boolean functions with uniformly distributed as well as product distributed input variables

evolutionary constrained optimization using an addition of ranking method and a percentage based tolerance value adjustment scheme one of the most important issues in developing an evolutionary optimization algorithm is the proper handling of any constraints on the problem one must balance the objective function against the degree of constraint violation in such a way that neither is dominant common approaches to strike this balance include implementing a penalty function and the more recent stochastic ranking method but these methods require an extra tuning parameter which must be chosen by the user the present paper demonstrates that a proper balance can be achieved using an addition of ranking method through the ranking of the individuals with respect to the objective function and constraint violation independently we convert these two properties into numerical values of the same order of magnitude this removes the requirement of a user specified penalty coefficient or any other tuning parameters direct addition of the ranking terms is then performed to integrate all information into a single decision variable this approach is incorporated into a m l evolution strategy and tested on thirteen benchmark problems one engineering design problem and five difficult problems with a high dimensionality or many constraints the performance of the proposed strategy is similar to that of the stochastic ranking method when dealing with inequality constraints but it has a much simpler ranking procedure and does not require any tuning parameters a percentage based tolerance value adjustment scheme is also proposed to enable feasible search when dealing with equality constraints

exact solution of kauffman s model with connectivity one kauffman s model is a randomly assembled network of boolean automata each automaton receives inputs from at most k other automata its state at discrete time t 1 is determined by a randomly chosen but fixed boolean function of the k inputs at time t the resulting quenched random dynamics of the network demonstrates two phases a frozen and a chaotic phase the authors give an exact solution of the model for connectivity k 1 valid everywhere in the frozen phase and at a critical point valid for finite as well as for infinite networks they discuss the network s critical behaviour and finite size effects the results for the frozen phase presented complement recent exact results for the chaotic phase obtained for k infinity

differential evolution in constrained numerical optimization an empirical study motivated by the recent success of diverse approaches based on differential evolution de to solve constrained numerical optimization problems in this paper the performance of this novel evolutionary algorithm is evaluated three experiments are designed to study the behavior of different de variants on a set of benchmark problems by using different performance measures proposed in the specialized literature the first experiment analyzes the behavior of four de variants in 24 test functions considering dimensionality and the type of constraints of the problem the second experiment presents a more in depth analysis on two de variants by varying two parameters the scale factor f and the population size np which control the convergence of the algorithm from the results obtained a simple but competitive combination of two de variants is proposed and compared against state of the art de based algorithms for constrained optimization in the third experiment the study in this paper shows 1 important information about the behavior of de in constrained search spaces and 2 the role of this knowledge in the correct combination of variants based on their capabilities to generate simple but competitive approaches

adding a single state memory optimally accelerates symmetric linear maps previous papers have proposed to add memory registers to the dynamics of discrete time linear systems in order to accelerate their convergence in particular it has been proved that adding one memory slot per agent allows faster convergence towards average consensus we here prove that this situation cannot be improved by adding more memory slots when the knowledge about the self adjoint linear map to be accelerated reduces to bounds on its extreme eigenvalues

characterizing short term stability for boolean networks over any distribution of transfer functions we present a characterization of short term stability of kauffman s nk random boolean networks under arbitrary distributions of transfer functions given such a boolean network where each transfer function is drawn from the same distribution we present a formula that determines whether short term chaos damage spreading will happen our main technical tool which enables the formal proof of this formula is the fourier analysis of boolean functions which describes such functions as multilinear polynomials over the inputs numerical simulations on mixtures of threshold functions and nested canalyzing functions demonstrate the formula s correctness

stability margin scaling laws for distributed formation control as a function of network structure we describe a methodology for modeling analysis and distributed control design of a large vehicular formation whose information graph is a d dimensional lattice we derive asymptotic formulae for the closed loop stability margin based on a partial differential equation pde approximation of the formation we show that the exponent in the scaling law for the stability margin is influenced by the structure of the information graph and by the control architecture symmetric or asymmetric for a given fixed number of vehicles we show that the scaling law can be improved significantly by employing a higher dimensional information graph and or by introducing small asymmetry mistuning in the nominally symmetric proportional control gains we also provide a characterization of the error introduced by the pde approximation

boolean nested canalizing functions a comprehensive analysis abstract boolean network models of molecular regulatory networks have been used successfully in computational systems biology the boolean functions that appear in published models tend to have special properties in particular the property of being nested canalizing a concept inspired by the concept of canalization in evolutionary biology it has been shown that networks comprised of nested canalizing functions have dynamic properties that make them suitable for modeling molecular regulatory networks namely a small number of large attractors as well as relatively short limit cycles this paper contains a detailed analysis of this class of functions based on a novel normal form as polynomial functions over the boolean field the concept of layer is introduced that stratifies variables into different classes depending on their level of dominance using this layer concept a closed form formula is derived for the number of nested canalizing functions with a given number of variables additional metrics considered include hamming weight the activity number of any variable and the average sensitivity of the function it is also shown that the average sensitivity of any nested canalizing function is between 0 and 2 this provides a rationale for why nested canalizing functions are stable since a random boolean function in n variables has average sensitivity n 2 the paper also contains experimental evidence that the layer number is an important factor in network stability

an improved differential evolution algorithm with fitness based adaptation of the control parameters differential evolution de is arguably one of the most powerful stochastic real parameter optimization algorithms of current interest de operates through the similar computational steps as employed by a standard evolutionary algorithm ea however unlike the traditional eas the de variants perturb the current generation population members with the scaled differences of randomly selected and distinct population members therefore no separate probability distribution has to be used which makes the scheme self organizing in this respect scale factor f and crossover rate cr are two very important control parameters of de since the former regulates the step size taken while mutating a population member in de and the latter controls the number of search variables inherited by an offspring from its parent during recombination this article describes a very simple yet very much effective adaptation technique for tuning both f and cr on the run without any user intervention the adaptation strategy is based on the objective function value of individuals in the de population comparison with the best known and expensive variants of de over fourteen well known numerical benchmarks and one real life engineering problem reflects the superiority of proposed parameter tuning scheme in terms of accuracy convergence speed and robustness