an improved multi objective population based extremal optimization algorithm with polynomial mutation as a recently developed evolutionary algorithm inspired by far from equilibrium dynamics of self organized criticality extremal optimization eo has been successfully applied to a variety of benchmark and engineering optimization problems however there are only few reported research works concerning the applications of eo in the field of multi objective optimization this paper presents an improved multi objective population based eo algorithm with polynomial mutation called imopeo plm to solve multi objective optimization problems mops unlike the previous multi objective versions based on eo the proposed imopeo plm adopts population based iterated optimization a more effective mutation operation called polynomial mutation and a novel and more effective mechanism of generating new population from the design perspective of multi objective evolutionary algorithms moeas imopeo plm is relatively simpler than other reported competitive moeas due to its fewer adjustable parameters and only mutation operation furthermore the extensive experimental results on some benchmark mops show that imopeo plm performs better than or at least competitive with these reported popular moeas such as mopeo moeo nsga ii a moclpso paes spea spea2 sms emoa smpso and moea d de by using nonparametric statistical tests e g kruskal wallis test mann whitney u test friedman and quade tests in terms of some commonly used quantitative performance metrics e g convergence diversity spread hypervolume generational distance inverted generational distance

robust adaptive path following of underactuated ships robust path following is an issue of vital practical importance to the ship industry in this paper a nonlinear robust adaptive control strategy is developed to force an underactuated surface ship to follow a predefined path at a desired speed despite the presence of environmental disturbances induced by wave wind and ocean current the proposed controller is scalable and is designed using lyapunov s direct method and the popular backstepping and parameter projection techniques along the way of proving closed loop stability we obtain a new stability result for nonlinear cascade systems with non vanishing uncertainties interestingly it is shown in this paper that our developed control strategy is easily extendible to situations of practical importance such as parking and point to point navigation numerical simulations using the real data of a monohull ship are provided to illustrate the effectiveness of the proposed methodology for path following of underactuated ships

lyapunov formulation of the large scale iss cyclic small gain theorem the discrete time case abstract this paper presents a lyapunov formulation of the cyclic small gain theorem for dynamical networks composed of discrete time input to state stable iss subsystems iss lyapunov functions for dynamical networks satisfying the cyclic small gain condition are constructed from the iss lyapunov functions of the subsystems

extremal optimization for graph partitioning extremal optimization is a new general purpose method for approximating solutions to hard optimization problems we study the method in detail by way of the computationally hard np hard graph partitioning problem we discuss the scaling behavior of extremal optimization focusing on the convergence of the average run as a function of run time and system size the method has a single free parameter which we determine numerically and justify using a simple argument on random graphs our numerical results demonstrate that extremal optimization maintains consistent accuracy for increasing system sizes with an approximation error decreasing over run time roughly as a power law t 20 4 on geometrically structured graphs the scaling of results from the average run suggests that these are far from optimal with large fluctuations between individual trials but when only the best runs are considered results consistent with theoretical arguments are recovered

sms emoa multiobjective selection based on dominated hypervolume abstract the hypervolume measure or s metric is a frequently applied quality measure for comparing the results of evolutionary multiobjective optimisation algorithms emoa the new idea is to aim explicitly for the maximisation of the dominated hypervolume within the optimisation process a steady state emoa is proposed that features a selection operator based on the hypervolume measure combined with the concept of non dominated sorting the algorithm s population evolves to a well distributed set of solutions thereby focussing on interesting regions of the pareto front the performance of the devised s metric selection emoa sms emoa is compared to state of the art methods on two and three objective benchmark suites as well as on aeronautical real world applications

nonlinear small gain theorems for discrete time feedback systems and applications we derive in this work a local nonlinear small gain theorem in the framework of input to state stability for discrete time systems our primary objective is to show that as in the continuous time context these discrete time nonlinear small gain theorems are very effective in stability analysis and synthesis for various classes of discrete time control systems two converse lyapunov theorems for discrete exponential stability are developed to assist these applications new results in stability and stabilization presented in this paper are significant extensions of previous work by other authors ieee trans automat control 38 1993 1398 39 1994 2340 33 1988 1082

extremal optimization at the phase transition of the three coloring problem we investigate the phase transition in vertex coloring on random graphs using the extremal optimization heuristic three coloring is among the hardest combinatorial optimization problems and is equivalent to a 3 state anti ferromagnetic potts model like many other such optimization problems it has been shown to exhibit a phase transition in its ground state behavior under variation of a system parameter the graph s mean vertex degree this phase transition is often associated with the instances of highest complexity we use extremal optimization to measure the ground state cost and the backbone an order parameter related to ground state overlap averaged over a large number of instances near the transition for random graphs of size n up to 512 for these graphs benchmarks show that extremal optimization reaches ground states and explores a sufficient number of them to give the correct backbone value after about osn 3 5 d update steps finite size scaling yields a critical mean degree value ac 4 703s28d furthermore the exploration of the degenerate ground states indicates that the backbone order parameter measuring the constrainedness of the problem exhibits a first order phase transition

lyapunov formulation of iss cyclic small gain in continuous time dynamical networks this paper provides a lyapunov formulation of the cyclic small gain theorem for general dynamical networks large scale systems composed of continuous time input to state stable iss subsystems iss lyapunov functions for continuous time dynamical networks satisfying cyclic small gain conditions are constructed from the iss lyapunov functions of the subsystems

global exponential stabilisation of acyclic traffic networks abstractthis work is devoted to the construction of explicit feedback control laws for the robust global exponential stabilisation of general uncertain discrete time acyclic networks we consider discrete time uncertain network models which satisfy very weak assumptions the construction of the controllers and the rigorous proof of the robust global exponential stability for the closed loop system are based on recently proposed vector lyapunov function criteria as well as the fact that the network is acyclic it is shown in this study that the latter requirement is necessary for the existence of a robust global exponential stabiliser of the desired uncongested equilibrium point of the network our main focus is on traffic networks and all assumptions are related to features appearing in traffic models an illustrative example demonstrates the applicability of the obtained results to realistic traffic flow networks

exponential stabilization of an underactuated autonomous surface vessel this paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters it is first shown that although the system is not asymptotically stabilizable to a given configuration using a time invariant continuous feedback it is strongly accessible and small time locally controllable at any equilibrium time invariant discontinuous feedback laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates a simulation example is included to demonstrate the results

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

multi objective robust pid controller tuning using two lbests multi objective particle swarm optimization in this paper two lbests multi objective particle swarm optimization 2lb mopso is applied to design multi objective robust proportional integral derivative pid controllers for two mimo systems namely distillation column plant and longitudinal control system of the super maneuverable f18 harv fighter aircraft multi objective robust pid controller design problem is formulated by minimizing integral squared error ise and balanced robust performance criteria during the search 2lb mopso can focus on small regions in the parameter space in the vicinity of the best existing fronts as the lbests are chosen from the top fronts in a non domination sorted external archive of reasonably large size the offspring obtained can be more diverse with good fitness the performance of various optimal pid controllers is compared in terms of the sum of ise and balanced robust performance criteria for the purpose of comparison 2lb mopso nsga ii as well as earlier reported riccati iga and osa methods are considered the performance of pid controllers obtained using 2lb mopso is better than that of others in addition hypervolume based comparisons are carried out to show the superior performance of 2lb mopso over nsga ii the results reveal that 2lb mopso yields better robustness and consistency in terms of the sum of ise and balanced robust performance criteria than various optimal pid controllers

nature s way of optimizing we propose a general purpose method for finding high quality solutions to hard optimization problems inspired by self organizing processes often found in nature the method called extremal optimization successively eliminates extremely undesirable components of sub optimal solutions drawing upon models used to simulate far from equilibrium dynamics it complements approximation methods inspired by equilibrium statistical physics such as simulated annealing with only one adjustable parameter its performance proves competitive with and often superior to more elaborate stochastic optimization procedures we demonstrate it here on two classic hard optimization problems graph partitioning and the traveling salesman problem 2000 elsevier science b v all rights reserved

optimization with extremal dynamics for the traveling salesman problem abstract by mapping the optimization problems to physical systems the paper presents a general purpose stochastic optimization method with extremal dynamics it is built up with the traveling salesman problem tsp being a typical np complete problem as self organized critical processes of extremal dynamics the optimization dynamics successively updates the states of those cities with high energy consequently a near optimal solution can be quickly obtained through the optimization processes combining the two phases of greedy searching and fluctuated explorations ergodic walk near the phase transition the computational results demonstrate that the proposed optimization method may provide much better performance than other optimization techniques developed from statistical physics such as simulated annealing sa since the proposed fundamental solution is based on the principles and micromechanisms of computational systems it can provide systematic viewpoints and effective computational methods on a wide spectrum of combinatorial and physical optimization problems

characterizations of input to state stability for hybrid systems abstract we study input to state stability iss for a broad class of hybrid systems which are combinations of a differential equation on a constraint set and a difference equation on another constraint set for this class of hybrid systems we establish the equivalence of iss nonuniform iss and the existence of a smooth iss lyapunov function by additionally assuming that the right hand side of the differential equation has a convex property with respect to inputs moreover we demonstrate by examples that the equivalence may fail when such a convexity assumption is removed

a fully discrete state kinetic theory approach to modeling vehicular traffic this paper presents a new mathematical model of vehicular traffic based on the methods of the generalized kinetic theory in which the space of microscopic states position and speed of the vehicles is genuinely discrete while in the recent literature discrete velocity kinetic models of car traffic have already been successfully proposed this is to our knowledge the first attempt to account for all aspects of the physical granularity of car flow within the formalism of the aforesaid mathematical theory thanks to a rich but handy structure the resulting model allows one to easily implement and simulate various realistic scenarios giving rise to characteristic traffic phenomena of practical interest e g queue formation due to roadwork or to a traffic light moreover it is analytically tractable under quite general assumptions whereby fundamental properties of the solutions can be rigorously proved

global robust adaptive path following of underactuated ships we propose a method for designing a global robust adaptive controller that forces an underactuated ship to follow a reference path under both constant and time varying disturbances induced by waves wind and ocean currents both linear and nonlinear damping terms are included to cover both low and high speed applications all nonlinear damping coefficients are assumed unknown but lie in a known compact set the new results are derived using a choice of an appropriate body fixed frame origin a smooth approximation of nonsmooth damping terms several nonlinear coordinate changes the backstepping technique and utilization of the ship dynamic structure experiments on a model ship illustrate the results

path tracking of underactuated ships with general form of dynamics abstractthis article considers the path tracking problem for underactuated ships with general form of dynamics including uncertainties by introducing certain two polar coordinate transformations the ship s tracking kinematics and dynamics can be transformed into certain two inputs two outputs nonlinear strict feedback form to avoid possible singularity problem in the backstepping control design we introduce an asymptotic modification of orientation concept presented tracking scheme can guarantee the uniformly ultimately boundedness of closed loop system in terms of polar coordinates for the convenience of comparison with previous related works where all tracking schemes were discussed in the cartesian frame we carry out some case studies to investigate the conditions under which the proposed tracking method can guarantee the same stability and convergence properties of tracking errors in the cartesian frame numerical simulation studies are also carried out to demonstrate the effectiveness of pres

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

a generalization of the small gain theorem for nonlinear feedback systems abstract a generalization is given of the usual small gain theorem which allows greater flexibility in use of gain bounds for stability analysis of nonlinear feedback systems

achieving balance between proximity and diversity in multi objective evolutionary algorithm currently an alternative framework using the hypervolume indicator to guide the search for elite solutions of a multi objective problem is studied in the evolutionary multi objective optimization community very actively comparing to the traditional pareto dominance based approach in this paper we present a dynamic neighborhood multi objective evolutionary algorithm based on hypervolume indicator dnmoea hi which benefits from both pareto dominance and hypervolume indicator based frameworks dnmoea hi is featured by the employment of hypervolume indicator as a truncation operator to prune the exceeded population while a well designed density estimator i e tree neighborhood density is combined with the pareto strength value to perform fitness assignment moreover a novel algorithm is proposed to directly evaluate the hypervolume contribution of a single individual the performance of dnmoea hi is verified on a comprehensive benchmark suite in comparison with six other multi objective evolutionary algorithms experimental results demonstrate the efficiency of our proposed algorithm solutions obtained by dnmoea hi well approach the pareto optimal front and are evenly distributed over the front simultaneously

small gain conditions and the comparison principle the general input to state stability iss small gain condition for networks in a trajectory formulation is shown to be equivalent to the requirement that a discrete time comparison system induced by the gain matrix of the network is iss this leads to a comparison principle relating input to state stability of an artificial discrete time system to the same stability property of a continuous time nominal system as a consequence general small gain conditions can now be verified by finding iss lyapunov functions

generalized decomposition and cross entropy methods for many objective optimization decomposition based algorithms for multi objective optimization problems have increased in popularity in the past decade although convergence to the pareto optimal front pf for such algorithms can often be superior to that of pareto based alternatives the problem of effectively distributing pareto optimal solutions in a high dimensional space has not been solved in this work we introduce a novel concept which we call generalized decomposition generalized decomposition provides a framework with which the decision maker dm can guide the underlying search algorithm toward specific regions of interest or the entire pareto front with the desired distribution of pareto optimal solutions the method simplifies many objective problems by unifying the three performance objectives of an a posteriori multi objective optimizer convergence to the pf evenly distributed pareto optimal solutions and coverage of the entire front to only one that of convergence a framework established on generalized decomposition and an estimation of distribution algorithm eda based on low order statistics namely the cross entropy method is created to illustrate the benefits of the proposed concept for many objective problems the algorithm mace gd is shown to be highly competitive with the existing best in class decomposition based algorithm moea d and a more elaborate eda method rm meda

a multiobjective evolutionary algorithm based on decomposition with normal boundary intersection for traffic grooming in optical networks abstract this paper presents a multiobjective optimization algorithm for solving tri objective optimization problems with objectives of very different scales as a version of the multiobjective evolutionary algorithm based on decomposition moea d it adopts the normal boundary intersection nbi based tchebycheff approach to decompose a multiobjective optimization problem into a number of single objective subproblems particular attention has been paid to set the weight vectors of these subproblems for handling disparately scaled objectives we have applied our proposed algorithm to a traffic grooming problem in the telecommunication fields we also propose to use an indirect encoding approach to handle this very complicated problem our experimental studies show that our proposed method is able to produce very promising results for this real world telecommunication problem

multistage extremal optimization for hard travelling salesman problem abstract the adjustable parameters of probability distributions adopted by extremal optimization eo and its modified versions play a critical role in controlling their performances unlike the traditional static probability distribution based strategy this paper presents a novel method called multistage eo to explore the configuration space of hard travelling salesman problem tsp by using different values of the parameters in different stages this method is to optimize with multi start techniques starting from random states in the first stage in all later stages it always selects the best configuration obtained from the last stage as the initial one for optimization in the current stage the superior performance of the proposed method is proved by the experimental tests with the well known hard tsp instances

on the index of convergence of a class of boolean matrices with structural properties boolean matrices are of prime importance in the study of discrete event systems des which allow us to model systems across a variety of applications the index of convergence i e the number of

technical communique point to point navigation of underactuated ships this paper considers point to point navigation of underactuated ships where only surge force and yaw moment are available in general a ship s sway motion satisfies a passive boundedness property which is expressed in terms of a lyapunov function under this kind of consideration a certain concise nonlinear scheme is proposed to guarantee the closed loop system to be uniformly ultimately bounded uub a numerical simulation study is also performed to illustrate the effectiveness of the proposed scheme

an improved shuffled frog leaping algorithm with extremal optimisation for continuous optimisation several types of evolutionary computing methods are documented in the literature and are well known for solving unconstrained optimisation problems this paper proposes a hybrid scheme that combines the merits of a global search algorithm the shuffled frog leaping algorithm sfla and local exploration extremal optimisation eo and that exhibits strong robustness and fast convergence for high dimensional continuous function optimisation a modified shuffled frog leaping algorithm msfla is investigated that improves the leaping rule by properly extending the leaping step size and adding a leaping inertia component to account for social behaviour to further improve the local search ability of msfla and speed up convergence we occasionally introduce eo which has an excellent local exploration capability in the local exploration process of the msfla it is characterised by alternating the coarse grained cauchy mutation and the fine grained gaussian mutation compared with standard particle swarm optimisation pso sfla and msfla for six widely used benchmark examples the hybrid msfla eo is shown to be a good and robust choice for solving high dimensional continuous function optimisation problems it possesses excellent performance in terms of the mean function values the success rate and the fitness function evaluations ffe which is a rough measure of the complexity of the algorithm

a novel elitist multiobjective optimization algorithm multiobjective extremal optimization abstract recently a general purpose local search heuristic method called extremal optimization eo has been successfully applied to some np hard combinatorial optimization problems this paper presents an investigation on eo with its application in numerical multiobjective optimization and proposes a new novel elitist 1 multiobjective algorithm called multiobjective extremal optimization moeo in order to extend eo to solve the multiobjective optimization problems the pareto dominance strategy is introduced to the fitness assignment of the proposed approach we also present a new hybrid mutation operator that enhances the exploratory capabilities of our algorithm the proposed approach is validated using five popular benchmark functions the simulation results indicate that the proposed approach is highly competitive with the state of the art multiobjective evolutionary algorithms thus moeo can be considered a good alternative to solve numerical multiobjective optimization problems

general framework for localised multi objective evolutionary algorithms many real world problems have multiple competing objectives and can often be formulated as multi objective optimisation problems multi objective evolutionary algorithms moeas have proven very effective in obtaining a set of trade off solutions for such problems this research seeks to improve both the accuracy and the diversity of these solutions through the local application of evolutionary operators to selected sub populations a local operation based implementation framework is presented in which a population is partitioned using hierarchical clustering into a pre defined number of sub populations environment selection and genetic variation are then applied to each sub population the effectiveness of this approach is demonstrated on 2 and 4 objective benchmark problems the performance of each of four best in class moeas is compared with their modified local operation based versions derived from this framework in each case the introduction of the local operation based approach improves performance further it is shown that the combined use of local environment selection and local genetic variation is better than the application of either local environment selection or local genetic variation alone preliminary results indicate that the selection of a suitable number of sub populations is related to problem dimension as well as to population size