complex temperature singularities in potts models on the square lattice we report some results on the complex temperature ct singularities of q state potts models on the square lattice we concentrate on the problematic region mathrm re a l0 where a e k in which ct zeros of the partition function are sensitive to finite lattice artifacts from analyses of low temperature series expansions for 3l ql 8 we establish the existence in this region of complex conjugate ct singularities at which the magnetization and susceptibility diverge from calculations of zeros of the partition function we obtain evidence consistent with the inference that these singularities occur at endpoints a e a e of arcs protruding into the complex temperature extension of the ferromagnetic phase exponents for these singularities are determined e g for q 3 we find ensuremath beta e ensuremath 0 125 1 consistent with ensuremath beta e ensuremath frac 1 8 by duality these results also imply associated arcs extending into the ct extension of the symmetric paramagnetic phase analytic expressions are suggested for the positions of some of these singularities e g for q 5 our finding is consistent with the exact value a e a e 2 ensuremath 1 ensuremath mp i further discussions of complex temperature phase diagrams are given

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

omni optimizer a generic evolutionary algorithm for single and multi objective optimization due to the vagaries of optimization problems encountered in practice users resort to different algorithms for solving different optimization problems in this paper we suggest and evaluate an optimization procedure which specializes in solving a wide variety of optimization problems the proposed algorithm is designed as a generic multi objective multi optima optimizer care has been taken while designing the algorithm such that it automatically degenerates to efficient algorithms for solving other simpler optimization problems such as single objective uni optimal problems single objective multi optima problems and multi objective uni optimal problems the efficacy of the proposed algorithm in solving various problems is demonstrated on a number of test problems chosen from the literature because of its efficiency in handling different types of problems with equal ease this algorithm should find increasing use in real world optimization problems

quantization of models with non compact quantum group symmetry modular xxz magnet and lattice sinh gordon model we define and study certain integrable lattice models with non compact quantum group symmetry the modular double of including an integrable lattice regularization of the sinh gordon model and a non compact version of the xxz model their fundamental r matrices are constructed in terms of the non compact quantum dilogarithm our choice of the quantum group representations naturally ensures self adjointness of the hamiltonian and the higher integrals of motion these models are studied with the help of the separation of variables method we show that the spectral problem for the integrals of motion can be reformulated as the problem to determine a subset among the solutions to certain finite difference equations baxter equation and quantum wronskian equation which is characterized by suitable analytic and asymptotic properties a key technical tool is the so called operator for which we give an explicit construction our results allow us to establish some connections to related results and conjectures on the sinh gordon theory in continuous spacetime our approach also sheds some light on the relations between massive and massless models in particular the sinh gordon and liouville theories from the point of view of their integrable structures

a combined global and local search method to deal with constrained optimization for continuous tabu search heuristic methods such as tabu search are efficient for global optimizations most studies however have focused on constraint free optimizations penalty functions are commonly used to deal with constraints for global optimization algorithms in dealing with constraints this is sometimes inefficient especially for equality constraints as it is difficult to keep the global search within the feasible region by purely adding a penalty to the objective function a combined global and local search method is proposed in this paper to deal with constrained optimizations it is demonstrated by combining continuous tabu search cts and sequential quadratic programming sqp methods first a nested inner and outer loop method is presented to lead the search within the feasible region sqp a typical local search method is used to quickly solve a non linear programming purely for constraints in the inner loop and provides feasible neighbors for the outer loop cts in the outer loop is used to seek for the global optimal finally another local search using sqp is conducted with the results of cts as initials to refine the global search results efficiency is demonstrated by a number of benchmark problems

on the equality constraints tolerance of constrained optimization problems the tolerance value plays an important role when converting equality constraints into inequality constraints in solving constrained optimization problems many researchers use a fixed or dynamic setting directly based on trial or experiments without systematic study as a well known constraint handling technique deb s feasibility based rule is widely adopted but it has one drawback as the ranking is not consistent with the actual ranking after introducing the tolerance value after carefully analyzing how the tolerance value influences the ranking difference a novel strategy named ranking adjustment strategy ras is proposed which can be considered as a complement of deb s feasibility based rule the experiment has verified the effectiveness of the proposed strategy this is the first time to analyze the inner mechanism of the tolerance value for equality constraints systematically which can give some guide for future research

complex temperature phase diagrams for the q state potts model on self dual families of graphs and the nature of the q limit exact calculations of the potts model partition function z g q v have been presented for arbitrary q and temperature like variable v on self dual strip graphs g of the square lattice with fixed width l y and arbitrarily great length lx with two types of boundary conditions letting lx infinity the resultant free energy and complex temperature phase diagram have been computed including the locus b where the free energy is nonanalytic results are analyzed for widths l y 1 2 3 these results have been used to study the approach to the large q limit of b

multi objective design optimization using cascade evolutionary computations the consideration of uncertainties in conjunction with the probability of violation of the constraints imposed by the design codes is examined in the framework of structural optimization the optimum design achieved based on a deterministic formulation is compared in terms of the optimum weight the probability of violation of the constraints and the probability of failure with the optimum designs achieved through a robust design formulation where the variance of the response is considered as an additional criterion the stochastic finite element problem is solved using the monte carlo simulation method combined with the latin hypercube sampling technique for improving its computational efficiency a non dominant cascade evolutionary algorithm based methodology is adopted for the solution of the multi objective optimization problem encountered in order to obtain the global pareto front curve

a combined nlp differential evolution algorithm approach for the optimization of looped water distribution systems 1 this paper proposes a novel optimization approach for the least cost design of looped water distribution systems wdss three distinct steps are involved in the proposed optimization approach in the first step the shortest distance tree within the looped network is identified using the dijkstra graph theory algorithm for which an extension is proposed to find the shortest distance tree for multisource wdss in the second step a nonlinear programming nlp solver is employed to optimize the pipe diameters for the shortest distance tree chords of the shortest distance tree are allocated the minimum allowable pipe sizes finally in the third step the original looped water network is optimized using a differential evolution de algorithm seeded with diameters in the proximity of the continuous pipe sizes obtained in step two as such the proposed optimization approach combines the traditional deterministic optimization technique of nlp with the emerging evolutionary algorithm de via the proposed network decomposition the proposed methodology has been tested on four looped wdss with the number of decision variables ranging from 21 to 454 results obtained show the proposed approach is able to find optimal solutions with significantly less computational effort than other optimization techniques

asymptotic limits and zeros of chromatic polynomials and ground state entropy of potts antiferromagnets we study the asymptotic limiting function w g q lim n to infty p g q 1 n where p g q is the chromatic polynomial for a graph g with n vertices we first discuss a subtlety in the definition of w g q resulting from the fact that at certain special points q s the following limits do not commute lim n to infty lim q to q s p g q 1 n ne lim q to q s lim n to infty p g q 1 n we then present exact calculations of w g q and determine the corresponding analytic structure in the complex q plane for a number of families of graphs g including circuits wheels biwheels bipyramids and cyclic and twisted ladders we study the zeros of the corresponding chromatic polynomials and prove a theorem that for certain families of graphs all but a finite number of the zeros lie exactly on a unit circle whose position depends on the family using the connection of p g q with the zero temperature potts antiferromagnet we derive a theorem concerning the maximal finite real point of non analyticity in w g q denoted q c and apply this theorem to deduce that q c sq 3 and q c hc 3 sqrt 5 2 for the square and honeycomb lattices finally numerical calculations of w hc q and w sq q are presented and compared with series expansions and bounds

exact potts model partition functions on strips of the honeycomb lattice abstract we present exact calculations of the partition function of the q state potts model on i open ii cyclic and iii mobius strips of the honeycomb brick lattice of width l y 2 and arbitrarily great length in the infinite length limit the thermodynamic properties are discussed the continuous locus of singularities of the free energy is determined in the q plane for fixed temperature and in the complex temperature plane for fixed q values we also give exact calculations of the zero temperature partition function chromatic polynomial and w q the exponent of the ground state entropy for the potts antiferromagnet for honeycomb strips of type iv l y 3 cyclic v l y 3 mobius vi l y 4 cylindrical and vii l y 4 open in the infinite length limit we calculate w q and determine the continuous locus of points where it is nonanalytic we show that our exact calculation of the entropy for the l y 4 strip with cylindrical boundary conditions provides an extremely accurate approximation to a few parts in 10 5 for moderate q values to the entropy for the full 2d honeycomb lattice where the latter is determined by monte carlo measurements since no exact analytic form is known

cooperative coevolutionary differential evolution with improved augmented lagrangian to solve constrained optimisation problems propose the improved augmented lagrangian method ialf to deal with constraints in a more efficient way propose cooperative coevolutionary method using improved augmented lagrangian ccialf approach for solving constrained optimisation problems solve the cec 2006 constrained optimisation test suite with proposed ccialf algorithm with higher solution quality compared to the state of the art algorithms solve practical engineering problems by proposed ccialf algorithm and improve the best known objective function value that exists in the literature in constrained optimisation the augmented lagrangian method is considered as one of the most effective and efficient methods this paper studies the behaviour of augmented lagrangian function alf in the solution space and then proposes an improved augmented lagrangian method we have shown that our proposed method can overcome some of the drawbacks of the conventional augmented lagrangian method with the improved augmented lagrangian approach this paper then proposes a cooperative coevolutionary differential evolution algorithm for solving constrained optimisation problems the proposed algorithm is evaluated on a set of 24 well known benchmark functions and five practical engineering problems experimental results demonstrate that the proposed algorithm outperforms the state of the art algorithms with respect to solution quality as well as efficiency

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

pareto optimal sensor locations for structural identification theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed the objective is to optimally locate sensors in the structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling for a single model class the information entropy is used as the optimality criterion for selecting the best sensor configuration for multiple model classes the problem is formulated as a multi objective optimization problem of finding the pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices a heuristic algorithm is proposed for constructing effective pareto optimal sensor configurations that are superior in terms of computational efficiency and accuracy to the pareto sensor configurations predicted by evolutionary algorithms suitable for solving general multi objective optimisation problems the theoretical developments and the effectiveness of the proposed algorithms are illustrated for a 10 dof chain like spring mass model and a 32 dof truss structure

on the thermodynamic bethe ansatz equation in the sinh gordon model two implicit periodic structures in the solution of the sinh gordon thermodynamic bethe ansatz tba equation are considered the analytic structure of the solution as a function of complex is studied to some extent both analytically and numerically the results hint at how the cft integrable structures can be relevant in the sinh gordon and staircase models more motivations are figured out for subsequent studies of the massless sinh gordon i e liouville tba equation

partition function zeros of a restricted potts model on lattice strips and effects of boundary conditions we calculate exactly the partition function z g q v of the q state potts model with temperature like boltzmann variable v for strip graphs g of the square and triangular lattices of various widths ly and arbitrarily great lengths lx with a variety of boundary conditions and with q and v restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two dimensional lattices from these calculations in the limit lx we determine the continuous accumulation loci of the partition function zeros in the v and q planes strips of the honeycomb lattice are also considered we discuss some general features of these loci

a hybrid particle swarm optimization with a feasibility based rule for constrained optimization during the past decade hybrid algorithms combining evolutionary computation and constraint handling techniques have shown to be effective to solve constrained optimization problems for constrained optimization the penalty function method has been regarded as one of the most popular constraint handling technique so far whereas its drawback lies in the determination of suitable penalty factors which greatly weakens the efficiency of the method as a novel population based algorithm particle swarm optimization pso has gained wide applications in a variety of fields especially for unconstrained optimization problems in this paper a hybrid pso hpso with a feasibility based rule is proposed to solve constrained optimization problems in contrast to the penalty function method the rule requires no additional parameters and can guide the swarm to the feasible region quickly in addition to avoid the premature convergence simulated annealing sa is applied to the best solution of the swarm to help the algorithm escape from local optima simulation and comparisons based on several well studied benchmarks demonstrate the effectiveness efficiency and robustness of the proposed hpso moreover the effects of several crucial parameters on the performance of the hpso are studied as well

improved novel global harmony search with a new relaxation method for reliability optimization problems reliability engineers often try to achieve a high reliability level of electronic systems reliability optimization problem involves setting reliability objectives for components or subsystems in order to meet the resource consumption constraint e g the total cost weight the reliability optimization has been an active area of research for the past decades in this paper an improved novel global harmony search inghs approach is proposed to solve reliability optimization problem the inghs employs a stochastic position updating strategy to replace the position updating of nghs and thus the balance between the exploration and exploitation ability further improved and more search space are observed during the algorithms performance moreover a new constraint relaxation method also is integrated into the proposed approach applying the proposed approach to several well known benchmark problems results indicate that the inghs algorithm can find better solution effectively and efficiently furthermore the inghs algorithm is used to solve reliability optimization problems numerical results demonstrated that the inghs algorithm performs better than several state of the art algorithms in most cases

control of the optimum synthesis process of a four bar linkage whose point on the working member generates the given path this paper presents the optimum synthesis of a four bar linkage in which the coupler point performs a path composed of rectilinear segments and a circular arc the grashof four bar linkage whose geometry provides minimum deviations from the given problem for certain parts of the crank cycle is chosen the motion of the coupler point of the four bar linkage is controlled within the given values of allowed deviations so that it is always in the prescribed environment of the given point on the observed segment the synthesis process tends to bring only those path segments that are beyond the boundaries within the prescribed boundary deviations during the synthesis allowed deviations change from the initial maximum values to the given minimum ones groups of mechanisms realising satisfactory approximation to the desired motion can be obtained by the method of controlled decrease of allowed deviations with the application of the differential evolution de algorithm

application of particle swarm optimization based on chks smoothing function for solving nonlinear bilevel programming problem particle swarm optimization pso is a new optimization technique originating from artificial life and evolutionary computation it completes optimization through following the personal best solution of each particle and the global best value of the whole swarm pso can be used to solve nonlinear programming problems for global optimal solutions efficiently so a novel approach based on particle swarm optimization is proposed to solve nonlinear bilevel programming problem nblp in the proposed approach applying karush kuhn tucker kkt condition to the lower level problem we transform the nblp into a regular nonlinear programming with complementary constraints which is sequentially smoothed by chen harker kanzow smale chks smoothing function the pso approach is then applied to solve the smoothed nonlinear programming for getting the approximate optimal solution of the nblp problem simulations on 5 benchmark problems and practical example about watershed water trading decision making problem are made and the results demonstrate the effectiveness of the proposed method for solving nblp

a local exploration based differential evolution algorithm for constrained global optimization abstract we propose a modified differential evolution de algorithm for constrained global optimization the modification is based on the mutation rule of de the new algorithm also incorporates a periodic local exploration technique the local technique used is a limited version of the pattern search ps method the penalty functions such as the superiority of feasible points sfp and the parameter free penalty pfp are used for handling constraints we numerically study sfp and pfp and based on a drawback observed we adapt the selection rule of de the new algorithm is tested on 45 test problems comparisons are made with some recent algorithms

self adaptive mix of particle swarm methodologies for constrained optimization abstract in recent years many different variants of the particle swarm optimizer pso for solving optimization problems have been proposed however pso has an inherent drawback in handling constrained problems mainly because of its complexity and dependency on parameters furthermore one pso variant may perform well for some test problems but not obtain good results for others in this paper our purpose is to develop a new pso algorithm that can efficiently solve a variety of constrained optimization problems it considers a mix of different pso variants each of which evolves with a different number of individuals from the current population in each generation the algorithm assigns more individuals to the better performing variants and fewer to the worse performing ones also a new pso variant is developed for use in the proposed algorithm to maintain a better balance between its local and global pso versions a new methodology for adapting pso parameters is presented and the proposed self adaptive pso algorithm tested and analyzed on two sets of test problems namely the cec2006 and cec2010 constrained optimization problems based on the results the proposed algorithm shows significantly better performance than the same global and local pso variants as well as other state of the art algorithms although based on our analysis it cannot guarantee an optimal solution for any unknown problem it is expected to be able to solve a wide variety of practical problems

complex temperature properties of the 2d ising model with beta h or i pi 2 we study the complex temperature properties of a rare example of a statistical mechanical model which is exactly solvable in an external symmetry breaking field namely the ising model on the square lattice with beta h or i pi 2 this model was solved by lee and yang 1952 we first determine the complex temperature phases and their boundaries from a low temperature high field series expansion of the partition function we extract the low temperature series for the susceptibility chi to o u23 where u e 4k analysing this series we conclude that chi has divergent singularities i at u u3 3 232 with exponent gamma e 5 4 ii at u 1 with exponent gamma 1 5 2 and iii at u us 1 with exponent gamma s 1 we also extract a shorter series for the staggered susceptibility and investigate its singularities using the exact result of lee and yang for the free energy we calculate the specific heat and determine its complex temperature singularities we also carry this out for the uniform and staggered magnetization

truss optimization on shape and sizing with frequency constraints based on orthogonal multi gravitational search algorithm abstract structural optimization on shape and sizing with frequency constraints is well known as a highly nonlinear dynamic optimization problem with several local optimum solutions hence efficient optimization algorithms should be utilized to solve this problem in this study orthogonal multi gravitational search algorithm omgsa as a meta heuristic algorithm is introduced to solve truss optimization on shape and sizing with frequency constraints the omgsa is a hybrid approach based on a combination of multi gravitational search algorithm multi gsa and an orthogonal crossover oc in multi gsa the population is split into several sub populations then each sub population is independently evaluated by an improved gravitational search algorithm igsa furthermore the oc is used in the proposed omgsa in order to find and exploit the global solution in the search space the capability of omgsa is demonstrated through six benchmark examples numerical results show that the proposed omgsa outperform the other optimization techniques

zeros of jones polynomials for families of knots and links abstract we calculate jones polynomials v l t for several families of alternating knots and links by computing the tutte polynomials t g x y for the associated graphs g and then obtaining v l t as a special case of the tutte polynomial for each of these families we determine the zeros of the jones polynomial including the accumulation set in the limit of infinitely many crossings a discussion is also given of the calculation of jones polynomials for non alternating links

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

a new fuzzy programming approach for multi period portfolio optimization with return demand and risk control abstract this paper considers a multi period portfolio selection problem imposed by return demand and risk control in a fuzzy investment environment in which the returns of assets are characterized by fuzzy numbers a fuzzy lower semi deviation is originally defined as the risk control of portfolio a proportion entropy constraint is added as the divergence measure of portfolio based on the theories of possibility and necessity measures a new multi period portfolio optimization model with return demand and risk control is proposed and then the proposed model is transformed into a crisp nonlinear programming problem by using fuzzy programming approach furthermore an improved differential evolution algorithm is designed for obtaining the optimal strategy finally a numerical example is given to illustrate the practicality and efficiency of the proposed model and the corresponding algorithm

a decremental stochastic fractal differential evolution for global numerical optimization the aim of hybridization in the context of evolutionary computation is to combine appropriate operators from different evolutionary computation paradigms to form a single technique that enjoys a statistically superior performance over a wide range of optimization problems this paper introduces a novel hybridization between differential evolution and update processes of the stochastic fractal search algorithm the diffusion property of the fractal search algorithm is applied in random fractals followed by two novel update processes to explore the search space more efficiently in this algorithm a diffusion process based on differential evolution algorithm is used instead of random fractals in the original stochastic fractal search algorithm a new success based scheme is used to utilize the update processes and to solve the burden of extra computations during the search this new algorithm captures the strengths of both component algorithms and produces a greater explorative power as compared to the original algorithms to verify the performance of our algorithm a challenging test suite of 30 benchmark functions from the ieee cec2014 real parameter single objective competition is used the results affirm the effectiveness and robustness of the proposed approach compared to the original stochastic fractal search and other recent state of the art algorithms the proposed algorithm enjoys a statistically superior performance over most of the tested benchmarks especially hybrid and composition test functions compared to the other contestant algorithms

accelerated random search for constrained global optimization assisted by radial basis function surrogates abstract the accelerated random search ars algorithm appel et al 2004 is a stochastic algorithm for the global optimization of black box functions subject only to bound constraints ars iteratively samples uniformly within a box centered at the current best point if the sample point is worse than the current best point then the size of the box is reduced thereby making it more likely to generate an improving solution if the current best point is not yet a local minimum otherwise if the sample point is an improvement over the current best point then the size of the box is reset to the initial value so that the box covers the entire search space ars has been shown theoretically and numerically to converge to the global minimum faster than the pure random search prs algorithm on bound constrained problems this article develops the constrained ars cars algorithm which is an extension of ars for optimization problems with black box inequality constraints under some mild conditions on the constrained optimization problem we prove the convergence to the global minimum in a probabilistic sense of a class of stochastic search algorithms called scattered uniform random search scat urs algorithms which includes cars as a special case to improve performance of cars on computationally expensive simulation based problems we incorporate radial basis function rbf surrogate models to approximate the objective and constrained functions and refer to the resulting algorithm as cars rbf numerical experiments show that cars consistently and substantially outperforms both the pure random search prs and accelerated particle swarm optimization apso algorithms yang 2010 on 31 test problems with dimensions ranging from 2 to 20 moreover cars rbf is an improvement over cars outperforms a sequential penalty derivative algorithm and competes with constrlmsrbf regis 2011 on the same test problems finally sensitivity analysis of cars rbf to the type of rbf model used shows that the cubic rbf model generally yields the best results on the test problems among six types of rbf models considered including the thin plate spline gaussian and multiquadric models

flow polynomials and their asymptotic limits for lattice strip graphs we present exact calculations of flow polynomials f g q for lattice strips of various fixed widths l y 4 and arbitrarily great lengths l x with several different boundary conditions square honeycomb and triangular lattice strips are considered we introduce the notion of flows per face fl in the infinite length limit we study the zeros of f g q in the complex q plane and determine exactly the asymptotic accumulation sets of these zeros in the infinite length limit for the various families of strips the function fl is nonanalytic on this locus the loci are found to be noncompact for many strip graphs with periodic or twisted periodic longitudinal boundary conditions and compact for strips with free longitudinal boundary conditions we also find the interesting feature that aside from the trivial case l y 1 the maximal point q cf where crosses the real axis is universal on cyclic and mobius strips of the square lattice for all widths for which we have calculated it and is equal to the asymptotic value q cf 3 for the infinite square lattice

complex temperature singularities in the d 2 ising model triangular and honeycomb lattices we study complex temperature singularities of the ising model on the triangular and honeycomb lattices we first discuss the complex t phases and their boundaries from exact results we determine the complex t singularities in the specific heat and magnetization for the triangular lattice we discuss the implications of the divergence of the magnetization at the point u d 1 where u d z 2 d e 4k and extend a previous study by guttmann of the susceptibility at this point with the use of differential approximants for the honeycomb lattice from an analysis of low temperature series expansions we have found evidence that the uniform and staggered susceptibilities n and n a both have divergent singularities at z d 1 z and our numerical values for the exponents are consistent with the hypothesis that the exact values are 0 d 0 a d 5 2 the critical amplitudes at this singularity were calculated using our exact results for 0 and together with numerical values for 0 from series analyses we find that the exponent relation 0 c 2 c 0 d 2 is violated at z d 1 on the honeycomb lattice the right hand side is consistent with being equal to 4 rather than 2 the connections of the critical exponents at these two singularities on the triangular and honeycomb lattice are discussed

enhancing the search ability of differential evolution through orthogonal crossover differential evolution de is a class of simple yet powerful evolutionary algorithms for global numerical optimization binomial crossover and exponential crossover are two commonly used crossover operators in current popular de it is noteworthy that these two operators can only generate a vertex of a hyper rectangle defined by the mutant and target vectors therefore the search ability of de may be limited orthogonal crossover ox operators which are based on orthogonal design can make a systematic and rational search in a region defined by the parent solutions in this paper we have suggested a framework for using an ox in de variants and proposed oxde a combination of de rand 1 bin and ox extensive experiments have been carried out to study oxde and to demonstrate that our framework can also be used for improving the performance of other de variants

triangular lattice potts models in this paper we study the 3 state potts model on the triangular lattice which has two and three site interactions using a peierls argument we obtain a rigorous bound on the transition temperature thereby disproving a conjecture on the location of its critical point low temperature series are generated and analyzed for three particular choices of the coupling constants a phase diagram is then drawn on the basis of these considerations our analysis indicates that the antiferromagnetic transition and the transition along the coexistence line are of first order implying the existence of a multicritical point in the ferromagnetic region relation of the triangularq state potts model with other lattice statistical problems is also discussed in particular an ashkin teller model and the hard hexagon lattice gas solved by baxter emerge as special cases in appropriate limits

single and multiobjective frame optimization by evolutionary algorithms and the auto adaptive rebirth operator abstract the constrained minimum mass problem of middle size frames is taken into account for both continuous and discrete cases with ideal without buckling effect and own gravitational load and real with both models comparing three strategies of evolutionary algorithms some proposals to obtain appropriate results in middle sized frames are exposed optimization considerations about coding and structure and the introduction of the auto adaptive rebirth operator moreover the introduction in the initial population of high quality single optimization solutions obtained via the auto adaptive rebirth operator is proposed as a way to improve the final non dominated fronts obtained in structural frame multicriteria optimization number of different cross section types as second criteria the results through three test cases 55 35 bar sized show the advantageous use of the auto adaptive rebirth operator in frame optimization

single row facility layout problem using a permutation based genetic algorithm in this paper a permutation based genetic algorithm ga is applied to the np hard problem of arranging a number of facilities on a line with minimum cost known as the single row facility layout problem srflp the ga individuals are obtained by using some rule based as well as random permutations of the facilities which are then improved towards the optimum by means of specially designed crossover and mutation operators such schemes led the ga to handle the srflp as an unconstrained optimization problem in the computational experiments carried out with large size instances of sizes from 60 to 80 available in the literature the proposed ga improved several previously known best solutions

a modified real coded genetic algorithm for constrained optimization abstract the performance of a genetic algorithm ga largely depends upon crossover and mutation operators deep and thakur 2007 14 15 proposed a real coded genetic algorithm rcga incorporating laplace crossover lx and power mutation pm operator and shown that the resulting ga named lx pm outperforms many existing rcgas on a large set of scalable test problems of varying difficulty level in this paper lx pm is modified by improving the lx operator the modified lx operator named as bounded exponential crossover bex operator always creates offspring within the variable bounds a new rcga named bex pm incorporating bex and pm operator is proposed the performance of the modified ga is tested against the original algorithm lx pm and three other popular constrained optimization algorithms hx num hx mptm and sbx pol over a test suite containing twenty five constrained optimization problems collected from global optimization literature the performance of all rcgas and quality of solution obtained is compared on the basis of standard criteria used in ga literature the comparative study shows that bex pm performs significantly better than the original algorithm lx pm and outperforms all rcgas considered in this study

improving benders decomposition using a genetic algorithm we develop and investigate the performance of a hybrid solution framework for solving mixed integer linear programming problems benders decomposition and a genetic algorithm are combined to develop a framework to compute feasible solutions we decompose the problem into a master problem and a subproblem a genetic algorithm along with a heuristic are used to obtain feasible solutions to the master problem whereas the subproblem is solved to optimality using a linear programming solver over successive iterations the master problem is refined by adding cutting planes that are implied by the subproblem we compare the performance of the approach against a standard benders decomposition approach as well as against a stand alone solver cplex on miplib test problems

a mapping relating complex and physical temperatures in the 2d q state potts model and some applications we show an exact equivalence of the free energy of the q state potts antiferromagnet on a lattice for the full temperature interval and the free energy of the q state potts model on the dual lattice for a semi infinite interval of complex temperatures cts this implies the existence of two quite different types of ct singularities the generic kind which does not obey universality or various scaling relations and a special kind which does obey such properties and encodes information of direct physical relevance we apply this observation to characterize ct properties of the potts model on several lattices to rule out two existing conjectures and to determine the critical value of q above which the potts antiferromagnet on the diced lattice has no phase transition

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

decomposition based evolutionary algorithm for large scale constrained problems cooperative coevolutionary algorithms cc have been successful in solving large scale optimization problems the performance of cc can be improved by decreasing the number of interdependent variables among decomposed subproblems this is achieved by first identifying dependent variables and by then grouping them in common subproblems this approach has potential because so far no grouping technique has been mainly developed for constrained problems in this paper a new variable interaction identification technique to identify the dependent variables in large scale constrained problems is proposed the proposed technique is tested on both a new test suite of constrained problems with medium and high dimensions which include overlapping subproblems and different levels of complexity and nonseparability and also the established ded problem the experimental results have shown that the proposed technique contributes to the decomposition approach over a range of high dimensions in comparison with other state of the art grouping techniques it achieves better performance with higher feasibility ratios and less computational time

adaptive memetic differential evolution with global and local neighborhood based mutation operators differential evolution de is one of the most popular optimization methods for real valued problems and a large number of its variants have been proposed so far however bringing together different ideas that already led to successful de versions is rare in the literature in the present paper a novel de algorithm is proposed in which three among the most efficient concepts already applied separately within de framework are gathered together namely 1 the adaptation of algorithm control parameters and probabilities of using different mutation strategies 2 the use of nelder mead algorithm as a local search method hybridized with de and 3 the splitting mutation into global and local models when local mutation model is based on the concept of neighborhood of individuals organized on a ring topology the performance of the novel algorithm called adaptive memetic de with global and local neighborhood based mutation operators is compared with 13 different de variants on a set of 25 popular problems which include rotated shifted and hybrid composition functions it is found that although none de algorithm outperforms all the others for the majority of problems on average the proposed approach perform better than all 13 de algorithms selected for comparison the proposed algorithm is another heuristic approach developed to solve optimization problems the question may arise whether proposing novel methods is useful as no free lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal in the last section of the paper the limitations and implications of no free lunch theorems are discussed based on rich but unfortunately frequently neglected literature a very simple continuous and differentiable minimization problem is proposed for which it is empirically verified that each among considered 14 de algorithms perform poorer than random sampling it is also empirically shown that when all considered de algorithms search for the maximum of the proposed problem they found lower minimum than de algorithms searching for the minimum such result is not unexpected according to no free lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods

dimensional reduction in constrained global optimization on smooth manifolds display omitted approach to reduce the dimension of search domains in constrained global optimization on smooth manifolds more equality constraints more dimensional reduction mappings under optimization do not need to be differentiable or even continuous optimization task is executed while keeping candidate points populations within feasible submanifolds the proposed paradigm may be employed jointly with an extensive family of already established metaheuristics this work introduces an approach aimed at reducing the dimension of search domains in constrained global optimization of real valued functions defined on smooth manifolds and subject also and mainly to equality constraints the functions expressing the cited constraints must satisfy certain smoothness conditions and other types of restrictions are simultaneously possible but the effect of dimensional reduction will be proportional to the number of equality constraints the objective functions under study do not need to be differentiable or even continuous and it is shown that the optimization task will be executed so that candidate points remain in the corresponding submanifolds evolving there during the whole optimization process the proposed paradigm may be employed jointly with an extensive family of already established metaheuristics after introducing the fundamental ideas and establishing the theoretical basis some examples will illustrate the effectiveness of the proposed method

exact potts model partition functions on ladder graphs abstract we present exact calculations of the partition function z of the q state potts model and its generalization to real q for arbitrary temperature on n vertex ladder graphs i e strips of the square lattice with width ly 2 and arbitrary length lx with free cyclic and mobius longitudinal boundary conditions these partition functions are equivalent to tutte whitney polynomials for these graphs the free energy is calculated exactly for the infinite length limit of these ladder graphs and the thermodynamics is discussed by comparison with strip graphs of other widths we analyze how the singularities at the zero temperature critical point of the ferromagnet on infinite length finite width strips depend on the width we point out and study the following noncommutativity at certain special values q s lim n lim q q s z 1 n lim q q s lim n z 1 n it is shown that the potts antiferromagnet on both the infinite length line and ladder graphs with cyclic or mobius boundary conditions exhibits a phase transition at finite temperature if 0 b in the corresponding c 2 space arising as the accumulation set of partition function zeros as n in particular we study the connection with the t 0 limit of the potts antiferromagnet where b reduces to the accumulation set of chromatic zeros certain properties of the complex temperature phase diagrams are shown to exhibit close connections with those of the model on the square lattice showing that exact solutions on infinite length strips provide a way of gaining insight into these complex temperature phase diagrams

potts model partition functions for self dual families of strip graphs abstract we consider the q state potts model on families of self dual strip graphs g d of the square lattice of width l y and arbitrarily great length l x with periodic longitudinal boundary conditions the general partition function z and the t 0 antiferromagnetic special case p chromatic polynomial have the respective forms j 1 n f l y c f l y j f l y j l x with f z p for arbitrary l y we determine i the general coefficient c f l y j in terms of chebyshev polynomials ii the number n f l y d of terms with each type of coefficient and iii the total number of terms n f l y we point out interesting connections between the n z l y d and temperley lieb algebras and between the n f l y and enumerations of directed lattice animals exact calculations of p are presented for 2 l y 4 in the limit of infinite length we calculate the ground state degeneracy per site exponent of the ground state entropy w q generalizing q from z to c we determine the continuous locus b in the complex q plane where w q is singular we find the interesting result that for all l y values considered the maximal point at which b crosses the real q axis denoted q c is the same and is equal to the value for the infinite square lattice q c 3 this is the first family of strip graphs of which we are aware that exhibits this type of universality of q c

zeros of the partition function for the triangular lattice three state potts model the authors obtain the zeros of the partition function for the isotropic triangular lattice three state potts model in a finite lattice the distribution exhibits new points on the real axis which are well fitted by an algebraic equation deduced from the inversion relation and the symmetries of the anisotropic model they identify a symmetry approximately relating all six transition points

complex temperature properties of the two dimensional ising model for nonzero magnetic field we study the complex temperature phase diagram of the square lattice ising model for nonzero external magnetic field h i e for 0 le mu le infty where mu e 2 beta h we also carry out a similar analysis for infty le mu le 0 the results for the interval 1 le mu le 1 provide a new way of continuously connecting the two known exact solutions of this model viz at mu 1 onsager yang and mu 1 lee and yang our methods include calculations of complex temperature zeros of the partition function and analysis of low temperature series expansions for real nonzero h the inner branch of a lima c c on bounding the fm phase breaks and forms two complex conjugate arcs we study the singularities and associated exponents of thermodynamic functions at the endpoints of these arcs for mu 0 there are two line segments of singularities on the negative and positive u axis and we carry out a similar study of the behavior at the inner endpoints of these arcs which constitute the nearest singularities to the origin in this case finally we also determine the exact complex temperature phase diagrams at mu 1 on the honeycomb and triangular lattices and discuss the relation between these and the corresponding zero field phase diagrams

an improved self adaptive constraint sequencing approach for constrained optimization problems real life optimization problems involve a number of constraints arising out of user requirements physical laws statutory requirements resource limitations etc such constraints are routinely evaluated using computationally expensive analysis i e solvers relying on finite element methods computational fluid dynamics computational electro magnetic etc existing optimization approaches adopt a full evaluation policy i e all the constraints corresponding to a solution are evaluated throughout the course of search furthermore a common sequence of constraint evaluation is used for all the solutions in this paper we introduce a novel scheme for constraint handling wherein every solution is assigned a random sequence of constraints and the evaluation process is aborted whenever a constraint is violated the solutions are sorted based on two measures i e the number of satisfied constraints and the violation measure the number of satisfied constraints takes precedence over the amount of violation and the most efficient sequence of constraint evaluation is evolved during the course of search the performance of the proposed scheme is rigorously compared with other state of the art constraint handling methods using single objective inequality constrained test problems of cec 2006 and cec 2010 the constraint handling approach is generic and can be easily used for the solution of constrained multiobjective optimization problems or even problems with equality constraints a bi objective welded beam design problem a tri objective car side impact problem and an equality constrained optimization problem of cec 2006 is solved as an illustration the results clearly highlight potential savings offered by the proposed strategy and more importantly the paper provides a detailed insight on why such a strategy performs better than others

two dimensional optimization of material composition of functionally graded materials using meshless analyses and a genetic algorithm abstract we propose a methodology for the two dimensional simulation and optimization of material distribution of functionally graded materials for thermomechanical processes the proposed approach focuses on metal ceramic functionally graded materials which offer great promise in applications where the operating conditions are severe the two dimensional quasi static heat conduction and thermoelasticity problems are analyzed using the element free galerkin method the spatial distribution of ceramic volume fraction is obtained by piecewise bicubic interpolation of volume fractions defined at a finite number of grid points the effective material properties at a point in the domain are estimated from the local volume fractions of the material constituents using the mori tanaka and self consistent homogenization schemes the volume fraction distribution is optimized using a real coded genetic algorithm the element free galerkin code is validated by comparing the results with an exact thermoelasticity solution for a simply supported plate subsequently we use the genetic algorithm and element free galerkin analyses to optimize the material composition for two model problems in the first problem we minimize the peak residual stress when the functionally graded component is cooled from a high fabrication temperature the goal of the second model problem is to minimize the mass of a graded component with constraints on the peak effective stress and maximum temperature experienced by the metal

a hybrid genetic pattern search augmented lagrangian method for constrained global optimization abstract hybridization of genetic algorithms with local search approaches can enhance their performance in global optimization genetic algorithms as most population based algorithms require a considerable number of function evaluations this may be an important drawback when the functions involved in the problem are computationally expensive as it occurs in most real world problems thus in order to reduce the total number of function evaluations local and global techniques may be combined moreover the hybridization may provide a more effective trade off between exploitation and exploration of the search space in this study we propose a new hybrid genetic algorithm based on a local pattern search that relies on an augmented lagrangian function for constraint handling the local search strategy is used to improve the best approximation found by the genetic algorithm convergence to an e global minimizer is proved numerical results and comparisons with other stochastic algorithms using a set of benchmark constrained problems are provided

improved versions of the lede algorithm for constrained global optimization two modified versions of the authors recent differential evolution algorithm for constrained global optimization are proposed they incorporate a filter set which results in more efficient implementations of the original algorithm numerical results are presented which suggest that the new algorithms are competitive

coupled eagle strategy and differential evolution for unconstrained and constrained global optimization the performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process the fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve modern metaheuristic algorithms are generally more suitable for global optimization this paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by yang and deb in combination with the efficient differential evolution after a detailed formulation and explanation of its implementation the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks for the validation against constrained problems this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature the performance of the proposed algorithm is further compared with various state of the art algorithms in the area the optimal solutions obtained in this study are better than the best solutions obtained by the existing methods the unique search features used in the proposed algorithm are analyzed and their implications for future research are also discussed in detail

consolidated optimization algorithm for resource constrained project scheduling problems abstract resource constrained project scheduling problems rcpsps represent an important class of practical problems over the years many optimization algorithms for solving them have been proposed with their performances evaluated using well established test instances with various levels of complexity while it is desirable to obtain a high quality solution and fast rate of convergence from an optimization algorithm no single one performs well across the entire space of instances furthermore even for a given algorithm the optimal choice of its operators and control parameters may vary from one problem to another to deal with this issue we present a generic framework for solving rcpsps in which various meta heuristics each with multiple search operators are self adaptively used during the search process and more emphasis is placed on the better performing algorithms and their underlying search operators to further improve the rate of convergence and introduce good quality solutions into the population earlier a local search approach is introduced the experimental results clearly indicate the capability of the proposed algorithm to attain high quality results using a small population compared with several state of the art algorithms the proposed one delivers the best solutions for problems with 30 and 60 activities and is very competitive for those involving 120 activities

integrable discretizations of the 2 1 dimensional sinh gordon equation in this paper we propose two semi discrete equations and one fully discrete equation and study them by hirota s bilinear method these equations have continuum limits into a system which admits the 2 1 dimensional generalization of the sinh gordon equation as a result two integrable semi discrete versions and one fully discrete version for the sinh gordon equation are found backlund transformations nonlinear superposition formulae determinant solution and lax pairs for these discrete versions are presented

continuous symmetries of difference equations lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations in this article we review the results of a much more recent program the use of lie groups to study difference equations we show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners one is to use generalized symmetries acting on solutions of difference equations but leaving the lattice invariant the other is to restrict them to point symmetries but to allow them to also transform the lattice

a novel modified differential evolution algorithm for constrained optimization problems a novel modified differential evolution algorithm nmde is proposed to solve constrained optimization problems in this paper the nmde algorithm modifies scale factor and crossover rate using an adaptive strategy for any solution if it is at a standstill its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions we can obtain satisfactory feasible solutions for constrained optimization problems by combining the nmde algorithm and a common penalty function method experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems and it can be an efficient alternative to solving constrained optimization problems

hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems this study presents a hybrid harmony search algorithm hhsa to solve engineering optimization problems with continuous design variables although the harmony search algorithm hsa has proven its ability of finding near global regions within a reasonable time it is comparatively inefficient in performing local search in this study sequential quadratic programming sqp is employed to speed up local search and improve precision of the hsa solutions moreover an empirical study is performed in order to determine the impact of various parameters of the hsa on convergence behavior various benchmark engineering optimization problems are used to illustrate the effectiveness and robustness of the proposed algorithm numerical results reveal that the proposed hybrid algorithm in most cases is more effective than the hsa and other meta heuristic or deterministic methods

exact potts model partition function on strips of the triangular lattice abstract in this paper we present exact calculations of the partition function z of the q state potts model and its generalization to real q for arbitrary temperature on n vertex strip graphs of width ly 2 and arbitrary length of the triangular lattice with free cyclic and mobius longitudinal boundary conditions these partition functions are equivalent to tutte whitney polynomials for these graphs the free energy is calculated exactly for the infinite length limit of the graphs and the thermodynamics is discussed considering the full generalization to arbitrary complex q and temperature we determine the singular locus b in the corresponding c 2 space arising as the accumulation set of partition function zeros as n in particular we study the connection with the t 0 limit of the potts antiferromagnet where b reduces to the accumulation set of chromatic zeros comparisons are made with our previous exact calculation of potts model partition functions for the corresponding strips of the square lattice our present calculations yield as special cases several quantities of graph theoretic interest

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

upper and lower bounds for the ground state entropy of antiferromagnetic potts models we derive rigorous upper and lower bounds for the ground state entropy of the q state potts antiferromagnet on the honeycomb and triangular lattices these bounds are quite restrictive especially for large q copyright ital 1997 ital the american physical society

spanning forests and the q state potts model in the limit q 0 we study the q state potts model with nearest neighbor coupling v e j 1 in the limit q v 0 with the ratio w v q held fixed combinatorially this limit gives rise to the generating polynomial of spanning forests physically it provides information about the potts model phase diagram in the neighborhood of q v 0 0 we have studied this model on the square and triangular lattices using a transfer matrix approach at both real and complex values of w for both lattices we have computed the symbolic transfer matrices for cylindrical strips of widths 2 l 10 as well as the limiting curves b of partition function zeros in the complex w plane for real w we find two distinct phases separated by a transition point w w0 where w0 1 4 resp w0 0 1753 0 0002 for the square resp triangular lattice for w w0 we find a non critical disordered phase that is compatible with the predicted asymptotic freedom as w for w w0 our results are compatible with a massless berker kadanoff phase with central charge c 2 and leading thermal scaling dimension xt 1 2 marginally irrelevant operator at w w0 we find a first order critical point the first derivative of the free energy is discontinuous at w0 while the correlation length diverges as w w0 and is infinite at w w0 the critical ehavior at w w0 seems to be the same for both lattices and it differs from that of the berker kadanoff phase our results suggest that the central charge is c 1 the leading thermal scaling dimension is xt 1 0 and the critical exponents are 1 d 1 2 and 1

study of the potts model on the honeycomb and triangular lattices low temperature series and partition function zeros we present and analyse low temperature series and complex temperature partition function zeros for the q state potts model with q 4 on the honeycomb lattice and q 3 4 on the triangular lattice a discussion is given on how the locations of the singularities obtained from the series analysis correlate with the complex temperature phase boundary extending our earlier work we include a similar discussion for the potts model with q 3 on the honeycomb lattice and with q 3 4 on the kagom lattice

reliability polynomials and their asymptotic limits for families of graphs we present exact calculations of reliability polynomials r g p for lattice strips g of fixed widths l y 4 and arbitrarily great length l x with various boundary conditions we introduce the notion of a reliability per vertex r g p lim v r g p 1 v where v denotes the number of vertices in g and g denotes the formal limit lim v g we calculate this exactly for various families of graphs we also study the zeros of r g p in the complex p plane and determine exactly the asymptotic accumulation set of these zeros b across which r g is nonanalytic

a real coded genetic algorithm for solving integer and mixed integer optimization problems in this paper a real coded genetic algorithm named mi lxpm is proposed for solving integer and mixed integer constrained optimization problems the proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm lxpm of deep and thakur k deep m thakur a new crossover operator for real coded genetic algorithms applied mathematics and computation 188 2007 895 912 k deep m thakur a new mutation operator for real coded genetic algorithms applied mathematics and computation 193 2007 211 230 the algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm rst2anu incorporating annealing concept the proposed mi lxpm outperforms both the algorithms in most of the cases which are considered

a note on teaching learning based optimization algorithm teaching learning based optimization tlbo seems to be a rising star from amongst a number of metaheuristics with relatively competitive performances it is reported that it outperforms some of the well known metaheuristics regarding constrained benchmark functions constrained mechanical design and continuous non linear numerical optimization problems such a breakthrough has steered us towards investigating the secrets of tlbo s dominance this paper reports our findings on tlbo qualitatively and quantitatively through code reviews and experiments respectively our findings have revealed three important mistakes regarding tlbo 1 at least one unreported but important step 2 incorrect formulae on a number of fitness function evaluations and 3 misconceptions about parameter less control additionally unfair experimental settings conditions were used to conduct experimental comparisons e g different stopping criteria the experimental results for constrained and unconstrained benchmark functions under fairly equal conditions failed to validate its performance supremacy the ultimate goal of this paper is to provide reminders for metaheuristics researchers and practitioners in order to avoid similar mistakes regarding both the qualitative and quantitative aspects and to allow fair comparisons of the tlbo algorithm to be made with other metaheuristic algorithms

investigating a hybrid simulated annealing and local search algorithm for constrained optimization constrained optimization problems cop often take place in many practical applications such as kinematics chemical process optimization power systems and so on these problems are challenging in terms of identifying feasible solutions when constraints are non linear and non convex therefore finding the location of the global optimum in the non convex cop is more difficult as compared to non convex bound constrained global optimization problems this paper proposes a hybrid simulated annealing method hsa for solving the general cop hsa has features that address both feasibility and optimality issues and here it is supported by a local search procedure feasible sequential quadratic programming fsqp we develop two versions of hsa the first version hsap incorporates penalty methods for constraint handling and the second one hsad eliminates the need for imposing penalties in the objective function by tracing feasible and infeasible solution sequences independently numerical experiments show that the second version is more reliable in the worst case performance

three state potts antiferromagnet on the triangular lattice the three state potts antiferromagnetic model on the triangular lattice 3paft has a weak first order transition in the pure case the first order nature follows from analytic arguments and while it has been observed in some simulations the precision of and internal disagreement between these observations has left much to be desired the 3paft is the only two dimensional nearest neighbour potts model with an ordered phase that does not have an infinite degeneracy that remains without an exact value for its critical point this model is expected to exhibit interesting glassy behaviour and a possible crossover to a second order transition upon dilution a careful characterization of the nature of the pure transition is needed in order to explore the physics of the dilute model we find clear indication of a first order transition at tt 0 62731 or 0 00006 using a cluster method that can be extended to the dilute case and histogram reweighting analysis our estimate is two orders of magnitude more precise than previous simulations and falls within the error bounds of a reanalysis of existing series expansion tt 0 628 or 0 004 reported on herein

exact results on potts model partition functions in a generalized external field and weighted set graph colorings we present exact results on the partition function of the q state potts model on various families of graphs g in a generalized external magnetic field that favors or disfavors spin values in a subset i s 1 s of the total set of possible spin values z g q s v w where v and w are temperature and field dependent boltzmann variables we remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the potts model with a conventional magnetic field that favors or disfavors a single spin value exact results are also given for the interesting special case of the zero temperature potts antiferromagnet corresponding to a set weighted chromatic polynomial ph g q s w that counts the number of colorings of the vertices of g subject to the condition that colors of adjacent vertices are different with a weighting w that favors or disfavors colors in the interval i s we derive powerful new upper and lower bounds on z g q s v w for the ferromagnetic case in terms of zero field potts partition functions with certain transformed arguments we also prove general inequalities for z g q s v w on different families of tree graphs as part of our analysis we elucidate how the field dependent potts partition function and weighted set chromatic polynomial distinguish respectively between tutte equivalent and chromatically equivalent pairs of graphs

solving constrained optimization problems using a novel genetic algorithm a novel genetic algorithm is described in this paper for the problem of constrained optimization the algorithm incorporates modified genetic operators that preserve the feasibility of the trial solutions encoded in the chromosomes the stochastic application of a local search procedure and a stopping rule which is based on asymptotic considerations the algorithm is tested on a series of well known test problems and a comparison is made against the algorithms c somga and donlp2

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

an evidential classifier based on feature selection and two step classification strategy in this paper we investigate ways to learn efficiently from uncertain data using belief functions in order to extract more knowledge from imperfect and insufficient information and to improve classification accuracy we propose a supervised learning method composed of a feature selection procedure and a two step classification strategy using training information the proposed feature selection procedure automatically determines the most informative feature subset by minimizing an objective function the proposed two step classification strategy further improves the decision making accuracy by using complementary information obtained during the classification process the performance of the proposed method was evaluated on various synthetic and real datasets a comparison with other classification methods is also presented highlightsa classifier is based on belief functions to tackle uncertain data the classifier composed by feature selection and a two step classification a new combination rule to better represent data uncertainty a new feature selection is based on minimizing uncertainty with sparse constraint two step classification improving accuracy of decision making

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

balanced ranking method for constrained optimization problems using evolutionary algorithms this work presents a new technique to handle constraints in the solution of optimization problems by evolutionary algorithms the balanced ranking method brm in this method the fitness function is based on two rankings for feasible and infeasible solutions respectively the rankings are merged according to deterministic criteria that consider the status of the search process and specific properties of the population the focus of the brm method is to comprise a constraint handling technique cht that is not coupled to the optimization algorithm and thus can be implemented into different algorithms the method is compared with other well known chts that follow this same uncoupled approach all implemented into a canonical genetic algorithm two well known suites of benchmark functions and five engineering problems are used as case studies the performance of the different chts is assessed by nonparametric statistical tests including the sign test and the wilcoxon signed ranks test the results indicate that the brm presents a good performance being reliable and efficient while maintaining its uncoupled characteristic leading to an easy implementation and hybridization with any search algorithm

complex temperature singularities of the susceptibility in the d 2 ising model i square lattice we investigate the complex temperature singularities of the susceptibility of the 2d ising model on a square lattice from an analysis of low temperature series expansions we find evidence that as one approaches the point u us 1 where u e 4k from within the complex extensions of the fm or afm phases the susceptibility has a divergent singularity of the form x approximately as 1 u gamma s with exponent gamma s 3 2 the critical amplitude as is calculated other critical exponents are found to be alpha s sigma s 0 and beta s 1 4 so that the scaling relation alpha s 2 beta s gamma s is satisfied however using exact results for beta s on the square triangular and honeycomb lattices we show that universality is violated at this singularity beta s is lattice dependent finally from an analysis of spin spin correlation functions we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point u 1 from within the symmetric phase this is confirmed by an explicit study of high temperature series expansions

the potts model on kagome and honeycomb lattices low temperature series have been derived for theq state potts model on the kagom e lattice qd 3 and 4 and for the 3 state honeycomb lattice the series are derived by the finite lattice method with many additional terms obtained by noting the structure of the correction terms accurate estimates of the critical points are found which confirm exact but not rigorous results in the case of the honeycomb lattice and refute previous conjectures in the case of the kagom e lattice in this paper we report on the derivation and analysis of low temperature series for the 3 state honeycomb and 3 and 4 state kagomlattice potts model from the series we obtain estimates for the critical points which for the honeycomb model confirms the validity of the exact but not rigorous result 7 and for the kagomlattice provides accurate results against which conjectures can be tested and found not to hold we comment on properties that the solution must have in an unsuccessful attempt to find an alternative conjecture in addition we obtain estimates for the location of various non physical singularities the remainder of the paper is organized as follows in section 2 we briefly describe the finite lattice method of series expansions give details regarding the specific implementations for the kagomand honeycomb lattices and show how the finite lattice method can be supplemented by an extension procedure allowing us to derive more series terms details regarding the analysis of the series are given in section 3 and the implications for possible conjectures for the critical point on the kagom

structural topology design optimization using genetic algorithms with a bit array representation abstract in this paper a bit array representation method for structural topology optimization using the genetic algorithm ga is implemented the importance of structural connectivity in a design is further emphasized by considering the total number of connected objects of each individual explicitly in an equality constraint function to evaluate the constrained objective function deb s constraint handling approach is further developed to ensure that feasible individuals are always better than infeasible ones in the population to improve the efficiency of the ga a violation penalty method is proposed to drive the ga search towards the topologies with higher structural performance less unusable material and fewer separate objects in the design domain an identical initialization method is also proposed to improve the ga performance in dealing with problems with long narrow design domains numerical results of structural topology optimization problems of minimum weight and minimum compliance designs show the success of this bit array representation method and suggest that the ga performance can be significantly improved by handling the design connectivity properly