example based learning particle swarm optimization for continuous optimization particle swarm optimization pso is a heuristic optimization technique based on swarm intelligence that is inspired by the behavior of bird flocking the canonical pso has the disadvantage of premature convergence several improved pso versions do well in keeping the diversity of the particles during the searching process but at the expense of rapid convergence this paper proposes an example based learning pso elpso to overcome these shortcomings by keeping a balance between swarm diversity and convergence speed inspired by a social phenomenon that multiple good examples can guide a crowd towards making progress elpso uses an example set of multiple global best particles to update the positions of the particles in this study the particles of the example set were selected from the best particles and updated by the better particles in the first in first out order in each iteration the particles in the example set are different and are usually of high quality in terms of the target optimization function elpso has better diversity and convergence speed than single gbest and non gbest pso algorithms which is proved by mathematical and numerical results finally computational experiments on benchmark problems show that elpso outperforms all of the tested pso algorithms in terms of both solution quality and convergence time

a basic analog of a theorem of polya we derive a q analog of a theorem of george polya 1918 0 q 1 concer ning the zeros of basic cosine and sine transforms the results are established without further restrictions on q

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

two dimensional q differential transformation and its application the one dimensional q differential transformation was introduced in 8 for solving the ordinary q differential equations here we present the definition and operation of the two dimensional q differential transform a distinctive feature of the q differential transform is its ability to solve linear and nonlinear partial q differential equations

an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

on hardy s inequality for symmetric integral transforms and analogous abstract in this paper we give a generalization of hardy s theorem for a class of symmetric transforms in both classical and quantum calculus as applications we give q analogues of hardy s theorem for the q fourier cosine q bessel fourier and q dunkl transforms

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

κ deformed fourier transform abstract we present a new formulation of fourier transform in the picture of the algebra derived in the framework of the generalized statistical mechanics the fourier transform is obtained from a fourier series recently introduced by scarfone 2013 the kernel of this transform that reduces to the usual exponential phase in the 0 limit is composed by a deformed phase and a damping factor that gives a wavelet like behaviour we show that the fourier transform is isomorph to the standard fourier transform through a changing of time and frequency variables nevertheless the new formalism is useful to study according to fourier analysis those functions defined in the realm of the algebra as a relevant application we discuss the central limit theorem for the sum of n iterate statistically independent random variables

difference ladder operators for a harmonic schrodinger oscillator using unitary linear lattices the formalism of raising and lowering operators is developed for the difference operator analogue of a quantum harmonic oscillator which acts on functions on a discrete support the grid under consideration is a mixed version of an equidistant lattice and a q linear grid several properties of the grid are described the grids under consideration are referred to by the name unitary linear lattices the ladder difference operators are derived and compared with the continuum situation the arising spectral problems for these operators are dealt by using the theory of bilateral jacobi operators in weighted l2 z spaces eventual applications to mathematical physics and numerical schrodinger theory are briefly discussed

ranges and inversion formulas for spherical mean operator and its dual abstract we consider the spherical mean operator r and its dual t r we establish some results from harmonic analysis for the generalized fourier transform associated with the operator r we deduce that the operators r and t r are transmutation operators on some spaces of functions next we give inversion formulas for these operators and a plancherel theorem for the operator t r

an adaptive parameter tuning of particle swarm optimization algorithm an adaptive parameter tuning of particle swarm optimization based on velocity information apso vi algorithm is proposed in this paper the velocity convergence of particles is first analyzed and the relationship between the velocity of particle and the search failures is pointed out which reveals the reasons why pso has relative poor global searching ability then this algorithm introduces the velocity information which is defined as the average absolute value of velocity of all the particles a new strategy is presented that the inertia weight is dynamically adjusted according to average absolute value of velocity which follows a given nonlinear ideal velocity by feedback control which can avoid the velocity closed to zero at the early stage under the guide of the nonlinear ideal velocity apso vi can maintain appropriate swarm diversity and alleviate the premature convergence validly numerical experiments are conducted to compare the proposed algorithm with different variants of pso on some benchmark functions experimental results show that the proposed algorithm remarkably improves the ability of pso to jump out of the local optima and significantly enhance the convergence speed and precision

a piecewise linear chaotic map and sequential quadratic programming based robust hybrid particle swarm optimization this paper presents a novel robust hybrid particle swarm optimization rhpso based on piecewise linear chaotic map pwlcm and sequential quadratic programming sqp the aim of the present research is to develop a new single objective optimization approach which requires no adjustment of its parameters for both unconstrained and constrained optimization problems this novel algorithm makes the best of ergodicity of pwlcm to help pso with the global search while employing the sqp to accelerate the local search five unconstrained benchmarks eighteen constrained benchmarks and three engineering optimization problems from the literature are solved by using the proposed hybrid approach the simulation results compared with other state of art methods demonstrate the effectiveness and robustness of the proposed rhpso for both unconstrained and constrained problems of different dimensions

a new evolutionary search strategy for global optimization of high dimensional problems global optimization of high dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation the weakness of randomization based evolutionary algorithms in searching high dimensional spaces is demonstrated in this paper a new strategy sp uci is developed to treat complexity caused by high dimensionalities this strategy features a slope based searching kernel and a scheme of maintaining the particle population s capability of searching over the full search space examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that sp uci surpasses two popular algorithms particle swarm optimizer pso and differential evolution de on high dimensional problems experimental results also corroborate the argument that in high dimensional optimization only problems with well formative fitness landscapes are solvable and slope based schemes are preferable to randomization based ones

a co evolutionary multi objective optimization algorithm based on direction vectors most real world multi objective problems mops have a complicated solution space facing such problems a direction vectors based co evolutionary multi objective optimization algorithm dvcmoa that introduces the decomposition idea from moea d to co evolutionary algorithms is proposed in this paper it is novel in the sense that dvcmoa applies the concept of direction vectors to co evolutionary algorithms dvcmoa first divides the entire population into several subpopulations on the basis of the initial direction vectors in the objective space then it solves mops through the co evolutionary interaction among the subpopulations in which individuals are classified according to their direction vectors finally it explores the less developed regions to maintain the relatively uniform distribution of the solution space in this way dvcmoa has advantages in convergence diversity and uniform distribution of the non dominated solution set which are explained through comparison with other state of the art multi objective optimization evolutionary algorithms moeas in this paper dvcmoa is shown to be effective on 6 multi objective 0 1 knapsack problems

a hybrid multi objective immune algorithm for a flow shop scheduling problem with bi objectives weighted mean completion time and weighted mean tardiness this paper investigates a novel multi objective model for a no wait flow shop scheduling problem that minimizes both the weighted mean completion time c w and weighted mean tardiness t w obtaining an optimal solution for this type of complex large sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult this paper presents a new hybrid multi objective algorithm based on the features of a biological immune system is and bacterial optimization bo to find pareto optimal solutions for the given problem to validate the performance of the proposed hybrid multi objective immune algorithm hmoia in terms of solution quality and diversity level various test problems are examined further the efficiency of the proposed algorithm based on various metrics is compared against five prominent multi objective evolutionary algorithms ps nc ga nsga ii spea ii moia and misa our computational results suggest that our proposed hmoia outperforms the five foregoing algorithms especially for large sized problems

approximating pareto frontier using a hybrid line search approach the aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach but it is well known that this technique sometimes fail in different aspects for determining the pareto frontier this paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point once the first pareto solution is obtained a simplified version of the former one is used in the context of pareto dominance to obtain a set of efficient points which will assure a thorough distribution of solutions on the pareto frontier in the current form the proposed technique is well suitable for problems having multiple objectives it is not limited to bi objective problems and require the functions to be continuous twice differentiable in order to assess the effectiveness of this approach some experiments were performed and compared with two recent well known population based metaheuristics namely parego and nsga ii when compared to parego and nsga ii the proposed approach not only assures a better convergence to the pareto frontier but also illustrates a good distribution of solutions from a computational point of view both stages of the line search converge within a short time average about 150ms for the first stage and about 20ms for the second stage apart from this the proposed technique is very simple easy to implement and use to solve multiobjective problems

green function on the quantum plane a green function which can be called q analogous of the hankel function on the quantum plane eq2 eq 2 u 1 is constructed

the zeros of basic bessel functions the functions jv ax x and associated orthogonal polynomials abstract the modified lommel polynomials are generalized and their orthogonality relation is obtained as a byproduct we prove that the non zero roots of jv ax x are real simple and interlace with those of jv ax 1 x the q lommel polynomials are shown to play in the theory of basic bessel function the role played by the lommel polynomials in the bessel function theory the q lommel polynomials are proved to be orthogonal with respect to a purely discrete measure with bounded support this is then used to prove that the prositive zeros of x j 2 v x q are real simple and interlace with the zeros of x 1j 2 v 1 x q when 1 we also establish the complete monotonicity of 1x 1 2 j v 1 2 i x q j v 2 i x q

enhancing particle swarm optimization using generalized opposition based learning particle swarm optimization pso has been shown to yield good performance for solving various optimization problems however it tends to suffer from premature convergence when solving complex problems this paper presents an enhanced pso algorithm called gopso which employs generalized opposition based learning gobl and cauchy mutation to overcome this problem gobl can provide a faster convergence and the cauchy mutation with a long tail helps trapped particles escape from local optima the proposed approach uses a similar scheme as opposition based differential evolution ode with opposition based population initialization and generation jumping using gobl experiments are conducted on a comprehensive set of benchmark functions including rotated multimodal problems and shifted large scale problems the results show that gopso obtains promising performance on a majority of the test problems

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

elements of harmonic analysis related to the third basic zero order bessel function this paper is devoted to the study of some q harmonic analysis related to the third q bessel function of order zero we establish a product formula leading to a q translation with some positive kernel as an application we provide a q analogue of the continuous wavelet transform related to this harmonic analysis

on a q paley wiener theorem abstract after the analysis of the q even translation and the q cosine fourier transform by a fitouhi and f bouzeffour in q cosine fourier transform and q heat equation ramanujan j in press it is natural to look for the q analogue of some well known classical theorems in this paper we purpose to give a q version of the paley wiener theorem related to this fourier transform using standard methods of the q calculus

q prolate spheroidal wave functions and q sampling theorem in this paper we introduce a q version of the prolate spheroidal wave functions which is the eigenfunction of the concentration problem related to sampling and interpolation of q hankel bandlimited functions as application we give a q sampling theorem which extrapolates functions in l 2 space with q n email protected z as sampling points

inversion formulas for q riemann liouville and q weyl transforms we study fractional transforms associated with q bessel operator which is useful to inverse q riemann liouville and q weyl transforms

multi objective particle swarm optimization with time variant inertia and acceleration coefficients in this article we describe a novel particle swarm optimization pso approach to multi objective optimization moo called time variant multi objective particle swarm optimization tv mopso tv mopso is made adaptive in nature by allowing its vital parameters viz inertia weight and acceleration coefficients to change with iterations this adaptiveness helps the algorithm to explore the search space more efficiently a new diversity parameter has been used to ensure sufficient diversity amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front tv mopso has been compared with some recently developed multi objective pso techniques and evolutionary algorithms for 11 function optimization problems using different performance measures

completeness special functions and uncertainty principles over q linear grids we derive completeness criteria for sequences of functions of the form f x n where n is the nth zero of a suitably chosen entire function using these criteria we construct complete nonorthogonal systems of fourier bessel functions and their q analogues as well as other complete sets of q special functions we discuss connections with uncertainty principles over q linear grids and the completeness of certain sets of q bessel functions is used to prove that if a function f and its q hankel transform both vanish at the points q n n 1 0 q 1 then f must vanish on the whole q linear grid qn n

toeplitz matrices and classical and q bessel functions we use biinfinite toeplitz matrix analogues of classical and q binomial identities in a commutative banach algebra setting to characterize classical and q bessel functions of integer order and to establish properties of these functions

on no wait and no idle flow shops with makespan criterion the paper deals with the np hard problems of minimizing the makespan in m machine no wait and no idle permutation flow shops we identify networks whose longest path lengths represent the makespans these networks reveal the duality between the two problems and show graphical explanations of the fact that under no wait and no idle conditions the makespan can be a decreasing function of some job processing times moreover they also lead to a natural reduction of the no wait flow shop problem to the traveling salesman problem some lower bounds on the shortest makespan and new efficiently solvable special cases

moss multiobjective scatter search applied to non linear multiple criteria optimization abstract this paper introduces a multiple criteria scatter search to deal with bounded constrained non linear continuous vector optimization problems of high dimension applying a multistart tabu search ts as a diversification generation method each ts works with its own starting point recency memory and aspiration threshold frequency memory is used to diversify the search and it is shared between the ts a pareto relation is applied in order to designate a subset of the best generated solutions to be reference solutions a choice function called kramer choice function is used to divide the reference solutions in two subsets the euclidean distance is used as a measure of dissimilarity in order to find diverse solutions to be combined linear combinations of the reference solutions are used as a solution combination method balls in the decision space and the objective space are used to avoid duplications different tabu sets with different tabu tenures are employed in the scatter phase to enhance the diversity of the search the performance of our approach is compared with pareto optimal frontiers and three other state of the art moeas for a suite test problems taken from the literature

convergence of multi objective evolutionary algorithms to a uniformly distributed representation of the pareto front in evolutionary multi objective optimization emo the convergence to the pareto set of a multi objective optimization problem mop and the diversity of the final approximation of the pareto front are two important issues in the existing definitions and analyses of convergence in multi objective evolutionary algorithms moeas convergence with probability is easily obtained because diversity is not considered however diversity cannot be guaranteed by combining the convergence with diversity this paper presents a new definition for the finite representation of a pareto set the b pareto set and a convergence metric for moeas based on a new archive updating strategy the convergence of one such moea to the b pareto sets of mops is proved numerical results show that the obtained b pareto front is uniformly distributed along the pareto front when according to the new definition of convergence the algorithm is convergent

an algorithmic method to extend topsis for decision making problems with interval data in this paper from among multi criteria models in making complex decisions and multiple attribute models for the most preferable choice technique for order preference by similarity ideal solution topsis approach has been dealt with in some cases determining precisely the exact value of the attributes is difficult and that as a result of this their values are considered as intervals therefore the aim of this paper is to extend the topsis method for decision making problems with interval data by extension of topsis method an algorithm to determine the most preferable choice among all possible choices when data is interval is presented finally an example is shown to highlight the procedure of the proposed algorithm at the end of this paper 2005 elsevier inc all rights reserved

uncertainty relation in quantum mechanics with quantum group symmetry the commutation relations uncertainty relations and spectra of position and momentum operators were studied within the framework of quantum group symmetric heisenberg algebras and their bargmann fock representations as an effect of the underlying noncommutative geometry a length and a momentum scale appear leading to the existence of nonzero minimal uncertainties in the positions and momenta the usual quantum mechanical behavior is recovered as a limiting case for not too small and not too large distances and momenta

on a regularization scheme for linear operators in distribution spaces with an application to the spherical radon transform this article provides a framework to regularize operator equations of the first kind where the underlying operator is linear and continuous between distribution spaces the dual spaces of smooth functions to regularize such a problem the authors extend louis method of approximate inverse from hilbert spaces to distribution spaces the idea is to approximate the exact solution in the weak topology by a smooth function where the smooth function is generated by a mollifier the resulting regularization scheme consists of the evaluation of the given data at so called reconstruction kernels which solve the dual operator equation with the mollifier as right hand side a nontrivial example of such an operator is given by the spherical radon transform which maps a function to its mean values over spheres centered on a line or plane this transform is one of the mathematical models in sonar and radar after establishing the theory of the approximate inverse for distributions we apply it to the spherical radon

on q analogues of the fourier and hankel transforms for h exton s q analogue of the bessel function going back to w hahn in a special case but different from f h jackson s q bessel functions we derive hansen lommel type orthogonality relations which by a symmetry turn out to be equivalent to orthogonality relations which are q analogues of the hankel integral transform pair these results are implicit in the context of quantum groups in a paper by vaksman and korogodskii as a specialization we get q cosines and q sines which admit q analogues of the fourier cosine and fourier sine transforms

genetic local search for multi objective combinatorial optimization abstract the paper presents a new genetic local search gls algorithm for multi objective combinatorial optimization moco the goal of the algorithm is to generate in a short time a set of approximately efficient solutions that will allow the decision maker to choose a good compromise solution in each iteration the algorithm draws at random a utility function and constructs a temporary population composed of a number of best solutions among the prior generated solutions then a pair of solutions selected at random from the temporary population is recombined local search procedure is applied to each offspring results of the presented experiment indicate that the algorithm outperforms other multi objective methods based on gls and a pareto ranking based multi objective genetic algorithm ga on travelling salesperson problem tsp

on the braided fourier transform on the n dimensional quantum space we work out in detail a theory of integrability on the braided covector hopf algebra and the braided vector hopf algebra of type an introduced by majid using a braided fourier transform very similar to the one defined by kempf and majid we obtain n dimensional analogs of results by koornwinder expressing the correspondence between products of the q2 gaussian gq2 x times monomials and products of the q2 gaussian gq2 times q2 hermite polynomials under the transform we invert the correspondence by finding a suitable inversion different from the one of kempf and majid we show that with this transforms whenever n 2 the plancherel measure will depend on the parity of the power series that we are transforming

on the zeros of basic finite hankel transforms in this article we prove that the basic finite hankel transform whose kernel is the third type jackson q bessel function has only infinitely many real and simple zeros provided that q satisfies a condition additional to the standard one we also study the asymptotic behavior of the zeros the obtained results are applied to investigate the zeros of q bessel functions as well as the zeros of q trigonometric functions a basic analog of a theorem of g polya 1918 on the zeros of sine and cosine transformations is also given

using the hamming distance to extend topsis in a fuzzy environment considering the fact that in some cases determining precisely the exact value of attributes is difficult and that their values can be considered as fuzzy data this paper extends the topsis method for dealing with fuzzy data and an algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented in this approach to identify the fuzzy ideal solution and fuzzy negative ideal solution one of the yager indices which is used for ordering fuzzy quantities in 0 1 is applied using yager s index leads to a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives then the hamming distance is proposed for calculating the distance between two triangular fuzzy numbers finally an application is given to clarify the main results developed in the paper

two machine flow shop scheduling with two criteria maximum earliness and makespan abstract in this study we address the problem of minimizing makespan and maximum earliness simultaneously in a two machine flow shop environment we develop a branch and bound procedure that generates all efficient solutions with respect to two criteria we propose several lower and upper bounding schemes to enhance the efficiency of the algorithm we also propose a heuristic procedure that generates approximate efficient solutions our computational results reveal that the branch and bound procedure is capable of solving problems with up to 25 jobs and the heuristic procedure produces approximate efficient solutions that are very close to exact efficient solutions in very small computation times

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

yet another basic analogue of graf s addition formula an identity involving basic bessel functions and al salam chihara polynomials is proved for which we recover graf s addition formula for the bessel function as the base q tends to 1 the corresponding product formula is derived some known identities for jackson s q bessel functions are obtained as limiting cases as special cases we prove identities for q charlier polynomials

increasing selective pressure towards the best compromise in evolutionary multiobjective optimization the extended nosga method most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the pareto frontier however finding this set does not solve the problem the decision maker still has to choose the best compromise solution out of that set here we introduce a new characterization of the best compromise solution of a multiobjective optimization problem by using a relational system of preferences based on a multicriteria decision aid way of thinking and an outranked based dominance generalization we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise such conditions define a lexicographic minimum of a bi objective optimization problem which is a map of the original one the nosga ii method is a nsga ii inspired efficient way of solving the resulting mapped problem

a fuzzy satisficing method for large scale linear programming problems with block angular structure abstract in this paper we focus on large scale linear programming problems with block angular structure for which the dantzig wolfe decomposition method has been successfully applied by considering the vague nature of human judgements we assume that the decision maker may have a fuzzy goal for the objective function and fuzzy constraints for the coupling constraints having elicited the corresponding linear membership functions through the interaction with the decision maker if we adopt the convex fuzzy decision for combining them it is shown that under some appropriate conditions the formulated problem can be reduced to a number of independent linear subproblems and the overall satisficing solution for the decision maker is directly obtained just only solving the subproblems

a multi objective portfolio selection model with fuzzy value at risk ratio considering nonstatistical uncertainties and or insufficient historical data in security return forecasts fuzzy set theory has been applied in the past decades to build portfolio selection models meanwhile various risk measurements such as variance entropy and value at risk have been proposed in fuzzy environments to evaluate investment risks from different perspectives sharpe ratio also known as the reward to variability ratio which measures the risk premium per unit of the nonsystematic risk asset deviation has received great attention in modern portfolio theory in this study the sharpe ratio in fuzzy environments is introduced whereafter a fuzzy value at risk ratio is proposed compared with sharpe ratio value at risk ratio is an index with dimensional knowledge that reflects the risk premium per unit of the systematic risk the greatest loss under a given confidence level on the basis of the two ratios a multi objective model is built to evaluate their joint impact on portfolio selection then the proposed model is solved by a fuzzy simulation based multi objective particle swarm optimization algorithm where the global best of each iteration is determined by an improved dominance times based method finally the algorithm superiority is justified via comparing with existing solvers on benchmark problems and the model effectiveness is exemplified by using three case studies on portfolio selection

radii of starlikeness and convexity of some q bessel functions abstract geometric properties of the jackson and hahn exton q bessel functions are studied for each of them three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane for each of the six functions we determine the radii of starlikeness and convexity precisely by using their hadamard factorization these are q generalizations of some known results for bessel functions of the first kind the characterization of entire functions from the laguerre polya class via hyperbolic polynomials plays an important role in this paper moreover the interlacing property of the zeros of jackson and hahn exton q bessel functions and their derivatives is also useful in the proof of the main results we also deduce a necessary and sufficient condition for the close to convexity of a normalized jackson q bessel function and its derivatives some open problems are proposed at the end of the paper

design of mixed h2 h control systems using algorithms inspired by the immune system we utilize optimization algorithms inspired by the immune system for treating the mixed h 2 h control problem both precisely known systems and uncertain systems with polytopic uncertainties are investigated for the latter a novel methodology is proposed to compute the worst case norms within the polytope of matrices this methodology consists in defining the worst case norm computation as an implicit optimization problem with a special structure we exploit this structure of the problem for its solution the paper presents both mono and multiobjective optimization algorithms developed from the clonal selection principle the former is the real coded clonal selection algorithm rcsa and the latter is the multiobjective clonal selection algorithm mocsa the complete design process involves the combination of synthesis and analysis the rcsa is used for analysis through the worst case norm computation for a given provided controller the mocsa is used for synthesis working on a population of candidate controllers until providing an estimate of the pareto set for the mixed h 2 h control problem the numerical examples illustrate the power and the validity of the proposed approach for robust control design moreover our approach for worst case norm evaluation is compared with other approaches available in literature

seclusion factor method to solve fuzzy multiple criteria decision making problems this paper incorporates the basic concepts of subjectivity with the objective of decision theory to develop a method which intellectualizes ambiguity into multiple criteria decision making mcdm problems an outranking intensity is introduced to determine the degree of overall outranking between competing alternatives which are represented by fuzzy numbers the comparison of these degrees is made through the concept of overall existence ranking index comparative examples as well as a case study are given to illustrate the approach

a study of particle swarm optimization particle trajectories particle swarm optimization pso has shown to be an efficient robust and simple optimization algorithm most of the pso studies are empirical with only a few theoretical analyses that concentrate on understanding particle trajectories these theoretical studies concentrate mainly on simplified pso systems this paper overviews current theoretical studies and extend these studies to investigate particle trajectories for general swarms to include the influence of the inertia term the paper also provides a formal proof that each particle converges to a stable point an empirical analysis of multi dimensional stochastic particles is also presented experimental results are provided to support the conclusions drawn from the theoretical findings

on q newton kantorovich method for solving systems of equations starting from q taylor formula for the functions of several variables and mean value theorems in q calculus which we prove by ourselves we develop a new methods for solving the systems of equations we will prove its convergence and we will give an estimation of the error

decomposition of the parametric space in multiobjective convex programs using the generalized tchebycheff norm abstract a method for decomposing the parametric space in multiobjective convex programs with or without parameters in the constraints using the generalized tchebycheff norm is presented this approach is rather simpler than the corresponding one using the nonnegative weighted sum of objectives also several results are introduced which relate two convex programs with each other one with parameters in the constraints and the other with parameters in the objective function such results make the study of the first type of problems rather simple

asymptotic expansions for a class of q integral transforms abstract using the q mellin transform studied in a fitouhi n bettaibi k brahim the mellin transform in quantum calculus constructive approximation 23 3 2006 305 323 we provide an asymptotic expansion for a class of q integral transforms having the form 0 f t h xt d q t in particular we are interested with the q laplace q fourier cosine and q hankel transforms we adopt the method of handelsman and lew r wong asymptotic approximations of integrals computer science and scientific computing academic press new york 1989

elements of q harmonic analysis abstract measures that act as q analogs of lebesgue measure are introduced some q analogs of fourier and laplace transforms are studied last the connection between certain spaces of q exponential type and discrete q fourier transforms is discussed

a dominance tree and its application in evolutionary multi objective optimization most contemporary multi objective evolutionary algorithms moeas store and handle a population with a linear list and this may impose high computational complexities on the comparisons of solutions and the fitness assignment processes this paper presents a data structure for storing the whole population and their dominating information in moeas this structure called a dominance tree dt is a binary tree that can effectively and efficiently store three valued relations namely dominating dominated or non dominated among vector values this paper further demonstrates dt s potential applications in evolutionary multi objective optimization with two cases the first case utilizes the dt to improve nsga ii as a fitness assignment strategy the second case demonstrates a dt based moea called a dtea which is designed by leveraging the favorable properties of the dt the simulation results show that the dt improved nsga ii is significantly faster than nsga ii meanwhile dtea is much faster than spea2 nsga ii and an improved version of nsga ii on the other hand in regard to converging to the pareto optimal front and maintaining the diversity of solutions dt improved nsga ii and dtea are found to be competitive with nsga ii and spea2

an interactive algorithm for large scale multiple objective programming problems with fuzzy parameters through topsis approach in this paper we extend technique for order preference by similarity ideal solution topsis for solving large scale multiple objective programming problems involving fuzzy parameters these fuzzy parameters are characterized as fuzzy numbers for such problems the pareto optimality is introduced by extending the ordinary pareto optimality on the basis of the level sets of fuzzy numbers an interactive fuzzy decision making algorithm for generating pareto optimal solution through topsis approach is provided where the decision maker dm is asked to specify the degree and the relative importance of objectives finally a numerical example is given to clarify the main results developed in the paper

a class of multi objective expected value decision making model with birandom coefficients and its application to flow shop scheduling problem in this paper we establish multi objective decision making models with birandom coefficients for the flow shop scheduling problem furthermore we introduce the general multi objective decision making model under a birandom environment and transform the birandom uncertain model into a deterministic model through an expected value operator and some properties of the expected value model are also researched we extend some theories of birandom variables and especially devote ourselves to researching the expected value of two kinds of birandom variables the expected value goal model is also proposed in order to compute the expected value of birandom variables birandom simulation is presented combined with the genetic algorithm it is applied in dealing with objective functions and constraint functions and to obtain the optimal solution finally an application to flow shop scheduling at geely haoqing automatic company is provided as an illustration

a new pso algorithm with random c d switchings abstract this paper investigates the overall convergence analysis and proposes a novel random c d switchings pso algorithm with random switchings between convergence operator and divergence operator with respect to the standard pso algorithm its convergence analysis provides a fundamental theory of selecting convergence operator and divergence operator during the process of finding the suboptimal or global solution the random switchings between two typical operators namely operator c and operator d which are two different ways to update velocities of all particles are conducted by a so called convergence ratio parameter which can determine the tradeoff between exploration ability and exploitation ability from the quantitative perspective numerical results on several benchmark functions demonstrate the following observations 1 the proper convergence ratio is closely related to the landscape of objective function the dimension of solution space and the number of local optimums 2 small convergence ratio setting to 0 60 or 0 65 may benefit the optimization problem which has many local optimums in the high dimensional space while large convergence ratio setting to 0 85 or 0 9 is probably helpful for the optimization problem with few local optimums or flat landscape

extensions of topsis for multi objective large scale nonlinear programming problems in this paper we focus on multi objective large scale nonlinear programming molsnlp problems with block angular structure we extend technique for order preference by similarity ideal solution topsis approach to solve molsnlp problems compromise topsis control minimizes the measure of distance providing that the closest solution should have the shortest distance from the positive ideal solution pis as well as the longest distance from the negative ideal solution nis as the measure of closeness l p metric is used thus we reduce a q dimensional objective space to a two dimensional space by a first order compromise procedure the concept of membership function of fuzzy set theory is used to represent the satisfaction level for both criteria also we get a single objective large scale nonlinear programming lsnlp problem using the max min operator for the second order compromise operation finally a numerical illustrative example is given to clarify the main results developed in the paper

spectral zeta functions for q bessel equations explicit formulae for the zeta functions of the zeros of hahn exton and jackson s q bessel functions are derived they can be regarded as spectral sum rules for some discrete quantum billiards

extension of the topsis method for decision making problems with fuzzy data decision making problem is the process of finding the best option from all of the feasible alternatives in this paper from among multicriteria models in making complex decisions and multiple attribute models for the most preferable choice technique for order preference by similarity to ideal solution topsis approach has been dealt with in real word situation because of incomplete or non obtainable information the data attributes are often not so deterministic there for they usually are fuzzy imprecise therefore the aim of this paper is to extend the topsis method to decision making problems with fuzzy data in this paper the rating of each alternative and the weight of each criterion are expressed in triangular fuzzy numbers the normalized fuzzy numbers is calculated by using the concept of a cuts finally a numerical experiment is used to illustrate the procedure of the proposed approach at the end of this paper

real paley wiener theorems for the koornwinder swarttouw q hankel transform abstract we derive two real paley wiener theorems in the setting of quantum calculus the first uses techniques due to tuan and zayed v k tuan a i zayed paley wiener type theorems for a class of integral transforms j math anal appl 266 1 2002 200 226 in order to describe the image of the space l q 2 0 r under koornwinder and swarttouw q hankel transform t h koornwinder r f swarttouw on q analogues of the fourier and hankel transforms trans amer math soc 333 1 1992 445 461 and contains as a special case a description of the domain of the q sampling theorem associated with the q hankel transform l d abreu a q sampling theorem related to the q hankel transform proc amer math soc 133 4 2005 1197 1203 the second characterizes the image of compactly supported q smooth functions under a rescaled version of the q hankel transform and is a q analogue of a recent result due to andersen n b andersen real paley wiener theorems for the hankel transform j fourier anal appl 12 1 2006 17 25

extensions of the topsis for group decision making under fuzzy environment the aim of this paper is to extend the topsis to the fuzzy environment owing to vague concepts frequently represented in decision data the crisp value are inadequate to model real life situations in this paper the rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers then a vertex method is proposed to calculate the distance between two triangular fuzzy numbers according to the concept of the topsis a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the fuzzy positive ideal solution fpis and fuzzy negative ideal solution fnis simultaneously finally an example is shown to highlight the procedure of the proposed method at the end of this paper

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

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

range descriptions for the spherical mean radon transform abstract the transform considered in the paper averages a function supported in a ball in r n over all spheres centered at the boundary of the ball this radon type transform arises in several contemporary applications e g in thermoacoustic tomography and sonar and radar imaging range descriptions for such transforms are important in all these areas for instance when dealing with incomplete data error correction and other issues four different types of complete range descriptions are provided some of which also suggest inversion procedures necessity of three of these appropriately formulated conditions holds also in general domains while the complete discussion of the case of general domains would require another publication

summation formulae for the product of the q kummer functions from e q 2 using the representation of eq 2 on the non commutative space zz qz z q 0 summation formulae for the product of two three and four q kummer functions are derived

models of q algebra representations q integral transforms and addition theorems oscillator lie algebras with respect to countable bases of eigenfunctions of the car tan subalgebras and he computed the summation identities for bessel functions and laguerre polynomials associated with the addition theorems for these matrix elements he also studied matrix elements of the pseudo euclidean and pseudo oscillator algebras with respect to the continuum bases of generalized eigenfunctions of the cartan subalgebras of these lie algebras and this resulted in realizations of the addition theorems for the matrix elements as integral transform identities for bessel functions and for confluent hypergeometric functions here we work out q analogs of these results in which the usual exponential function mapping from the lie algebra to the lie group is replaced by the q exponential mappings e4 and e this study of representations of the euclidean quantum algebra and the q oscillator algebra not a quantum algebra leads to summation integral transform and q integral transform identities for q analogs of the bessel and confluent hypergeometric functions extending the results of vile in for the q 1 case

applications of the mellin transform in quantum calculus abstract in this paper we study in quantum calculus the correspondence between poles of the q mellin transform see a fitouhi n bettaibi k brahim the mellin transform in quantum calculus constr approx 23 3 2006 305 323 and the asymptotic behaviour of the original function at 0 and as applications we give a new technique in q analysis to derive the asymptotic expansion of some functions defined by q integrals or by q harmonic sums finally a q analogue of the mellin perron formula is given

operator representations of a q deformed heisenberg algebra a class of well behaved representations of a q deformed heisenberg algebra previously introduced phys lett b 291 273 1992 z phys c 64 335 1994 is studied and classified

notes on some single machine scheduling problems with general position dependent and time dependent learning effects this paper provides a continuation of the idea presented by yin et al yin et al some scheduling problems with general position dependent and time dependent learning effects inform sci 179 2009 2416 2425 for each of the following three objectives total weighted completion time maximum lateness and discounted total weighted completion time this paper presents an approximation algorithm which is based on the optimal algorithm for the corresponding single machine scheduling problem and analyzes its worst case bound it shows that the single machine scheduling problems under the proposed model can be solved in polynomial time if the objective is to minimize the total lateness or minimize the sum of earliness penalties it also shows that the problems of minimizing the total tardiness discounted total weighted completion time and total weighted earliness penalty are polynomially solvable under some agreeable conditions on the problem parameters

topsis for modm abstract in this study we extend topsis to solve a multiple objective decision making problem the principle of compromise of topsis for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution thus we reduce a k dimensional objective space to a two dimensional objective space by a first order compromise procedure we then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria we obtain a single objective programming problem by using the max min operator for the second order compromise operation to illustrate the procedure the bow river valley water quality management problem is solved by use of topsis