memetic algorithm based on improved inver over operator and lin kernighan local search for the euclidean traveling salesman problem in this study an improved inver over operator is proposed to solve the euclidean traveling salesman problem tsp problem the improved inver over operator is tested on 14 different tsp examples selected from tsplib the application of the improved inver over operator gives much more effective results regarding to the best and average error values than the basic inver over operator then an effective memetic algorithm based on improved inver over operator and lin kernighan local search is implemented to speed up the convergence capability of the presented algorithm a restart technique is employed we evaluate the proposed algorithm based on standard tsp test problems and show that the proposed algorithm performs better than other memetic algorithm in terms of solution quality and computational effort

exterior point algorithms for nearest points and convex quadratic programs we consider the problem of finding the nearest point by euclidean distance in a simplicial cone to a given point and develop an exterior penalty algorithm for it each iteration in the algorithm consists of a single newton step following a reduction in the value of the penalty parameter proofs of convergence of the algorithm are given various other versions of exterior penalty algorithms for nearest point problems in nonsimplicial polyhedral cones and for convex quadratic programs all based on a single descent step following a reduction in the value of the penalty parameter per iteration are discussed the performance of these algorithms in large scale computational experiments is very encouraging it shows that the number of iterations grows very slowly if at all with the dimension of the problem

geometric superalgebra and the dirac equation a unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form useful to study the mathematical description of matter and its interaction fields the formalism then encompasses both points of view multivectors for the description of space time geometry and the description of the integer spin interaction fields and spinor representations suitable for the description of half odd integer matter fields an application is made to study the change of the dirac equation under the spinors to multivectors to scalars mapping the physical and geometric content of the multivector solutions of the dirac hestenes equation is clearly shown

on the classification of clifford algebras and their relation to spinors in n dimensions a classification of all the clifford algebras is given in terms of kronecker products of the quaternion and dihedral groups the relationship to spinors in n dimensions is explicitly determined we show that the real clifford algebra in minkowski spacetime is distinct from both the algebra of dirac matrices and the algebra of majorana matrices and cannot be realized by the spinor framework the matrix representations of clifford algebras are discussed and are utilized to give a classification of the real forms of lie algebras we are thus able to relate clifford lie and spinor algebras in an intrinsic geometrical setting

multivectorial generalization of the cartan map a multivectorial generalization of the spinors to vectors cartan map is constructed with space time as a base space constructed from spinors dirac spinors and spinors pairs being particular cases onto a multivector space with two internal symmetries one of them is the fundamental space time clifford group c 1 3 and the other an isotopic space in multivectorial representation related with the more common gauge groups the algebraic properties of this map and of the operators representing observables are studied the inversion map is also presented the quaternion projection of the map is shown as are its properties and its mathematical and physical meaning the procedure presented here is compared with other spinor vector maps used in the literature

algebraic spinor solution to the kahler equation the kahler equation for an inhomogeneous differential form is analyzed in some detail algebraic spinorial solution to the kahler equation lying in a minimal left ideal characterized by a certain idempotent projector has been examined

a new hybrid heuristic approach for solving large traveling salesman problem this paper presents a new metaheuristic approach called acomac algorithm for solving the traveling salesman problem tsp we introduce multiple ant clans concept from parallel genetic algorithm to search solution space utilizing various islands to avoid local minima and thus can yield global minimum for solving the traveling salesman problem moreover we present two approaches named the multiple nearest neighbor nn and the dual nearest neighbor dnn to acomac to enhance large tsps to validate the proposed methods numerous simulations were conducted to compare acomac and dorigo s acs with and without the addition of the multiple nearest neighbor nn method or the dual nearest neighbor dnn approach using a range of tsp benchmark problems according to the results of the simulation adding the nn or dnn approach to acomac or acs as initial solutions also significantly enhances the performance of acomac and acs in solving the traveling salesman problem meanwhile using acomac dnn with tsp can yield better solutions than the other stated approaches additionally acomac or acomac nn utilizing five ant clans with a total of 20 ants is verified to yield better solutions furthermore acomac with a local weighting w set to 0 6 can yield better solutions in terms of length

k out of n systems reliability and availability analyses are recognized as essential for guiding decision makers in the implementation of actions addressed to improve the technical and economical performance of complex systems for industrial systems with reparable components the most interesting parameter used to drive maintenance is the stationary availability in this regard the present paper proposes an exact formula for computing the system stationary availability of a k out of n system such a formula is proved to be in agreement with the fundamental theorem of markov chains then a multi objective mathematical model is formulated for choosing the optimal system configuration design the pareto front is developed using the lexicographic goal programming lgp method and the topsis method is successively implemented to choose the k out of n configuration that represents the best compromise between the considered objective functions a numerical example is provided stationary availability formula proposed for k out of n systems validation of the proposed formula by markov chains design of a k out of n system selection of pareto solution by means of topsis multi criteria method

bilinear covariants and spinor fields duality in quantum clifford algebras classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum clifford algebras on minkowski spacetime once the bilinear covariants are expressed in terms of algebraic spinor fields the duality between spinor and quantum spinor fields can be discussed thus by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric quantum algebraic spinor fields and deformed bilinear covariants can be constructed they are thus compared to the classical non quantum ones classes of quantum spinor fields classes are introduced and compared with lounesto s spinor field classification a physical interpretation of the deformed parts and the underlying z grading is proposed the existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity s w hawking the unpredictability of quantum gravity commun

guided local search and its application to the traveling salesman problem abstract the traveling salesman problem tsp is one of the most famous problems in combinatorial optimization in this paper we are going to examine how the techniques of guided local search gls and fast local search fls can be applied to the problem gls sits on top of local search heuristics and has as a main aim to guide these procedures in exploring efficiently and effectively the vast search spaces of combinatorial optimization problems gls can be combined with the neighborhood reduction scheme of fls which significantly speeds up the operations of the algorithm the combination of gls and fls with tsp local search heuristics of different eiciency and effectiveness is studied in an effort to determine the dependence of gls on the underlying local search heuristic used comparisons are made with some of the best tsp heuristic algorithms and general optimization techniques which demonstrate the advantages of gls over alternative heuristic approaches suggested for the problem

new approach using ant colony optimization with ant set partition for fuzzy control design applied to the ball and beam system in this paper we describe the design of a fuzzy logic controller for the ball and beam system using a modified ant colony optimization aco method for optimizing the type of membership functions the parameters of the membership functions and the fuzzy rules this is achieved by applying a systematic and hierarchical optimization approach modifying the conventional aco algorithm using an ant set partition strategy the simulation results show that the proposed algorithm achieves better results than the classical aco algorithm for the design of the fuzzy controller

finite geometries and clifford algebras ii the pleasant incidence properties of m dimensional projective geometry enable us upon employing the finite geometry over the field rm f rm 2 to deal nicely with certain commutativity anti commutativity aspects of clifford algebras cl o d in dimensions d 2m 1 1 m 2 3

realization extension and classification of certain physically important groups and algebras an associative algebra of differential forms with division has been constructed the algebra of forms in each different space provides a practical realization of the universal clifford algebra of that space a classification of all such algebras is given in terms of two distinct types of algebras nk and sk the former include the dihedral quaternion and majorana algebras the latter include the complex spinor and dirac algebras the associative product expresses hodge duality as multiplication by a basis element this makes possible the realization of higher order algebras in a calculationally useful algebraic setting the fact that the associative algebras as well as the enveloped lie algebras are precisely those arising in physics suggests that this formalism may be a convenient setting for the formulation of basic physical laws

fluctuation driven computing on number conserving cellular automata a number conserving cellular automaton ncca is a cellular automaton in which the states of cells are denoted by integers and the sum of all of the numbers in a configuration is conserved throughout its evolution nccas have been widely used to model physical systems that are ruled by conservation laws of mass or energy imai et al 13 showed that the local transition function of ncca can be effectively translated into the sum of a binary flow function over pairs of neighboring cells in this paper we explore the computability of nccas in which the pairwise number flows are performed at fully asynchronous timings despite the randomness that is associated with asynchronous transitions useful computation still can be accomplished efficiently in the cellular automata through the active exploitation of fluctuations 18 specifically certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space as if they were subject to brownian motion because random fluctuations promise a powerful resource for searching through a computational state space the brownian like flow of the numbers allows for efficient embedding of logic circuits into our novel asynchronous ncca

projection onto simplicial cones by picard s method abstract by using moreau s decomposition theorem for projecting onto cones the problem of projecting onto a simplicial cone is reduced to finding the unique solution of a nonsmooth system of equations it is shown that picard s method applied to the system of equations associated with the problem of projecting onto a simplicial cone generates a sequence that converges linearly to the solution of the system numerical experiments are presented making the comparison between picard s and semi smooth newton s methods to solve the nonsmooth system associated with the problem of projecting a point onto a simplicial cone

analytical and numerical comparisons of biogeography based optimization and genetic algorithms we show that biogeography based optimization bbo is a generalization of a genetic algorithm with global uniform recombination ga gur based on the common features of bbo and ga gur we use a previously derived bbo markov model to obtain a ga gur markov model one bbo characteristic which makes it distinctive from ga gur is its migration mechanism which affects selection pressure i e the probability of retaining certain features in the population from one generation to the next we compare the bbo and ga gur algorithms using results from analytical markov models and continuous optimization benchmark problems we show that the unique selection pressure provided by bbo generally results in better optimization results for a set of standard benchmark problems we also present comparisons between bbo and ga gur for combinatorial optimization problems include the traveling salesman the graph coloring and the bin packing problems

a novel bio inspired approach based on the behavior of mosquitoes this paper proposes a new nature inspired algorithm na mosquito host seeking algorithm mhsa the inspiration for which comes from the host seeking behavior of mosquitoes applying the algorithm to the traveling salesman problem tsp every city pair is treated as an artificial mosquito and the tsp solving process is transformed into the host seeking behavior of a swarm of artificial mosquitoes we study the evolution of swarms the artificial mosquitoes microcosmic actions and macroscopic swarm intelligence and present efficient solutions to tsp using mhsa the proposed mhsa is fundamentally different from the other popular nas in its motivation principle the optimization mechanism its elements and their states and the biological model the mathematical model and theoretical foundation on which it is based we show that 1 mhsa can converge 2 its parameter setting does not depend on algorithm learning or prior knowledge and 3 mhsa can describe complex behaviors and dynamics the properties of mhsa including correctness convergence and stability are discussed in details simulation results attest to the effectiveness and suitability of mhsa

the relationship between finite groups and clifford algebras clifford algebras are traditionally realized in terms of a specific set of representation matrices this paper provides a more effective alternative by giving the finite group associated with each clifford algebra all the representation independent algebraic results which are really direct consequences of the underlying group structure can thus be derived in an easier and more general manner there are five related but distinct classes of finite groups associated with the clifford algebras these groups are constructed from the complex cyclic quaternion and dihedral groups in a way which is discussed here in detail of particular utility is a table which lists the order structure of each group this permits the immediate identification of any clifford algebra in any dimension

path planning on a cuboid using genetic algorithms the traveling salesman problem tsp is one of the most extensively studied problems in the fields of combinatorial optimization and global search heuristics a variety of heuristic algorithms are available for solving euclidean tsp and planar tsps however optimization on a cuboid has potential applications for areas like path planning on the faces of buildings rooms furniture books and products or simulating the behaviors of insects in this paper we address a variant of the tsp in which all points cities and paths solution are on the faces of a cuboid we develop an effective hybrid method based on genetic algorithms and 2 opt to adapt the euclidean tsp to the surface of a cuboid the method was tested on some benchmark problems from tsplib with satisfactory results a web based interactive visualization tool has also been developed using java 3d and optimization results for different point densities on the cuboid are presented

artificial neural network approach for solving fuzzy differential equations the current research attempts to offer a novel method for solving fuzzy differential equations with initial conditions based on the use of feed forward neural networks first the fuzzy differential equation is replaced by a system of ordinary differential equations a trial solution of this system is written as a sum of two parts the first part satisfies the initial condition and contains no adjustable parameters the second part involves a feed forward neural network containing adjustable parameters the weights hence by construction the initial condition is satisfied and the network is trained to satisfy the differential equations this method in comparison with existing numerical methods shows that the use of neural networks provides solutions with good generalization and high accuracy the proposed method is illustrated by several examples

finite dimensional guaranteed cost sampled data fuzzy control for a class of nonlinear distributed parameter systems in this paper a finite dimensional guaranteed cost sampled data fuzzy control gcsdfc problem is addressed for a class of nonlinear parabolic partial differential equation pde systems initially applying the galerkin s method to the pde system a nonlinear ordinary differential equation ode system is derived the resulting nonlinear ode system can accurately describe the dominant dynamics of the pde system which is subsequently expressed by the takagi sugeno t s fuzzy model then a guaranteed cost sampled data fuzzy controller is developed to stabilize exponentially the closed loop slow fuzzy system while providing an upper bound for the quadratic cost function a novel time dependent functional is constructed to derive the condition for the existence of the proposed controller which is presented by bilinear matrix inequalities bmis moreover a suboptimal gcsdfc problem to minimize the cost bound can be formulated as a bmi optimization problem a local optimization algorithm that views the bmi as a double linear matrix inequality lmi is given to solve this bmi optimization problem in which a latin hypercube sampling lhs method is proposed to find an initially feasible solution for starting the algorithm furthermore it is shown that the proposed controller can ensure the exponential stability of the closed loop pde system finally simulation results on the fisher equation and the temperature profile of a catalytic rod show that the proposed design strategy is effective

hybrid evolutionary fuzzy learning scheme in the applications of traveling salesman problems abstract this study develops a hybrid evolutionary fuzzy learning algorithm that automatically determines the near optimal traveling path in large scale traveling salesman problems lstsps identifying solutions for lstsps is one of the most complicated topics in the field of global combinatorial optimization problems the proposed hybrid evolutionary fuzzy learning scheme combines the advantages of the adaptive fuzzy c means fcm simple max min merging concept simulated annealing sa learning algorithm and an efficient table transform based particle swarm optimization tpso this study uses the proposed method to deal with the large size tsp routing system the evolutionary tpso learning algorithm is applied to optimize the traveling table which in turn extracts the appropriate traveling table sequence codes for approaching the shorter traveling path the sa local optimal learning algorithm works after the tpso learning scheme using three operators to acquire the optimal traveling solution inversion translation and switching the other considerable notation is to divide the large scale cities into suitable subgroup cities to improve the efficiency of training machine the popular fcm algorithm is a valid unsupervised clustering method that identifies the relational grades of a given traveling city dataset separating them into popular categories based on the critical issue in maximal city number to break the city nodes of the traveling loop and reconnect suitable nodes again with the minimal distance searching procedure the proposed simple but powerful max min merging algorithm to rebuild the new traveling path various sizes of tsp testing instances reveal that the developed hybrid evolutionary fuzzy learning algorithm achieves better results than other learning methods in both the quality of routing and computing time

a vertex algorithm for collision detection abstract an algorithm for detecting the collision of moving objects is presented the algorithm applies to polyhedral objects that can be represented as convex hulls of finite number of vertices in two or three dimensional space this is then extended to a three or four dimensional space respectively to represent the objects and their motion nonlinear programming techniques are then employed to detect possible interference the algorithm detects in one step whether or not the objects will interfere during their motion which may involve pure translations or rotations or both a subalgorithm for computing the minimum distance between the objects is also presented this can be used to solve the interference detection problem or for more general applications

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

collision detection for moving polyhedra we consider the collision detection problem for a three dimensional solid object moving among polyhedral obstacles the configuration space for this problem is six dimensional and the traditional representation of the space uses three translational parameters and three angles typically euler angles the constraints between the object and obstacles then involve trigonometric functions we show that a quaternion representation of rotation yields constraints which are purely algebraic in a seven dimensional space by simple manipulation the constraints may be projected down into a six dimensional space with no increase in complexity the algebraic form of the constraints greatly simplifies computation of collision points and allows us to derive an efficient exact intersection test for an object which is translating and rotating among obstacles

clifford algebras and finite groups the structure of finite groups associated with clifford algebras of signatures 0 d d identical to 3 mod 4 is outlined a speculation by another author concerning the possible exceptional nature of the group associated with d 7 is seen to be false

singular solutions to the seiberg witten and freund equations on flat space from an iterative method although it is well known that the seiberg witten equations do not admit nontrivial l2 solutions in flat space singular solutions to them have been previously exhibited either in r3 or in the dimensionally reduced spaces r2 and r1 which have physical interest in this work we employ an extension of the hopf fibration to obtain an iterative procedure to generate particular singular solutions to the seiberg witten and freund equations on flat space examples of solutions obtained by such method are presented and briefly discussed

observers observables spinors and the confusion of tongues choquet bruhat was the first to give a proper physical definition of covariant spinors taking into account the reference system and treating them as equivalence classes defined from the transformation laws of the representatives when the reference system is changed recently rodriguez et al int j theor phys 35 1849 1996 have adapted this procedure from covariant spinors to the case of algebraic and operator spinors these approaches are restrained in the sense that the type of spinor is chosen from the beginning and it does not admit a general formulation in this paper we present a unified definition that is valid for any type of the space of representation being independent of its particular properties in our formulation the three types of spinors appear as particular cases of the general definition moreover we stick out the importance of the bilinear covariants in the definition of spinors from this we recognize a completely different kind of spinor characterized by the different n

on the performance of self organizing maps for the non euclidean traveling salesman problem in the polygonal domain in this paper two state of the art algorithms for the traveling salesman problem tsp are examined in the multi goal path planning problem motivated by inspection planning in the polygonal domain w both algorithms are based on the self organizing map som for which an application in w is not typical the first is somhom s algorithm and the second is the co adaptive net these algorithms are augmented by a simple approximation of the shortest path among obstacles in w moreover the competitive and cooperative rules are modified by recent adaptation rules for the euclidean tsp and by proposed enhancements to improve the algorithms performance in the non euclidean tsp based on the modifications two new variants of the algorithms are proposed that reduce the required computational time of their predecessors by an order of magnitude therefore making som more competitive with combinatorial heuristics the results show how som approaches can be used in the polygonal domain so they can provide additional features over the classical combinatorial approaches based on the complete visibility graph

n dimensional spinors their properties in terms of finite groups a classification scheme is presented for the finite multiplicative group generated by the gamma matrices associated with a given clifford algebra this group reflects the periodicities observed in n dimensional spinors and its representations and other properties are studied thus highlighting the dependence on the number of spacelike and timelike vectors the reality of the representations is examined and tabulated application is made to the imposition of majorana and weyl conditions

an extension of karmarkar projective algorithm for convex quadratic programming we present an extension of karmarkar s linear programming algorithm for solving a more general group of optimization problems convex quadratic programs this extension is based on the iterated application of the objective augmentation and the projective transformation followed by optimization over an inscribing ellipsoid centered at the current solution it creates a sequence of interior feasible points that converge to the optimal feasible solution in o ln iterations each iteration can be computed in o ln3 arithmetic operations wheren is the number of variables andl is the number of bits in the input in this paper we emphasize its convergence property practical efficiency and relation to the ellipsoid method

a general method of generating and classifying clifford algebras a general construction program is given for the generation of higher order clifford algebras of various signatures together with their faithful representations in terms of pauli type operators the analysis is based upon several isomorphism theorems that provide a simpler understanding of the standard classification scheme of these algebras and an improved signature index notation is suggested that identifies each of the five types of clifford algebras

the complete reduction of clifford algebras the complete reduction of simple clifford algebras is spanned by matrix bases considered as generators of an algebra the basis elements pij satisfy the product relations pijpkl jkpil it follows that subsets of pij with subscript or superscript fixed span minimal left or right ideals the expression of the basis elements pij in the usual multivector basis is derived from isomorphic matrix algebras spinors and hermitian conjugate spinors are defined as members of minimal left and right ideals spinor scalar products are defined these scalar products are in fact scalar multiples of an idempotent

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

toward solving the steiner travelling salesman problem on urban road maps using the branch decomposition of graphs the steiner travelling salesman problem stsp is an important issue in intelligent transportation systems and has various practical applications such as travelling and parcel delivery in this study we consider the stsp in real world road maps i e given a road map with a set of service points or intersections selection of the representative vertices of a graph g to determine a closed route so a vehicle can visit each service point at least once with the minimum cost it has been theoretically proved that the stsp and its ancestor travelling salesman problem are np hard however it has been empirically demonstrated that they can be solved efficiently on planar graphs with small branchwidths therefore we propose a branch decomposition based extraction algorithm for the stsp in planar graphs our algorithm can solve the stsp in a planar graph g with a time complexity of 2o bw g no 1 where bw g is the branchwidth of g in the case of planar graphs with a small branchwidth our algorithm performs efficiently we evaluated our algorithm by applying it to real world urban road maps which demonstrated the suitability of our method for real world applications

fock space description of simple spinors cartan s simple often called pure spinors corresponding to even dimensional complex vector spaces are defined in terms of the associated maximal totally null planes their geometrical properties are derived and described using notions familiar to physicists dirac and weyl spinors gamma matrices tensors formed bilinearly from pairs of spinors and creation and annihilation operators of fermi states a new theorem characterizes a simple spinor by the properties of the vector t b where is an arbitrary spinor and b is the matrix connecting the gamma matrices with their transposes the cartan constraint equations on the components of simple spinors are given a new geometrically transparent derivation based on the action on simple spinors of a maximal abelian subgroup of the group spin

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

on the algebra of dirac bispinor densities factorization and inversion theorems the algebraic system formed by dirac bispinor densities i i is discussed the inverse problem given a set of 16 real functions i which satisfy the bispinor algebra find the spinor to which they correspond is solved an expedient solution to this problem is obtained by introducing a general representation of dirac spinors it is shown that this form factorizes into the product of two noncommuting projection operators acting on an arbitrary constant spinor

a proof of convergence for ant algorithms a proof of convergence for ant algorithms is developed ant algorithms were modeled as branching random processes the branching random walk and branching wiener process to derive rates of birth and death of ant paths substitution is then carried out in birth death processes which proves that a stable distribution is surely reached this indicates that ant algorithms converge with probability one this analogy models ant algorithms complexity parameters such as the number of cycles the degrees of freedom of problem and the number of ants

a new approach to solving the multiple traveling salesperson problem using genetic algorithms the multiple traveling salesperson problem mtsp involves scheduling m 1 salespersons to visit a set of n m locations so that each location is visited exactly once while minimizing the total or maximum distance traveled by the salespersons the mtsp is similar to the notoriously difficult traveling salesperson problem tsp with the added complication that each location may be visited by any one of the salespersons previous studies investigated solving the mtsp with genetic algorithms gas using standard tsp chromosomes and operators this paper proposes a new ga chromosome and related operators for the mtsp and compares the theoretical properties and computational performance of the proposed technique to previous work computational testing shows the new approach results in a smaller search space and in many cases produces better solutions than previous techniques

the remarkable algebra so 2n its representations its clifford algebra and potential applications properties of the real lie algebra so 2n and its finite dimensional representations are described the structure of the clifford algebras associated with the two fundamental spinor representations are determined and it is found in particular that for so 4n there is a remarkable asymmetry one representation is real the other complex though equivalent to its complex conjugate and the associated clifford algebras are inequivalent generalised dirac matrices are defined acting within the direct sum of these two spinor representations of so 2n these matrices generate a different clifford algebra not determined uniquely by those representations and their commutators do not span a representation of so 2n the isomorphisms of so 6 with su 3 1 and of so 8 with so 6 2 are described together with the corresponding mappings between finite dimensional irreducible representations a possible application to unified field theory is discussed

an algorithm for linear least squares problems with equality and nonnegativity constraints we present a new algorithm for solving a linear least squares problem with linear constraints these are equality constraint equations and nonnegativity constraints on selected variables this problem while appearing to be quite special is the core problem arising in the solution of the general linearly constrained linear least squares problem the reduction process of the general problem to the core problem can be done in many ways we discuss three such techniques

a clifford algebra quantization of dirac s electron positron field the quantum field theory of free dirac particles four component massive spin 1 2 particles is derived by a segal quantization procedure first details are given on how the spinor space of dirac is actually a minimal left ideal of the clifford algebra associated with a lorentz inner product space and how the homogeneous group actions break the natural two component quaternion structure to give familiar four component complex spinors second wigner s procedure for constructing unitary representations of the poincare group is used to construct the appropriately induced infinite dimensional representation of the inhomogeneous group starting from the above four dimensional nonunitary representation third and finally segal s procedure for quantizing classical fermion fields is adapted to this infinite dimensional hilbert space to obtain the clifford algebra of annihilation creation operators for spin 1 2 particles the familiar fock space appears as a minimal left ideal in this second clifford algebra

collision computation of moving bodies abstract in this paper an explicit mathematical representation of n dimensional bodies moving in translation along general trajectories is derived this representation is used to find out if two moving bodies are going to collide an optimization problem is developed for finding the time and location of collision we consider the special cases of linear and piece wise linear trajectories the collision in this case can be obtained by solving a linear program or a sequence of linear programs respectively the problem of finding the collision time and location of several moving bodies is cast as an integer programming problem a comprehensive simulation study shows that this approach requires much lesser computation time when compared with the current approach of finding the collision between all pairs of bodies

a null space method for computing the search direction in the general inertia controlling method for dense quadratic programming the inertia controlling strategy in active set methods consists of choosing the working set so that the reduced hessian never has more than one non positive eigenvalue usually this strategy has been implemented by permitting to delete constraints only at stationary points in a general inertia controlling method constraints may be deleted at non stationary points a null space method for dense quadratic programming is presented in which only one triangular system has to be solved at each iteration for computing the search direction this method takes advantage of previously developed recurrence formulas for updating the search direction when the working set changes

gauge transformations of spinors within a clifford algebraic structure algebraic spinors can be defined as minimal left ideals of clifford algebras we consider gauge transformations which are two sided equivalence transformations of a complete algebra including the spinors these transformations of the spinors introduce new interaction terms which appear hard to interpret we establish algebraic theorems which allow these new interaction terms to be evaluated and use these ideas to provide a new formulation of glashow s electroweak interactions of leptons the theorems also lead us to propose a new clifford algebraic definition of spinors based on nilpotents rather than idempotents

on using lp to collision detection between a manipulator arm and surrounding obstacles abstract this paper is concerned with two linear programming lp models for the detection of a collision between a manipulator arm and its surrounding obstacles on the basis of a real case study in particular the first model finds the intersections between two convex polyhedra while the second one finds the intersections between suitable representations of the objects a comparison between the two approaches is presented on the basis of experimental data 9200 test cases have been analyzed

new insertion and postoptimization procedures for the traveling salesman problem this paper describes a new insertion procedure and a new postoptimization routine for the traveling salesman problem the combination of the two methods results in an efficient algorithm genius which outperforms known alternative heuristics in terms of solution quality and computing time

a search algorithm for motion planning with six degrees of freedom abstract the motion planning problem is of central importance to the fields of robotics spatial planning and automated design in robotics we are interested in the automatic synthesis of robot motions given high level specifications of tasks and geometric models of the robot and obstacles the movers problem is to find a continuous collision free path for a moving object through an environment containing obstacles we present an implemented algorithm for the classical formulation of the three dimensional movers problem given an arbitrary rigid polyhedral moving object p with three translational and three rotational degrees of freedom find a continuous collision free path taking p from some initial configuration to a desired goal configuration this paper describes an implementation of a complete algorithm at a given resolution for the full six degree of freedom movers problem the algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six dimensional configuration space called c space the c space obstacles which characterize the physically unachievable configurations are directly represented by six dimensional manifolds whose boundaries are five dimensional c surfaces by characterizing these surfaces and their intersections collision free paths may be found by the closure of three operators which i slide along five dimensional level c surfaces parallel to c space obstacles ii slide along one to four dimensional intersections of level c surfaces and iii jump between six dimensional obstacles these operators are employed by a best first search algorithm in c space we will discuss theoretical properties of the algorithm including completeness at a resolution this paper describes the heuristic search with particular emphasis on the heuristic strategies that evaluate local geometric information at the heart of this paper lie the design and implementation of these strategies for planning paths along level c surfaces and their intersection manifolds and for reasoning about motions with three degrees of rotational freedom the problems of controlling the interaction of these strategies and of integrating diverse local experts for geometric reasoning provide an interesting application of search to a difficult domain with significant practical implications the representations and algorithms we develop impact many geometric planning problems and extend to cartesian manipulators with six degrees of freedom

algebraic and dirac hestenes spinors and spinor fields almost all presentations of dirac theory in first or second quantization in physics and mathematics textbooks make use of covariant dirac spinor fields an exception is the presentation of that theory first quantization offered originally by hestenes and now used by many authors there a new concept of spinor field as a sum of nonhomogeneous even multivectors fields is used however a careful analysis detailed below shows that the original hestenes definition cannot be correct since it conflicts with the meaning of the fierz identities in this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by hestenes in order to do that we give a preliminary definition of algebraic spinor fields asf and dirac hestenes spinor fields dhsf on minkowski space time as some equivalence classes of pairs u u where u is a spinorial frame field and u is an appropriate sum of multivectors fields to be specified below the necessity of our definitions are shown by a careful analysis of possible formulations of dirac theory and the meaning of the set of fierz identities associated with the bilinear covariants on minkowski space time made with asf or dhsf we believe that the present paper clarifies some misunderstandings past and recent appearing on the literature of the subject it will be followed by a sequel paper where definitive definitions of asf and dhsf are given as appropriate sections of a vector bundle called the left spin clifford bundle the bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary riemann cartan space times the present paper contains also appendixes a e which exhibits a truly useful collection of results concerning the theory of clifford algebras including many tricks of the trade necessary for the intelligibility of the text

using a tsp heuristic for routing order pickers in warehouses in this paper we deal with the sequencing and routing problem of order pickers in conventional multi parallel aisle warehouse systems for this np hard steiner travelling salesman problem tsp exact algorithms only exist for warehouses with at most three cross aisles while for other warehouse types literature provides a selection of dedicated construction heuristics we evaluate to what extent reformulating and solving the problem as a classical tsp leads to performance improvements compared to existing dedicated heuristics we report average savings in route distance of up to 47 when using the lkh lin kernighan helsgaun tsp heuristic additionally we examine if combining problem specific solution concepts from dedicated heuristics with high quality local search features could be useful lastly we verify whether the sophistication of state of the art local search heuristics is necessary for routing order pickers in warehouses or whether a subset of features suffices to generate high quality solutions

genetic algorithm for the personnel assignment problem with multiple objectives the assignment problem is a well known graph optimization problem defined on weighted bipartite graphs the objective of the standard assignment problem is to maximize the summation of the weights of the matched edges of the bipartite graph in the standard assignment problem any node in one partition can be matched with any node in the other partition without any restriction in this paper variations of the standard assignment problem are defined with matching constraints by introducing structures in the partitions of the bipartite graph and by defining constraints on these structures according to the first constraint the matching between the two partitions should respect the hierarchical ordering constraints defined by forest and level graph structures produced by using the nodes of the two partitions respectively in order to define the second constraint the nodes of the partitions of the bipartite graph are distributed into mutually exclusive sets the set restriction constraint enforces the rule that in one of the partitions all the elements of each set should be matched with the elements of a set in the other partition even with one of these constraints the assignment problem becomes an np hard problem therefore the extended assignment problem with both the hierarchical ordering and set restriction constraints becomes an np hard multi objective optimization problem with three conflicting objectives namely minimizing the numbers of hierarchical ordering and set restriction violations and maximizing the summation of the weights of the edges of the matching genetic algorithms are proven to be very successful for np hard multi objective optimization problems in this paper we also propose genetic algorithm solutions for different versions of the assignment problem with multiple objectives based on hierarchical and set constraints and we empirically show the performance of these solutions

reliability evaluation and optimal design in heterogeneous multi state series parallel systems this paper addresses the heterogeneous redundancy allocation problem in multi state series parallel reliability structures with the objective to minimize the total cost of system design satisfying the given reliability constraint and the consumer load demand the demand distribution is presented as a piecewise cumulative load curve and each subsystem is allowed to consist of parallel redundant components of not more than three types the system uses binary capacitated components chosen from a list of available products to provide redundancy so as to increase system performance and reliability the components are characterized by their feeding capacity reliability and cost a system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of constituent components a binomial probability based method to compute exact system reliability index is suggested to analyze the problem and suggest an optimal near optimal system structure an ant colony optimization algorithm has been presented the solution approach consists of a series of simple steps as used in early ant colony optimization algorithms dealing with other optimization problems and offers straightforward analysis four multi state system design problems have been solved for illustration two problems are taken from the literature and solved to compare the algorithm with the other existing methods the other two problems are based upon randomly generated data the results show that the method can be appealing to many researchers with regard to the time efficiency and yet without compromising over the solution quality

fast collision detection in four dimensional space abstract in this paper we consider the collision detection problem for general objects a four dimensional approach is proposed for this problem which detects exactly and in one step when and where the earliest collison will occur between the objects this is done by using four dimensional sets to represent the objects in both space and time the problem is then posed as a nonlinear programming problem the algorithm can handle the case of a rigid body moving on a general path in r 2 or r 3 with simultaneous translation and rotation simulation results on some example problems are given and show that the algorithm is superior to those available in the literature

zero order tsk type fuzzy system learning using a two phase swarm intelligence algorithm this paper proposes zero order takagi sugeno kang tsk type fuzzy system learning using a two phase swarm intelligence algorithm tpsia the first phase of tpsia learns fuzzy system structure and parameters by on line clustering aided ant colony optimization aco phase two aims to further optimize all of the free parameters in the fuzzy system using particle swarm optimization pso in clustering aided aco caco fuzzy system structure is learned through on line clustering once a new rule is generated by clustering the consequent is selected from a discrete set of candidate values by aco in aco the path of an ant is regarded as a combination of consequent values selected from every rule caco helps to locate good initial fuzzy systems for subsequent phase learning in phase two initial particles in pso are randomly generated according to the best solution found by caco all free parameters in the designed fuzzy system are optimally tuned by pso simulations on fuzzy control of three nonlinear plants are conducted to verify tpsia performance comparisons with other learning algorithms demonstrate tpsia performance

a recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes for a given pair of finite point setsp andq in some euclidean space we consider two problems problem 1 of finding the minimum euclidean norm point in the convex hull ofp and problem 2 of finding a minimum euclidean distance pair of points in the convex hulls ofp andq we propose a finite recursive algorithm for these problems the algorithm is not based on the simplicial decomposition of convex sets and does not require to solve systems of linear equations

hybrid parallel tempering and simulated annealing method in this paper we propose a new hybrid scheme of parallel tempering and simulated annealing hybrid pt sa within the hybrid pt sa scheme a composite system with multiple conformations is evolving in parallel on a temperature ladder with various transition step sizes the simulated annealing sa process uses a cooling scheme to decrease the temperature values in the temperature ladder to the target temperature the parallel tempering pt scheme is employed to reduce the equilibration relaxation time of the composite system at a particular temperature ladder configuration in the sa process the hybrid pt sa method reduces the waiting time in deep local minima and thus leads to a more efficient sampling capability on high dimensional complicated objective function landscapes compared to the approaches pt and parallel sa with the same temperature ladder transition step sizes and cooling scheme parallel sa configurations our preliminary results obtained with the hybrid pt sa method confirm the expected improvements in simulations of several test objective functions including the rosenbrock s function and the rugged funnel like function and several instantiations of the traveling salesman problem the hybrid pt sa may have slower convergence than genetic algorithms ga with good crossover heuristics but it has the advantage of tolerating bad initial values and displaying robust sampling capability even in the absence of additional information moreover the hybrid pt sa has natural parallelization potential

a semi smooth newton method for a special piecewise linear system with application to positively constrained convex quadratic programming in this paper a special piecewise linear system is studied it is shown that under a mild assumption the semi smooth newton method applied to this system is well defined and the method generates a sequence that converges linearly to a solution besides we also show that the generated sequence is bounded for any starting point and a formula for any accumulation point of this sequence is presented as an application we study the convex quadratic programming problem under positive constraints the numerical results suggest that the semi smooth newton method achieves accurate solutions to large scale problems in few iterations

a new penalty function algorithm for convex quadratic programming in this paper we develop an exterior point algorithm for convex quadratic programming using a penalty function approach each iteration in the algorithm consists of a single newton step followed by a reduction in the value of the penalty parameter the points generated by the algorithm follow an exterior path that we define convergence of the algorithm is established the proposed algorithm was motivated by the work of al sultan and murty on nearest point problems a special quadratic program a preliminary implementation of the algorithm produced encouraging results in particular the algorithm requires a small and almost constant number of iterations to solve the small to medium size problems tested

an effective implementation of the lin kernighan traveling salesman heuristic abstract this paper describes an implementation of the lin kernighan heuristic one of the most successful methods for generating optimal or near optimal solutions for the symmetric traveling salesman problem tsp computational tests show that the implementation is highly effective it has found optimal solutions for all solved problem instances we have been able to obtain including a 13 509 city problem the largest non trivial problem instance solved to optimality today

a critical index algorithm for nearest point problems on simplicial cones we consider the linear complementarity problem q m in whichm is a positive definite symmetric matrix of ordern this problem is equivalent to a nearest point problem b in which a 1 a n is a basis for r n b is a given point in r n and it is required to find the nearest point in the simplicial cone pos tob we develop an algorithm for solving the linear complementarity problem q m or the equivalent nearest point problem b computational experience in comparison with an existing algorithm is presented

spatial planning a configuration space approach this paper presents algorithms for computing constraints on the position of an object due to the presence of ther objects this problem arises in applications that require choosing how to arrange or how to move objects without collisions the approach presented here is based on characterizing the position and orientation of an object as a single point in a configuration space in which each coordinate represents a degree of freedom in the position or orientation of the object the configurations forbidden to this object due to the presence of other objects can then be characterized as regions in the configuration space called configuration space obstacles the paper presents algorithms for computing these configuration space obstacles when the objects are polygons or polyhedra

clifford algebra notes on the spinor metric and lorentz poincare and conformal groups a particular normalization for the set of basis elements i of the complex clifford algebrasc p q is motivated and defined by demanding that the physical bispinor densities i i be real this condition referred to here as dirac normalization also necessitates the introduction of the spinor metric and the solution of the metric conditions is given for arbitrary p q when n p q is even the metric is unique and when n is odd there are two distinct metrics then the dirac normalization preserving automorphism group of the basis is explored this is also the group of transformations leaving the spinor metric invariant in particular the physically important cases of the lorentz poincare and conformal groups are sought as subgroups of the automorphism group as expected it is found that the lorentz group is always contained in the automorphism group however it is found that the poincare and conformal groups are contained only in the cases where n is even and q is odd furthermore when n is odd these groups may be found in the full isomorphism group but only for one of the two possible spinor metrics possible physical implications of these results are discussed

iterative two step genetic algorithm based method for efficient polynomial b spline surface reconstruction surface reconstruction is a very challenging problem arising in a wide variety of applications such as cad design data visualization virtual reality medical imaging computer animation reverse engineering and so on given partial information about an unknown surface its goal is to construct to the extent possible a compact representation of the surface model in most cases available information about the surface consists of a dense set of either organized or scattered 3d data points obtained by using scanner devices a today s prevalent technology in many reverse engineering applications in such a case surface reconstruction consists of two main stages 1 surface parameterization and 2 surface fitting both tasks are critical in order to recover surface geometry and topology and to obtain a proper fitting to data points they are also pretty troublesome leading to a high dimensional nonlinear optimization problem in this context present paper introduces a new method for surface reconstruction from clouds of noisy 3d data points our method applies the genetic algorithm paradigm iteratively to fit a given cloud of data points by using strictly polynomial b spline surfaces genetic algorithms are applied in two steps the first one determines the parametric values of data points the later computes surface knot vectors then the fitting surface is calculated by least squares through either svd singular value decomposition or lu methods the method yields very accurate results even for surfaces with singularities concavities complicated shapes or nonzero genus six examples including open semi closed and closed surfaces with singular points illustrate the good performance of our approach our experiments show that our proposal outperforms all previous approaches in terms of accuracy and flexibility

convex hull representations of models for computing collisions between multiple bodies abstract in this paper we consider a collision detection problem that frequently arises in the field of robotics given a set of bodies with their initial positions and trajectories we wish to identify the first collision that occurs between any two bodies or to determine that none exists for the case of bodies having linear trajectories we construct a convex hull representation of the integer programming model of s z selim and h a almohamad european journal of operational research 119 1 1999 121 129 and compare the relative effectiveness in solving this problem via the resultant linear program we also extend this analysis to model a situation in which bodies move along piecewise linear trajectories possibly rotating at the end of each linear segment for this case we again compare an integer programming approach with its linear programming convex hull representation and exhibit the effectiveness of solving a sequence of mathematical programs for each time segment over a global programming scheme which considers all segments at once we provide computational results to illustrate the effect of various numbers of bodies present in the collision scenarios as well as the times at which the first collision occurs

optimized annealing of traveling salesman problem from the nth nearest neighbor distribution abstract we report a new statistical general property in traveling salesman problem that the n th nearest neighbor distribution of optimal tours verifies with very high accuracy an exponential decay as a function of the order of neighbor n defining the energy function as deviation from this exponential decay which is different to the tour length d in normal annealing processes we propose a distinct highly optimized annealing scheme which is performed in space and d space by turns the simulation results of some standard traveling salesman problems in tsplib95 are presented it is shown that our annealing recipe is superior to the canonical simulated annealing

the multi criteria minimum spanning tree problem based genetic algorithm abstract minimum spanning tree mst problem is of high importance in network optimization and can be solved efficiently the multi criteria mst mc mst is a more realistic representation of the practical problems in the real world but it is difficult for traditional optimization technique to deal with in this paper a non generational genetic algorithm ga for mc mst is proposed to keep the population diversity this paper designs an efficient crossover operator by using dislocation a crossover technique and builds a niche evolution procedure where a better offspring does not replace the whole or most individuals but replaces the worse ones of the current population to evaluate the non generational ga the solution sets generated by it are compared with solution sets from an improved algorithm for enumerating all pareto optimal spanning trees the improved enumeration algorithm is proved to find all pareto optimal solutions and experimental results show that the non generational ga is efficient

polynomial time approximation schemes for euclidean traveling salesman and other geometric problems we present a polynomial time approximation scheme for euclidean tsp in fixed dimensions for every fixed c 1 and given any n nodes in r 2 a randomized version of the scheme finds a 1 1 c approximation to the optimum traveling salesman tour in o n log n o c time when the nodes are in r d the running time increases to o n log n o d c d 1 for every fixed c d the running time is n poly log n that is nearly linear in n the algorithmm can be derandomized but this increases the running time by a factor o n d the previous best approximation algorithm for the problem due to christofides achieves a 3 2 aproximation in polynomial time we also give similar approximation schemes for some other np hard euclidean problems minimum steiner tree k tsp and k mst the running times of the algorithm for k tsp and k mst involve an additional multiplicative factor k the previous best approximation algorithms for all these problems achieved a constant factor approximation we also give efficient approximation schemes for euclidean min cost matching a problem that can be solved exactly in polynomial time all our algorithms also work with almost no modification when distance is measured using any geometric norm such as e p for p 1 or other minkowski norms they also have simple parallel i e nc implementations

collision detection of a moving polygon in the presence of polygonal obstacles in the plane this paper presents a new approach for the following collision detection problem in the plane let a simple polygon p rotate at a center spl ogr with constant angular velocity spl omega and translate towards a set of polygonal obstacles s with constant velocity spl nu given p and s as well as their initial positions and given also the velocities of p determine whether or not p will collide with any element of s and report the collided elements of s if collisions occurred an o mn worst case optimal algorithm is proposed to solve this problem where n is the number of vertices of p and m is the number of vertices of the obstacles in s

distance estimation and collision prediction for on line robotic motion planning abstract an efficient method for computing the minimum distance and predicting collisions between moving objects is presented this problem has been incorporated in the framework of an in line motion planning algorithm to satisfy collision avoidance between a robot and moving objects modelled as convex polyhedra in the beginning the deterministic problem where the information about the objects is assumed to be certain is examined if instead of the euclidean norm l 1 or l norms are used to represent distance the problem becomes a linear programming problem the stochastic problem is formulated where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles two problems are considered first filtering of the distance between the robot and the moving object at the present time second prediction of the minimum distance in the future in order to predict the collision time

structure of spin groups associated with degenerate clifford algebras clifford algebras over finite dimensional vector spaces endowed with degenerate quadratic form contain a nontrivial two sided nilpotent ideal the jacobson radical generated by the orthogonal complement of such spaces thus they cannot be faithfully represented by matrix algebras following the theory of spin representations of classical clifford algebras the left regular spin representations of these degenerate algebras can be studied in suitably constructed left ideals first structure of the group of units of such algebras is examined for a quadratic form of arbitrary rank it is shown to be a semidirect product of a group generated by the radical and the group of units of a maximal nondegenerate clifford subalgebra next in the special case of corank 1 clifford pin and spin groups are defined an their structures are described as an example a galilei clifford algebra over the galilei space time is considered a covering theorem is then proved analogous to the one well known in the theory of