a variable grouping based genetic algorithm for large scale integer programming to effectively reduce the dimensionality of search space this paper proposes a variable grouping based genetic algorithm vgga for large scale integer programming problems ips the vgga first groups ip s decision variables based on the optimal solution to the ip s continuous relaxation problem and then applies a standard genetic algorithm ga to the subproblem for each group of variables we compare the vgga with the standard ga and gas based on even variable grouping by applying them to solve randomly generated convex quadratic knapsack problems and integer knapsack problems numerical results suggest that the vgga is superior to the standard ga and gas based on even variable grouping both on computation time and solution quality

an interactive fuzzy satisficing method for multiobjective 0 1 programming problems with fuzzy numbers through genetic algorithms with double strings abstract in this paper by considering the experts vague or fuzzy understanding of the nature of the parameters in the problem formulation process multiobjective 0 1 programming problems involving fuzzy numbers are formulated using the a level sets of fuzzy numbers the corresponding nonfuzzy programming problem is introduced the fuzzy goals of the decision maker dm for the objective functions are quantified by eliciting the corresponding linear membership functions through the introduction of an extended pareto optimality concept if the dm specifies the degree and the reference membership values the corresponding extended pareto optimal solution can be obtained by solving the augmented minimax problems through genetic algorithms with double strings then an interactive fuzzy satisficing method for deriving a satisficing solution for the dm efficiently from an extended pareto optimal solution set is presented an illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method

distribution properties of compressing sequences derived from primitive sequences over bbz p e let z pe be the integer residue ring with odd prime p and integer e 2 any sequence a over z pe has a unique p adic expansion a a0 a1 p ae 1 pe 1 where ai can be regarded as a sequence over z p for 0 i e 1 let f x be a strongly primitive polynomial over z pe and a b be two primitive sequences generated by f x over z pe assume x0 xe 1 xe 1 x0 xe 2 is an e variable function over z p with the monomial p 1 2 xe 2 p 1 x1 p 1 not pearing in the expression of x0 x1 xe 2 it is shown that if there exists an s z p such that a0 t ae 1 t s if and only if b0 t be 1 t s for all nonnegative t with i 0 where is an m sequence determined by f x and a0 then a b this implies that for compressing sequences derived from primitive sequences generated by f x over z pe single element distribution is unique on all positions t with t 0 in particular when x0 x1 xe 2 0 it is a completion of the former result on the uniqueness of distribution of element 0 in highest level sequences

isometries for the induced c norm on square matrices and some related results abstract let fn be the linear space of column vectors with n coordinates over f r or c denote by gp n the group of n n generalized permutation matrices i e matrices with exactly one nonzero entry with magnitude 1 in each row and column given a nonzero vector c c1 cn t fn define the c norm of x x1 xn t fn by x c max c t p x p gp n and the induced c norm of a fn n by a c max a y c y c 1 we characterize the isometries for induced c norms to achieve our goal we study the geometric properties of fn n and obtain some inequalities related to the induced c norm as by products these results are of independent interest

genetic algorithms with double strings for 0 1 programming problems abstract in this paper genetic algorithms with double strings for 0 1 knapsack problems are first revisited together with some modifications and computational experiments then the genetic algorithms with double strings for 0 1 knapsack problems are extended to deal with more general 0 1 programming problems involving both positive and negative coefficients in the constraints especially new decoding algorithms for double strings using reference solutions both without and with the reference solution updating procedure are proposed so that each of individuals is decoded to the corresponding feasible solution for the general 0 1 programming problems the efficiency and effectiveness of the proposed methods are investigated by comparing them with a branch and bound method with respect to the accuracy of an approximate solution and the processing time through a number of numerical experiments

l subinvariant norms abstract let l be a compact semigroup of operators on f n where f r or f c a norm p on f n is said to be l subinvariant if p s x p x for all s l x f n if l is a closed subgroup of unitary operators on f n the concept of l subinvariant norm coincides with the concept of l invariant norm studied in c k li n k tsing linear algebra appl 150 1991 179 194 in this paper some basic properties of l subinvariant norms are studied and several results of li and tsing c k li n k tsing linear algebra appl 150 1991 179 194 on group invariant norms are extended to semigroup subinvariant norms as an application necessary and sufficient conditions on a pair of vectors x y f n are obtained such that p x p y holds for each weakly monotonic norm p

the isometries of certain maximum norms abstract let a 1 a m be nonsingular n n matrices over f r or c and let 1 p j for j 1 m we characterize the linear isometries for the norm n on f n defined by n x max l p j a j x 1 j m where l p y denotes the l p norm of y f n as an application we study the conditions on matrices a 1 a m for which n is absolute or a symmetric gauge function

certain isometries on rn abstract let r n be the linear space of all real column vectors with n coordinates given x x 1 x n t r n its p k norm is defined by x p k max x i 1 p x i k p 1 p 1 i 1 k n where k is a positive integer satisfying 1 k n and p satisfies 1 p whereas its c norm is defined by x c max c t px p is a generalized permutation matrix for any nonzero c r n this paper characterizes the isometries for c norms and p k norms some related results are also considered

lieb functions and m positivity of norms abstract some properties of 2 or 3 positive maps on matrix spaces are proved where special attention is given to norms it is shown that for a locally bounded function the definition of a lieb function can be simplified somewhat unitarily invariant norms are characterized by a certain monotonicity property the set of 2 positive numerical radii is described and an example of a 3 positive norm is obtained

duality between some linear preserver problems ii isometries with respect to c special norms and matrices with fixed singular values let fm n m n denote the linear space of all m n complex or real matrices according as f c or r let c c1 cm 0 be such that c1 cm 0 the c spectral norm of a matrix a fm n is the quantity a c i imci i a where 1 a m a are the singular values of a let d d1 dm 0 where d1 dm 0 we consider the linear isometries between the normed spaces fm n c and fm n d and prove that they are dual transformations of the linear operators which map l d onto l c where l c x fm n x has singular values c1 cm

solving the knapsack problem with imprecise weight coefficients using genetic algorithms this paper investigates solving the knapsack problem with imprecise weight coefficients using genetic algorithms this work is based on the assumption that each weight coefficient is imprecise due to decimal truncation or coefficient rough estimation by the decision maker to deal with this kind of imprecise data fuzzy sets provide a powerful tool to model and solve this problem we investigate the possibility of using genetic algorithms in solving the fuzzy knapsack problem without defining membership functions for each imprecise weight coefficient the proposed approach simulates a fuzzy number by distributing it into some partition points we use genetic algorithms to evolve the values in each partition point so that the final values represent the membership grade of a fuzzy number the empirical results show that the proposed approach can obtain very good solutions within the given bound of each imprecise weight coefficient than the fuzzy knapsack approach the fuzzy genetic algorithm concept approach is different but gives better results than the traditional fuzzy approach

a unified method for a class of convex separable nonlinear knapsack problems abstract in this paper a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems which are characterized by positive marginal cost pmc and increasing marginal loss cost ratio imlcr by taking advantage of these two characteristics the proposed algorithm is applicable to the problem with equality or inequality constraints in contrast to the methods based on karush kuhn tucker kkt conditions our approach has linear computation complexity numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems

interactive fuzzy programming for multi level 0 1 programming problems through genetic algorithms abstract in this paper we propose interactive fuzzy programming for multi level 0 1 programming problems through genetic algorithms our method is supposed to apply to hierarchical decision problems in which decision making at each level is sequential from upper to lower level and decision makers are essentially cooperative after determining the fuzzy goals of the decision makers at all levels a satisfactory solution is derived efficiently by updating the satisfactory degrees of the decision makers at the upper level with considerations of overall satisfactory balance among all levels an illustrative numerical example for three level 0 1 programming problems is provided to demonstrate the feasibility of the proposed method

g invariant norms and g c radii abstract let v be a finite dimensional inner product space over f r or c and let g be a closed subgroup of the group of unitary operators on v a norm or a seminorm on v is said to be g invariant if g x x for all g g x v the concept of g invariant norm specializes to many interesting particular cases such as the absolute norms on f n symmetric gauge functions on r n unitarily invariant norms on f m n etc which are of wide research interest in this paper we study the general properties of g invariant norms our main strategy is to study g invariant norms via the g c radius rg c on v defined by r g c x max x g c g g where c v it is shown that the g c radii are very important g invariant seminorms because every g invariant norm or seminorm admits a representation in terms of them as a result one may focus attention on g c radii in order to get results on g invariant norms we study the norm properties of g c radii and obtain various results relating g invariant norms and g c radii the linear operators on v that preserve g invariant norms g invariant seminorms or g c radii are also investigated several open questions are mentioned

linear maps relating different unitary similarity orbits or different generalized numerical ranges abstract let m be the complex linear space m n of n n complex matrices or the real linear space h n of n n hermitian matrices for c m its unitary similarity orbit is the set u c ucu u unitary and its circular unitary similarity orbit is the set v c x f 1 x u c where f is the scalar field c or r according as m m n or m h n related to u c and v c are the c numerical range and the c numerical radius of a m defined by w c a tr ax x u c and r c a max z z w c a respectively let c d h n we study the linear operators t on m satisfying one of the following properties i w d t a w c a for all a m ii r d t a r c a for all a m iii t u d u c iv t v d v c in particular we determine the conditions on c and d for the existence of a linear operator t on m satisfying any one of the conditions i iv and characterize such an operator if it exists

compression mappings on primitive sequences over z p sup e let z p sup e be the integer residue ring with odd prime p spl ges 5 and integer e spl ges 2 for a sequence a over z p sup e there is a unique p adic expansion a a sub 0 a spl middot p a sub e 1 spl middot p sup e 1 where each a sub i is a sequence over 0 1 p 1 and can be regarded as a sequence over the finite field gf p naturally let f x be a primitive polynomial over z p sup e and g f x p sup e the set of all primitive sequences generated by f x over z p sup e set spl phi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 1 x sub 0 x sub 1 x sub e 2 spl psi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 2 x sub 0 x sub 1 x sub e 2 where spl eta sub e 2 1 and spl eta sub e 2 2 are arbitrary functions of e 1 variables over gf p and 2 spl les k spl les p 1 then the compression mapping spl phi sub e 1 g f x p sup e spl rarr gf p sup spl infin a spl rarr spl phi sub e 1 a sub 0 a sub e 1 is injective that is a b if and only if spl phi sub e 1 a sub 0 a sub e 1 spl phi sub e 1 b sub 0 b sub e 1 for a b spl isin g f x p sup e furthermore if f x is a strongly primitive polynomial over z p sup e then spl phi sub e 1 a sub 0 a sub e 1 spl psi sub e 1 b sub 0 b sub e 1 if and only if a b and spl phi sub e 1 x sub 0 x sub e 1 spl psi sub e 1 x sub 0 x sub e 1 for a b spl isin g f x p sup e

a class of rough multiple objective programming and its application to solid transportation problem this paper establishes a rough multiple objective programming model for a solid transportation problem furthermore a general model for rough multiple objective programming problem is presented properties of the feasible and efficient solutions of rough multiple objective programming problems are investigated in addition compromise solutions are obtained by using the interactive fuzzy satisfying method to solve the rough multiple objective solid transportation problem the rough simulation based genetic algorithm is proposed in which the rough simulation is embedded into the genetic algorithm finally an application of the solid transportation problem at xiluodu hydropower station is provided as an illustration

permutation invariant norms abstract a norm or seminorm on on r n is permutation invariant if px x for all n n permutation matrices p and for all x r n we present a systematic study of permutation invariant seminorms their relations with other types of norms on matrices are discussed in addition we consider a special class of permutation invariant seminorms the c radii defined and denoted by r c x max c t px p a permutation for any given c r n it is shown that r c are the building blocks of all permutation invariant seminorms if the entries of c are not all equal and their sum is not 0 then r c is a norm on r n for such r c we study their norm properties and characterize their isometry groups

on the distinctness of binary sequences derived from primitive sequences modulo square free odd integers let m be a square free odd integer and z m the integer residue ring modulo m this paper studies the distinctness of primitive sequences over z m modulo 2 recently for the case of m pq a product of two distinct prime numbers p and q the problem has been almost completely solved as for the case that m is a product of more prime numbers the problem has been quite resistant to proof in this paper a partial proof is given by showing that a class of primitive sequences of order 2n 1 over z m is distinct modulo 2 where n is a positive integer besides as an independent interest this paper also involves two distribution properties of primitive sequences over z m which are related closely to our main results

on the distinctness of modular reductions of maximal length sequences modulo odd prime powers we discuss the distinctness problem of the reductions modulo m of maximal length sequences modulo powers of an odd prime p where the integer m has a prime factor different from p for any two different maximal length sequences generated by the same polynomial we prove that their reductions modulo m are distinct in other words the reduction modulo m of a maximal length sequence is proved to contain all the information of the original sequence

fuzzy programming for multiobjective 0 1 programming problems through revised genetic algorithms abstract recently genetic algorithms gas a new learning paradigm that models a natural evolution mechanism have received a great deal of attention regarding their potential as optimization techniques for solving combinatorial optimization problems in this paper we focus on multiobjective 0 1 programming problems as a generalization of the traditional single objective ones by considering the imprecise nature of human judgements we assume that the decision maker may have fuzzy goal for each of the objective functions after eliciting the linear membership functions through the interaction with the decision maker we adopt the fuzzy decision of bellman and zadeh or minimum operator for combining them in order to investigate the applicability of the conventional gas for the solution of the formulated problems a lot of numerical simulations are performed by assuming several genetic operators then instead of using the penalty function for treating the constraints we propose three types of revised gas which generate only feasible solutions illustrative numerical examples demonstrate both feasibility and efficiency of the proposed methods

operation planning of district heating and cooling plants through genetic algorithms for nonlinear 0 1 programming abstract in recent years the operation planning of district heating and cooling plants has been arousing interest as a result of development of cooling load prediction methods for district heating and cooling systems in this paper we formulate an operation planning problem of a district heating and cooling plant as a nonlinear 0 1 programming problem realizing that there does not exist an efficient exact solution method and the problem involves hundreds of variables we propose an approximate solution method using genetic algorithms for the formulated nonlinear 0 1 programming problem furthermore we investigate the feasibility and effectiveness of the proposed method for an operation planning problem of an actual district heating and cooling plant

an effective genetic algorithm approach to large scale mixed integer programming problems abstract to effectively reduce the search space of gas on large scale mip problems this paper proposed a new variable grouping method based on structure properties of a problem taking the capacity expansion and technology selection problem as a typical example this method groups problem s decision variables over time period and machine line based on this new variable grouping method we developed a variable grouping based genetic algorithm according to problem s structure properties vgga s we tested the performance of vgga s by applying it on the capacity expansion and technology selection problem numerical experiments suggested that vgga s outperforms the standard ga and variable grouping based gas without considering problem s structure properties both on computation time and solution quality although vgga s is proposed based on structure properties of a specific mip problem it is a general optimization algorithm and theoretically applicable to other large scale mip problems

fuzzy multicriteria integer programming via fuzzy generalized networks recent advances in network based mathematical programming methods have given rise to practical economical and computationally efficient solution methodologies for truly large scale problems today a wide variety of real world problems have been solved in such a manner even though on the surface they do not have an apparent network structure one type of network the generalized network has been successfully applied to solve large scale zero one or mixed integer mathematical programming models however one drawback to such approaches is their typical focus on but a single objective the purpose of this paper then is to document the results of an ongoing research effort which combines the generalized network concept with the technique of fuzzy programming the resultant hybrid approach has been found to provide a computationally efficient approach to multi objective zero one or integer programming problems

some aspects of the theory of norms abstract let v be a finite dimensional vector space motivated by theory or applications one might want to consider different kinds of norms on v in this paper we discuss some results and problems involving different classes of norms on a vector space studied by this author in the past few years the paper consists of five sections section 1 concerns the conditions on two vectors x y v satisfying x y for all in a certain class of norms section 2 concerns the isometry groups of g invariant norms i e norms that satisfy g x x for all x v and for all g g where g is a group of unitary orthogonal operators on v section 3 concerns g invariant norms that satisfy some special properties section 4 concerns the best approximation s x 0 t of y where y t v with respect to different kinds of norms additional open problems topics and references are mentioned in section 5

an approximate dynamic programming approach to multidimensional knapsack problems we present an approximate dynamic programming adp approach for the multidimensional knapsack problem mkp we approximate the value function a using parametric and nonparametric methods and busing a base heuristic we propose a new heuristic which adaptively rounds the solution of the linear programming relaxation our computational study suggests athe new heuristic produces high quality solutions fast and robustly bstate of the art commercial packages like cplex require significantly larger computational time to achieve the same quality of solutions c the adp approach using the new heuristic competes successfully with alternative heuristic methods such as genetic algorithms dthe adp approach based on parametric and nonparametric approximations while producing reasonable solutions is not competitive overall this research illustrates that the base heuristic approach is a promising computational approach for mkps worthy of further investigation

the isometries and the g invariance of certain seminorms abstract let f be the field of real or complex numbers and let g be a subgroup of the general linear group gl n f if a is an m n matrix over f let a be the seminorm on f n defined by x a ax for all x f n in this paper we characterize the linear isometries for the seminorm a and study the conditions on a for which a is g invariant that is sx a x a for all x f n and all s g as a special case we describe all matrices a for which a is absolute or a symmetric gauge function

duality between some linear preserver problems iii c spectral norms and skew symmetric matrices with fixed singular values abstract let f denote either the complex field c or the real field r let v be sn f or kn f the vector spaces of all n n symmetric and skew symmetric matrices respectively over f for c c1 cn 0 with c1 cn 0 the c spectral norm of a matrix a v is the quantity a c i l n c i i a where 1 a n a are the singular values of a let d d1 dn 0 with d1 dn 0 we study the linear isometries between the normed spaces v c and v d by using the fact that they are dual transformations of the linear operators which map d onto c where c x v x has singular values c 1 c n it is shown that such isometries and hence their dual transformations exist if and only if c and d are scalar multiples of each other in such case we completely determine the structure of such isometries and prove that they and their dual transformations belong to a same class of operators in the proof we obtain characterizations of the extreme points of the unit ball in v for different cases with respect to c which is of independent interest

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

solving 0 1 knapsack problems based on amoeboid organism algorithm the 0 1 knapsack problem is an open issue in discrete optimization problems which plays an important role in real applications in this paper a new bio inspired model is proposed to solve this problem the proposed method has three main steps first the 0 1 knapsack problem is converted into a directed graph by the network converting algorithm then for the purpose of using the amoeboid organism model the longest path problem is transformed into the shortest path problem finally the shortest path problem can be well handled by the amoeboid organism algorithm numerical examples are given to illustrate the efficiency of the proposed model

arithmetic crosscorrelations of feedback with carry shift register sequences an arithmetic version of the crosscorrelation of two sequences is defined generalizing mandelbaum s 1967 arithmetic autocorrelations large families of sequences are constructed with ideal vanishing arithmetic crosscorrelations these sequences are decimations of the 2 adic expansions of rational numbers p q such that 2 is a primitive root module q

a solution to the optimal power flow using genetic algorithm optimal power flow opf is one of the main functions of power generation operation and control it determines the optimal setting of generating units it is therefore of great importance to solve this problem as quickly and accurately as possible this paper presents the solution of the opf using genetic algorithm technique this paper proposes a new methodology for solving opf this methodology is divided into two parts the first part employs the genetic algorithm ga to obtain a feasible solution subject to desired load convergence while the other part employs ga to obtain the optimal solution the main goal of this paper is to verify the viability of using genetic algorithm to solve the opf problem simultaneously composed by the load flow and the economic dispatch problem six buses system are used to highlight the goodness of this solution technique

a multiperiod two echelon multicommodity capacitated plant location problem abstract in this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses we address this problem by means of a formulation as a mixed integer programming problem a lagrangean relaxation is proposed to solve the problem together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems computational tests are provided showing the good performance of this approach for a wide range of problems

further result on distribution properties of compressing sequences derived from primitive sequences over bf z p e let p be an odd prime number e an integer greater than 1 and z pe the integer residue ring modulo pe in this paper we obtain an improved result of the previous paper ieee trans inf theory 56 1 2010 555 563 on distribution properties of compressing sequences derived from primitive sequences over z pe it is shown that two primitive sequences and b generated by a strongly primitive polynomial f x over z pe are the same if there exist s z p and k z p such that the distribution of in their compressing sequences ae 1 a0 ae 2 and be 1 b0 be 2 is coincident at the positions t with t k where x0 xe 2 is an e variable polynomial over z p with the coefficient of xe 2p 1 x1p 1x0p 1 not equal to 1 e p 1 2 and is an m sequence over z p determined by f x and a compared with the previous result this gives a more precise characterization on the positions of a compressing sequence i e of the form ae 1 a0 ae 2 derived from a primitive sequence a over z pe that completely determines a in particular the result is also true for the highest level sequence ae 1 by taking x0 xe 2 0

translation invariant maps and applications in this paper we study translation invariant maps on a linear space a method for estimating quantities induced by such maps is presented applications for differences of operators commutators g contractive maps and gruss type inequalities are also given

on g invariant norms abstract a result of r mathias and horn cf linear algebra appl 142 1990 63 on the representation of the unitarily invariant norm is extended in the context of eaton triples and of real semisimple lie algebras the representation is related to a function criteria for being a norm is given in terms of and the longest element of the underlying finite reflection group in particular for the real simple lie algebras is a norm on its cartan subspace for a given nonzero if and only if 0 where 0 is the longest element of the weyl group this is the case if the weyl group contains id some related results are obtained

partial period distribution of fcsr sequences klapper and goresky 1995 introduced feedback with carry shift register fcsr and presented a significant kind of fcsr sequences that is l sequences they showed that the number of 0s and 1s occurring in one of their periods are equal we discuss the partial period distribution of l sequences and show that when the periods become large the proportion of 1s resp 0s occurring in any of their partial periods approximates 50

an interactive fuzzy satisficing method for large scale multiobjective 0 1 programming problems with fuzzy parameters through genetic algorithms abstract in this paper by considering the experts imprecise or fuzzy understanding of the nature of the parameters in the problem formulation process multiobjective block angular 0 1 programming problems involving fuzzy numbers are formulated using the level sets of fuzzy numbers the corresponding nonfuzzy multiobjective 0 1 programming problem is introduced and an extended pareto optimality concept is defined for the multiobjective 0 1 programming problem the fuzzy goal of the decision maker for each objective function quantified by eliciting the corresponding membership function is considered since the decision maker must select a compromise or satisficing solution from the extended pareto optimal solution set including an infinite number of elements in general an interactive fuzzy satisficing method through genetic algorithms for deriving a satisficing solution for the decision maker from an extended pareto optimal solution set is presented then for fixed and reference membership levels the corresponding extended pareto optimal solution can be obtained by solving a minimax problem with block angular structure in order to solve the minimax problem efficiently we adopt a genetic algorithm with decomposition procedures finally both feasibility and effectiveness of the proposed method is discussed on the basis of results of simple numerical experiments

a comparison of genetic and conventional methods for the solution of integer goal programmes abstract this paper discusses two different approaches to the solution of difficult goal programming gp models an integer goal programming igp solver and some genetically driven multi objective methods are developed specialised gp speed up techniques and analysis tools are employed in the design and development of the solution systems a selection of linear integer models of small to medium size with an internal structure that makes solution difficult are considered these problems are solved by both methods in order to assess their computational performance over several criteria and to compare the differences between them from the results obtained in this research it is observed that genetic algorithms ga have performed in general less efficiently than the integer goal programming system for the sample of problems analysed

norm hull of vectors and matrices let v be a real or complex finite dimensional vector space and let n be a set of norms on v the norm hull of a vector x v with respect to n is the set of vectors y v that satisfy y x for all n we study and give characterization of the norm hull for some sets of well known norms on general vector spaces and for the set of algebra norms and the set of induced norms on the algebra of n n real or complex matrices

a new genetic algorithm for solving nonconvex nonlinear programming problems abstract in nonlinear programming problems especially nonconvex problems attaining the global optimum is crucial to reach this purpose the current paper represents a new genetic algorithm for solving nonconvex nonlinear programming problems the new method is simpler and more intuitive than the existing models and finds the global optimum of the problem in a reasonable time the proposed technique to attain the global optimum of problem especially in large scale problems instead of increasing the size of population which usually conduces to the curse of dimensionality that is widespread in usual genetic algorithms decomposes the main problem into several sub problems but with lower size of population in each sub problem this decomposition has been formed in such a way that it could envelop the total solution space the proposed genetic algorithm which determines the sufficient sub problems could converge to global optimum of problem to be able to measure the proposed genetic algorithm several problems have been solved in different spectrums herein it has been shown that the proposed technique both in run time and in solution quality is preferred to the usual genetic algorithm in this domain nonlinear continuous programming problems

further results on the distinctness of binary sequences derived from primitive sequences modulo square free odd integers this paper studies the distinctness of primitive sequences over z m modulo 2 where m is an odd integer that is composite and square free and z m is the integer residue ring modulo m a new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomial f x over z m are pairwise distinct modulo 2 such result improves a recent result obtained in our previous paper and consequently the set of primitive sequences over z m that can be proven to be distinct modulo 2 is greatly enlarged

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

genetic algorithms and traveling salesman problems abstract a genetic algorithm ga with an asexual reproduction plan through a generalized mutation for an evolutionary operator is developed that can be directly applied to a permutation of n numbers for an approximate global optimal solution of a traveling salesman problem tsp schema analysis of the algorithm shows that a sexual reproduction with the generalized mutation operator preserves the global convergence property of a genetic algorithm thus establishing the fundamental theorem of the ga for the algorithm avoiding an intermediate step of encoding through random keys to preserve crossover or permuting n and using fixing states for legal crossover are the chief benefits of the innovations reported in this paper the algorithm has been applied to a number of natural and artificial problems and the results are encouraging

distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers let a and b be primitive sequences over z pe with odd prime p and e 2 for certain compressing maps we consider the distribution properties of compressing sequences of a and b and prove that a b if the compressing sequences are equal at the times t such that t k where is a sequence related to a we also discuss the s uniform distribution property of compressing sequences for some compressing maps we have that there exist different primitive sequences such that the compressing sequences are s uniform we also discuss that compressing sequences can be s uniform for how many elements s

on the norm property of g c radii and eaton triples abstract let v be a euclidean space and o v be the orthogonal group the norm criterion of the g c radius is studied in the framework of an eaton triple v g d

an effective genetic algorithm approach to multiobjective routing problems morps dynamic programming dp is a mathematical procedure designed primarily to improve the computational efficiency of solving select mathematical programming problems by decomposing them into smaller and hence computationally simpler subproblems in solving multiple objectives dynamic programming problem modp classical approaches reduce the multiple objectives into a single objective of minimizing a weighted sum of objectives the determination of these weights indicate the relative importance of the various objective also if the problem scale increases it becomes difficult to be dealt with even in the case of single objective because of the rapid expansion of the number of states to be considered in this paper we investigated the possibility of using genetic algorithms gas to solve multiobjective routing problems morps this procedure eliminates the need of any user defined weight factor for each objective also the proposed approach is developed to deal with the problems with both single or multiple objectives the simulation results for morps shows that genetic algorithms gas may hopefully be a new approach for such kinds of difficult to solve problems

scheduling of design projects with uncertain number of iterations abstract a short product design cycle is critical to the success of companies in the era of time based competition the underlying design activities however are often interlinked and quite uncertain for example some activities may have to be iterated several times to meet the design criteria furthermore time critical projects suffer the risk of failure if they cannot meet established target dates generating good and robust schedules is thus critical especially under the concurrent engineering paradigm where the delay of a single task may have a domino effect on subsequent tasks and on other projects sharing designers and or resources this paper studies the scheduling of design projects with uncertain number of iterations while managing design risks a separable problem formulation that balances modeling accuracy and computation complexity is created with the goal to minimize project tardiness and risk penalties an optimization based methodology that combines lagrangian relaxation stochastic dynamic programming and ordinal optimization is developed numerical results supported by simulation demonstrate that near optimal solutions are obtained and uncertainties are effectively managed for problems of practical sizes

an evolutionary heuristic for quadratic 0 1 programming abstract in this paper we present a heuristic algorithm for the well known unconstrained quadratic 0 1 programming problem the approach is based on combining solutions in a genetic paradigm and incorporates intensification algorithms used to improve solutions and speed up the method extensive computational experiments on instances with up to 500 variables are presented and we compare our approach both with powerful heuristic and exact algorithms from the literature establishing the effectiveness of the method in terms of solutions quality and computing time

search space division in gas using phenotypic properties in this article we study a new type of forking ga fga the phenotypic forking ga p fga the fga divides the whole search space into subspaces depending on the convergence status of the population and the solutions obtained so far and is intended to deal with multimodal problems which are difficult to solve using conventional ga we use a multi population scheme which includes one parent population that explores one subspace and one or more child population s exploiting the other subspace the p fga divides the search space using phenotypic properties only and defines a search subspace to be exploited by a child population by a neighborhood hypercube around the current best individual in the phenotypic feature space empirical results on complex function optimization problems show that the p fga performs fairly well compared to a conventional ga two other variants of the p fga the moving window p fga to accelerate the speed of convergence in the child populations and the variable resolution p fga to solve multimodal problems with high precision are also studied in this article

an interactive fuzzy satisficing method for general multiobjective 0 1 programming problems through genetic algorithms with double strings based on a reference solution in this paper focusing on general multiobjective 0 1 programming problems involving positive and negative coefficients we propose an interactive fuzzy satisficing method by extending our previous genetic algorithms with double strings for multiobjective multidimensional 0 1 knapsack problems in the extended genetic algorithms a new decoding algorithm for individuals represented by double strings which maps each individual to a feasible solution is proposed through the introduction of backtracking and individual modification after examining the feasibility and efficiency of the extended genetic algorithms with double strings using a lot of 0 1 programming problems involving positive and negative coefficients an illustrative numerical example demonstrated the feasibility and efficiency of the proposed interactive fuzzy satisficing method

a lower bound on the linear span of an fcsr we have derived a lower bound on the linear span of a binary sequence generated by a feedback with carry shift register fcsr under the following condition q is a power of a prime such that q r sup e e spl ges 2 and r 2p 1 where both r and p are 2 prime this allows us to design fcsr stream ciphers similar to previously proposed linear feedback shift register lfsr stream ciphers