new constructive methods in classical ideal theory abstract the recent development of computer algebra allows us to take up problems of classical ideal theory for which constructive solutions by nearly unfeasible algorithms exist like the problem of deciding whether a polynomial belongs to a given ideal g hermann math ann 95 1926 736 788 even macaulay s methods by using h bases are not satisfactory at least when considering modules the concept of grobner bases introduced in computer algebra by buchberger allows us to find feasible algorithms for many problems of classical ideal theory by transforming them into some low dimensional systems of linear equations our aim is to demonstrate the effectivity of this new concept considering only polynomial rings p k x 1 x n k a field we generalize in part i the notion of grobner bases to modules present some equivalent properties characterizing these bases and show their good computational qualities in part ii we construct starting with grobner bases of ideals explicit free solutions where all the bases of submodules under consideration are also grobner bases and present a reduction strategy for obtaining shorter resolutions where all the bases have also favourable properties t bases part iii deals with applications we propose a method for constructing minimal resolutions starting with the resolutions of part ii and present a convenient way for computing the hilbert function

compact location problems we consider the problem of placing a specified number p of facilities on the nodes of a network so as to minimize some measure of the distances between facilities this formulation models a number of problems arising in facility location statistical clustering pattern recognition and also a processor allocation problem in multiprocessor systems

location on tree networks p centre and n dispersion problems we consider two problems of locating facilities on trees in the first we wish to determine the location of n points so as to maximize the minimum distance between any pair in the second we wish to locate p centers of a single type of facility so as to minimize the maximum distance between any point and the center nearest to it we provide polynomial algorithms for both problems of o n 2 log n log n for the first problem and of o n 2 log p for the second where n is the number of nodes in the tree

on polynomial ideals of finite codimension with applications to box spline theory we investigate the relation between an ideal i of finite codimension in the space of multivariate polynomials and ideals which are generated by lower order perturbations of some generators for i of particular interest are the codimension of these ideals and the local approximation order of their kernels the discussion stimulated by recent results in approximation theory allows us to provide a simple analysis of the polynomial and exponential spaces associated with box splines we describe their structure dimension and local approximation order and an algorithm for their construction the resulting theory is extended to subspaces of the above exponential polynomial spaces

real bargmann spaces fischer decompositions and sets of uniqueness for polyharmonic functions in this paper a positive answer is given to the following question of w k hayman if a polyharmonic entire function of order k vanishes on k distinct ellipsoids in the euclidean space r n then it vanishes everywhere moreover a characterization of ellipsoids is given in terms of an extension property of solutions of entire data functions for the dirichlet problem answering a question of d khavinson and h s shapiro these results are consequences from a more general result in the context of direct sum decom positions fischer decompositions of polynomials or functions in the algebra a br of all real analytic functions defined on the ball br of radius r and center 0 whose taylor series of homogeneous polynomials converges compactly in br the main result states that for a given elliptic polynomial p of degree 2k and suciently

the edge weighted clique problem valid inequalities facets and polyhedral computations abstract let kn v e be the complete undirected graph with weights ce associated to the edges in e we consider the problem of finding the subclique c u f of kn such that the sum of the weights of the edges in f is maximized and u b for some b 1 n this problem is called the maximum edge weighted clique problem mewcp and is np hard in this paper we investigate the facial structure of the polytope associated to the mewcp introducing new classes of facet defining inequalities computational experiments with a branch and cut algorithm are reported confirming the strength of these inequalities all instances with up to 48 nodes could be solved without entering into the branching phase moreover we show that some of these new inequalities also define facets of the boolean quadric polytope and generalize many of the previously known inequalities for this well studied polytope

randomized heuristics for the capacitated clustering problem in this paper we investigate the adaptation of the greedy randomized adaptive search procedure grasp and iterated greedy methodologies to the capacitated clustering problem ccp in particular we focus on the effect of the balance between randomization and greediness on the performance of these multi start heuristic search methods when solving this np hard problem the former is a memory less approach that constructs independent solutions while the latter is a memory based method that constructs linked solutions obtained by partially rebuilding previous ones both are based on the combination of greediness and randomization in the constructive process and coupled with a subsequent local search phase we propose these two multi start methods and their hybridization and compare their performance on the ccp additionally we propose a heuristic based on the mathematical programming formulation of this problem which constitutes a so called matheuristic we also implement a classical randomized method based on simulated annealing to complete the picture of randomized heuristics our extensive experimentation reveals that iterated greedy performs better than grasp in this problem and improved outcomes are obtained when both methods are hybridized and coupled with the matheuristic in fact the hybridization is able to outperform the best approaches previously published for the ccp this study shows that memory based construction is an effective mechanism within multi start heuristic search techniques

truncated power method for sparse eigenvalue problems this paper considers the sparse eigenvalue problem which is to extract dominant largest sparse eigenvectors with at most k non zero components we propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem a strong sparse recovery result is proved for the truncated power method and this theory is our key motivation for developing the new algorithm the proposed method is tested on applications such as sparse principal component analysis and the densest k subgraph problem extensive experiments on several synthetic and real world data sets demonstrate the competitive empirical performance of our method

an integer programming approach for solving the p dispersion problem abstract given a collection of n items elements and an associated symmetric distance dij between each pair of items i and j we seek a subset p of these items with a given cardinality p so that the minimum pairwise distance among the selected items is maximized this problem is known as the max min diversity problem or the p dispersion problem and it is shown to be np hard we define a collection of node packing problems associated with each instance of this problem and employ a binary search among these node packing problems to devise an effective procedure for solving the original problem we employ existing integer programming techniques i e branch and bound and strong valid inequalities to solve these node packing problems through a computational experiment we show that this approach can be used to solve relatively large instances of the p dispersion problem i e instances with more than 1000 items we also discuss an application of this problem in the context of locating traffic sensors in a highway network

integer friendly formulations for the r separation problem abstract in this paper we consider different formulations for the r separation problem where the objective is to choose as as many points as possible from a given set of points subject to the constraint that no two selected points can be closer than r units to one another our goal is to devise a mathematical programming formulation with an lp relaxation which yields integer solutions with great frequency we consider six different formulations of the r separation problem we show that the lp relaxations of the most obvious formulations will yield fractional results in all instances of the problem if an optimal solution contains fewer than half of the given points to build computationally effective formulations for the r separation problem we write dense constraints with unit right hand sides the lp formulation that performs the best in our computational tests almost always finds 0 1 solutions to the problem

optimizing network attacks by artificial bee colony abstract over the past few years the task of conceiving effective attacks to complex networks has arisen as an optimization problem attacks are modelled as the process of removing a number k of vertices from the graph that represents the network and the goal is to maximise or minimise the value of a predefined metric over the graph in this work we present an optimization problem that concerns the selection of nodes to be removed to minimise the maximum betweenness centrality value of the residual graph this metric evaluates the participation of the nodes in the communications through the shortest paths of the network to address the problem we propose an artificial bee colony algorithm which is a swarm intelligence approach inspired in the foraging behaviour of honeybees in this framework bees produce new candidate solutions for the problem by exploring the vicinity of previous ones called food sources the proposed method exploits useful problem knowledge in this neighbourhood exploration by considering the partial destruction and heuristic reconstruction of selected solutions the performance of the method with respect to other models from the literature that can be adapted to face this problem such as sequential centrality based attacks module based attacks a genetic algorithm a simulated annealing approach and a variable neighbourhood search is empirically shown

the equitable dispersion problem most optimization problems focus on efficiency based objectives given the increasing awareness of system inequity resulting from solely pursuing efficiency we conceptualize a number of new element based equity oriented measures in the dispersion context we propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter element distances given the proposed optimization framework we develop corresponding mathematical programming formulations as well as their mixed integer linear reformulations we also discuss computational complexity issues related graph theoretic interpretations and provide some preliminary computational results

on the unified dispersion problem efficient formulations and exact algorithms abstract facility dispersion problems involve placing a number of facilities as far apart from each other as possible four different criteria of facility dispersal have been proposed in the literature erkut neuman 1991 despite their formal differences these four classic dispersion objectives can be expressed in a unified model called the partial sum dispersion model lei church 2013 in this paper we focus on the unweighted partial sum dispersion problem and introduce an efficient formulation for this generalized dispersion problem based on a construct by ogryczak and tamir 2003 we also present a fast branch and bound based exact algorithm

mean square error criteria to multiresponse process optimization by a new genetic algorithm the recent push for quality in industry has brought response surface methodology to the attention of many users most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers for most products however quality is multidimensional so it is common to observe multiple responses in an experimental situation in this paper we present a methodology for analyzing several quality characteristics simultaneously using the mean square error mse criterion when data are collected from a combined array problems with highly nonlinear or multimodal objective functions are extremely difficult to solve and are further complicated by the presence of multiple objectives an alternative approach is to use a heuristic search procedure such as a genetic algorithm ga the ga generates a string of solutions using genetics like operators such as selection crossover and mutation in this paper a genetic algorithm based on arithmetic crossover for the multiresponse problem is proposed the string of solutions highlight the trade offs that one needs to consider in order to obtain a compromise solution a numerical example has been presented to illustrate the performance and the applicability of the proposed method

mathematical optimization ideas for biodiversity conservation several major environmental issues like biodiversity loss and climate change currently concern the international community these topics that are related to the development of human societies have become increasingly important since the united nations conference on environment and development unced or earth summit in rio de janeiro in 1992 in this article we are interested in the first issue we present here many examples of the help that using mathematical programming can provide to decision makers in the protection of biodiversity the examples we have chosen concern the selection of nature reserves the control of adverse effects caused by landscape fragmentation including the creation or restoration of biological corridors the ecological exploitation of forests the control of invasive species and the maintenance of genetic diversity most of the presented models are or can be approximated with linear quadratic or fractional integer formulations and emphasize spatial aspects of conservation planning many of them represent decisions taken in a static context but temporal dimension is also considered the problems presented are generally difficult combinatorial optimization problems some are well solved and others less well research is still needed to progress in solving them in order to deal with real instances satisfactorily moreover relations between researchers and practitioners have to be strengthened furthermore many recent achievements in the field of robust optimization could probably be successfully used for biodiversity protection a domain in which many data are uncertain

finding connected k subgraphs with high density abstract given an edge weighted connected graph g on n vertices and a positive integer k n a subgraph of g on k vertices is called a k subgraph in g we design combinatorial approximation algorithms for finding a connected k subgraph in g such that its weighted density is at least a factor max 1 k k 2 n 2 of the maximum weighted density among all k subgraph in g which are not necessarily connected where max 1 k k 2 n 2 n 2 3 implies an o n 2 3 approximation ratio we obtain improved o n 2 5 approximation for unit weights these particularly provide the first non trivial approximations for the heaviest densest connected k subgraph problem on general graphs we also give o n log n approximation for the problem on general weighted interval graphs

locating an undesirable facility with a minimax criterion abstract the problem considered in this paper involves the location of an undesirable facility such that the maximum weighted inverse square distance from the facility to n given points is minimized the region in which the facility is to be located is bounded and contains the n points with which the facility to be located will interact applications can include siting an undesirable facility that produces some form of pollutant such as radiation noise and some gases any problem that involves the location of a facility that emits pollutants whose concentrations follow the inverse square law is a candidate for the use of this work a mathematical programming algorithm is developed for the situation in which the location problem involves a convex polygonal region an interactive computer graphics approach is described for the case when the location problem involves a general region

tabu enhanced iterated greedy algorithm a case study in the quadratic multiple knapsack problem abstract iterated greedy search is a simple and effective metaheuristic for combinatorial problems its flexibility enables the incorporation of components from other metaheuristics with the aim of obtaining effective and powerful hybrid approaches we propose a tabu enhanced destruction mechanism for iterated greedy search that records the last removed objects and avoids removing them again in subsequent iterations the aim is to provide a more diversified and successful search process with regards to the standard destruction mechanism which selects the solution components for removal completely at random we have considered the quadratic multiple knapsack problem as the application domain for which we also propose a novel local search procedure and have developed experiments in order to assess the benefits of the proposal the results show that the tabu enhanced iterated greedy approach in conjunction with the new local search operator effectively exploits the problem knowledge associated with the requirements of the problem considered attaining competitive results with regard to the corresponding state of the art algorithms

multivariate refinable functions differences and ideals a simple tutorial this paper summarizes the algebraic quotient ideal approach to polynomial generation by refinable functions and connects it to strang fix conditions and factorization with respect to difference operators motivated by the latter one we also consider vector subdivision schemes with matrix valued coefficients and review some of their properties

it cemop an iterative co evolutionary algorithm for multiobjective optimization problem with nonlinear constraints over the past few years researchers have developed a number of multiobjective evolutionary algorithms moeas although most studies concentrate on solving unconstrained optimization problems there exit a few studies where moeas have been extended to solve constrained optimization problems most of them were based on penalty functions for handling nonlinear constraints by genetic algorithms however the performance of these methods is highly problem dependent many methods require additional tuning of several parameters in this paper we present a new optimization algorithm which is based on concept of co evolution and repair algorithm for handling nonlinear constraints the algorithm maintains a finite sized archive of nondominated solutions which gets iteratively updated in the presence of new solutions based on the concept of e dominance the use of e dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the pareto set approximation by choosing an appropriate e value which guarantees convergence and diversity the results provided by the proposed algorithm for six benchmark problems are promising when compared with exiting well known algorithms also our results suggest that our algorithm is better applicable for solving real world application problems

on multiplicities in polynomial system solving this paper deals with the description of the solutions of zero dimensional systems of polynomial equations based on different models for describing solutions we consider suitable representations of a multiple root or more precisely suitable descriptions of the primary component of the system at a root we analyse the complexity of finding the representations and of algorithms which perform transformations between the different representations

tabu search and grasp for the maximum diversity problem in this paper we develop new heuristic procedures for the maximum diversity problem mdp this np hard problem has a significant number of practical applications such as environmental balance telecommunication services or genetic engineering the proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement although proposed in seminal tabu search papers memory based constructions have often been implemented in naive ways that disregard important elements of the fundamental tabu search proposals we will compare our tabu search construction with a memory less design and with previous algorithms recently developed for this problem the constructive method can be coupled with a local search procedure or a short term tabu search for improved outcomes extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times

an artificial bee colony algorithm for the maximally diverse grouping problem in this paper an artificial bee colony algorithm is proposed to solve the maximally diverse grouping problem this complex optimisation problem consists of forming maximally diverse groups with restricted sizes from a given set of elements the artificial bee colony algorithm is a new swarm intelligence technique based on the intelligent foraging behaviour of honeybees the behaviour of this algorithm is determined by two search strategies an initialisation scheme employed to construct initial solutions and a method for generating neighbouring solutions more specifically the proposed approach employs a greedy constructive method to accomplish the initialisation task and also employs different neighbourhood operators inspired by the iterated greedy algorithm in addition it incorporates an improvement procedure to enhance the intensification capability through an analysis of the experimental results the highly effective performance of the proposed algorithm is shown in comparison to the current state of the art algorithms which address the problem

a variable iterated greedy algorithm for the traveling salesman problem with time windows this paper presents a variable iterated greedy algorithm for solving the traveling salesman problem with time windows tsptw to identify a tour minimizing the total travel cost or the makespan separately the tsptw has several practical applications in both production scheduling and logistic operations the proposed algorithm basically relies on a greedy algorithm generating an increasing number of neighboring solutions through the use of the idea of neighborhood change in variable neighborhood search vns algorithms in other words neighboring solutions are generated by destructing a solution component and re constructing the solution again with variable destruction sizes in addition the proposed algorithm is hybridized with a vns algorithm employing backward and forward 1 opt local searches to further enhance the solution quality the performance of the proposed algorithm was tested on several benchmark suites from the literature experimental results confirm that the proposed algorithm is either competitive to or even better than the best performing algorithms from the literature ultimately new best known solutions are obtained for 38 out of 125 problem instances of the recently proposed benchmark suite whereas 15 out of 31 problem instances are also further improved for the makespan criterion

a branch and bound algorithm for the maximum diversity problem this article begins with a review of previously proposed integer formulations for the maximum diversity problem mdp this problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized we propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial solutions to the mdp empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the medium sized instances with 50 elements as well as some large sized instances with 100 elements we compare our method with the best previous linear integer formulation solved with the well known software cplex the comparison favors the proposed procedure

greedy randomized adaptive search procedure with exterior path relinking for differential dispersion minimization we propose several new hybrid heuristics for the differential dispersion problem the best of which consists of a grasp with sampled greedy construction with variable neighborhood search for local improvement the heuristic maintains an elite set of high quality solutions throughout the search after a fixed number of grasp iterations exterior path relinking is applied between all pairs of elite set solutions and the best solution found is returned exterior path relinking or path separation a variant of the more common interior path relinking is first applied in this paper in interior path relinking paths in the neighborhood solution space connecting good solutions are explored between these solutions in the search for improvements exterior path relinking as opposed to exploring paths between pairs of solutions explores paths beyond those solutions this is accomplished by considering an initiating solution and a guiding solution and introducing in the initiating solution attributes not present in the guiding solution to complete the process the roles of initiating and guiding solutions are exchanged extensive computational experiments on 190 instances from the literature demonstrate the competitiveness of this algorithm

effective metaheuristic algorithms for the minimum differential dispersion problem abstract this paper presents tabu search and memetic search algorithms for solving the minimum differential dispersion problem the tabu search algorithm employs a neighborhood decomposition candidate list strategy and a rarely used solution based tabu memory unlike the typical attribute based tabu list the solution based tabu strategy leads to a more highly focused intensification process and avoids tuning the tabu tenure while employing coordinated hash functions that accelerate the determination of tabu status the memetic search algorithm incorporates the tabu search procedure within it and makes use of a crossover operator that generates solution assignments by an evaluation mechanism that includes both quality and distance criteria experimental results on a benchmark testbed of 250 problems reveal that our tabu search algorithm is capable of discovering better solutions for 179 71 6 of the problem instances while our memetic search algorithm finds better solutions for 157 62 8 of the instances collectively yielding better solutions for 181 72 4 of the test problems than recently reported state of the art algorithms

polynomial interpolation of minimal degree minimal degree interpolation spaces with respect to a finite set of points are subspaces of multivariate polynomials of least possible degree for which lagrange interpolation with respect to the given points is uniquely solvable and degree reducing this is a generalization of the concept of least interpolation introduced by de boor and ron this paper investigates the behavior of lagrange interpolation with respect to these spaces giving a newton interpolation method and a remainder formula for the error of interpolation moreover a special minimal degree interpolation space will be introduced which is particularly beneficial from the numerical point of view

a comment on on prime factor mapping for the discrete hartley transform lun and sin see ieee trans signal processing vol 40 no 6 p 1399 1411 1982 describe a method of computing prime factor decomposed discrete hartley transform dht over n points with 2n less additions compared to the existing algorithms of bracewell and sorensen 1976 the author shows how the method of lun and siu ran be extended to eliminate the 2n extra additions in the algorithms of bracewell and sorenson

a simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem over the last decade many metaheuristics have been applied to the flowshop scheduling problem ranging from simulated annealing or tabu search to complex hybrid techniques some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated in fact several published methods require substantial implementation efforts exploit problem specific speed up techniques that cannot be applied to slight variations of the original problem and often re implementations of these methods by other researchers produce results that are quite different from the original ones in this work we present a new iterated greedy algorithm that applies two phases iteratively named destruction were some jobs are eliminated from the incumbent solution and construction where the eliminated jobs are reinserted into the sequence using the well known neh construction heuristic optionally a local search can be applied after the construction phase our iterated greedy algorithm is both very simple to implement and as shown by experimental results highly effective when compared to state of the art methods

a hybrid metaheuristic approach to solving the ubqp problem this paper presents a hybrid metaheuristic approach hma for solving the unconstrained binary quadratic programming ubqp problem by incorporating a tabu search procedure into the framework of evolutionary algorithms the proposed approach exhibits several distinguishing features including a diversification based combination operator and a distance and quality based replacement criterion for pool updating the proposed algorithm is able to easily obtain the best known solutions for 31 large random instances up to 7000 variables which no previous algorithm has done and find new best solutions for three of nine instances derived from the set partitioning problem demonstrating the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency furthermore some key elements and properties of the hma algorithm are also analyzed

a lagrangian relaxation approach to the edge weighted clique problem the b clique polytope cp n b is the convex hull of the node and edge incidence vectors of all subcliques of size at most b of a complete graph on n nodes including the boolean quadric polytope qp n as a special case and being closely related to the quadratic knapsack polytope it has received considerable attention in the literature in particular the max cut problem is equivalent with optimizing a linear function over qp n n the problem of optimizing linear functions over cp n b has so far been approached via heuristic combinatorial algorithms and cutting plane methods we study the structure of cp n b in further detail and present a new computational approach to the linear optimization problem based on lucena s suggestion of integrating cutting planes into a lagrangian relaxation of an integer programming problem in particular we show that the separation problem for tree inequalities becomes polynomial in our lagrangian framework finally computational results are presented

construction and improvement algorithms for dispersion problems abstract given a set n a pairwise distance function d and an integer number m the dispersion problems dps require to extract from n a subset m of cardinality m so as to optimize a suitable function of the distances between the elements in m different functions give rise to a whole family of combinatorial optimization problems in particular the max sum dp and the max min dp have received strong attention in the literature other problems e g the max minsum dp and the min diffsum dp have been recently proposed with the aim to model the optimization of equity requirements as opposed to that of more classical efficiency requirements building on the main ideas which underly some state of the art methods for the max sum dp and the max min dp this work proposes some constructive procedures and a tabu search algorithm for the new problems in particular we investigate the extension to the new context of key features such as initialization tenure management and diversification mechanisms the computational experiments show that the algorithms applying these ideas perform effectively on the publicly available benchmarks but also that there are some interesting differences with respect to the dps more studied in the literature as a result of this investigation we also provide optimal results and bounds as a useful reference for further studies

an iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives iterated greedy ig algorithms are based on a very simple principle are easy to implement and can show excellent performance in this paper we propose two new ig algorithms for a complex flowshop problem that results from the consideration of sequence dependent setup times on machines a characteristic that is often found in industrial settings the first ig algorithm is a straightforward adaption of the ig principle while the second incorporates a simple descent local search furthermore we consider two different optimization objectives the minimization of the maximum completion time or makespan and the minimization of the total weighted tardiness extensive experiments and statistical analyses demonstrate that despite their simplicity the ig algorithms are new state of the art methods for both objectives

on computing the discrete hartley transform the discrete hartley transform dht is a real valued transform closely related to the dft of a real valued sequence bracewell has recently demonstrated a radix 2 decimation in time fast hartley transform fht algorithm in this paper a complete set of fast algorithms for computing the dht is developed including decimation in frequency radix 4 split radix prime factor and winograd transform algorithms the philosophies of all common fft algorithms are shown to be equally applicable to the computation of the dht and the fht algorithms closely resemble their fft counterparts the operation counts for the fht algorithms are determined and compared to the counts for corresponding real valued fft algorithms the fht algorithms are shown to always require the same number of multiplications the same storage and a few more additions than the real valued fft algorithms even though computation of the fht takes more operations in some situations the inherently real valued nature of the discrete hartley transform may justify this extra cost

clique relaxations in social network analysis the maximum k plex problem this paper introduces and studies the maximum k plex problem which arises in social network analysis and has wider applicability in several important areas employing graph based data mining after establishing np completeness of the decision version of the problem on arbitrary graphs an integer programming formulation is presented followed by a polyhedral study to identify combinatorial valid inequalities and facets a branch and cut algorithm is implemented and tested on proposed benchmark instances an algorithmic approach is developed exploiting the graph theoretic properties of a k plex that is effective in solving the problem to optimality on very large sparse graphs such as the power law graphs frequently encountered in the applications of interest

an iterated greedy heuristic for a market segmentation problem with multiple attributes this research has been supported by the mexican national council for science and technology conacyt through grants cb2005 01 48499y and cb2011 01 166397 and a scholarship for graduate studies and by the universidad autonoma de nuevo leon through its scientific and technological research support program paicyt grants ca1478 07 ce012 09 it511 10 and ce331 15 ruben ruiz is partially supported by the spanish ministry of economy and competitiveness under the project scheyard optimization of scheduling problems in container yards no dpi2015 65895 r financed by feder funds we would like to thank rafael frinhani richard fuchshuber and their corresponding research teams for providing us the source code of their algorithms to carry out the corresponding tests furthermore we are grateful to the editor and the four anonymous reviewers for their careful reading of our manuscript and their constructive comments and suggestions which helped us improve its quality

multivariate polynomial equations with multiple zeros solved by matrix eigenproblems the eigenproblem method calculates the solutions of systems of polynomial equations f 1 x 1 ldots x s 0 ldots f m x 1 ldots x s 0 it consists in fixing a suitable polynomial f and in considering the matrix a f corresponding to the mapping p mapsto f cdot p where the equivalence classes are modulo the ideal generated by f 1 ldots f m the eigenspaces contain vectors from which all solutions of the system can be read off this access was investigated in 1 and 16 mainly for the case that is nonderogatory in the present paper we study the case where f 1 ldots f m have multiple zeros in common we establish a kind of jordan decomposition of a f reflecting the multiplicity structure and describe the conditions under which a f is nonderogatory the algorithmic analysis of the eigenproblem in the general case is indicated

a hybrid metaheuristic method for the maximum diversity problem abstract the maximum diversity problem mdp consists in selecting a subset of m elements from a given set of n elements n m in such a way that the sum of the pairwise distances between the m chosen elements is maximized we present a hybrid metaheuristic algorithm denoted by mamdp for mdp the algorithm uses a dedicated crossover operator to generate new solutions and a constrained neighborhood tabu search procedure for local optimization mamdp applies also a distance and quality based replacement strategy to maintain population diversity extensive evaluations on a large set of 120 benchmark instances show that the proposed approach competes very favorably with the current state of art methods for mdp in particular it consistently and easily attains all the best known lower bounds and yields improved lower bounds for 6 large mdp instances the key components of mamdp are analyzed to shed light on their influence on the performance of the algorithm

an extended formulation approach to the edge weighted maximal clique problem we consider an extended formulation approach to the edge weighted maximal clique problem the problem is formulated by using additional variables for the set of nodes with the natural variables for the set of edges we show that the proposed formulation is superior to the natural formulation both theoretically and practically by using the projection technique we can also derive new classes of facet defining inequalities for the lower dimensional polytope of the natural variables computational results are reported

a review on algorithms for maximum clique problems the maximum clique problem mcp is to determine in a graph a clique i e a complete subgraph of maximum cardinality the mcp is notable for its capability of modeling other combinatorial problems and real world applications as one of the most studied np hard problems many algorithms are available in the literature and new methods are continually being proposed given that the two existing surveys on the mcp date back to 1994 and 1999 respectively one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic mcp algorithms with a special focus on recent developments to be informative we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful by classifying the main search strategies and putting forward the critical elements of the most relevant clique methods this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches

on prime factor mapping for the discrete hartley transform the authors propose a new prime factor mapping scheme which requires no extra arithmetic operations for the realization of prime factor mapping for the computation of the discrete hartley transform dht it is achieved by embedding all the extra arithmetic operations into the subsequent short length computations with the computational complexities of these embedded short lengths remaining unchanged consequently the present approach significantly eliminates the burden which is introduced by the extra arithmetic operations with this mapping scheme it is further demonstrated that a prime factor mapped dht would have superb performance compared with other fast dht algorithms

shifting representation search for hybrid flexible flowline problems this paper considers the hybrid flexible flowline scheduling problem with a set of additional restrictions and generalizations that are common in practice these include precedence constraints sequence dependent setup times time lags machine eligibility and release times there are many potential solution representations for this problem ranging from simple and compact to more complex and complete typically when choosing the degree of detail of the solution representation a tradeoff can be found between efficiency of the algorithm and the size of the search space several adaptations of existing methods are introduced memetic algorithm iterated local search iterated greedy as well as a novel algorithm called shifting representation search srs this new method starts with an iterated greedy algorithm applied to a permutation version of the problem and at a given time switches to an iterated local search on the full search space as far as we know this shift of the solution representation is new in the scheduling literature experimental results and statistical tests clearly prove the superiority of srs compared with classical and existing methods

grobner bases h bases and interpolation the paper is concerned with a construction for h bases of polynomial ideals without relying on term orders the main ingredient is a homogeneous reduction algorithm which orthogonalizes leading terms instead of completely canceling them this allows for an extension of buchberger s algorithm to construct these h bases algorithmically in addition the close connection of this approach to minimal degree interpolation and in particular to the least interpolation scheme due to de boor and ron is pointed out

iterated greedy for the maximum diversity problem abstract the problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best so far metaheuristics for the problem under consideration

prony s method in several variables the paper gives an extension of prony s method to the multivariate case which is based on the relationship between polynomial interpolation normal forms modulo ideals and h bases though the approach is mainly of algebraic nature we also give an algorithm using techniques from numerical linear algebra to solve the problem in a fast and efficient way

solving the maximum edge weight clique problem via unconstrained quadratic programming the unconstrained quadratic binary program uqp is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times often rivaling and sometimes surpassing more traditional methods in this paper we report on the application of uqp to the maximum edge weighted clique problem computational experience is reported illustrating the attractiveness of the approach

on the singularity of multivariate hermite interpolation in this paper we study the singularity of multivariate hermite interpolation of type total degree we present two methods to judge the singularity of the interpolation schemes considered and by methods to be developed we show that all hermite interpolation of type total degree on m d k points in r d is singular if d 2k and then we solve the hermite interpolation problem on email protected d 3 nodes completely precisely all hermite interpolations of type total degree on email protected d 1 points with d 2 are singular only three cases for m d 2 and one case for m d 3 can produce regular hermite interpolation schemes respectively besides we also present a method to compute the interpolation space for hermite interpolation of type total degree

lagrange interpolation on subgrids of tensor product grids this note shows that a wide class of algebraically motivated constructions for lagrange interpolation polynomials always yields a tensor product interpolation space as long as the nodes form a tensor product grid or a lower subset thereof

the discrete p dispersion problem considered is the problem of selecting p out of n given points in some space such that the minimum distance between pairs of selected points is maximized this objective may be appropriate if the selected points correspond to facility sites and the objective is to have as dispersed a set as possible this problem is np complete related graph theoretical problems are discussed integer programming models are proposed and an outline is given on a line search procedure to solve this problem optimally using a branch and bound procedure problems with n 40 and p 16 can be solved on a microcomputer the heuristic developed to get an initial lower bound finds an optimal solution for most of our random test problems also described is an extension to the basic problem that allows for preselected points which may correspond to existing facility locations this more general version can be solved by slight modifications of the algorithms

new facets and a branch and cut algorithm for the weighted clique problem abstract we consider a polyhedral approach to the weighted maximal b clique problem given a node and edge weighted complete graph the problem is to find a complete subgraph clique with no more than b nodes such that the sum of the weights of all nodes and edges in the clique is maximal we introduce four new classes of facet defining inequalities for the associated b clique polytope one of these inequality classes constitutes a generalization of the well known tree inequalities the other classes are associated with multistars we use these inequalities together with other classes of facet defining inequalities in a branch and cut algorithm for the problem we give a description of this algorithm including some separation procedures and present the computational results for different sets of test problems the computation times that are obtained indicate that this algorithm is more efficient than previously described algorithms for the problem

multivariate hermite interpolation by algebraic polynomials a survey abstract this is a survey of that theory of multivariate lagrange and hermite interpolation by algebraic polynomials which has been developed in the past 20 years its purpose is not to be encyclopedic but to present the basic concepts and techniques which have been developed in that period of time and to illustrate them with examples it takes classical hermite interpolation as a starting point but then successively broadens the assumptions so that finally interpolation of arbitrary functionals and the theory of singularities from algebraic geometry is discussed

heuristic and special case algorithms for dispersion problems the dispersion problem arises in selecting facilities to maximize some function of the distances between the facilities the problem also arises in selecting nondominated solutions for multiobjective decision making it is known to be np hard under two objectives maximizing the minimum distance max min between any pair of facilities and maximizing the average distance max avg we consider the question of obtaining near optimal solutions for max min we show that if the distances do not satisfy the triangle inequality there is no polynomial time relative approximation algorithm unless p np when the distances satisfy the triangle inequality we analyze an efficient heuristic and show that it provides a performance guarantee of two we also prove that obtaining a performance guarantee of less than two is np hard for max avg we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality we also present a polynomial ti

iterated tabu search for the maximum diversity problem in this paper we deal with the maximum diversity problem mdp which asks to select a specified number of elements from a given set so that the sum of distances between the selected elements is as large as possible we develop an iterated tabu search its algorithm for solving this problem we also present a steepest ascent algorithm which is well suited in application settings where solutions of satisfactory quality are required to be provided very quickly computational results for problem instances involving up to 5000 elements show that the its algorithm is a very attractive alternative to the existing approaches in particular we demonstrate the outstanding performance of its on the mdp instances taken from the literature for 69 such instances new best solutions were found

less is more basic variable neighborhood search for minimum differential dispersion problem abstract in this paper we propose a basic variable neighborhood search for solving minimum differential dispersion problem using only the swap neighborhood structure in both descent intensification and shaking diversification steps it has become a trend in the metaheuristic literature to use hybrid metaheuristics i e combination of several metaheuristic paradigms for solving some particular optimization problem we show that our simple method which relies on the basic variable neighborhood search significantly outperforms the hybrid one that combines grasp variable neighborhood search and exterior path relinking metaheuristics thus simplicity is not only the desired user friendly property of a heuristic but can lead to more efficient and effective method than if complex hybrid metaheuristic is used less is more

iterated greedy local search methods for unrelated parallel machine scheduling abstract this work deals with the parallel machine scheduling problem which consists in the assignment of n jobs on m parallel machines the most general variant of this problem is when the processing time depends on the machine to which each job is assigned to this case is known as the unrelated parallel machine problem similarly to most of the literature this paper deals with the minimization of the maximum completion time of the jobs commonly referred to as makespan c max many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time extensive computational campaigns show that these solutions are most of the time better than the current state of the art methodologies by a statistically significant margin

a new bounding procedure and an improved exact algorithm for the max 2 sat problem given a cnf conjunctive normal form boolean expression with clauses of size at most two the max 2 sat problem asks to find a truth assignment to the boolean variables that makes true the maximum number of clauses in this paper we describe an innovative upper bound computation procedure which is centered around the use of equations and inequalities that are satisfied by all solutions to the problem the procedure is incorporated in a branch and bound algorithm for max 2 sat an initial solution to the problem is provided by an iterated tabu search heuristic we present computational experience on the max 2 sat benchmark instances from the max sat evaluation 2007 the results show that the developed branch and bound algorithm is very competitive with the best previously reported techniques