two continuous models for the dynamics of sandpile surfaces we consider a modified bouchaud cates ravi prakash edwards model for pile surface dynamics and show that in the long scale limit this model converges to a quasistationary model of pile growth in the form of an evolutionary variational inequality

stability theorem for delay differential equations with impulses abstract in this paper we obtain sufficient conditions for the stability of the zero solution of the delay differential equation with impulses formula

probabilistic analysis of output cost of a heuristic search algorithm abstract by proposing a new restricted type of network model we compute the probability distribution of output costs generated by the heuristic search algorithm a of bagchi and mohanti a of nilsson in terms of the heuristic distribution

the improvement of razumikhin type theorems for impulsive functional differential equations abstract in this paper by using lyapunov functions and razumikhin techniques the stability of impulsive functional differential equations is investigated the obtained results avoid the difficulty of constructing a p function in razumikhin s condition and they generalize and improve the existing theorems an example is given to illustrate the importance of the obtained results

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

stress distribution in quasi crystalline granular piles the main goal of this paper is a rigorous consideration of the stress problem in some simple models of granular piles discrete models are considered and the transition to the continuous description is accomplished in order to find the coarse grained average stress some phenomenological rules are formulated on basis of a rigorous consideration of the simple models and applied to more complicated situations

new razumikhin type theorems on the stability for impulsive functional differential systems in this paper we investigate the stability of the trivial solution for impulsive functional differential systems using several lyapunov functions including partial components coupled with the razumikhin technique and obtained some new razumikhin type theorems which avoid using the auxiliary function p under less restrictive conditions our results improve some of the earlier findings and are suitable for many applications some examples are given to illustrate the advantages of the theorems obtained

weighted a search unifying view and application the a algorithm is a well known heuristic best first search method several performance accelerated extensions of the exact a approach are known interesting examples are approximate algorithms where the heuristic function used is inflated by a weight often referred to as weighted a these methods guarantee a bounded suboptimality as a technical contribution this paper presents the previous results related to weighted a from authors like pohl pearl kim likhachev and others in a more condensed and unifying form with this unified view a novel general bound on suboptimality of the result is derived in the case of avoiding any reopening of expanded states for e 0 this bound is 1 e n 2 where n is an upper bound on an optimal solution length binary decision diagrams bdds are well known to ai e g from set based exploration of sparse memory and symbolic manipulation of state spaces the problem of exact or approximate bdd minimization is introduced as a possible new challenge for heuristic search like many classical ai domains this problem is motivated by real world applications several variants of weighted a search are applied to problems of bdd minimization and the more classical domains like blocksworld and sliding tile puzzles for bdd minimization the comparison of the evaluated methods also includes previous heuristic and simulation based methods such as rudell s hill climbing based sifting algorithm simulated annealing and evolutionary algorithms a discussion of the results obtained in the different problem domains gives our experiences with weighted a which is of value for the ai practitioner

some results of the worst case analysis for flow shop scheduling abstract known approximation algorithms recommended for the permutation flow shop problem with the weighted sum of completion times have a worst case performance ratio which is unknown or known but unlimited we propose new algorithms with this ratio equal to m k k where k is the worst case performance ratio of an algorithm which solves an auxiliary k machine problem worst case analyses of other approximation algorithms for the mean completion time and the makespan criteria are also presented

strip generation algorithms for constrained two dimensional two staged cutting problems abstract the constrained two dimensional cutting c tdc problem consists of determining a cutting pattern of a set of n small rectangular piece types on a rectangular stock plate of length l and width w as to maximize the sum of the profits of the pieces to be cut each piece type i i 1 n is characterized by a length l i a width w i a profit or weight c i and an upper demand value b i the upper demand value is the maximum number of pieces of type i which can be cut on rectangle l w in this paper we study the two staged fixed orientation c tdc noted fc 2tdc it is a classical variant of the c tdc where each piece is produced in the final cutting pattern by at most two guillotine cuts and each piece has a fixed orientation we solve the fc 2tdc problem using several approximate algorithms that are mainly based upon a strip generation procedure we evaluate the performance of these algorithms on instances extracted from the literature

minimizing the sum of squares lateness on a single machine abstract this paper proposes a new procedure that considers the use of inserted idle time to optimally solve the single machine scheduling problem where the objective is to minimize the sum of squares lateness a heuristic procedure is also proposed for this problem these procedures and an existing procedure developed by gupta and sen are tested using problems of various sizes in terms of the number of jobs to be scheduled and for different degrees of due date tightness the performance measures are cpu time and sum of squares lateness of the solutions generated the results show that a simple descent procedure yields very good results and is efficient even on large problems

an exact two dimensional non guillotine cutting tree search procedure we consider the two dimensional cutting problem of cutting a number of rectangular pieces from a single large rectangle so as to maximize the value of the pieces cut we develop a lagrangean relaxation of a zero one integer programming formulation of the problem and use it as a bound in a tree search procedure subgradient optimization is used to optimize the bound derived from the lagrangean relaxation problem reduction tests derived from both the original problem and the lagrangean relaxation are given incorporating the bound and the reduction tests into a tree search procedure enables moderately sized problems to be solved

stability of functional differential equations with impulses abstract in this paper the stability of functional differential equations fde with impulses is investigated some comparison theorems are given several lyapunov razumikhin functions of partial components of the state variable x which can be much easier constructed are used so that the conditions ensuring that stability are simpler and less restrictive the results improve and generalize the ones in the literature an example is also given to illustrate the importance of our results

efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation in this paper we analyse the performance of flowshop sequencing heuristics with respect to the objectives of makespan and flowtime minimisation for flowtime minimisation we propose the strategy employed by the neh heuristic to construct partial solutions results show that this approach outperforms the common fast heuristics for flowtime minimisation while performing similarly or slightly worse than others which on reward prove to be much more cpu time consuming additionally the suggested approach is well balanced with respect to makespan and flowtime minimisation based on the previous results two algorithms are proposed for the sequencing problem with multiple objectives makespan and flowtime minimisation these algorithms provide the decision maker with a set of heuristically efficient solutions such that he she may choose the most suitable sequence for a given ratio between costs associated with makespan and those assigned to flowtime computational experience shows both algorithms to perform better than the current heuristics designed for the two criteria problem

uniform stability theorems for delay differential equations with impulses abstract in the paper we obtain sufficient conditions for the uniform stability of the zero solution of the delay differential equation with impulses x t h t x t f t x t t t 0 t t k x t k x t k i k x t k k n

search algorithms under different kinds of heuristics a comparative study three heuristic search algorithms called algorithms a b and c are presented their performance with the admissibility condition relaxed is compared using the following two criteria i number of node expansions and ii cost of solution found first a general comparison is made in this process some variations and extensions of c are also considered subsequently two types of heuristic estimates called proper and path dependent are defined and the algorithms are reexamined it is shown that on the whole a nilsson s algorithm and b martelli s algorithm are inferior to c which is a slightly modified version of b 7 references

minimizing non decreasing separable objective functions for the unit time open shop scheduling problem in this paper we study both the non preemptive and preemptive versions of the popular unit time open shop scheduling problem for the set of feasible schedules which satisfy a predetermined order of job completion times we construct the linear description of the convex hull of the vectors of the job completion times based on the properties of the resulting scheduling polyhedron we show that the problem of constructing an optimal schedule minimizing an arbitrary non decreasing separable cost function of job completion times is polynomially solvable

performance enhancements to tabu search for the early tardy scheduling problem abstract tabu search ts has been used to solve a number of np hard problems including the single machine early tardy scheduling problem previous research has solved this particular problem using two different solution spaces one solution space manipulates the order of jobs in the schedule to create new neighbours while the other uses a binary solution space to specify which jobs are early and which jobs are tardy this paper presents techniques for improving the performance of ts in solving large early tardy scheduling problems with a view to developing generalized ts enhancement strategies three specific techniques are investigated the first uses a combination of two previously published candidate selection strategies the second incorporates an extra diversification phase in the search and the third uses a hybrid ts method that uses two different solution spaces results show that these performance enhancement strategies produce similar results all consistently better by at least 5 on the original ts methods used to solve this problem the applicability of these enhancements to ts generally is discussed

graph search methods for non order preserving evaluation functions applications to job sequencing problems abstract graph search with a is frequently faster than tree search but a graph search operates correctly only when the evaluation function is order preserving in the non orderpreserving case no paths can be discarded and the entire explicit graph must be stored in memory such situations arise in one machine minimum penalty job sequencing problems when setup times are sequence dependent grec the unlimited memory version of a memory constrained search algorithm of the authors called mrec has a clear advantage over a in that it is able to find optimal solutions to such problems at the same time it is as efficient as a in solving graph search problems with order preserving evaluation functions experimental results indicate that in the non order preserving case grec is faster than both best first and depth first tree search and can solve problem instances of larger size than best first tree search

an effective quasi human based heuristic for solving the rectangle packing problem abstract in this paper we introduce an effective deterministic heuristic less flexibility first for solving the classical np complete rectangle packing problem many effective heuristics implemented for this problem are cpu intensive and non deterministic in nature others including the polynomial approximation methodology j assoc comput mach 32 1 1985 130 are too laborious for practical problem sizes the technique we propose is inspired and developed by enhancing some rule of thumb guidelines resulting from the generation long work experience of human professionals in ancient days although the less flexibility first heuristic is a deterministic algorithm the results are very encouraging this algorithm can consistently produce packing densities of around 99 on most randomly generated large examples as compared with the recent results of a well known simulated annealing based rectangle packing rp algorithm ieee trans computer aided design integrated circuits systems 17 1 1998 60 the results are much better both in less dead space 2 4 vs 6 7 and much less cpu time 9 57 vs 331 78 seconds experimenting our heuristics on a public rectangle packing data set covering instances of 16 97 rectangles the average unpack ratio is quite satisfactory 0 92 for bounding boxes limited to be optimum and 2 68 for the completed packing while most cases spend only a few minutes in cpu time

algorithms for searching explicit and or graphs and their applications to problem reduction search abstract we present algorithms for finding out optimal cost solutions of an explicit and or graph we show that these new algorithms can work on and or graphs containing cycles finally we show how these algorithms can be incorporated in implicit graph search schemes like ao so that they work for transformation rules which lead to graphs with cycles

a fast tabu search algorithm for the permutation flow shop problem abstract a fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in the permutation flow shop is presented the algorithm is based on a tabu search technique with a specific neighborhood definition which employs a block of jobs notion computational experiments up to 500 jobs and 20 machines show its excellent numerical properties

a bidirectional building approach for the 2d constrained guillotine knapsack packing problem abstract this paper investigates the 2d guillotine knapsack packing problem in which the objective is to select and cut a set of rectangles from a sheet with fixed size and maximize the total profit of the selected rectangles the orientation of the rectangles is fixed and the guillotine cut in which the cut must be parallel to the sides of the sheet to divide it into two completely separated sheets is required two well known methods namely the top down and bottom up approaches are combined into a coherent algorithm to address this problem computational experiments on benchmark test sets show that the approach finds the optimal solution for almost all moderately sized instances and outperforms all existing approaches for larger instances

improvement heuristic for the flow shop scheduling problem an adaptive learning approach abstract we propose an improvement heuristic approach for the general flow shop problem n m cmax based on the idea of adaptive learning the approach employs a one pass heuristic to give a good starting solution in the search space and uses a weight parameter to perturb the data of the original problem to obtain improved solutions the weights are then adjusted employing a learning strategy which involves reinforcement and backtracking the learning is similar to that in neural networks the random perturbation allows a non deterministic local search we apply the improvement heuristic approach in conjunction with three well known heuristics in the literature namely palmer s slope index cds and neh we test our approach on several benchmark problem sets including taillard s carlier s heller s and reeves we compare our results to the best known upper bound solutions and find that for many problems we match the best known upper bound for one problem we discover a new upper bound

best first search methods for constrained two dimensional cutting stock problems best first search is a widely used problem solving technique in the field of artificial intelligence the method has useful applications in operations research as well here we describe an application to constrained two dimensional cutting stock problems of the following type a stock rectangle s of dimensions l w is supplied there are n types of demanded rectangles r1 r2 rn with the ith type having length li width wi value vi and demand constraint bi it is required to produce from the stock rectangle s ai copies of ri 1 i n to maximize a1v1 a2v2 anvn subject to the constraints ai bi only orthogonal guillotine cuts are permitted all parameters are integers a best first tree search algorithm based on wang s bottom up approach is described that guarantees optimal solutions and is more efficient than existing methods

two hybrid meta heuristics for the finite horizon elsp in flexible flow lines with unrelated parallel machines this article addresses the economic lot sizing and scheduling problem in flexible flow lines with unrelated parallel machines over a finite planning horizon the objective is determination of a cyclic schedule that minimizes the sum of setup and inventory holding costs per unit time without any stock out a new mixed zero one nonlinear mathematical programming has been developed for the problem due to difficulty of obtaining the optimal solution especially for medium and large sized problems we have also proposed two algorithms a hybrid genetic algorithm hga and a simulated annealing sa two efficient constructive heuristic algorithms have been also proposed that provide some initial solutions for the algorithms moreover a new local search approach has been proposed to improve solution quality of algorithms the two proposed solution methods are compared on 180 randomly generated problems computational results indicate the superiority of the proposed hga in compare to the sa with respect to the solution quality but the proposed sa outperforms the proposed hga with respect to the required computations time

some aspects of scatter search in the flow shop problem abstract the flow shop scheduling problem with the makespan criterion is a certain strongly np hard case from the domain of or this problem having simple formulation contrasting with its troublesome complex and time consuming solution methods is ideal for testing the quality of advanced combinatorial optimization algorithms although many excellent approximate algorithms for the flow shop problem have been provided up till now in the literature some theoretical and experimental problems associated with an algorithm s activity still remain unexamined in this paper we provide a new view on the solution space and the search process relying upon it we are proposing the new approximate algorithm which applies some properties of neighborhoods refers to the big valley phenomenon uses some elements of the scatter search as well as the path relinking technique this algorithm shows up to now unprecedented accuracy obtainable within a short time on a pc which has been confirmed in a wide variety of computer tests good properties of the algorithm remain scalable if the size of instances increases

case study on statistically estimating minimum makespan for flow line scheduling problems abstract lower bounds are typically used to evaluate the performance of heuristics for solving combinatorial minimization problems in the absence of tight analytical lower bounds optimal objective function values may be estimated statistically in this paper extreme value theory is used to construct confidence interval estimates of the minimum makespan achievable when scheduling nonsimilar groups of jobs on a two stage flow line experimental results based on randomly sampled solutions to each of 180 randomly generated test problems revealed that i least squares parameter estimators outperformed standard analytical estimators for the weibull approximation to the distribution of the sample minimum makespan ii to evaluate each weibull fit reliably both the anderson darling and kolmogorov smirnov goodness of fit tests should be used and iii applying a local improvement procedure to a large sample of randomly generated initial solutions improved the probability that the resulting weibull fit yielded a confidence interval covering the minimum makespan

a new heuristic method for the flow shop sequencing problem abstract a new heuristic method is presented for solving the m machine n job flow shop scheduling problem this method named spirit is composed of two phases the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques the results of the heuristic are compared with those from other well known methods

dynamics of a freely evolving two dimensional granular medium we consider the dynamics of an ensemble of identical inelastic hard disks in a doubly periodic domain because there is no external forcing the total energy of the system is monotonically decreasing so that this idealized granular medium is cooling down there are three nondimensional control parameters the coefficient of restitution r the solid fraction ensuremath nu and the total number of disks in the domain n our goal is a comprehensive description of the phenomenology of granular cooling in the r ensuremath nu n parameter space previous studies have shown that granular cooling results in the formation of structures both the mass and the momentum spontaneously become nonuniform four different regimes kinetic shearing clustered and collapsed have been identified starting with the almost elastic case in which r is just less than 1 the kinetic regime resembles a classical nondissipative gas in which there are no structures when r is decreased with fixed n and ensuremath nu the system evolves into the shearing regime in which most of the energy and momentum resides in the gravest hydrodynamic shear mode at still smaller values of r the clustered regime appears as an extended transient large clusters of disks form collide breakup and reform from the clustered state the gas eventually either evolves into the shearing regime or alternatively collapses the collapsed regime is characterized by a dynamical singularity in which a group of particles collides infinitely often in a finite time while each individual collision is binary the space and time scales decrease geometrically with the cumulative number of collisions so that a multiparticle interaction occurs the regime boundaries i e the critical values of r in the n ensuremath nu plane have been delineated using event driven numerical simulations analytic considerations show that the results of the simulations can be condensed by supposing that the critical values of r depend only on n and ensuremath nu through the optical depth ensuremath lambda ensuremath equiv d ensuremath surd n ensuremath pi ensuremath nu 2 where d is the disk diameter textcopyright 1996 the american physical society

best first minimax search we describe a very simple selective search algorithm for two player games called best first minimax it always expands next the node at the end of the expected line of play which determines the minimax value of the root it uses the same information as alpha beta minimax and takes roughly the same time per node generation we present an implementation of the algorithm that reduces its space complexity from exponential to linear in the search depth but at significant time cost our actual implementation saves the subtree generated for one move that is still relevant after the player and opponent move pruning subtrees below moves not chosen by either player we also show how to efficiently generate a class of incremental random game trees on uniform random game trees best first minimax outperforms alpha beta when both algorithms are given the same amount of computation on random trees with random branching factors best first outperforms alpha beta for shallow depths but eventually loses at greater depths we obtain similar results in the game of othello finally we present a hybrid best first extension algorithm that combines alpha beta with best first minimax and performs significantly better than alpha beta in both domains even at greater depths in othello it beats alpha beta in two out of three games

numerical tests of constitutive laws for dense granular flows we numerically and theoretically study the macroscopic properties of dense sheared granular materials in this process we first consider an invariance in newton s equations explain how it leads to bagnold s scaling and discuss how it relates to the dynamics of granular temperature next we implement numerical simulations of granular materials in two different geometries simple shear and flow down an incline and show that measurements can be extrapolated from one geometry to the other then we observe nonaffine rearrangements of clusters of grains in response to shear strain and show that fundamental observations which served as a basis for the shear transformation zone stz theory of amorphous solids m l falk and j s langer phys rev e 57 7192 1998 m r s bull 25 4 02000 can be reproduced in granular materials finally we present constitutive equations for granular materials as proposed by lemaitre phys rev lett 89 064303 2002 based on the dynamics of granular temperature and stz theory and show that they match remarkably well with our numerical data from both geometries

note on the single machine scheduling problem with quadratic penalty function of completion times an improved branching procedure this paper gives optimality conditions to obtain a priori precedence relationships among some of the jobs in a single machine scheduling problem so as to curtail the enumeration while using branch and bound technique the objective is to minimize a quadratic or generalized quadratic penalty function of job completion times

memory intensive and or search for combinatorial optimization in graphical models in this paper we explore the impact of caching during search in the context of the recent framework of and or search in graphical models specifically we extend the depth first and or branch and bound tree search algorithm to explore an and or search graph by equipping it with an adaptive caching scheme similar to good and no good recording furthermore we present best first search algorithms for traversing the same underlying and or search graph and compare both algorithms empirically we focus on two common optimization problems in graphical models finding the most probable explanation mpe in belief networks and solving weighted csps wcsp in an extensive empirical evaluation we demonstrate conclusively the superiority of the memory intensive and or search algorithms on a variety of benchmarks

performance of linear space search algorithms abstract search algorithms that use space linear in the search depth are widely employed in practice to solve difficult problems optimally such as planning and scheduling in this paper we study the average case performance of linear space search algorithms including depth first branch and bound dfbnb iterative deepening id and recursive best first search rbfs to facilitate our analyses we use a random tree t b d that has mean branching factor b depth d and node costs that are the sum of the costs of the edges from the root to the nodes we prove that the expected number of nodes expanded by dfbnb on a random tree is no more than bd times the expected number of nodes expanded by best first search bfs on the same tree which usually requires space that is exponential in depth d we also show that dfbnb is asymptotically optimal when bfs runs in exponential time and id and rbfs are asymptotically optimal when the edge costs of t b d are integers if bp 0 is the expected number of children of a node whose costs are the same as that of their parent then the expected number of nodes expanded by these three linear space algorithms is exponential when bp o d 4 when bp 0 1 and at most quadratic when bp 0 1 in addition we study the heuristic branching factor of t b d and the effective branching factor of bfs dfbnb id and rbfs on t b d furthermore we use our analytic results to explain a surprising anomaly in the performance of these algorithms and to predict the existence of a complexity transition in the asymmetric traveling salesman problem

local search methods for the flowshop scheduling problem with flowtime minimization abstract flowshop scheduling is a very active research area this problem still attracts a considerable amount of interest despite the sheer amount of available results total flowtime minimization of a flowshop has been actively studied and many effective algorithms have been proposed in the last few years new best solutions have been found for common benchmarks at a rapid pace however these improvements many times come at the cost of sophisticated algorithms complex methods hinder potential applications and are difficult to extend to small problem variations replicability of results is also a challenge in this paper we examine simple and easy to implement methods that at the same time result in state of the art performance the first two proposed methods are based on the well known iterated local search ils and iterated greedy ig frameworks which have been applied with great success to other flowshop problems additionally we present extensions of these methods that work over populations something that we refer to as population based ils pils and population based ig piga respectively we calibrate the presented algorithms by means of the design of experiments doe approach extensive comparative evaluations are carried out against the most recent techniques for the considered problem in the literature the results of a comprehensive computational and statistical analysis show that the presented algorithms are very effective furthermore we show that despite their simplicity the presented methods are able to improve 12 out of 120 best known solutions of taillard s flowshop benchmark with total flowtime criterion

average case analysis of best first search in two representative directed acyclic graphs many problems that arise in the real world have search spaces that are graphs rather than trees understanding the properties of search algorithms and analyzing their performance have been major objectives of research in ai but most published work on the analysis of search algorithms has been focused on tree search and comparatively little has been reported on graph search one of the major obstacles in analyzing average case complexity of graph search is that no single graph can serve as a suitable representative of graph search problems in this paper we propose one possible approach to analyzing graph search we take two problem domains for which the search graphs are directed acyclic graphs of similar structure and determine the average case performance of the best first search algorithm a on these graphs the first domain relates to one machine job sequencing problems in which a set of jobs must be sequenced on a machine in such a way that a penalty function is minimized the second domain concerns the traveling salesman problem our mathematical formulation extends a technique that has been used previously for analyzing tree search we demonstrate the existence of a gap in computational cost between two classes of problem instances one class has exponential complexity and the other has polynomial complexity for the job sequencing domain we provide supporting experimental evidence showing that problems exhibit a huge difference in computational cost under different conditions for the traveling salesman problem our theoretical results reflect on the long standing debate on the expected complexity of branch and bound algorithms for solving the problem indicating that the complexity can be polynomial or exponential depending on the accuracy of the heuristic function used

new razumikhin type theorems for impulsive functional differential equations in this paper we investigate stability and boundedness for a class of impulsive functional differential equations by using liapunov functions and razumikhin technique some new razumikhin type theorems on stability and boundedness are obtained the corresponding results obtained recently in j shen j yan nonlinear anal 33 1998 519 531 x liu j shen to appear are improved

reducing reexpansions in iterative deepening search by controlling cutoff bounds abstract it is known that a best first search algorithm like a 5 6 requires too much space which often renders it unusable and a depth first search strategy does not guarantee an optimal cost solution the iterative deepening algorithm ida 4 achieves both space and cost optimality for a class of tree searching problems however for many other problems it takes too much of computation time due to excessive reexpansion of nodes this paper presents a modification of ida to an admissible iterative depth first branch and bound algorithm ida cr for trees which overcomes this drawback of ida and operates much faster using the same amount of storage algorithm ida cra a bounded suboptimal cost variation of ida cr is also presented in order to reduce the execution time still further results with the 0 1 knapsack problem traveling salesman problem and the flow shop scheduling problem are shown

accelerated tabu search for no wait flowshop scheduling problem with maximum lateness criterion abstract for the no wait flowshop scheduling problem with maximum lateness criterion properties are developed to speed up three kinds of basic operations generating candidate solutions i e the insertion of a new job into a partial sequence and the insertion and exchange neighborhood moves the properties reduce the time to evaluate a candidate from o nm to o 1 and simplify the implementation of the heuristics based on the basic operations by evaluating candidates before their generation the properties also reduce from o n 3 m to o n 2 the time complexity of well known neh heuristic and the complete evaluation of the insertion and exchange neighborhoods tabu search ts is applied to the considered problem since ts tries to find the best neighbor of the current solution in each iteration and therefore can much benefit from the speedups three different ways to use insertion and exchange neighborhoods are compared in ts computational experiments show that the speedups are more helpful as job number increases and all proposed ts algorithms are more effective and robust than the existing algorithms although two and single neighborhood ts algorithms are not significantly different two neighborhood ts algorithms are more preferable

boundedness of the solutions of impulsive differential systems with time varying delay in this paper we investigate boundedness of the solutions of impulsive functional differential equations with time varying delay by using lyapunov functions and razumikhin techniques we will see that impulses do contribute to the solutions boundedness property

an algorithm for the two dimensional assortment problem abstract in this paper we consider the two dimensional assortment problem this is the problem of choosing from a set of stock rectangles a subset which can be used for cutting into a number of smaller rectangular pieces constraints are imposed upon the number of such pieces which result from the cutting a heuristic algorithm for the guillotine cutting version of the problem is developed based on a greedy procedure for generating two dimensional cutting patterns a linear program for choosing the cutting patterns to use and an interchange procedure to decide the best subset of stock rectangles to cut computational results are presented for a number of test problems which indicate that the algorithm developed produces good quality results both for assortment problems and for two dimensional cutting problems

improving the efficiency of a best first bottom up approach for the constrained 2d cutting problem abstract this work introduces several improvements in the solution of the constrained 2d cutting problem such improvements combine the detection of dominated and duplicated cutting patterns with the implementation of parallel approaches for best first search methods the analysis of symmetries and dominances among the cutting patterns is able to discard some non optimal or redundant builds thus reducing the search space to be explored the experimental evaluation demonstrates that when the domination duplication rules are applied to an efficient parallel approach the obtained reduction in the number of managed nodes involves a noticeable decrease in the computational effort associated with the final search process

restricted neighborhood in the tabu search for the flowshop problem this paper deals with the minimizing weighted tardiness of jobs in a scheduling problem where the structure is that of the proportionate flowshop a modified version of the widmer hertz algorithm for the makespan problem is presented improving the computational performance by reducing the size of the neighborhoods the heuristic tests were applied to 720 flowshop problems from 10 to 50 jobs

frontier search the critical resource that limits the application of best first search is memory we present a new class of best first search algorithms that reduce the space complexity the key idea is to store only the open list of generated nodes but not the closed list of expanded nodes the solution path can be recovered by a divide and conquer technique either as a bidirectional or unidirectional search for many problems frontier search dramatically reduces the memory required by best first search we apply frontier search to breadth first search of sliding tile puzzles and the 4 peg towers of hanoi problem dijkstra s algorithm on a grid with random edge costs and the a algorithm on the fifteen puzzle the four peg towers of hanoi problem and optimal sequence alignment in computational biology

hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization in this paper a hga hybrid genetic algorithm is proposed for permutation flowshop scheduling problems pfsp with total flowtime minimization which are known to be np hard one of the chromosomes in the initial population is constructed by a suitable heuristic and the others are yielded randomly an artificial chromosome is generated by a weighted simple mining gene structure with which a new crossover operator is presented additionally two effective heuristics are adopted as local search to improve all generated chromosomes in each generation the hga is compared with one of the most effective heuristics and a recent meta heuristic on 120 benchmark instances experimental results show that the hga outperforms the other two algorithms for all cases furthermore hga obtains 115 best solutions for the benchmark instances 92 of which are newly discovered

solving the flowshop scheduling problem with sequence dependent setup times using advanced metaheuristics abstract this paper deals with the permutation flowshop scheduling problem in which there are sequence dependent setup times on each machine commonly known as the sdst flowshop the optimisation criteria considered is the minimisation of the makespan or cmax genetic algorithms have been successfully applied to regular flowshops before and the objective of this paper is to assess their effectiveness in a more realistic and complex environment we present two advanced genetic algorithms as well as several adaptations of existing advanced metaheuristics that have shown superior performance when applied to regular flowshops we show a calibration of the genetic algorithm s parameters and operators by means of a design of experiments doe approach for evaluating the proposed algorithms we have coded several if not all known sdst flowshop specific algorithms all methods are tested against an augmented benchmark based on the instances of taillard the results show a clear superiority of the algorithms proposed especially for the genetic algorithms regardless of instance type and size

nonlinear elasticity and pressure dependent wave speeds in granular media following is an analysis of the small strain nonlinear elasticity of granular media near states of zero stress as it relates to the pressure dependent incremental linear elasticity and wave speeds the main object is elucidation of the p dependence of incremental elastic moduli on pressure p a dependence observed in numerous experiments but found to be at odds with the p scaling predicted by various micromechanical models based on hertzian contact after presenting a power law continuum model for small strain nonlinear elasticity the present work develops micromechanical models based on two alternative mechanisms for the anomalous pressure scaling namely 1 departures at the single contact level from the hertzian contact due to point like or conical asphericity 2 variation in the number density of hertzian contacts due to buckling of particle chains both mechanisms result in p pressure scaling at low pressure and both exhibit a high pressure transition to p scaling at a characteristic transition pressure p for assemblages of nearly equal spheres a non hertzian contact model for mechanism 1 and percolation type model for 2 yield estimates of p of the form p c 3 here c is a non dimensional coefficient depending only on granular contact geometry while 1 is a small parameter representing spherical imperfections and is an appropriate elastic modulus of the particles then with r representing particle radius and h a characteristic spherical tolerance or asperity height it is found that h r for mechanism 1 as opposed to h r for 2 limited data from the classic experiments of duffy mindlin on sphere assemblages tend to support mechanism 1 but more exhaustive experiments are called for in addition to the above analysis of reversible elastic effects a percolation model of inelastic shake down or consolidation is given it serves to describe how prolonged mechanical vibration leading to the replacement of point like or inactive contacts by stiffer hertz contacts may change the pressure scaling behaviour of particulate media the present analysis suggests that pressure dependence of elasticity may provide a useful means of characterizing the state of consolidation and stability of dense particulate media

depth first iterative deepening an optimal admissible tree search abstract the complexities of various search algorithms are considered in terms of time space and cost of solution path it is known that breadth first search requires too much space and depth first search can use too much time and doesn t always find a cheapest path a depth first iterative deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches the algorithm has been used successfully in chess programs has been effectively combined with bi directional search and has been applied to best first heuristic search as well this heuristic depth first iterative deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the fifteen puzzle within practical resource limits

the frictional flow of a dense granular material based on the dilatant double shearing model slow flow of granular materials which typically occurs during the emptying of industrial storage hoppers and bins has great industrial relevance in the present study we have employed our newly developed dilatant double shearing model h zhu m m mehrabadi m massoudi incorporating the effects of fabric in the dilatant double shearing model for granular materials int j plast 22 2006 628 653 to study the slow flow of a frictional dense granular material although most models pertain only to the fully developed granular flow the application of the dilatant double shearing model is shown to be valid from the onset of granular flow to the fully developed granular flow in this paper we use the finite element program abaqus explicit to numerically simulate the granular couette flow and the frictional granular flow in a silo for the granular couette flow the relative density variation and the velocity profile obtained by using the dilatant double shearing model are in good quantitative agreement with those obtained from a dem simulation for the frictional flow in a silo the major principal stress directions are obtained at various time steps after the onset of silo discharge we find that in the hopper zone the arching of the granular material between the sloping hopper walls is clearly demonstrated by the change in direction of the major principal stress we also compare the pressure distribution along the wall before and after the onset of silo discharge the numerical results show that the dilatant double shearing model is capable of capturing the essential features of the frictional granular flow

agent searching in a tree and the optimality of iterative deepening the agent searching framework models the effort of a search strategy in terms of the distance traversed by an agent while exploring the search space the framework has been found to be useful in modeling search problems where the cost of backtracking and retracing search paths is important in determining search complexity in this paper we show that depth first iterative deepening dfid strategies are optimal for an agent searching in a line in m concurrent rays and in uniform b ary trees in the conventional search model it is known that dfid is asymptotically optimal for uninformed search of uniform b ary trees in this paper we prove the stronger result that for agent searching in uniform b ary trees iterative deepening is optimal up to lower order terms we also discuss the problems involved in optimally performing agent search in a graph

a scatter search algorithm for the distributed permutation flowshop scheduling problem abstract the distributed permutation flowshop problem has been recently proposed as a generalization of the regular flowshop setting where more than one factory is available to process jobs distributed manufacturing is a common situation for large enterprises that compete in a globalized market the problem has two dimensions assigning jobs to factories and scheduling the jobs assigned to each factory despite being recently introduced this interesting scheduling problem has attracted attention and several heuristic and metaheuristic methods have been proposed in the literature in this paper we present a scatter search ss method for this problem to optimize makespan ss has seldom been explored for flowshop settings in the proposed algorithm we employ some advanced techniques like a reference set made up of complete and partial solutions along with other features like restarts and local search a comprehensive computational campaign including 10 existing algorithms together with statistical analyses shows that the proposed scatter search algorithm produces better results than existing algorithms by a significant margin moreover all 720 known best solutions for this problem are improved

a three dimensional numerical model for dense granular flows based on the µ i rheology this paper presents a three dimensional implementation of the so called i rheology to accurately and efficiently compute steady state dense granular flows the tricky pressure dependent visco plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the newton raphson algorithm the computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution then two application examples dealing with actual lab experiments have also been considered the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder in both configurations the obtained computational results are in good agreement with available experimental data

linear space best first search abstract best first search is a general heuristic search algorithm that always expands next a frontier node of lowest cost it includes as special cases breadth first search dijkstra s single source shortest path algorithm and the a algorithm its applicability however is limited by its exponential memory requirement previous approaches to this problem such as iterative deepening do not expand nodes in best first order if the cost function can decrease along a path we present a linear space best first search algorithm rbfs that always explores new nodes in best first order regardless of the cost function and expands fewer nodes than iterative deepening with a nondecreasing cost function on the sliding tile puzzles rbfs with a nonmonotonic weighted evaluation function dramatically reduces computation time with only a small penalty in solution cost in general rbfs reduces the space complexity of best first search from exponential to linear at the cost of only a constant factor in time complexity in our experiments

the two machine flow shop problem with arbitrary precedence relations abstract the scheduling problem n 3 f c max with arbitrary precedence constraints between the jobs is studied a branch and bound algorithm is described bounds are obtained by solving 2 machine subproblems which are relaxed versions of the current 3 machine problem these 2 machine problems which have precedence constraints can be quickly solved in an optimal fashion only if the constraints are of a series parallel s p form using methods described in 5 we find an s p constraints subgraph which may be solved to obtain a lower bound for each 2 machine subproblem this provides the basis for the calculation of an effective lower bound for the 3 machine case computational experience with the algorithm is reported

handling flexibility in a generalised job shop with a fuzzy approach abstract in this paper we deal with a particular scheduling problem inspired by a practical case coming from a belgian pharmaceutical company this problem has some particularities with respect to the classical job shop problem the principal one is the existence of a delay between the end of an operation and the start of the next operation of the same job this delay is not fixed but belongs generally to an interval range of possible values a resolution method the horizon method has been proposed in the deterministic case fixed data and strict constraints in this method the horizon time of each machine is discretised by unit times and at each unit time a binary value is associated all the operations applied on the machines horizons are logic operations or and right or left shifting and so on unfortunately this method does not take into account several aspects of the problem the existence of a preference relation on the possible values of the delay between successive operations and of flexible due dates in this work we modelise such flexible parameters using the fuzzy logic we propose a new method generalizing the horizon method this new method try to find for the realisation of the jobs a compromise between the choice of good values for the delay between couples of successive operations of the same job and good values for the completion time of the jobs

reflections on the mechanics of granular matter during recent years a rather basic conflict has emerged between departments of mechanics physics concerning the description of granular media experts from mechanics measure stress strain relations using the so called triaxial tests and then use these data to predict the behavior of a sample under given boundary conditions some physicists have a different view they have claimed that it is not possible to define a proper displacement field in a heap of sand and that the notion of strains is thus ambiguous in the present text we conclude that the crucial features are the following a a heap is usually formed from a flowing phase of sand b there is empirically a sharp interface between the flowing phase and the frozen heap below c we may define for each grain a displacement which is measured from the moment when it froze this displacement is due for instance to a compaction of the heap under its own weight we also present some aspects of the dynamics including dune motions and surface flows of grains bouchaud cates and coworkers have constructed a very compact description for thin flows we discuss the practical consequences of this picture emphasizing some possible extensions for thicker flows this suggests a number of possible experiments on avalanches

some efficient heuristic methods for the flow shop sequencing problem abstract in this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one next this problem is applied to taboo search a new technique to solve combinatorial optimization problems and computational experiments are reported finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed up

sequencing of jobs in some production system abstract we consider a real life problem of scheduling clients orders in the production of concrete blocks in a factory of building industry this problem can be modelled as a hybrid flow shop scheduling problem with mixed no wait no store constraints and mixed bottleneck non bottleneck machines the objective function is to minimize maximum completion time to solve the problem we propose an approximation algorithm based on the tabu search approach

the dh kd algorithm a hybrid approach for unconstrained two dimensional cutting problems abstract we study both weighted and unweighted unconstrained two dimensional guillotine cutting problems we develop a hybrid approach which combines two heuristics from the literature the first one dh uses a tree search procedure introducing two strategies depth first search and hill climbing the second one kd is based on a series of one dimensional knapsack problems using dynamic programming techniques the dh kd algorithm starts with a good initial lower bound obtained by using the kd algorithm at each level of the tree search the proposed algorithm uses also the kd algorithm for constructing new lower bounds and uses another one dimensional knapsack for constructing refinement upper bounds the resulting algorithm can be seen as a generalization of the two heuristics and solves large problem instances very well within small computational time our algorithm is compared to morabito et al s algorithm the unweighted case and to beasley s 2 approach the weighted case on some examples taken from the literature as well as randomly generated instances

admissibility of ao when heuristics overestimate les techniques de reduction de problemes utilisant des graphes and or sont souvent appliquees dans la resolution de problemes les strategies de recherche dans les graphes aud or sont etudiees de maniere a assurer leur admissibilite l algorithme ao est alors analyse en utilisant des graphes aud or mixtes il est montre que la decomposition de l estimation du cout permet une analyse des strategies de recherche dans les graphes and or semblable a celle concernant les graphes ordinaires ou l estimation de cout est optimale quelques methodes permettant d obtenir des solutions admissibles sont proposees

heuristic search in restricted memory research note abstract this paper presents heuristic search algorithms which work within memory constraints these algorithms ma for ordinary graphs and mao for and or graphs guarantee admissible solutions within specified memory limitations above the minimum required the memory versus node expansions tradeoff is analyzed for the worst case in the case of ordinary graphs some experiments using the fifteen puzzle problem are carried out under various pruning conditions these parameterized algorithms are found to encompass a wide class of best first search algorithms

a genetic algorithm for the two dimensional strip packing problem with rectangular pieces given a set of rectangular pieces and a container of fixed width and variable length the two dimensional strip packing problem 2d spp consists of orthogonally placing all the pieces within the container without overlapping such that the overall length of the layout is minimised until now mainly heuristics for example genetic algorithms ga were proposed for the 2d spp which use encoded solutions that are manipulated by standard operators in this paper a ga for the 2d spp is suggested that works without any encoding of solutions rather fully defined layouts are manipulated as such by means of specific genetic operators two additional constraints namely the orientation constraint and the guillotine constraint can be taken into account the ga is subjected to a comprehensive test using benchmark instances with up to 5000 pieces compared to eleven competing methods from the literature the ga performs best

heuristic search through islands abstract a heuristic search strategy via islands is suggested to significantly decrease the number of nodes expanded algorithm i which searches through a set of island nodes island set is presented assuming that the island set contains at least one node on an optimal cost path this algorithm is shown to be admissible and expands no more nodes than a for cases where the island set does not contain an optimal cost path or any path algorithm i a modification of algorithm i is suggested this algorithm ensures a suboptimal cost path which may be optimal and in extreme cases falls back to a

inconsistent heuristics in theory and practice in the field of heuristic search it is usually assumed that admissible heuristics are consistent implying that consistency is a desirable attribute the term inconsistent heuristic has at times been portrayed negatively as something to be avoided part of this is historical early research discovered that inconsistency can lead to poor performance for a nodes might be re expanded many times however the issue has never been fully investigated and was not re considered after the invention of ida this paper shows that many of the preconceived notions about inconsistent heuristics are outdated the worst case exponential time of inconsistent heuristics is shown to only occur on contrived graphs with edge weights that are exponential in the size of the graph furthermore the paper shows that rather than being something to be avoided inconsistent heuristics often add a diversity of heuristic values into a search which can lead to a reduction in the number of node expansions inconsistent heuristics are easy to create contrary to the common perception in the ai literature to demonstrate this a number of methods for achieving effective inconsistent heuristics are presented pathmax is a way of propagating inconsistent heuristic values in the search from parent to children this technique is generalized into bidirectional pathmax bpmx which propagates values from a parent to a child node and vice versa bpmx can be integrated into ida and a when inconsistent heuristics are used with bpmx experimental results show a large reduction in the search effort required by ida positive results are also presented for a searches

boundary conditions in mixture theory and in cfd applications of higher order models we discuss the importance of and the need for additional boundary conditions in mixture theory also known as the theory of interacting continua specifically we will give an overview of the model due to rajagopal and massoudi which is appropriate for the flow of a linearly viscous fluid infused with solid particles the solid particles are modeled as granular materials in this formulation the need for additional boundary condition arises due to higher gradients of density or volume fraction the challenging issue of how to split the total stress or the total velocity at the boundary is also discussed

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

bida an improved perimeter search algorithm abstract in this paper we present a new bidirectional heuristic search algorithm our algorithm can be viewed as a perimeter search algorithm and it uses a new technique for reducing the number of heuristic evaluations we also prove some general results on the behavior of iterative deepening perimeter search algorithms and we discuss some new lazy evaluation techniques for improving their performance the theoretical and experimental results show that perimeter search algorithms outperform the other bidirectional algorithms and we believe it is worthwhile to give them a deep look in subsequent research

single facility resource allocation under capacity based economies and diseconomics of scope we consider the optimal allocation of a resource in a single facility production environment in the presence of capacity based economies and diseconomies of scope this setting generalizes the usual approach to single facility resource allocation by allowing for the effective capacity of a facility to be a nonlinear function of the number of different items produced or the services delivered by the facility economies or diseconomies of scope are attributable to factors such as production changeover time overall process management requirements and complementary production requirements that vary with the product or service mix we consider the problem setting in which the effective capacity depends on the number of tasks assigned to the facility the resulting model scope generalizes the well known 0 1 knapsack problem we also consider the more general problem gencap in which capacity consumption depends on the specific set of tasks assigned to the facility we define tabu search heuristics as well as exact branch and bound algorithms for scope and gencap on the basis of extensive computational experience the solution procedures are seen to be extremely effective in particular the heuristics consistently obtain high quality solutions to the test problems furthermore the tractability of solving problems to optimality is demonstrated through the solution of scope problems having as many as 500 tasks and gencap problems involving as many as 50 tasks and more than 16 500 nonlinear capacity interactions

and or graph heuristic search methods two new marking algorithms for and or graphs called cf and cs are presented for admissible heuristics cs is not needed and cf is shown to be preferable to the marking algorithms of martelli and montanari when the heuristic is not admissible the analysis is carried out with the help of the notion of the first and second discriminants of an and or graph it is proved that in this case cf can be followed by cs to get optimal solutions provided the sumcost criterion is used and the first discriminant equals the second estimates of time and storage requirements are given other cost measures such as maxcost are also considered and a number of interesting open problems are enumerated

proof number search abstract proof number search pn search is designed for finding the game theoretical value in game trees it is based on ideas derived from conspiracy number search and its variants such as applied cn search and cn search while in cn search the purpose is to continue searching until it is unlikely that the minimax value of the root will change pn search aims at proving the true value of the root therefore pn search does not consider interim minimax values pn search selects the next node to be expanded using two criteria the potential range of subtree values and the number of nodes which must conspire to prove or disprove that range of potential values these two criteria enable pn search to treat efficiently game trees with a non uniform branching factor it is shown that in non uniform trees pn search outperforms other types of search such as iterative deepening search even when enhanced with transposition tables move ordering for the full principal variation etc pn search has been used to establish the game theoretical values of connect four qubic and go moku there pn search was able to find a forced win for the player to move first the experiments described here are in the domain of awari a game which has not yet been solved the experiments are repeatable for other games with a non uniform branching factor this article describes the underlying principles of pn search presents an appropriate implementation and provides an analysis of its strengths and weaknesses