a tabu search approach to the constraint satisfaction problem as a general problem solver many combinatorial problems including a variety of combinatorial optimization problems can be naturally formulated as a constraint satisfaction problem csp we develop in this paper a tabu search based algorithm for the csp as a foundation for a general problem solver in addition to the basic components of tabu search we develop a number of elaborations such as an automatic control mechanism for the tabu tenure modification of the penalty function to handle objective functions and enlargement of the neighborhood by allowing swap operations computational results with our algorithm are reported for various problems selected from a wide range of applications i e graph coloring generalized assignment set covering timetabling and nurse scheduling our results appear to be competitive with those of existing algorithms specially developed for the respective problem domains

a metaheuristic algorithm to solve satellite broadcast scheduling problem in this paper a new effective and scalable differential evolution algorithm is proposed for optimizing the satellite broadcast s scheduling problem sbs the satellite broadcast s scheduling optimization problem is known to be an np complete problem in which the aim is to find a valid broadcasting pattern to earth stationed terminals which maximizes the number of timeslots utilized for broadcasting under certain constraints the algorithm proposed sd bde is a binary version of differential evolution hybridized with ideas extracted from stochastic diffusion search on top of that a repair heuristic mechanism is added to resolve constraint violations preliminary analysis shows that the repair heuristic is very effective as compared to other versions which include other heuristics further the performance of the proposed algorithm is tested thoroughly against published work toward solving sbs problem as well as state of the art existing binary coded population based similar algorithms in this paper we used along with instances reported in the literature for such problem randomly generated benchmark s instances of varying sizes for the sake of creating a unified large scale set to compare different algorithm against experimental results show that the proposed algorithm outperformed the existing algorithms by finding better or optimal solutions for almost all tested benchmarks

combining vns with constraint programming for solving anytime optimization problems abstract this paper presents an hybrid search method for solving on line optimization problems that are modelled using the vcsp valued constraint satisfaction problems framework to each constraint is associated a valuation representing the cost to pay when this constraint will be violated by a solution our method vns lds cp uses principles of vns variable neighborhood search and combines a partial tree search limited discrepancy search with constraint propagation in order to compute local optima experiments on the celar benchmarks demonstrate significant improvements on other competing methods lns cp gr lobjois l lemaitre m verfaillie g 2000 large neighbourhood search using constraint propagation and greedy reconstruction for valued csp resolution in proceedings of the ecai2000 workshop on modelling and solving problems with constraints another hybrid method using vcsp s and two standard versions of simulated annealing li y h 1997 directed annealing search in constraint satisfaction and optimization ph d thesis imperial college of science department of computing quick and medium moreover vns lds cp clearly satisfies the key properties of anytime algorithms finally vns lds cp has been successfully applied to a real life on line resource allocation problem in computer networks

epsilon transformation exploiting phase transitions to solve combinatorial optimization problems abstract it has been shown that there exists a transition in the average case complexity of tree search problems from exponential to polynomial in the search depth we develop a new method called e transformation which makes use of this complexity transition to find a suboptimal solution with a random tree model we show that as the tree depth approaches infinity the expected number of nodes expanded by branch and bound bnb using e transformation is at most cubic in the search depth and that the relative error of the solution cost found with respect to the optimal solution cost is bounded above by a small constant we also present an iterative version of e transformation that can be used to find both suboptimal and optimal goal nodes depth first bnb dfbnb using iterative e transformation significantly improves upon dfbnb on random trees with large branching factors and deep goal nodes finding a better solution sooner we then present experimental results for e transformation and iterative e transformation on the asymmetric traveling salesman problem atsp and the maximum boolean satisfiability problem and identify the conditions under which these two methods are effective on the atsp dfbnb using e transformation outperforms a well known local search method and dfbnb using iterative e transformation improves upon dfbnb

an improved exponential time algorithm for k sat we propose and analyze a simple new randomized algorithm called resolvesat for finding satisfying assignments of boolean formulas in conjunctive normal form the algorithm consists of two stages a preprocessing stage in which resolution is applied to enlarge the set of clauses of the formula followed by a search stage that uses a simple randomized greedy procedure to look for a satisfying assignment currently this is the fastest known probabilistic algorithm for k cnf satisfiability for k g 4 with a running time of o 20 5625n for 4 cnf in addition it is the fastest known probabilistic algorithm for k cnf k g 3 that have at most one satisfying assignment unique k sat with a running time o 2 2 ln 2 1 n p o n e o 20 386 n in the case of 3 cnf the analysis of the algorithm also gives an upper bound on the number of the codewords of a code defined by a k cnf this is applied to prove a lower bounds on depth 3 circuits accepting codes with nonconstant distance in particular we prove a lower bound 21 282 i i i i i i

solving satisfiability with less searching a new technique complement searching is given for reducing the amount of searching required to solve satisfiability constraint satisfaction problems search trees for these problems often contain subtrees that have approximately the same shape when this occurs knowledge that the first subtree does not have a solution can be used to reduce the searching in the second subtree only the part of the second subtree which is different from the first needs to be searched the pure literal rule of the davis putnam procedure is a special case of complement searching the new technique greatly reduces the amount of searching required to solve conjunctive normal form predicates that contain almost pure literals literals with a small number of occurrences

parameterized enumeration transversals and imperfect phylogeny reconstruction we study parameterized enumeration problems where we are interested in all solutions of limited size rather than just some solution of minimum cardinality actually we have to enumerate the inclusion minimal solutions in order to get fixed parameter tractable fpt results two novel concepts are the notion of a full kernel that contains all small solutions and implicit enumeration of solutions in form of compressed descriptions in particular we study combinatorial and computational bounds for the transversal hypergraph vertex covers in graphs is a special case restricted to hyperedges with at most k elements as an example we apply the results and further special purpose techniques to almost perfect phylogeny reconstruction a problem in computational biology

bose einstein condensation in satisfiability problems abstract this paper is concerned with the complex behavior arising in satisfiability problems we present a new statistical physics based characterization of the satisfiability problem specifically we design an algorithm that is able to produce graphs starting from a k sat instance in order to analyze them and show whether a bose einstein condensation occurs we observe that analogously to complex networks the networks of k sat instances follow bose statistics and can undergo bose einstein condensation in particular k sat instances move from a fit get rich network to a winner takes all network as the ratio of clauses to variables decreases and the phase transition of k sat approximates the critical temperature for the bose einstein condensation finally we employ the fitness based classification to enhance sat solvers e g chainsat and obtain the consistently highest performing sat solver for cnf formulas and therefore a new class of efficient hardware and software verification tools

a t o 2 n 2 s o 2 n 4 algorithm for certain np complete problems in this paper we develop a general purpose algorithm that can solve a number of np complete problems in time t o 2 n 2 and space s o 2 n 4 the algorithm can be generalized to a fam

local search with constraint propagation and conflict based heuristics search algorithms for solving csp constraint satisfaction problems usually fall into one of two main families local search algorithms and systematic algorithms both families have their advantages designing hybrid approaches seems promising since those advantages may be combined into a single approach in this paper we present a new hybrid technique it performs a local search over partial assignments instead of complete assignments and uses filtering techniques and conflict based techniques to efficiently guide the search this new technique benefits from both classical approaches a priori pruning of the search space from filtering based search and possible repair of early mistakes from local search we focus on a specific version of this technique tabu decision repair experiments done on open shop scheduling problems show that our approach competes well with the best highly specialized algorithms

computing the similarity of two sequences with nested arc annotations we present exact algorithms for the np complete longest common subsequence problem for sequences with nested arc annotations a problem occurring in structure comparison of rna given two sequences of length at most n and nested arc structure one of our algorithms determines if existent in o 3 31k1 k2 n time an arc preserving subsequence of both sequences which can be obtained by deleting together with corresponding arcs k1 letters from the first and k2 letters from the second sequence a second algorithm shows that in case of a four letter alphabet we can find a length l arc annotated subsequence in o 12l l n time this means that the problem is fixed parameter tractable when parameterized by the number of deletions as well as when parameterized by the subsequence length our findings complement known approximation results which give a quadratic time factor 2 approximation for the general and polynomial time approximation schemes for restricted versions of the problem in addition we obtain further fixed parameter tractability results for these restricted versions

a noisy self organizing neural network with bifurcation dynamics for combinatorial optimization the self organizing neural network sonn for solving general 0 1 combinatorial optimization problems cops is studied in this paper with the aim of overcoming existing limitations in convergence and solution quality this is achieved by incorporating two main features an efficient weight normalization process exhibiting bifurcation dynamics and neurons with additive noise the sonn is studied both theoretically and experimentally by using the n queen problem as an example to demonstrate and explain the dependence of optimization performance on annealing schedules and other system parameters an equilibrium model of the sonn with neuronal weight normalization is derived which explains observed bands of high feasibility in the normalization parameter space in terms of bifurcation dynamics of the normalization process and provides insights into the roles of different parameters in the optimization process under certain conditions this dynamical systems view of the sonn reveals cascades of period doubling bifurcations to chaos occurring in multidimensional space with the annealing temperature as the bifurcation parameter a strange attractor in the two dimensional 2 d case is also presented furthermore by adding random noise to the cost potentials of the network nodes it is demonstrated that unwanted oscillations between symmetrical and greedy nodes can be sufficiently reduced resulting in higher solution quality and feasibility

construction of image reduction operators using averaging aggregation functions in this work we present an image reduction algorithm based on averaging aggregation functions we axiomatically define the concepts of image reduction operator and local reduction operator we study the construction of the latter by means of averaging functions and we propose an image reduction algorithm image reduction operator we analyze the properties of several averaging functions and their effect on the image reduction algorithm finally we present experimental results where we apply our algorithm in two different applications analyzing the best operators for each concrete application

weak monotonicity of lehmer and gini means we analyze directional monotonicity of several mixture functions in the direction 1 1 1 called weak monotonicity our particular focus is on power weighting functions and the special cases of lehmer and gini means we establish limits on the number of arguments of these means for which they are weakly monotone these bounds significantly improve the earlier results and hence increase the range of applicability of gini and lehmer means we also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions

strengthened ordered directionally monotone functions links between the different notions of monotonicity abstract in this work we propose a new notion of monotonicity strengthened ordered directional monotonicity this generalization of monotonicity is based on directional monotonicity and ordered directional monotonicity two recent weaker forms of monotonicity we discuss the relation between those different notions of monotonicity from a theoretical point of view additionally along with the introduction of two families of functions and a study of their connection to the considered monotonicity notions we define an operation between functions that generalizes the choquet integral and the ukasiewicz implication

a computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers singularly perturbed turning point problems tpps for second order ordinary differential equations des exhibiting twin boundary layers are considered in order to obtain numerical solution of these problems a computational method is suggested in which exponentially fitted difference schemes are combined with classical numerical methods in this method the given internal domain of definition of differential equation is divided into four subintervals and we solve the differential equation in each interval and combine the solution the implementation of the method on parallel architectures is mentioned error estimates are derived and numerical examples are given

a lagrangian reconstruction of genet abstract genet is a heuristic repair algorithm which demonstrates impressive efficiency in solving some large scale and hard instances of constraint satisfaction problems csps in this paper we draw a surprising connection between genet and discrete lagrange multiplier methods based on the work of wah and shang we propose a discrete lagrangian based search scheme lsdl defining a class of search algorithms for solving csps we show how genet can be reconstructed from lsdl the dual viewpoint of genet as a heuristic repair method and a discrete lagrange multiplier method allows us to investigate variants of genet from both perspectives benchmarking results confirm that first our reconstructed genet has the same fast convergence behavior as the original genet implementation and has competitive performance with other local search solvers dlm walksat and w sat oip on a set of difficult benchmark problems second our improved variant which combines techniques from heuristic repair and discrete lagrangian methods is always more efficient than the reconstructed genet and can better it by an order of magnitude

the computational complexity of propositional strips planning abstract i present several computational complexity results for propositional strips planning i e strips planning restricted to ground formulas different planning problems can be defined by restricting the type of formulas placing limits on the number of pre and postconditions by restricting negation in pre and postconditions and by requiring optimal plans for these types of restrictions i show when planning is tractable polynomial and intractable np hard in general it is pspace complete to determine if a given planning instance has any solutions extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even np completeness for example when only ground literals are permitted determining plan existence is pspace complete even if operators are limited to two preconditions and two postconditions when definite horn ground formulas are permitted determining plan existence is pspace complete even if operators are limited to zero preconditions and one postcondition one of the interesting tractable problems is if each operator is restricted to positive preconditions and one postcondition only ground literals the blocks world problem slightly modified is a subproblem of this restricted planning problem these results in combination with previous analyses are not encouraging for domain independent planning

equilibria of iterative softmax and critical temperatures for intermittent search in self organizing neural networks kwok and smith 2005 recently proposed a new kind of optimization dynamics using self organizing neural networks sonn driven by softmax weight renormalization such dynamics is capable of powerful intermittent search for high quality solutions in difficult assignment optimization problems however the search is sensitive to temperature setting in the softmax renormalization step it has been hypothesized that the optimal temperature setting corresponds to the symmetry breaking bifurcation of equilibria of the renormalization step when viewed as an autonomous dynamical system called iterative softmax ism we rigorously analyze equilibria of ism by determining their number position and stability types it is shown that most fixed points exist in the neighborhood of the maximum entropy equilibrium n 1 n 1 n 1 where n is the ism dimensionality we calculate the exact rate of decrease in the number of ism equilibria as one moves away from bounds on temperatures guaranteeing different stability types of ism equilibria are also derived moreover we offer analytical approximations to the critical symmetry breaking bifurcation temperatures that are in good agreement with those found by numerical investigations so far the critical temperatures have been determined only by trial and error numerical simulations on a set of n queens problems for a wide range of problem sizes n the analytically determined critical temperatures predict the optimal working temperatures for sonn intermittent search very well it is also shown that no intermittent search can exist in sonn for temperatures greater than one half

new methods for 3 sat decision and worst case analysis abstract we prove the worst case upper bound 1 5045 n for the time complexity of 3 sat decision where n is the number of variables in the input formula introducing new methods for the analysis as well as new algorithmic techniques we add new 2 and 3 clauses called blocked clauses generalizing the extension rule of extended resolution our methods for estimating the size of trees lead to a refined measure of formula complexity of 3 clause sets and can be applied also to arbitrary trees

an o 2 0 304n algorithm for solving maximum independent set problem a faster algorithm for finding a maximum independent set in a graph is presented the algorithm is an improved version of the one by tarjan and trojanowski 7 a technique to further accelerate this algorithm is also described

algorithms for four variants of the exact satisfiability problem we present four polynomial space and exponential time algorithms for variants of the exact satisfiability problem first an o 1 1120n where n is the number of variables time algorithm for the np complete decision problem of exact 3 satisfiability and then an o 1 1907n time algorithm for the general decision problem of exact satisfiability the best previous algorithms run in o 1 1193n and o 1 2299n time respectively for the p complete problem of counting the number of models for exact 3 satisfiability we present an o 1 1487n time algorithm we also present an o 1 2190n time algorithm for the general problem of counting the number of models for exact satisfiability presenting a simple reduction we show how this algorithm can be used for computing the permanent of a 0 1 matrix

minimizing conflicts a heuristic repair method for constraint satisfaction and scheduling problems abstract the paper describes a simple heuristic approach to solving large scale constraint satisfaction and scheduling problems in this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs the search can be guided by a value ordering heuristic the min conflicts heuristic that attempts to minimize the number of constraint violations after each step the heuristic can be used with a variety of different search strategies we demonstrate empirically that on the n queens problem a technique based on this approach performs orders of magnitude better than traditional backtracking techniques we also describe a scheduling application where the approach has been used successfully a theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective

optimization by simulated annealing an experimental evaluation part ii graph coloring and number partitioning this is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well studied domains of combinatorial optimization simulated annealing is a randomized technique proposed by s kirkpatrick c d gelatt and m p vecchi for improving local optimization algorithms here we report on experiments at adapting simulated annealing to graph coloring and number partitioning two problems for which local optimization had not previously been thought suitable for graph coloring we report on three simulated annealing schemes all of which can dominate traditional techniques for certain types of graphs at least when large amounts of computing time are available for number partitioning simulated annealing is not competitive with the differencing algorithm of n karmarkar and r m karp except on relatively small instances moreover if running time is taken into account natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based in sharp contrast to the observed performance of annealing on other problems

counting models for 2 sat and 3 sat formulae we here present algorithms for counting models and max weight models for 2sat and 3sat formulae they use polynomial space and run in o 1 2561n and o 1 6737n time respectively where n is the number of variables this is faster than the previously best algorithms for counting nonweighted models for 2sat and 3sat which run in o 1 3247n and o 1 6894n time respectively in order to prove these time bounds we develop new measures of formula complexity allowing us to conveniently analyze the effects of certain factors with a large impact on the total running time we also provide an algorithm for the restricted case of separable 2sat formulae with fast running times for well studied input classes for all three algorithms we present interesting applications such as computing the permanent of sparse 0 1 matrices

an initial study of time complexity in infinite domain constraint satisfaction abstract the constraint satisfaction problem csp is a widely studied problem with numerous applications in computer science and artificial intelligence for infinite domain csps there are many results separating tractable and np hard cases while upper and lower bounds on the time complexity of hard cases are virtually unexplored hence we initiate a study of the worst case time complexity of such csps we analyze backtracking algorithms and determine upper bounds on their time complexity we present asymptotically faster algorithms based on enumeration techniques and we show that these algorithms are applicable to well studied problems in for instance temporal reasoning finally we prove non trivial lower bounds applicable to many interesting csps under the assumption that certain complexity theoretic assumptions hold the gap between upper and lower bounds is in many cases surprisingly small which suggests that our upper bounds cannot be significantly improved

a deterministic 2 2 k 1 n algorithm for k sat based on local search local search is widely used for solving the propositional satisfiability problem papadimitriou 1991 showed that randomized local search solves 2 sat in polynomial time recently schoning 1999 proved that a close algorithm for k sat takes time 2 2 k n up to a polynomial factor this is the best known worst case upper bound for randomized 3 sat algorithms cf also recent preprint by schuler et al we describe a deterministic local search algorithm for k sat running in time 2 2 k 1 n up to a polynomial factor the key point of our algorithm is the use of covering codes instead of random choice of initial assignments compared to other weakly exponential algorithms our algorithm is technically quite simple we also describe an improved version of local search for 3 sat the improved algorithm runs in time 1 481n up to a polynomial factor our bounds are better than all previous bounds for deterministic k sat algorithms

pointwise directional increasingness and geometric interpretation of directionally monotone functions abstract the relaxation of monotonicity requirements is a trend in the theory of aggregation functions in the recent literature we can find several relaxed forms of monotonicity such as weak directional cone ordered directional and strengthened directional monotonicity all these forms of monotonicity are global properties in the sense that they are imposed for all the points in the domain of a function in this work we introduce a local notion of monotonicity called pointwise directional monotonicity or directional monotonicity at a point based on this concept we characterize all the previously defined notions of monotonicity and in the final part of the paper we present some geometric aspects of the global weaker forms of monotonicity stressing their relations and singularities

a satisfiability tester for non clausal propositional calculus an algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2 25 e l is described where l can be either the length of the input expression or the number of occurrences of literals i e leaves in it this represents a new upper bound on the complexity of non clausal satisfiability testing the performance is achieved by using lemmas concerning assignments and pruning that preserve satisfiability together with choosing a good variable upon which to recur for expressions in clause form it is shown that the davis putnam procedure satisfies the same upper bound

number of models and satisfiability of sets of clauses abstract we present a way of calculating the number of models of propositional formulas represented by sets of clauses the complexity of such a procedure is o n k where k is the length of clauses and n is the number of variables in the clauses the value of 2 is approximately 1 619 value of 3 is approximately 1 840 and the value of k approaches 2 when k is large further we apply the theory on satisfiability problems especially on the 3 sat problems the complexity of the 3 sat problems is o n where n is the number of variables in the clauses the value of is approximately 1 571 which is better than the results in schiermeyer 1993 and monien and schiermeyer 1985

an improved deterministic local search algorithm for 3 sat we slightly improve the pruning technique presented in dantsin et al theoret comput sci 289 2002 69 to obtain an o 1 473n deterministic algorithm for 3 sat

speedup learning for repair based search by identifying redundant steps repair based search algorithms start with an initial solution and attempt to improve it by iteratively applying repair operators such algorithms can often handle large scale problems that may be difficult for systematic search algorithms nevertheless the computational cost of solving such problems is still very high we observed that many of the repair steps applied by such algorithms are redundant in the sense that they do not eventually contribute to finding a solution such redundant steps are particularly harmful in repair based search where each step carries high cost due to the very high branching factor typically associated with it accurately identifying and avoiding such redundant steps would result in faster local search without harming the algorithm s problem solving ability in this paper we propose a speedup learning methodology for attaining this goal it consists of the following steps defining the concept of a redundant step acquiring this concept during off line learning by analyzing solution paths for training problems tagging all the steps along the paths according to the redundancy definition and using an induction algorithm to infer a classifier based on the tagged examples and using the acquired classifier to filter out redundant steps while solving unseen problems our algorithm was empirically tested on instances of real world employee timetabling problems etp the problem solver to be improved is based on one of the best methods for solving some large etp instances our results show a significant improvement in speed for test problems that are similar to the given example problems

a survey of numerical techniques for solving singularly perturbed ordinary differential equations this survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the numerical methods developed by numerous researchers after 1984 2000 the work done in this area during the period 1905 1984 has already been surveyed by the first author of this paper see appl math comput 30 1989 223 for details due to the space constraints we have covered only singularly perturbed one dimensional problems

improved exact algorithms for mildly sparse instances of max sat abstract we present improved exponential time exact algorithms for max sat our algorithms run in time of the form o 2 1 c n for instances with n variables and m c n clauses in this setting there are three incomparable currently best algorithms a deterministic exponential space algorithm with c 1 o c log c due to dantsin and wolpert 2006 9 a randomized polynomial space algorithm with c 1 o c log 3 c and a deterministic polynomial space algorithm with c 1 o c 2 log 2 c due to sakai seto and tamaki 2015 30 our first result is a deterministic polynomial space algorithm with c 1 o c log c that achieves the previous best time complexity without exponential space or randomization furthermore this algorithm can handle instances with exponentially large weights and hard constraints the previous algorithms and our deterministic polynomial space algorithm run super polynomially faster than 2 n only if m o n 2 our second results are deterministic exponential space algorithms for max sat with c 1 o c log c 2 3 and for max 3 sat with c 1 o c 1 2 that run super polynomially faster than 2 n when m o n 5 2 log 5 2 n and m o n 3 log 2 n respectively our third result is a randomized exponential space algorithm for max sat with c 1 o c 1 2 log 3 2 c that run super polynomially faster than 2 n when m o n 3 log 5 n

multigrid applied to singular perturbation problems the solution of the singular perturbation problem email protected u b x u f 0 0 u 0 u 0 u 1 u 1 by a multigrid algorithm is considered theoretical and experimental results for a number of different discretizations are presented the theoretical and observed rates agree with the results developed in an earlier work of kamowitz and parter in addition the rate of convergence of the algorithm when the coarse grid operator is the natural finite difference analogue of the fine grid operator is presented this is in contrast to the case in the previous work where the galerkin choice i h hl hi h h was used for the coarse grid operators

exploring relaxation induced neighborhoods to improve mip solutions given a feasible solution to a mixed integer programming mip model a natural question is whether that solution can be improved using local search techniques local search has been applied very successfully in a variety of other combinatorial optimization domains unfortunately local search relies extensively on the notion of a solution neighborhood and this neighborhood is almost always tailored to the structure of the particular problem being solved a mip model typically conveys little information about the underlying problem structure this paper considers two new approaches to exploring interesting domain independent neighborhoods in mip the more effective of the two which we call relaxation induced neighborhood search rins constructs a promising neighborhood using information contained in the continuous relaxation of the mip model neighborhood exploration is then formulated as a mip model itself and solved recursively the second which we call guided dives is a simple modification of the mip tree traversal order loosely speaking it guides the search towards nodes that are close neighbors of the best known feasible solution extensive computational experiments on very difficult mip models show that both approaches outperform default cplex mip and a previously described approach for exploring mip neighborhoods local branching with respect to several different metrics the metrics we consider are quality of the best integer solution produced within a time limit ability to improve a given integer solution of both good and poor quality and time required to diversify the search in order to find a new solution

refining the phase transition in combinatorial search abstract many recent studies have identified phase transitions from under to overconstrained instances in classes of constraint satisfaction search problems and their relation to search cost for example cases that are difficult to solve with a variety of search methods are concentrated near these transitions these studies show that a simple parameter describing the problem structure predicts the difficulty of solving the problem on average however this prediction is associated with a large variance and depends on the somewhat arbitrary choice of the problem class thus these results are of limited direct use for individual instances to help address this limitation additional parameters describing problem structure as well as heuristic effectiveness are introduced these are shown to reduce the variation in some cases this also provides further insight into the nature of intrinsically hard search problems

multi agent oriented constraint satisfaction this paper presents a multi agent oriented method for solving csps constraint satisfaction problems in this method distributed agents represent variables and a two dimensional grid like environment in which the agents inhabit corresponds to the domains of the variables thus the positions of the agents in such an environment constitute the solution to a csp in order to reach a solution state the agents will rely on predefined local reactive behaviors namely better move least move and random move while presenting the formalisms and algorithm we will analyze the correctness and complexity of the algorithm and demonstrate the proposed method with two benchmark csps i e n queen problems and coloring problems in order to further determine the effectiveness of different reactive behaviors we will examine the performance of this method in deriving solutions based on behavior prioritization and different selection probabilities

an exact algorithm for the minimum dominating clique problem a subset of vertices d v of a graph g v e is a dominating clique if d is a dominating set and a clique of g the existence problem given a graph g is there a dominating clique in g is np complete and thus both the minimum and the maximum dominating clique problems are np hard we present an o 1 3387n time and polynomial space algorithm that for an input graph on n vertices either computes a minimum dominating clique or reports that the graph has no dominating clique the algorithm uses the branch reduce paradigm and its time analysis is based on the measure conquer approach we also establish a lower bound of 1 2599n for the worst case running time of the algorithm finally using memorization we obtain an o 1 3234n time and exponential space algorithm for the same problem

a framework for structured quantum search abstract a quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented this algorithm shows how coherent quantum systems can be matched to the underlying structure of abstract search spaces the algorithm is evaluated empirically with a variety of search problems and shown to be particularly effective for searches with many constraints furthermore the algorithm provides a simple framework for utilizing search heuristics it also exhibits the same phase transition in search difficulty as found for sophisticated classical search methods indicating that it is effectively using the problem structure

novel survival functions based on conditional aggregation operators abstract in this paper we define a novel survival function motivated by real life problems which generalizes the super level measure introduced by do and thiele 2015 this concept is based on conditional aggregation operators extending the definition of aggregation operators introduced by calvo et al 2002 for all bounded measurable functions and not only for finite sequences some basic properties and several examples of conditional aggregation operators are presented using the novel survival function the choquet stieltjes functional is introduced and the conditions are indicated under which this functional can be called an integral the new functional generalizes several known integrals including the choquet stieltjes integral as well as choquet integral with respect to level dependent capacity introduced by greco et al 2011

multigrid methods for variational problems this paper develops a very simple but powerful theory for multigrid methods which applies directly to variationally posed operator equations

a probabilistic analysis of prepositional strips planning abstract i present a probabilistic analysis of prepositional strips planning the analysis considers two assumptions one is that each possible precondition likewise postcondition of an operator is selected independently of other pre and postconditions the other is that each operator has a fixed number of preconditions likewise postconditions under both assumptions i derive bounds for when it is highly likely that a planning instance can be efficiently solved either by finding a plan or proving that no plan exists roughly if planning instances under either assumption have n propositions ground atoms and g goals and the number of operators is less than an o n in g bound then a simple efficient algorithm can prove that no plan exists for most instances if the number of operators is greater than an n in g bound then a simple efficient algorithm can find a plan for most instances the two bounds differ by a factor that is exponential in the number of pre and postconditions a similar result holds for plan modification i e solving a planning instance that is close to another planning instance with a known plan thus it appears that prepositional strips planning a pspace complete problem exhibits a easy hard easy pattern as the number of available operators increases with a narrow range of hard problems an empirical study demonstrates this pattern for particular parameter values because prepositional strips planning is pspace complete this extends previous phase transition analyses which have focused on np complete problems also the analysis shows that surprisingly simple algorithms can solve a large subset of the planning problem

backtracking algorithms for disjunctions of temporal constraints abstract we extend the framework of simple temporal problems studied originally by dechter meiri and pearl to consider constraints of the form x 1 y 1 r 1 x n y n r n where x 1 x n y 1 y n are variables ranging over the real numbers r 1 r n are real constants and n 1 this is a wide class of temporal constraints that can be used to model a variety of problems in temporal reasoning scheduling planning and temporal constraint databases we have implemented several progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints backtracking backjumping three variations of forward checking and forward checking with backjumping we have partially ordered the above algorithms according to the number of visited search nodes and the number of performed consistency checks although our problem is non binary our results agree with the results of kondrak and van beek who consider only binary constraints we have also studied the performance of the above algorithms experimentally using randomly generated sets of data and job shop scheduling problems the experiments with random instances allowed us to locate the hard region for this class of problems the results show that hard problems occur at a critical value of the ratio of disjunctions to variables

anytime learning of decision trees the majority of existing algorithms for learning decision trees are greedy a tree is induced top down making locally optimal decisions at each node in most cases however the constructed tree is not globally optimal even the few non greedy learners cannot learn good trees when the concept is difficult furthermore they require a fixed amount of time and are not able to generate a better tree if additional time is available we introduce a framework for anytime induction of decision trees that overcomes these problems by trading computation speed for better tree quality our proposed family of algorithms employs a novel strategy for evaluating candidate splits a biased sampling of the space of consistent trees rooted at an attribute is used to estimate the size of the minimal tree under that attribute and an attribute with the smallest expected tree is selected we present two types of anytime induction algorithms a contract algorithm that determines the sample size on the basis of a pre given allocation of time and an interruptible algorithm that starts with a greedy tree and continuously improves subtrees by additional sampling experimental results indicate that for several hard concepts our proposed approach exhibits good anytime behavior and yields significantly better decision trees when more time is available

a study of some multigrid ideas in an effort to understand certain ideas and concepts associated with multigrid iterations we give an in depth study of a particular simple problem we consider a standard finite difference system associated with the two point boundary value problem pu bu qu 0 u 0 u 1 0 the operators i 2 h h i h 2 h are operator based interpolation and projection operators while the smoothers are the damped jacobi iterations with parameter a 0 we determine the exact rates of convergence for the two grid scheme and upper bounds 1 for the multigrid schemes experimental results are discussed

fuzzy rr dfcsp and planning constraint satisfaction is a fundamental artificial intelligence technique for knowledge representation and inference however the formulation of a static constraint satisfaction problem csp with hard imperative constraints is insufficient to model many real problems fuzzy constraint satisfaction provides a more graded viewpoint priorities and preferences are placed on individual constraints and aggregated via fuzzy conjunction to obtain a satisfaction degree for a solution to the problem this paper examines methods for solving an important instance of dynamic flexible constraint satisfaction dfcsp combining fuzzy csp and restriction relaxation based dynamic csp fuzzy rrdfcsp this allows the modelling of complex situations where both the set of constraints may change over time and there is flexibility inherent in the definition of the problem this paper also presents a means by which classical planning can be extended via fuzzy sets to enable flexible goals and preferences to be placed on the use of planning operators a range of plans can be produced trading compromises made versus the length of the plan the flexible planning operators are close in definition to fuzzy constraints hence through a hierarchical decomposition of the planning graph the work shows how flexible planning reduces to the solution of a set of fuzzy rrdfcsps

exact algorithms for treewidth and minimum fill in we show that the treewidth and the minimum fill in of an n vertex graph can be computed in time mathcal o 1 8899 n our results are based on combinatorial proofs that an n vertex graph has mathcal o 1 7087 n minimal separators and mathcal o 1 8135 n potential maximal cliques we also show that for the class of asteroidal triple free graphs the running time of our algorithms can be reduced to mathcal o 1 4142 n

a measure conquer approach for the analysis of exact algorithms for more than 40 years branch reduce exponential time backtracking algorithms have been among the most common tools used for finding exact solutions of np hard problems despite that the way to analyze such recursive algorithms is still far from producing tight worst case running time bounds motivated by this we use an approach that we call measure conquer as an attempt to step beyond such limitations the approach is based on the careful design of a nonstandard measure of the subproblem size this measure is then used to lower bound the progress made by the algorithm at each branching step the idea is that a smarter measure may capture behaviors of the algorithm that a standard measure might not be able to exploit and hence lead to a significantly better worst case time analysis in order to show the potentialities of measure conquer we consider two well studied np hard problems minimum dominating set and maximum independent set for the first problem we consider the current best algorithm and prove thanks to a better measure a much tighter running time bound for it for the second problem we describe a new simple algorithm and show that its running time is competitive with the current best time bounds achieved with far more complicated algorithms and standard analysis our examples show that a good choice of the measure made in the very first stages of exact algorithms design can have a tremendous impact on the running time bounds achievable

cooperative updating in the hopfield model we propose a new method for updating units in the hopfield model with this method two or more units change at the same time so as to become the lowest energy state among all possible states since this updating algorithm is based on the detailed balance equation convergence to the boltzmann distribution is guaranteed if our algorithm is applied to finding the minimum energy in constraint satisfaction and combinatorial optimization problems then there is a faster convergence than those with the usual algorithm in the neural network this is shown by experiments with the travelling salesman problem the four color problem the n queen problem and the graph bi partitioning problem in constraint satisfaction problems for which earlier neural networks are effective in some cases our updating scheme works fine even though we still encounter the problem of ending up in local minima our updating scheme has a great advantage compared with the usual updating scheme used in combinatorial optimization problems also we discuss parallel computing using our updating algorithm