An optimal coarse-grained arc consistency algorithm

The use of constraint propagation is the main feature of any constraint solver. It is thus of prime importance to manage the propagation in an efficient and effective fashion. There are two classes of propagation algorithms for general constraints: fine-grained algorithms where the removal of a value for a variable will be propagated to the corresponding values for other variables, and coarse-grained algorithms where the removal of a value will be propagated to the related variables. One big advantage of coarse-grained algorithms, like AC-3, over fine-grained algorithms, like AC-4, is the ease of integration when implementing an algorithm in a constraint solver. However, fine-grained algorithms usually have optimal worst case time complexity while coarse-grained algorithms do not. For example, AC-3 is an algorithm with non-optimal worst case complexity although it is simple, efficient in practice, and widely used. In this paper we propose a coarse-grained algorithm, AC2001/3.1, that is worst case optimal and preserves as much as possible the ease of its integration into a solver (no heavy data structure to be maintained during search). Experimental results show that AC2001/3.1 is competitive with the best fine-grained algorithms such as AC-6. The idea behind the new algorithm can immediately be applied to obtain a path consistency algorithm that has the best-known time and space complexity. The same idea is then extended to non-binary constraints.     

Strong local consistency algorithms for table constraints

Table constraints are important in constraint programming as they are present in many real problems from areas such as configuration and databases. As a result, numerous specialized algorithms that achieve generalized arc consistency (GAC) on table constraints have been proposed. Since these algorithms achieve GAC, they operate on one constraint at a time. In this paper we propose new filtering algorithms for positive table constraints that achieve stronger local consistency properties than GAC by exploiting intersections between constraints. The first algorithm, called maxRPWC+, is a domain filtering algorithm that is based on the local consistency maxRPWC and extends the GAC algorithm of Lecoutre and Szymanek (2006). The second algorithm extends the state-of-the-art STR-based algorithms to stronger relation filtering consistencies, i.e., consistencies that can remove tuples from constraints’ relations. Experimental results from benchmark problems demonstrate that the proposed algorithms are quite competitive with standard GAC algorithms like STR2 in some classes of problems with intersecting table constraints, being orders of magnitude faster in some cases.     

An optimal arc consistency algorithm for a particular case of sequence constraint

The AtMostSeqCard constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n???q?+?1 constraints AtMost u on each subsequence of size q. This constraint is useful in car-sequencing and crew-rostering problems. In van Hoeve et al. (Constraints 14(2):273–292, 2009), two algorithms designed for the AmongSeq constraint were adapted to this constraint with an O(2 ^q n) and O(n ³) worst case time complexity, respectively. In Maher et al. (2008), another algorithm similarly adaptable to filter the AtMostSeqCard constraint with a time complexity of O(n ²) was proposed. In this paper, we introduce an algorithm for achieving arc consistency on the AtMostSeqCard constraint with an O(n) (hence optimal) worst case time complexity. Next, we show that this algorithm can be easily modified to achieve arc consistency on some extensions of this constraint. In particular, the conjunction of a set of m AtMostSeqCard constraints sharing the same scope can be filtered in O(nm). We then empirically study the efficiency of our propagator on instances of the car-sequencing and crew-rostering problems.     

An extended divide-and-conquer algorithm for a generalized class of multibody constraints

An extension to the divide-and-conquer algorithm (DCA) is presented in this paper to model constrained multibody systems. The constraints of interest are those applied to the system due to the inverse dynamics or control laws rather than the kinematically closed loops which have been studied in the literature. These imposed constraints are often expressed in terms of the generalized coordinates and speeds. A set of unknown generalized constraint forces must be considered in the equations of motion to enforce these algebraic constraints. In this paper dynamics of this class of multibody constrained systems is formulated using a Generalized-DCA. In this scheme, introducing dynamically equivalent forcing systems, each generalized constraint force is replaced by its dynamically equivalent spatial constraint force applied from the appropriate parent body to the associated child body at the connecting joint without violating the dynamics of the original system. The handle equations of motion are then formulated considering these dynamically equivalent spatial constraint forces. These equations in the GDCA scheme are used in the assembly and disassembly processes to solve for the states of the system, as well as the generalized constraint forces and/or Lagrange multipliers.     

Extending the relevant component analysis algorithm for metric learning using both positive and negative equivalence constraints

Relevant component analysis (RCA) is a recently proposed metric learning method for semi-supervised learning applications. It is a simple and efficient method that has been applied successfully to give impressive results. However, RCA can make use of supervisory information in the form of positive equivalence constraints only. In this paper, we propose an extension to RCA that allows both positive and negative equivalence constraints to be incorporated. Experimental results show that the extended RCA algorithm is effective.     

An efficient genetic algorithm for automated mining of both positive and negative quantitative association rules

In this paper, a genetic algorithm (GA) is proposed as a search strategy for not only positive but also negative quantitative association rule (AR) mining within databases. Contrary to the methods used as usual, ARs are directly mined without generating frequent itemsets. The proposed GA performs a database-independent approach that does not rely upon the minimum support and the minimum confidence thresholds that are hard to determine for each database. Instead of randomly generated initial population, uniform population that forces the initial population to be not far away from the solutions and distributes it in the feasible region uniformly is used. An adaptive mutation probability, a new operator called uniform operator that ensures the genetic diversity, and an efficient adjusted fitness function are used for mining all interesting ARs from the last population in only single run of GA. The efficiency of the proposed GA is validated upon synthetic and real databases.     

An algorithm for the generalized eigenproblem

A new method is presented that determines the eigenvalues and corresponding eigenvectors for the most general form of the eigenproblem. An example illustrating the technique is included. The appendix contains a listing of the Fortran program developed for use on a Data General Eclipse/S200 computing system.     

Generalised arc consistency for the AllDifferent constraint: An empirical survey

The AllDifferent constraint is a crucial component of any constraint toolkit, language or solver, since it is very widely used in a variety of constraint models. The literature contains many different versions of this constraint, which trade strength of inference against computational cost. In this paper, we focus on the highest strength of inference, enforcing a property known as generalised arc consistency (GAC). This work is an analytical survey of optimizations of the main algorithm for GAC for the AllDifferent constraint. We evaluate empirically a number of key techniques from the literature. We also report important implementation details of those techniques, which have often not been described in published papers. We pay particular attention to improving incrementality by exploiting the strongly-connected components discovered during the standard propagation process, since this has not been detailed before. Our empirical work represents by far the most extensive set of experiments on variants of GAC algorithms for AllDifferent. Overall, the best combination of optimizations gives a mean speedup of 168 times over the same implementation without the optimizations.     

An efficient three-point arc algorithm

For many applications a 2-D circular arc can be conveniently specified by three points that lie on the arc. Since the radius of curvature grows without bound as the three points become collinear, any practical algorithm must avoid calculating the arc's radius or functions of the radius. An algorithm that achieves this objective is presented. It is very efficient because it uses exclusively integer arithmetic and requires only addition, subtraction, comparison, and branch operation in the inner loop     

An efficient algorithm for positive realizations

We observe that successive applications of known results from the theory of positive systems lead to an efficient general algorithm for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one of which complements an earlier result of [L. Benvenuti, L. Farina, An example of how positivity may force realizations of ‘large’ dimensions, Systems Control Lett. 36 (1999) 261–266]. Finally, we improve a lower-bound of [B. Nagy, M. Matolcsi, A lower-bound on the dimension of positive realizations, IEEE Trans. Circuits Syst. I 50 (2003) 782–784] to indicate that the algorithm is indeed efficient in general.     

Existence and algorithm for solving some generalized mixed variational inequalities

In this paper, by applying the auxiliary variational principle technique, an existence theorem of solutions for a new class of generalized mixed variational inequalities is proved in Hilbert spaces. A novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed. The convergence criteria and error estimates are also given. These results of existence, algorithm, and convergence are new and generalize some corresponding results involving single-valued mappings in recent literatures.     

一种有效的完全加权正负关联模式挖掘算法AWAPM_SPRMI

完全加权正负关联模式在文本挖掘、信息检索等方面具有重要的理论和应用价值.针对现有挖掘算法的不足,构建完全加权正负关联模式评价框架SPRMII(support-probability ratio-mutual information-interest),提出完全加权项集双兴趣度阈值剪枝策略,然后基于该剪枝策略提出一种新的基于SPRMII框架的完全加权正负关联模式挖掘算法AWAPM_SPRMII(all-weighted association patterns mining based on SPRMII).该算法克服了传统挖掘算法缺陷并采用新剪枝方法从完全加权数据库中挖掘有趣的频繁项集和负项集,通过项集权重维数比的简单计算和SPRMII评价框架,从这些项集中挖掘有效的完全加权正负关联规则.理论分析和实验表明,该算法有效,具有良好的扩展性,与现有经典挖掘算法比较,获得了良好的挖掘性能.     

A RBF-based constrained global optimization algorithm for problems with computationally expensive objective and constraints

This paper presents a metamodel-based constrained optimization method, called Radial basis function-based Constrained Global Optimization (RCGO), to solve optimization problems involving computationally expensive objective function and inequality constraints. RCGO is an extension of the adaptive metamodel-based global optimization (AMGO) algorithm which can handle unconstrained black-box optimization problems. Firstly, a sequential sampling method is implemented to obtain the initial points for building the radial basis function (RBF) approximations to all computational expensive functions while enforcing a feasible solution. Then, an auxiliary objective function subject to the approximate constraints is constructed to determine the next iterative point and further improve the solution. During the process, a distance function with a group of exponents is introduced in the auxiliary function to balance the local exploitation and the global exploration. The RCGO method is tested on a series of benchmark problems, and the results demonstrate that RCGO needs fewer costly evaluations and can be applied for costly constrained problems with all infeasible start points. And the test results on the 30D problems demonstrate that RCGO has advantages in solving the problems. The proposed method is then applied to the design of a cycloid gear pump and desirable results are obtained.     

Optimal and efficient filtering algorithms for table constraints

Filtering algorithms for table constraints can be classified in two categories: constraint-based and value-based. In the constraint-based approaches, the propagation queue only contains information on the constraints that must be reconsidered. For the value-based approaches, the propagation queue also contains information on the removed values. This paper proposes five efficient value-based algorithms for table constraints. Two of them (AC5TCOpt-Tr and AC5TCOpt-Sparse) are proved to have an optimal time complexity of O(r·t+r·d) per table constraint. Substantial experimental results are presented. An empirical analysis is conducted on the effect of the arity of the tables. The experiments show that our propagators are the best when the arity of the table is 3 or 4. Indeed, on instances containing only binary constraints, our algorithms are outperformed by classical AC algorithm AC3rm. AC3rm is dedicated to binary constraints. However, all our algorithms outperform existing state-of-the-art constraint based STR2+ and MDD ^c and the optimal value-based STR3 algorithms on those instances. On instances with small arity tables (up to arity 4), all our algorithms are generally faster than STR2+, MDD ^c and than STR3. AC5TCOpt-Sparse is globally the best propagator on those benchmarks. On benchmarks containing large arity tables (arity 5 or more), each of the three existing state-of-the-art algorithms is the winning strategy on one different benchmark.     

An efficient dynamical evolutionary algorithm for global optimization

In this paper, we introduce a new dynamical evolutionary algorithm (DEA) that aims to find the global optimum and give the theoretical explanation from statistical mechanics. The algorithm has been evaluated numerically using a wide set of test functions which are nonlinear, multimodal and multidimensional. The numerical results show that it is possible to obtain global optimum or more accurate solutions than other methods for the investigated hard problems.     

An adaptive single-point algorithm for global numerical optimization

This paper describes a novel algorithm for numerical optimization, called Simple Adaptive Climbing (SAC). SAC is a simple efficient single-point approach that does not require a careful fine-tunning of its two parameters. SAC algorithm shares many similarities with local optimization heuristics, such as random walk, gradient descent, and hill-climbing. SAC has a restarting mechanism, and a powerful adaptive mutation process that resembles the one used in Differential Evolution. The algorithms SAC is capable of performing global unconstrained optimization efficiently in high dimensional test functions. This paper shows results on 15 well-known unconstrained problems. Test results confirm that SAC is competitive against state-of-the-art approaches such as micro-Particle Swarm Optimization, CMA-ES or Simple Adaptive Differential Evolution.     

Universal basis sets for low-lying excited states of some positive and negative ions

The generator coordinate Hartree-Fock method is used to generate universal basis sets (UBSs) of Gaussian- and Slater-type functions for low-lying excited states of some mono-positive and -negative ions. From our basis sets the total energies are calculated and compared with the corresponding results obtained with other UBSs and with fully-optimized basis sets of STFs.     

An effective subgradient algorithm for the generalized assignment problem

A modified subgradient algorithm is presented for the generalized assignment problem, which, like the classical assignment problem, is concerned with the minimum cost assignment of agents to jobs. The generalized assignment problem, however, permits differences in job performance efficiencies among agents and thereby allows the possibility that each agent may be assigned more than a single job, as long as each job is ultimately assigned and the total resources available to every agent are not exceeded. A two stage heuristic algorithm using a modified subgradient approach and branch and bound is developed for solving the problem. By computing step sizes precisely and using the dual as a bound, the algorithm is shown to be particularly effective and easy to program and implement. A numerical example is presented to illustrate the model and method, and computational experience is cited for problems containing up to 12,000 0–1 variables.