A parallel algorithm solving a tridiagonal Toeplitz linear system

A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver first decomposes an n-dimensional strictly diagonally dominant TTLS equation into a number of m-dimensional subsystems employing a modified Gaussian elimination method. An analytic solution of a continued fraction is obtained to derive the solver. The solver based on the modified Gaussian elimination method fully exploits parallelism. Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).     

A fully parallel block independent set algorithm for distributed sparse matrices

We present a fully parallel algorithm for constructing block independent set for general sparse matrices in a distributed environment. The block independent set is used in the construction of parallel multilevel preconditioners in solving large sparse matrices on distributed memory parallel computers. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set construction strategies. Numerical experiments indicate that the parallel block independent set algorithm is effective in reducing both the parallel multilevel preconditioner construction time and the size of the last level reduced system.     

A parallel algorithm for improving the maximal property of Poisson disk sampling

This paper presents a simple yet effective algorithm to improve an arbitrary Poisson disk sampling to reach the maximal property, i.e., no more Poisson disk can be inserted. Taking a non-maximal Poisson disk sampling as input, our algorithm efficiently detects the regions allowing additional samples and then generates Poisson disks in these regions. The key idea is to convert the complicated plane or space searching problem into a simple searching on circles or spheres, which is one dimensional lower than the original sampling domain. Our algorithm is memory efficient and flexible, which generates maximal Poisson disk sampling in an arbitrary 2D polygon or 3D polyhedron. Moreover, our parallel algorithm can be extended from the Euclidean space to curved surfaces in an intrinsic manner. Thanks to its parallel structure, our method can be implemented easily on modern graphics hardware. We have observed significance performance improvement compared to the existing techniques.     

A parallel algorithm for the 0–1 knapsack problem

Research efforts on parallel exact algorithms for the 0–1 knapsack problem have up to now concentrated on solving small problems (at most 1,000 objects) and in many cases results have only been obtained by simulation of the parallel algorithm. After a brief review of a well known sequential branch-and-bound algorithm we discuss a new parallel algorithm for the 0–1 knapsack problem which exploits the potential parallelism that exists during the backtracking steps of the branch-and-bound algorithm. We report results for our parallel algorithm on a transputer network for problems with up to 20,000 objects. The speedup obtained is nearly linear for 2, 4, and 8 processors except when there is a strong correlation between the profit and weight of the objects.     

A parallel immune algorithm for traveling salesman problem and its application on cold rolling scheduling

Parallel computing provides efficient solutions for combinatorial optimization problem. However, since the communications among computing processes are rather cost-consuming, the actual parallel or distributed algorithm comes with substantial expenditures, such as, hardware, management, and maintenance. In this study, a parallel immune algorithm based on graphic processing unit (GPU) that originally comes to process the computer graphics in display adapter is proposed. Genetic operators and a structure of vaccine taboo list are designed, and the internal memory utility of GPU structure is optimized. To verify the effectiveness and efficiency of the proposed algorithm, various middle-scale traveling salesman problems (TSP) are employed to demonstrate the potential of the proposed techniques. The simulation examples demonstrate that the developed method can greatly improve the computing efficiency for solving the TSP, and the results are more remarkable when the scale of TSP becomes higher. Furthermore, the derived algorithm is verified by a practical application in steel industry that arranges the cold rolling scheduling of a batch of steel coils.     

A parallel two-list algorithm for the knapsack problem

An n-element knapsack problem has 2ⁿ possible solutions to search over, so a task which can be accomplished in 2″ trials if an exhaustive search is used. Due to the exponential time in solving the knapsack problem, the problem is considered to be very hard. In the past decade, much effort has been done in order to find techniques which could lead to practical algorithms with reasonable running time. In 1994, Chang et al. proposed a brilliant parallel algorithm, which needs O(2^n/8) processors to solve the knapsack problem in O(2^n/2) time; that is, the cost of Chang et al.'s parallel algorithm is O(2^5n/8). In this paper, we propose a parallel algorithm to improve Chang et al.'s parallel algorithm by reducing the time complexity to be O(2^3n/8) under the same O(2^n/8) processors available. Thus, the proposed parallel algorithm has a cost of O(2^n/2). It is an improvement over previous literature. We believe that the proposed parallel algorithm is pragmatically feasible at the moment when multiprocessor systems become more and more popular.     

A parallel multistart algorithm for the closest string problem

In this paper we describe and implement a parallel algorithm to find approximate solutions for the Closest String Problem (CSP). The CSP, also known as Motif Finding problem, has applications in Coding Theory and Computational Biology. The CSP is NP-hard which motivates us to think about heuristics to solve large instances. Several approximation algorithms have been designed for the CSP, but all of them have a poor performance guarantee. Recently some researchers have shown empirically that integer programming techniques can be successfully used to solve moderate-size instances (10–30 strings each of which is 300–800 characters long) of the CSP. However, real-world instances are larger than those tested. In this paper we show how a simple heuristic can be used to find near-optimal solutions to that problem. We implemented a parallel version of this heuristic and report computational experiments on large-scale instances. These results show the effectiveness of our approach.     

三层并行遗传算法及装箱问题中的应用

提出了一个新的基于线程构建模块(TBB)的三层并行遗传算法(TPGA)。与传统遗传算法相比,在保证了算法正确性的前提下提高了运行效率,并将遗传算法的数据编码、任务处理和数据解码分别进行并行化,提高了收敛速度。TBB是Intel提供的能够完整表现并行性的代码库。采用C++语言实现了基于TBB的TPGA和串行遗传算法(SGA),通过大量实验证明,TPGA同SGA相比,不但提高了收敛速度,而且能够取得一致的最优解。     

求解异构并行机调度问题的混合多目标教-学优化算法

以异构并行机调度问题为研究对象,考虑了一类以优化总加权完工时间和加权延误总和的调度问题。首先,基于问题描述构建了该问题的混合整数规划模型。其次,提出了混合多目标教-学优化算法。在算法设计中,结合问题的特点设计序列编码方法,并采用分解技术来实现多目标调度问题的求解。此外,该算法通过融合多种交叉算子来定义个体进化过程,并通过与变邻域搜索算法的混合来提升其优化效果。最后,给出了仿真实验与分析,测试结果验证了多目标教-学优化算法求解该调度问题的优越性。     

A new optimal algorithm for the permutation flow-shop problem and its parallel implementation

This paper describes a new parallel algorithm for solving n-job, m-machine flow-shop problems. The algorithm is basically a parallelization of the usual branch-and-bound method. It also takes advantage of all search method to keep high efficiency of parallel processing, when the sub-problem becomes smaller than certain size. It is shown that its implementation on both nCUBE2 and LUNA88k2 gives very good performance characteristics.     

A parallel algorithm for solving the implicit diffusion difference equations

This paper presents a parallel algorithm for solving the implicit diffusion difference equations. The basic idea is based on vectorization of the tridiagonal Toeplitz difference equations. This method is superior to the algorithm showed by H. Stone [8]. We computed some examples on an NEC SX-3/44R supercomputer by our method. The results showed a good parallelism with this algorithm.     

A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet

Nowadays genetic algorithms stand as a trend to solve NP-complete and NP-hard problems. In this paper, we present a new hybrid metaheuristic which uses parallel genetic algorithms and scatter search coupled with a decomposition-into-petals procedure for solving a class of vehicle routing and scheduling problems. The parallel genetic algorithm presented is based on the island model and its performance is evaluated for a heterogeneous fleet problem, which is considered a problem much harder to solve than the homogeneous vehicle routing problem.     

A genetic algorithm application using fuzzy processing times in non-identical parallel machine scheduling problem

There are many scheduling problems which are NP-hard in the literature. Several heuristics and dispatching rules are proposed to solve such hard combinatorial optimization problems. Genetic algorithms (GA) have shown great advantages in solving the combinatorial optimization problems in view of its characteristic that has high efficiency and that is fit for practical application [1]. Two different scale numerical examples demonstrate the genetic algorithm proposed is efficient and fit for larger scale identical parallel machine scheduling problem for minimizing the makespan. But, even though it is a common problem in the industry, only a small number of studies deal with non-identical parallel machines. In this article, a kind of genetic algorithm based on machine code for minimizing the processing times in non-identical machine scheduling problem is presented. Also triangular fuzzy processing times are used in order to adapt the GA to non-identical parallel machine scheduling problem in the paper. Fuzzy systems are excellent tools for representing heuristic, commonsense rules. That is why we try to use fuzzy systems in this study.     

A novel parallel hybrid intelligence optimization algorithm for a function approximation problem

A novel parallel hybrid intelligence optimization algorithm (PHIOA) is proposed based on combining the merits of particle swarm optimization with genetic algorithms. The PHIOA uses the ideas of selection, crossover and mutation from genetic algorithms (GAs) and the update velocity and situation of particle swarm optimization (PSO) under the independence of PSO and GAs. The proposed algorithm divides the individuals into two equation groups according to their fitness values. The subgroup of the top fitness values is evolved by GAs and the other subgroup is evolved by the PSO algorithm. The optimal number is selected as a global optimum at every circulation which shows better results than both PSO and GAs, then improves the overall performance of the algorithm. The PHIOA is used to optimize the structure and parameters of the fuzzy neural network. Finally, the experimental results have demonstrated the superiority of the proposed PHIOA to search the global optimal solution. The PHIOA can improve the error accuracy while speeding up the convergence process, and effectively avoid the premature convergence to compare with the existing methods.     

A parametric filtering algorithm for the graph isomorphism problem

We introduce a new filtering algorithm, called IDL(d)-filtering, for a global constraint dedicated to the graph isomorphism problem—the goal of which is to decide if two given graphs have an identical structure. The basic idea of IDL(d)-filtering is to label every vertex with respect to its relationships with other vertices around it in the graph, and to use these labels to filter domains by removing values that have different labels. IDL(d)-filtering is parameterized by a positive integer value d which gives a limit on the distance between a vertex to be labelled and the set of vertices considered to build its label. We experimentally compare different instantiations of IDL(d)-filtering with state-of-the-art dedicated algorithms and show that IDL(d)-filtering is more efficient on regular sparse graphs and competitive on other kinds of graphs.     

A genetic algorithm for the minimum generating set problem

Given a set of positive integers S, the minimum generating set problem consists in finding a set of positive integers T with a minimum cardinality such that every element of S can be expressed as the sum of a subset of elements in T. It constitutes a natural problem in combinatorial number theory and is related to some real-world problems, such as planning radiation therapies.We present a new formulation to this problem (based on the terminology for the multiple knapsack problem) that is used to design an evolutionary approach whose performance is driven by three search strategies; a novel random greedy heuristic scheme that is employed to construct initial solutions, a specialized crossover operator inspired by real-parameter crossovers and a restart mechanism that is incorporated to avoid premature convergence. Computational results for problem instances involving up to 100,000 elements show that our innovative genetic algorithm is a very attractive alternative to the existing approaches.     

A tabu search-based algorithm for the fuzzy clustering problem

The Fuzzy Clustering Problem (FCP) is a mathematical program which is difficult to solve since it is nonconvex, which implies possession of many local minima. The fuzzy C-means heuristic is the widely known approach to this problem, but it is guaranteed only to yield local minima. In this paper, we propose a new approach to this problem which is based on tabu search technique, and aims at finding a global solution of FCP. We compare the performance of the algorithm with the fuzzy C-means algorithm.     

A hybrid genetic algorithm for mixed model assembly line balancing problem with parallel workstations and zoning constraints

In this paper, we propose a hybrid genetic algorithm to solve mixed model assembly line balancing problem of type I (MMALBP-I). There are three objectives to be achieved: to minimize the number of workstations, maximize the workload smoothness between workstations, and maximize the workload smoothness within workstations. The proposed approach is able to address some particular features of the problem such as parallel workstations and zoning constraints. The genetic algorithm may lack the capability of exploring the solution space effectively. We aim to improve its exploring capability by sequentially hybridizing the three well known heuristics, Kilbridge & Wester Heuristic, Phase-I of Moodie & Young Method, and Ranked Positional Weight Technique, with genetic algorithm. The proposed hybrid genetic algorithm is tested on 20 representatives MMALBP-I and the results are compared with those of other algorithms.