DNA labelled graphs with DNA computing

Let k≥2, 1≤i≤k andα≥1 be three integers. For any multiset which consists of some k-long oligonucleotides, a DNA labelled graph is defined as follows: each oligonucleotide from the multiset becomes a point; two points are connected by an arc from the first point to the second one if the i rightmost uucleotides of the first point overlap with the i leftmost nucleotides of the second one. We say that a directed graph D can be(k, i;α)-labelled if it is possible to assign a label(l_1(x),..., l_k(x))to each point x of D such that l_j(x)∈{0,...,a-1}for any j∈{1,...,k}and(x,y)∈E(D)if and only if(l_k-i 1(x),..., l_k(x))=(l_1(y),..., l_i(y)). By the biological background, a directed graph is a DNA labelled graph if there exist two integers k, i such that it is(k, i; 4)-labelled. In this paper, a detailed discussion of DNA labelled graphs is given. Firstly, we study the relationship between DNA labelled graphs and some existing directed graph classes. Secondly, it is shown that for any DNA labelled graph, there exists a positive integer i such that it is(2i, i; 4)-labelled. Furthermore, the smallest i is determined, and a polynomial-time algorithm is introduced to give a(2i, i; 4)-labelling for a given DNA labelled graph. Finally, a DNA algorithm is given to find all paths from one given point to another in a(2i, i; 4)-labelled directed graph.     

A polynomial-time algorithm for computing the yolk in fixed dimension

The yolk, developed in Ferejohn, McKelvey and Packel (1984) and McKelvey (1986), is a key solution concept in the Euclidean spatial model as the region of policies where a dynamic voting game will tend to reside. However, determining the yolk is NP-hard for arbitrary dimension. This paper derives an algorithm to compute the yolk in polynomial time for any fixed dimension.Research supported by a Presidential Young Investigator Award from the National Science Foundation (ECS-8451032), and a Senior Research Associateship from the National Research Council.During the academic year 1990–1991.     

A polynomial-time algorithm for the change-making problem

Optimally making change—representing a given value with the fewest coins from a set of denominations—is in general NP-hard. In most real money systems however, the greedy algorithm is optimal. We give a polynomial-time algorithm to determine, for a given coin system, whether the greedy algorithm is optimal.     

A polynomial-time algorithm for near-unanimity graphs

We present a simple polynomial-time algorithm that recognises reflexive, symmetric graphs admitting a near-unanimity operation. Several other characterisations of these graphs are also presented.     

A modified DNA genetic algorithm for parameter estimation of the 2-Chlorophenol oxidation in supercritical water

Based on the mechanism of biological DNA genetic information and evolution, a modified DNA genetic algorithm (MDNA-GA) is proposed to estimate the kinetic parameters of the 2-Chlorophenol oxidation in supercritical water. In this approach, DNA encoding method, choose crossover operator and frame-shift mutation operator inspired by the biological DNA are developed for improving the global searching ability. Besides, an adaptive mutation probability which can be adjusted automatically according to the diversity of population is also adopted. A local search method is used to explore the search space to accelerate the convergence towards global optimum. The performance of MDNA-GA in typical benchmark functions and kinetic parameter estimation is studied and compared with RNA-GA. The experimental results demonstrate that the proposed algorithm can overcome premature convergence and yield the global optimum with high efficiency.     

A new algorithm for the Integer Knapsack Problem and its parallelization

Summary A new sequential algorithm with complexityO(M ²+n) for an Integer Knapsack Problem with capacityM andn objects is proposed. The correspondentO(M ²/p+n) parallel algorithm runs on a ring machine withp processors. Computational results on both a local area network and a transputer network are reported.     

Partially separable optimization and parallel computing

Parallel processors are becoming an attractive option for meeting the requirements to solve large nonlinear optimization problems and the partially separable methods are ideal candidates for parallel computing. This paper proposes implementation techniques for such methods. Computational experiments on an IBM 3090-200 and on a simulated multiprocessor are presented. The performance of both implementations is compared against a reference serial implementation.     

A memetic algorithm for the Multi Trip Vehicle Routing Problem

We consider the Multi Trip Vehicle Routing Problem, in which a set of geographically scattered customers have to be served by a fleet of vehicles. Each vehicle can perform several trips during the working day. The objective is to minimize the total travel time while respecting temporal and capacity constraints.     

A multi-start algorithm for a balanced real-world Open Vehicle Routing Problem

The aim of this paper is to solve a real-world problem proposed by an international company operating in Spain and modeled as a variant of the Open Vehicle Routing Problem in which the makespan, i.e., the maximum time spent on the vehicle by one person, must be minimized. A competitive multi-start algorithm, able to obtain high quality solutions within reasonable computing time is proposed. The effectiveness of the algorithm is analyzed through computational testing on a set of 19 school-bus routing benchmark problems from the literature, and on 9 hard real-world problem instances.     

Transgenetic algorithm for the Traveling Purchaser Problem

In this paper an evolutionary algorithm is presented for the Traveling Purchaser Problem, an important variation of the Traveling Salesman Problem. The evolutionary approach proposed in this paper is called transgenetic algorithm. It is inspired on two significant evolutionary driving forces: horizontal gene transfer and endosymbiosis. The performance of the algorithm proposed for the investigated problem is compared with other recent works presented in the literature. Computational experiments show that the proposed approach is very effective for the investigated problem with 17 and 9 new best solutions reported for capacitated and uncapacitated instances, respectively.     

Simulated Annealing and Genetic Algorithms for the Facility Layout Problem: A Survey

The facility layout problem (FLP) has many practical applications and is known to be NP-hard. During recent decades exact and heuristic approaches have been proposed in the literature to solve FLPs. In this paper we review the most recent developments regardingsimulated annealing and genetic algorithms for solvingfacility layout problems approximately.     

Iterative algorithms of domain decomposition for the solution of a quasilinear elliptic problem

This paper deals with iterative algorithms for domain decomposition applied to the solution of a quasilinear elliptic problem. Two iterative algorithms are examined: the first one is the Schwarz alternating procedure and the second algorithm is suitable for parallel computing. Convergence results are established in the two-domain and multidomain decomposition cases. Some issues of parallel implementation of these algorithms are discussed.     

An effective hybrid algorithm for computing symbolic determinants

A hybrid algorithm for computing the determinant of a matrix whose entries are polynomials is presented. It is based on the dimension-decreasing algorithm [22] and the parallel algorithm for computing a symbolic determinant of [19]. First, through the dimension-decreasing algorithm, a given multivariate matrix can be converted to a bivariate matrix. Then, the parallel algorithm can be applied to effectively compute the determinant of the bivariate matrix. Experimental results show that the new algorithm can not only reduce enormously the intermediate expression swell in the process of symbolic computation, but also achieve higher degree of parallelism, compared with the single parallel algorithm given in [19].     

A polynomial-time algorithm for a class of linear complementarity problems

Given ann × n matrixM and ann-dimensional vectorq, the problem of findingn-dimensional vectorsx andy satisfyingy = Mx + q, x 0,y 0,x _i y _i = 0 (i = 1, 2,,n) is known as a linear complementarity problem. Under the assumption thatM is positive semidefinite, this paper presents an algorithm that solves the problem in O(n ³ L) arithmetic operations by tracing the path of centers,{(x, y) S: x _i y _i = (i = 1, 2,,n) for some > 0} of the feasible regionS = {(x, y) 0:y = Mx + q}, whereL denotes the size of the input data of the problem.     

New polynomial-time algorithms for Camion bases

Let M be a finite set of vectors in Rⁿ of cardinality m and H(M)={{x∈Rⁿ:c^Tx=0}:c∈M} the central hyperplane arrangement represented by M. An independent subset of M of cardinality n is called a Camion basis, if it determines a simplex region in the arrangement H(M). In this paper, we first present a new characterization of Camion bases, in the case where M is the column set of the node-edge incidence matrix (without one row) of a given connected digraph. Then, a general characterization of Camion bases as well as a recognition procedure which runs in O(n²m) are given. Finally, an algorithm which finds a Camion basis is presented. For certain classes of matrices, including totally unimodular matrices, it is proven to run in polynomial time and faster than the algorithm due to Fonlupt and Raco.     

Matching search in fractal video compression and its parallel implementation in distributed computing environments

Fractal video compression is a relatively new video compression method. Its attraction is due to the high compression ratio and the simple decompression algorithm. But its computational complexity is high and as a result parallel algorithms on high performance machines become one way out. In this study we partition the matching search, which occupies the majority of the work in a fractal video compression process, into small tasks and implement them in two distributed computing environments, one using DCOM and the other using .NET Remoting technology, based on a local area network consists of loosely coupled PCs. Experimental results show that the parallel algorithm is able to achieve a high speedup in these distributed environments.     

Biological computation of the solution to the quadratic assignment problem

Biological computing provides a promising approach to attacking computationally intractable problems. The quadratic assignment problem (QAP) is a well-known NP-hard combinatorial optimization problem. This paper addresses the problem of how to solve QAP under the Adleman–Lipton-sticker model. A theoretically efficient DNA algorithm for solving QAP is proposed, which is executed by performing O(Kn⁴) operations on test tubes of DNA molecular strands with n² + K + 1 bit regions, where n is the number of facilities, and K is the length of the binary representation of an upper bound on the objective function. With the rapid progress of molecular biology techniques, the proposed algorithm might be of practical use in treating medium-sized instances of QAP.     

三维装箱问题的模型与改进遗传算法

三维装箱问题是一类NP-hard的组合优化问题,构建一个适当的数学模型并设计高效快速的算法具有重要的理论和现实意义.该文将箱子空间划分为立方体单元,依此构建三维装箱问题的混合整数规划模型,并通过改进遗传算法求解,剔除大量不可行解提高了收敛速度.实验结果表明此算法运算过程及结果稳定,具有较强的实际应用价值,能有效解决复杂的三维装箱问题.     

Enhancement of membrane computing model implementation on GPU by introducing matrix representation for balancing occupancy and reducing inter-block communications

In previous studies, objects of each membrane were assigned to threads of one thread block of the graphic processing unit (GPU). The number of active threads was low if the number of objects inside a membrane was low. This study represents objects of membranes as entities of a matrix. Then a sub-matrix represents the appropriate number of objects assigned to threads of each thread block to balance the load and keep the occupancy high even when the number of objects per membrane is low. The size of the sub-matrix or the appropriate number of active threads is determined automatically. Furthermore, by this approach it is possible to assign more than one membrane to each thread block and to execute communication between membranes in the same thread block without the need for time-consuming inter-block communication. For example, using the previous algorithm, for two objects per membrane the speed up is 0.6×, while for the proposed algorithm the speed up is 32.4×.