A Review of the Application of Meta-Heuristic Algorithms to 2D Strip Packing Problems

This paper is a review of the approachesdeveloped to solve 2D packing problems withmeta-heuristic algorithms. As packing tasks arecombinatorial problems with very large searchspaces, the recent literature encourages theuse of meta-heuristic search methods, inparticular genetic algorithms. The objective ofthis paper is to present and categorise thesolution approaches in the literature for 2Dregular and irregular strip packing problems.The focus is hereby on the analysis of themethods involving genetic algorithms. Anoverview of the methods applying othermeta-heuristic algorithms including simulatedannealing, tabu search, and artificial neuralnetworks is also given.     

QDENSITY—A Mathematica Quantum Computer simulation

This Mathematica 5.2 package¹ is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc. Selected examples of the basic commands are presented here and a tutorial notebook, Tutorial.nb is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: QFT.nb, Teleportation.nb, Grover.nb and Shor.nb where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of “one way computing” ideas, are included as an additional tool in the notebook Cluster.nb. A Mathematica palette containing most commands in QDENSITY is also included: QDENSpalette.nb.

Program summary

Title of program: QDENSITYCatalogue identifier: ADXH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v1_0Program available from: CPC Program Library, Queen's University of Belfast, N. IrelandOperating systems: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4Programming language used: Mathematica 5.2No. of bytes in distributed program, including test data, etc.: 180 581No. of lines in distributed program, including test data, etc.: 19 382Distribution format: tar.gzMethod of solution: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed.     

Competitive exploration of rectilinear polygons

Exploring a polygon with robots when the robots do not have knowledge of the surroundings can be viewed as an online problem. Typical for online problems is that decisions must be made based on past events without complete information about the future. In our case the robots do not have complete information about the environment. Competitive analysis can be used to measure the performance of methods solving online problems. The competitive ratio of such a method is the ratio between the method's performance and the performance of the best method having full knowledge of the future. We prove constant competitive strategies and lower bounds for exploring a simple rectilinear polygon in the _L1$L_1$ metric.     

An Efficient Output-Size Sensitive Parallel Algorithm for Hidden-Surface Removal for Terrains

We describe an efficient parallel algorithm for hidden-surface removal for terrain maps. The algorithm runs in O(log ⁴ n) steps on the CREW PRAM model with a work bound of O((n+k) \polylog ( n)) where n and k are the input and output sizes, respectively. In order to achieve the work bound we use a number of techniques, among which our use of persistent data structures is somewhat novel in the context of parallel algorithms. Received July 29, 1998; revised October 5, 1999.     

Implementation of particle-in-cell stellar dynamics codes on the connection machine-2

The development of massively parallel supercomputers provides a unique opportunity to advance the state of the art inN-body simulations. TheseN-body codes are of great importance for simulations in stellar dynamics and plasma physics. For systems with long-range forces, such as gravity or electromagnetic forces, it is important to increase the number of particles toN 10⁷ particles. Significantly improved modeling ofN body systems can be expected by increasingN, arising from a more realistic representation of physical transport processes involving particle diffusion and energy and momentum transport. In addition, it will be possible to guarantee that physically significant portions of complex physical systems, such as Lindblad resonances of galaxies or current sheets in magnetospheres, will have an adequate population of particles for a realistic simulation. Particle-mesh (PM) and particle-particle particle-mesh (P³M) algorithms present the best prospects for the simulation of large-scaleN-body systems. As an example we present a two-dimensional PM simulation of a disk galaxy that we have developed on the Connection Machine-2, a massively parallel boolean hypercube supercomputer. The code is scalable to any CM-2 configuration available and, on the largest configuration, simulations withN = 128 M = 2²⁷ particles are possible in reasonable run times.     

Complexity and computability of solutions to linear programming systems

Through key examples and constructs, exact and approximate, complexity, computability, and solution of linear programming systems are reexamined in the light of Khachian's new notion of (approximate) solution. Algorithms, basic theorems, and alternate representations are reviewed. It is shown that the Klee-Minty example hasnever been exponential for (exact) adjacent extreme point algorithms and that the Balinski-Gomory (exact) algorithm continues to be polynomial in cases where (approximate) ellipsoidal centered-cutoff algorithms (Levin, Shor, Khachian, Gacs-Lovasz) are exponential. By model approximation, both the Klee-Minty and the new J. Clausen examples are shown to be trivial (explicitly solvable) interval programming problems. A new notion of computable (approximate) solution is proposed together with ana priori regularization for linear programming systems. New polyhedral constraint contraction algorithms are proposed for approximate solution and the relevance of interval programming for good starts or exact solution is brought forth. It is concluded from all this that the imposed problem ignorance of past complexity research is deleterious to research progress on computability or efficiency of computation.This research was partly supported by Project NR047-071, ONR Contract N00014-80-C-0242, and Project NR047-021, ONR Contract N00014-75-C-0569, with the Center for Cybernetic Studies, The University of Texas at Austin.     

基于新障碍参数更新的二阶Mehrotra型预估—校正算法

针对二阶Mehrotra型预估-校正算法的一种变型算法,本文介绍一种新的自适应障碍参数更新法。利用该更新方法提出了相应的算法。新算法与之前的二阶Mehrotra型预估-校正算法相比,不用根据预估步和校正步的步长来确定参数的更新,而是在每步迭代中都采用自适应更新。最后证明了该算法在没有引进任何＂保障措施＂的情况下也具有相同的多项式时间复杂度。     

Study of Quintic Spline Interpolation and Generated Velocity Profile for High Speed Machining

Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high ac- celerations,in order to deliver the rapid feed motion.This paper presents an interpolation algorithm to generate continuous quintic spline toolpaths,with a constant travel increment at each step,while the smoother accelerations and jerks of two-order curve are obtained.Then an approach for reducing the feedrate fluctuation in high speed spline interpolation is presented.The presented ap- proach has been validated to quickly,reliably and effective with the simulation.     

A bandwidth latency tradeoff for broadcast and reduction

The “fractional tree” algorithm for broadcasting and reduction is introduced. Its communication pattern interpolates between two well known patterns—sequential pipeline and pipelined binary tree. The speedup over the best of these simple methods can approach two for large systems and messages of intermediate size. For networks which are not very densely connected the new algorithm seems to be the best known method for the important case that each processor has only a single (possibly bidirectional) channel into the communication network.