Computer programs for plotting curves with various dashed-line sequences

Two FORTRAN-callable subprograms have been written to draw a smooth curve through a set of input points as a solid line or as a general sequence of long and short dashes. Subroutine LINSEQ draws conventional curves whereas subroutine CONSEQ draws smooth closed curves (contours). The subprograms are based on an approximate calculation of the arc length along the curve and spline interpolation along the arc length. Options are provided for smoothing of the input data and for offsetting the plotted curve from the input data points. The method of calculation of the arc length and the generation of the line sequence are described.Usage descriptions of the main subprograms, sample calling programs illustrating the various features of the subprograms, and sample plots are given. The subroutines should be readily adaptable to almost any computer-driven incremental plotter

One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh

Incremental evolution strategy for function optimization

This paper presents a novel evolutionary approach for function optimization Incremental Evolution Strategy (IES). Two strategies are proposed. One is to evolve the input variables incrementally. The whole evolution consists of several phases and one more variable is focused in each phase. The number of phases is equal to the number of variables in maximum. Each phase is composed of two stages: in the single-variable evolution (SVE) stage, evolution is taken on one independent variable in a series of cutting planes; in the multi-variable evolving (MVE) stage, the initial population is formed by integrating the populations obtained by the SVE and the MVE in the last phase. And the evolution is taken on the incremented variable set. The other strategy is a hybrid of particle swarm optimization (PSO) and evolution strategy (ES). PSO is applied to adjust the cutting planes/hyper-planes (in SVEs/MVEs) while (1+1)-ES is applied to searching optima in the cutting planes/hyper-planes. The results of experiments show that the performance of IES is generally better than that of three other evolutionary algorithms, improved normal GA, PSO and SADE_CERAF, in the sense that IES finds solutions closer to the true optima and with more optimal objective values

Experimental study on population-based incremental learning algorithms for dynamic optimization problems

Copyright @ Springer-Verlag 2005.Evolutionary algorithms have been widely used for stationary optimization problems. However, the environments of real world problems are often dynamic. This seriously challenges traditional evolutionary algorithms. In this paper, the application of population-based incremental learning (PBIL) algorithms, a class of evolutionary algorithms, for dynamic problems is investigated. Inspired by the complementarity mechanism in nature a Dual PBIL is proposed, which operates on two probability vectors that are dual to each other with respect to the central point in the genotype space. A diversity maintaining technique of combining the central probability vector into PBIL is also proposed to improve PBILs adaptability in dynamic environments. In this paper, a new dynamic problem generator that can create required dynamics from any binary-encoded stationary problem is also formalized. Using this generator, a series of dynamic problems were systematically constructed from several benchmark stationary problems and an experimental study was carried out to compare the performance of several PBIL algorithms and two variants of standard genetic algorithm. Based on the experimental results, we carried out algorithm performance analysis regarding the weakness and strength of studied PBIL algorithms and identified several potential improvements to PBIL for dynamic optimization problems.This work was was supported by UK EPSRC under Grant GR/S79718/01

Dual population-based incremental learning for problem optimization in dynamic environments

Copyright @ 2003 Asia Pacific Symposium on Intelligent and Evolutionary SystemsIn recent years there is a growing interest in the research of evolutionary algorithms for dynamic optimization problems since real world problems are usually dynamic, which presents serious challenges to traditional evolutionary algorithms. In this paper, we investigate the application of Population-Based Incremental Learning (PBIL) algorithms, a class of evolutionary algorithms, for problem optimization under dynamic environments. Inspired by the complementarity mechanism in nature, we propose a Dual PBIL that operates on two probability vectors that are dual to each other with respect to the central point in the search space. Using a dynamic problem generating technique we generate a series of dynamic knapsack problems from a randomly generated stationary knapsack problem and carry out experimental study comparing the performance of investigated PBILs and one traditional genetic algorithm. Experimental results show that the introduction of dualism into PBIL improves its adaptability under dynamic environments, especially when the environment is subject to significant changes in the sense of genotype space

A market-based transmission planning for HVDC grid—case study of the North Sea

There is significant interest in building HVDC transmission to carry out transnational power exchange and deliver cheaper electricity from renewable energy sources which are located far from the load centers. This paper presents a market-based approach to solve a long-term TEP for meshed VSC-HVDC grids that connect regional markets. This is in general a nonlinear, non-convex large-scale optimization problem with high computational burden, partly due to the many combinations of wind and load that become possible. We developed a two-step iterative algorithm that first selects a subset of operating hours using a clustering technique, and then seeks to maximize the social welfare of all regions and minimize the investment capital of transmission infrastructure subject to technical and economic constraints. The outcome of the optimization is an optimal grid design with a topology and transmission capacities that results in congestion revenue paying off investment by the end the project's economic lifetime. Approximations are made to allow an analytical solution to the problem and demonstrate that an HVDC pricing mechanism can be consistent with an AC counterpart. The model is used to investigate development of the offshore grid in the North Sea. Simulation results are interpreted in economic terms and show the effectiveness of our proposed two-step approach