Evolution Programs for Various Discrete Problems

1996 ◽  
pp. 239-266 ◽  
Author(s):  
Zbigniew Michalewicz
Keyword(s):  
Discrete Problems ◽  
Evolution Programs

An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

2015 ◽  
Vol 18 (5) ◽  
pp. 1313-1335 ◽  
Author(s):  
Xiaoqiang Yue ◽  
Shi Shu ◽  
Xiao wen Xu ◽  
Zhiyang Zhou
Keyword(s):  
Convergence Analysis ◽  
Estimation Theory ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Condition Numbers ◽  
Radiation Diffusion ◽  
Discrete Problems ◽  
Preconditioned Gmres

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

Nontrivial solutions of non-autonomous dirichlet fractional discrete problems

2020 ◽  
Vol 23 (4) ◽  
pp. 980-995
Author(s):  
Alberto Cabada ◽  
Nikolay Dimitrov
Keyword(s):  
Existence And Uniqueness ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Difference Equation ◽  
Discrete Problems ◽  
Series Of Functions

AbstractIn this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

scholarly journals Pioneer: A New Tool for Coding of Multi-Level Finite State Machines Based on Evolution Programming

VLSI Design ◽  
1994 ◽  
Vol 2 (2) ◽  
pp. 105-116
Author(s):  
S. Muddappa ◽  
R. Z. Makki ◽  
Z. Michalewicz ◽  
S. Isukapalli
Keyword(s):  
Finite State Machines ◽  
Mutation Rates ◽  
Natural Phenomenon ◽  
State Machines ◽  
State Assignment ◽  
Wide Range ◽  
Finite State ◽  
Multi Level ◽  
Crossover And Mutation ◽  
Evolution Programs

In this paper we present a new tool for the encoding of multi-level finite state machines based on the concept of evolution programming. Evolution programs are stochastic adaptive algorithms, based on the paradigm of genetic algorithms whose search methods model some natural phenomenon: genetic inheritance and Darwinian strife for survival. Crossover and mutation rates were tailored to the state assignment problem experimentally. We present results over a wide range of MCNC benchmarks which demonstrate the effectiveness of the new tool. The results show that evolution programs can be effectively applied to state assignment.

scholarly journals Packets routing and bandwidth sensing in a network traffic: Ant colony optimization tactic.

2018 ◽  
Vol 24 (2) ◽  
pp. 223-228
Author(s):  
Felix U. Ogban ◽  
Roy Nentui
Keyword(s):  
Ant Colony Optimization ◽  
Network Traffic ◽  
Priority Queue ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
Ant Colonies ◽  
Lower Priority ◽  
Link State ◽  
Discrete Problems ◽  
Network Platform

Packets routing and bandwidth sensing in a network platform remains an integral part of the study of signal flow.The algorithm to route packets in a network link called the AntNet algorithm was inspired by the behavior of real ant colonies. At each node in the network, a forward ant deposits some amount of pheromones at different links that responds to the node’s queue length. In this paper, we propose the inclusion of the computation of paths to adapt with the Depth Search Ant Explorer Network (DS-ANTENet) algorithm for discrete problems as an IP based mechanism. This method is tested and the efficiency is compared to the original AntNet algorithm and the Link-State algorithm to check the transmission of computing traffic flows between the nodes. We then made comparison with the algorithms proposed in the literature. The protocols were sorted out in terms of average number of lost packets ranging from the higher priority queue to the lower priority queue which then resulted to the fact that; First, AntNetBW (loss ratios reduction of 9.6% when compared to the AntNet and the Link-State algorithm respectively. Secondly,  SANTENetBW (loss ratios reduction of 8.3% and 36.7% when compared to the AntNet and the Link-State algorithm respectively. Finally, DS-ANTENet (loss ratios reduction 0.7% and 33.2% when compared to the AntNet and the Link- State algorithm respectively.Keywords: Packets Routing, Bandwidth Sensing, Network Traffic, Ant Colony Optimization Algorithm, AntNet

scholarly journals Finite element algorithms for nonlocal minimal graphs

2021 ◽  
Vol 4 (2) ◽  
pp. 1-29
Author(s):  
Juan Pablo Borthagaray ◽  
◽  
Wenbo Li ◽  
Ricardo H. Nochetto ◽  
◽  
...  
Keyword(s):  
Mean Curvature ◽  
Numerical Experiments ◽  
Piecewise Linear ◽  
Gradient Flow ◽  
Minimal Graphs ◽  
Qualitative And Quantitative ◽  
Dirichlet Data ◽  
Data Truncation ◽  
Discrete Problems ◽  
Newton Scheme

<abstract><p>We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.</p></abstract>

scholarly journals Novel Inferences in a Multidimensional Social Network Use a Grid-like Code

2020 ◽  
Author(s):  
Seongmin A. Park ◽  
Douglas S. Miller ◽  
Erie D. Boorman
Keyword(s):  
Decision Making ◽  
Prefrontal Cortex ◽  
Medial Prefrontal Cortex ◽  
Entorhinal Cortex ◽  
Brain Regions ◽  
Cognitive Map ◽  
General Mechanism ◽  
Temporoparietal Junction ◽  
Flexible Behavior ◽  
Discrete Problems

ABSTRACTGeneralizing experiences to guide decision making in novel situations is a hallmark of flexible behavior. It has been hypothesized such flexibility depends on a cognitive map of an environment or task, but directly linking the two has proven elusive. Here, we find that discretely sampled abstract relationships between entities in an unseen two-dimensional (2-D) social hierarchy are reconstructed into a unitary 2-D cognitive map in the hippocampus and entorhinal cortex. We further show that humans utilize a grid-like code in several brain regions, including entorhinal cortex and medial prefrontal cortex, for inferred direct trajectories between entities in the reconstructed abstract space during discrete decisions. Moreover, these neural grid-like codes in the entorhinal cortex predict neural decision value computations in the medial prefrontal cortex and temporoparietal junction area during choice. Collectively, these findings show that grid-like codes are used by the human brain to infer novel solutions, even in abstract and discrete problems, and suggest a general mechanism underpinning flexible decision making and generalization.

scholarly journals Recent Advances in Global Optimization for Combinatorial Discrete Problems

2015 ◽  
Vol 06 (11) ◽  
pp. 1842-1856
Author(s):  
Adel R. Awad ◽  
Samia O. Chiban
Keyword(s):  
Global Optimization ◽  
Recent Advances ◽  
Discrete Problems
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