Evolutionary Approaches to Optimization Problems in Chimera Topologies

Chimera graphs define the topology of one of the first commercially available quantum computers. A variety of optimization problems have been mapped to this topology to evaluate the behavior of quantum enhanced optimization heuristics in relation to other optimizers, being able to efficiently solve problems classically to use them as benchmarks for quantum machines. In this paper we investigate for the first time the use of Evolutionary Algorithms (EAs) on Ising spin glass instances defined on the Chimera topology. Three genetic algorithms (GAs) and three estimation of distribution algorithms (EDAs) are evaluated over $1000$ hard instances of the Ising spin glass constructed from Sidon sets. We focus on determining whether the information about the topology of the graph can be used to improve the results of EAs and on identifying the characteristics of the Ising instances that influence the success rate of GAs and EDAs.Comment: 8 pages, 5 figures, 3 table

Dynamic Site Periods for the Jackson Purchase Region of Western Kentucky

Bridges, overpasses, and other engineered structures in the Jackson Purchase region of Western Kentucky are, of necessity, built on a thick column of loose to semi-consolidated sediments. Because these sediments tend to amplify seismically induced ground motions at preferred periods, structures with natural periods close to the preferred periods of amplification of the ground motions are particularly vulnerable to damages during an earthquake because of in-phase resonance. For this report, conventional seismic refraction and reflection techniques were used to determine the shearwave velocities of the more poorly consolidated, near-surface sediments for a matrix of sites in the region. Conventional seismic P-wave reflections along with existing drill hole and seismic reflection data in the region were then used to determine the depth to the top of the bedrock at the sites investigated. These data were used in SHAKE91 to calculate the fundamental period of the ground motion at the sites. This period, identified in the study as the dynamic site period, is the period at which ground motions in the sedimentary column are most apt to be amplified as a result of a seismic shear wave propagating from the top of the bedrock to the surface. Based on the results in this report, it is recommended that bridges, overpasses, and other engineered structures built in the region be designed so that their natural periods do not coincide with the fundamental period of the sedimentary column, thereby avoiding damage during an earthquake as a result of in-phase resonance

High Order Multistep Methods with Improved Phase-Lag Characteristics for the Integration of the Schr\"odinger Equation

In this work we introduce a new family of twelve-step linear multistep methods for the integration of the Schr\"odinger equation. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. This results in decreasing the sensitivity of the integration method on the estimated frequency of the problem. The efficiency of the new family of methods is proved via error analysis and numerical applications.Comment: 36 pages, 6 figure

Population Sizing for the Redundant Trivial Voting Mapping

Mapping-Proble

An analysis of the local optima storage capacity of Hopfield network based fitness function models

A Hopfield Neural Network (HNN) with a new weight update rule can be treated as a second order Estimation of Distribution Algorithm (EDA) or Fitness Function Model (FFM) for solving optimisation problems. The HNN models promising solutions and has a capacity for storing a certain number of local optima as low energy attractors. Solutions are generated by sampling the patterns stored in the attractors. The number of attractors a network can store (its capacity) has an impact on solution diversity and, consequently solution quality. This paper introduces two new HNN learning rules and presents the Hopfield EDA (HEDA), which learns weight values from samples of the fitness function. It investigates the attractor storage capacity of the HEDA and shows it to be equal to that known in the literature for a standard HNN. The relationship between HEDA capacity and linkage order is also investigated

DICE: A New Family of Bivariate Estimation of Distribution Algorithms based on Dichotomised Multivariate Gaussian Distributions

A new family of Estimation of Distribution Algorithms (EDAs) for discrete search spaces is presented. The proposed algorithms, which we label DICE (Discrete Correlated Estimation of distribution algorithms) are based, like previous bivariate EDAs such as MIMIC and BMDA, on bivariate marginal distribution models. However, bivariate models previously used in similar discrete EDAs were only able to exploit an O(d) subset of all the O(d2) bivariate variable dependencies between d variables. We introduce, and utilize in DICE, a model based on dichotomised multivariate Gaussian distributions. These models are able to capture and make use of all O(d2) bivariate variable interactions in binary and multary search spaces. This paper tests the performances of these new EDA models and algorithms on a suite of challenging combinatorial optimization problems, and compares their performances to previously used discrete-space bivariate EDA models. EDAs utilizing these new dichotomised Gaussian (DG) models exhibit significantly superior optimization performances, with the performance gap becoming more marked with increasing dimensionality

Compact Optimization Algorithms with Re-sampled Inheritance

The file attached to this record is the author's final peer reviewed version.Compact optimization algorithms are a class of Estimation of Distribution Algorithms (EDAs) characterized by extremely limited memory requirements (hence they are called \compact"). As all EDAs, compact algorithms build and update a probabilistic model of the distribution of solutions within the search space, as opposed to population-based algorithms that instead make use of an explicit population of solutions. In addition to that, to keep their memory consumption low, compact algorithms purposely employ simple probabilistic models that can be described with a small number of parameters. Despite their simplicity, compact algorithms have shown good performances on a broad range of benchmark functions and real-world problems. However, compact algorithms also come with some drawbacks, i.e. they tend to premature convergence and show poorer performance on non-separable problems. To overcome these limitations, here we investigate a possible algorithmic scheme obtained by combining compact algorithms with a non-disruptive restart mechanism taken from the literature, named Re-Sampled Inheritance (RI). The resulting compact algorithms with RI are tested on the CEC 2014 benchmark functions. The numerical results show on the one hand that the use of RI consistently enhances the performances of compact algorithms, still keeping a limited usage of memory. On the other hand, our experiments show that among the tested algorithms, the best performance is obtained by compact Differential Evolution with RI