Evolutionary algorithm-based analysis of gravitational microlensing lightcurves

A new algorithm developed to perform autonomous fitting of gravitational microlensing lightcurves is presented. The new algorithm is conceptually simple, versatile and robust, and parallelises trivially; it combines features of extant evolutionary algorithms with some novel ones, and fares well on the problem of fitting binary-lens microlensing lightcurves, as well as on a number of other difficult optimisation problems. Success rates in excess of 90% are achieved when fitting synthetic though noisy binary-lens lightcurves, allowing no more than 20 minutes per fit on a desktop computer; this success rate is shown to compare very favourably with that of both a conventional (iterated simplex) algorithm, and a more state-of-the-art, artificial neural network-based approach. As such, this work provides proof of concept for the use of an evolutionary algorithm as the basis for real-time, autonomous modelling of microlensing events. Further work is required to investigate how the algorithm will fare when faced with more complex and realistic microlensing modelling problems; it is, however, argued here that the use of parallel computing platforms, such as inexpensive graphics processing units, should allow fitting times to be constrained to under an hour, even when dealing with complicated microlensing models. In any event, it is hoped that this work might stimulate some interest in evolutionary algorithms, and that the algorithm described here might prove useful for solving microlensing and/or more general model-fitting problems.Comment: 14 pages, 3 figures; accepted for publication in MNRA

Biased random-key genetic algorithm for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete orcontinuous domain. In this paper, we propose a biased random-key genetic algorithm for findingapproximate solutions for continuous global optimization problems subject to box constraints. Experimentalresults illustrate its effectiveness on the robot kinematics problem, a challenging problemaccording to [7]

Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution

Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate

Multiple roots of systems of equations by repulsion merit functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global min- imizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several ite- rations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.Fundação para a Ciência e a Tecnologia (FCT

Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.Fundação para a Ciência e Tecnologia (FCT

Nature-inspired algorithms for solving some hard numerical problems

Optimisation is a branch of mathematics that was developed to find the optimal solutions, among all the possible ones, for a given problem. Applications of optimisation techniques are currently employed in engineering, computing, and industrial problems. Therefore, optimisation is a very active research area, leading to the publication of a large number of methods to solve specific problems to its optimality. This dissertation focuses on the adaptation of two nature inspired algorithms that, based on optimisation techniques, are able to compute approximations for zeros of polynomials and roots of non-linear equations and systems of non-linear equations. Although many iterative methods for finding all the roots of a given function already exist, they usually require: (a) repeated deflations, that can lead to very inaccurate results due to the problem of accumulating rounding errors, (b) good initial approximations to the roots for the algorithm converge, or (c) the computation of first or second order derivatives, which besides being computationally intensive, it is not always possible. The drawbacks previously mentioned served as motivation for the use of Particle Swarm Optimisation (PSO) and Artificial Neural Networks (ANNs) for root-finding, since they are known, respectively, for their ability to explore high-dimensional spaces (not requiring good initial approximations) and for their capability to model complex problems. Besides that, both methods do not need repeated deflations, nor derivative information. The algorithms were described throughout this document and tested using a test suite of hard numerical problems in science and engineering. Results, in turn, were compared with several results available on the literature and with the well-known Durand–Kerner method, depicting that both algorithms are effective to solve the numerical problems considered.A Optimização é um ramo da matemática desenvolvido para encontrar as soluções óptimas, de entre todas as possíveis, para um determinado problema. Actualmente, são várias as técnicas de optimização aplicadas a problemas de engenharia, de informática e da indústria. Dada a grande panóplia de aplicações, existem inúmeros trabalhos publicados que propõem métodos para resolver, de forma óptima, problemas específicos. Esta dissertação foca-se na adaptação de dois algoritmos inspirados na natureza que, tendo como base técnicas de optimização, são capazes de calcular aproximações para zeros de polinómios e raízes de equações não lineares e sistemas de equações não lineares. Embora já existam muitos métodos iterativos para encontrar todas as raízes ou zeros de uma função, eles usualmente exigem: (a) deflações repetidas, que podem levar a resultados muito inexactos, devido ao problema da acumulação de erros de arredondamento a cada iteração; (b) boas aproximações iniciais para as raízes para o algoritmo convergir, ou (c) o cálculo de derivadas de primeira ou de segunda ordem que, além de ser computacionalmente intensivo, para muitas funções é impossível de se calcular. Estas desvantagens motivaram o uso da Optimização por Enxame de Partículas (PSO) e de Redes Neurais Artificiais (RNAs) para o cálculo de raízes. Estas técnicas são conhecidas, respectivamente, pela sua capacidade de explorar espaços de dimensão superior (não exigindo boas aproximações iniciais) e pela sua capacidade de modelar problemas complexos. Além disto, tais técnicas não necessitam de deflações repetidas, nem do cálculo de derivadas. Ao longo deste documento, os algoritmos são descritos e testados, usando um conjunto de problemas numéricos com aplicações nas ciências e na engenharia. Os resultados foram comparados com outros disponíveis na literatura e com o método de Durand–Kerner, e sugerem que ambos os algoritmos são capazes de resolver os problemas numéricos considerados

Distributed Location Estimation of a Moving Target Characterized by a Spatial Poisson Field

Wireless Sensor Networks (WSNs) are traditionally employed to collect spatial and temporal data characterizing various events. These data are then used to solve inference problems such as object detection, counting, classification, estimation and tracking. Distributed solutions provided by WSNs are often cost effective and characterized by high performance indices.;In this work, we model and simulate a distributed sensor network composed of radiation detectors and analyze its ability to make inferences. Radiation detectors are deployed over a known area. A radiological point source is positioned in the interior of the area. Detectors take measurements of the field generated by the point source and transmit them (without any interaction with one another) to a remotely installed super computer (called here Fusion Center) for a joint processing. To minimize consumption of resources such as power in the network and transmission bandwidth, the measurements are locally preprocessed prior to transmission. Our model assumes two Gaussian channels, observation and transmission. The first channel distorts data at the receiver end of each sensor during data acquisition. The second channel distorts data during transmission. Sensor measurements are modeled as an inhomogeneous spatial counting random process (Poisson process). The location of the radiological point source in the area and the strength of the field generated by the substance are unknown parameters. The goal of the FC is to estimate these parameters from the distributed measurements provided by the WSN. To find the distributed estimates, we adopt the Maximum Likelihood approach. This approach requires knowledge of the joint probability density function of the distributed measurements observed by the FC. Since the joint probability density of the data observed at the FC is nonlinear in unknown parameters, we propose an iterative approach to solve for the maximum likelihood estimates of these parameters. The solution is a combination of the Bisection and Secant approaches adjusted to seek solution in a multidimensional parameter space. The performance of the distributed estimator is measured in terms of the mean square error. It is analyzed with respect to various parameters of the WSN. We vary the following parameters of the network: (1) the number of sensors in the WSN, (2) signal to noise ratio in observation and transmission channels, (3) the strength of the original field, and (4) the number of quantization levels used by a sensor to convert an analog measurement into a digital signal. We also propose a distributed tracking algorithm for monitoring position of the object in real time

Inclusion of Geometrically Nonlinear Aeroelastic Effects into Gradient-Based Aircraft Optimization

While aircraft have largely featured flexible wings for decades, more recently, aircraft structures have rapidly become more flexible. The pursuit of longer ranges and higher efficiency through higher aspect ratio wings, as well as the introduction of modern, light-weight materials has yielded moderately and very flexible aircraft configurations. Past accidents, such as the loss of the Helios High Altitude Long Endurance (HALE) aircraft have highlighted the limitations of linear analysis methods and demonstrated the peril of neglecting nonlinear effects when designing such aircraft. In particular, accounting for geometrical nonlinearities in flutter analyses become necessary in aircraft optimization, including transport aircraft, or future aircraft may require costly modifications late in the design process to fulfill certification requirements. As a result, there is a need to account for geometrical nonlinearities earlier in the design process and integrate these analyses directly into the multi-disciplinary design optimization (MDO) problems. This thesis investigates geometrically nonlinear flutter problems and how these should be integrated into aircraft MDO problems. First, flutter problems with and without geometrical nonlinearities are discussed and a unifying interpretation is presented. Furthermore, methods for interpreting nonlinear flutter problems are proposed and differences between linear and nonlinear flutter problem interpretation are discussed. Next, a flutter constraint formulation which accounts for geometrically nonlinear effects using beam-based analyses is presented. The resulting constraint uses a Kreisselmeiser-Steinhauser aggregation function to yield a scalar constraint from flight envelope flutter damping values. While the constraint enforces feasibility over the entire flight envelope, how the flight envelope is sampled largely determines the flutter constraint’s accuracy. To this end, a constrained Maximin approach, which is applicable for non-hypercube spaces, is used to sample the flight envelope and obtain a low-discrepancy sample set. The flutter constraint is then implemented using a beam-based geometrically nonlinear aeroelastic simulation code, UM/NAST. As gradient-based optimization methods are used in MDO due to the large number of design variables in aircraft design problems, the flutter constraint requires the recovery of flutter damping sensitivities. These are obtained by applying algorithmic differentiation (AD) to the UM/NAST code base. This enables the recovery of gradients for any solution type (static, modal, dynamic, and flutter/stability) with respect to any local design variable available within UM/NAST. The performance of the gradient prediction is studied and a hybrid primal-AD scheme is developed to obtain the coupled nonlinear aeroelastic sensitivities. After verifying the accuracy and performance of the gradient evaluation, the flutter constraint was implemented in a sample optimization problem. Finally, a roadmap for including the beam-based flutter constraint within an aircraft design problem is presented using analyses of varying fidelity. To this end, analyses of appropriate fidelity are used depending on the output of interest. While a shell-based FEM model can recover stress distributions, and is therefore well-suited for strength constraints, they are ill-suited for geometrically nonlinear flutter constraints due to their computational cost. Analyses are presented for a high aspect ratio transport aircraft configuration to illustrate the proposed approach and highlight the necessity for the inclusion of a geometrically nonlinear flutter constraint.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163259/1/clupp_1.pd

Penyelesaian Capacitated Closed Vehicle Routing Problem With Time Windows (Ccvrptw) Menggunakan Brkga Dengan Local Search

Determining the shortest route sequence for distributing productfrom depot to a number of outlets to minimize the total distribution cost is the main problem to deal with in Vehicle Routing Problem (VRP). Capacitated Closed Vehicle Routing Problem with Time Windows (CCVRPTW) is a variant of VRPthat accommodates the truck capacity and the working hours at the distribution. As CCVRPTW falls into NP-hard problem, it requires an efficient and effective algorithm to find the optimal solution. This research is aimed at designing Biased Random Key Genetic Algorithm (BRKGA) combined with a local search to solve CCVRPTW. The proposed algorithm is then coded in MATLAB. Using extensive numerical tests, the best setting of the algorithm parameters is obtained. The performance of the algorithm is then compared to a heuristic for solving a soft drink distribution problem. The result shows that BRKGA hybridized with a local search returns a lower total distribution cost compared to that of resulting from the heuristic. in addition, it is demonstrated that the proposed algorithm could further improve the performance of the standard BRKGA