A Multi-Layer Line Search Method to Improve the Initialization of Optimization Algorithms (Preprint submitted to Optimization Online)

We introduce a novel metaheuristic methodology to improve the initialization of a given deterministic or stochastic optimization algorithm. Our objective is to improve the performance of the considered algorithm, called core optimization algorithm, by reducing its number of cost function evaluations, by increasing its success rate and by boosting the precision of its results. In our approach, the core optimization is considered as a suboptimization problem for a multi-layer line search method. The approach is presented and implemented for various particular core optimization algorithms: Steepest Descent, Heavy-Ball, Genetic Algorithm, Differential Evolution and Controlled Random Search. We validate our methodology by considering a set of low and high dimensional benchmark problems (i.e., problems of dimension between 2 and 1000). The results are compared to those obtained with the core optimization algorithms alone and with two additional global optimization methods (Direct Tabu Search and Continuous Greedy Randomized Adaptive Search). These latter also aim at improving the initial condition for the core algorithms. The numerical results seem to indicate that our approach improves the performances of the core optimization algorithms and allows to generate algorithms more efficient than the other optimization methods studied here. A Matlab optimization package called ”Global Optimization Platform” (GOP), implementing the algorithms presented here, has been developed and can be downloaded at: http://www.mat.ucm.es/momat/software.ht

A Platform for Antenna Optimization with Numerical Electromagnetics Code Incorporated with Genetic Algorithms

This thesis investigation presents a unique incorporation of the Method of Moments (MoM) with a Genetic Algorithm (GA). A GA is used in accord with the Numerical Electromagnetics Code, Version 4 (NEC4) to create and optimize typical wire antenna designs, including single elements and arrays. Design parameters for the antenna are defined and encoded into a chromosome composed of a series of numbers. The cost function associated with the specific antenna of interest is what quantifies improvement and, eventually, optimization. This cost function is created and used by the GA to evaluate the performance of a population of antenna designs. The most successful designs of each generation are kept and altered through crossover and mutation. Through the course of generations, convergence upon a best design is attained. The Yagi-Uda and the Log Periodic Dipole Array (LPDA) antennas are the focus of this study. The objectives for each antenna are to maximize the main power gain while minimizing the Voltage Standing Wave Ratio (VSWR) and the antenna\u27s length. Results for the Yagi-Uda exceed previous designs by as much as 40 dB in the main lobe while maintaining respectable length and VSWR values. The improvements made in the LPDA antenna were not as drastic, finding a nominal increase in power gain while truncating original allowance in the length by more than half, along with nominal VSWR values that were close to the ideal value of one. The percentage of bandwidth covered for the frequencies of interest are 8.11% for the Yagi-Uda and 10.7% for the LPDA. GA performance is evaluated and, based on previous results, implemented with real-numbered chromosomes as opposed to the classic binary encoding. This methodology is very robust and is improved upon in this research, all while using a novel approach with an optimization program platform called iSIGHT, developed by Engineous Software

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

A Multi-Layer Line Search Method to Improve the Initialization of Optimization Algorithms

International audienceWe introduce a novel metaheuristic methodology to improve the initializationof a given deterministic or stochastic optimization algorithm. Our objectiveis to improve the performance of the considered algorithm, calledcore optimization algorithm, by reducing its number of cost function evaluations,by increasing its success rate and by boosting the precision of itsresults. In our approach, the core optimization is considered as a suboptimizationproblem for a multi-layer line search method. The approachis presented and implemented for various particular core optimization algorithms:Steepest Descent, Heavy-Ball, Genetic Algorithm, Differential Evolutionand Controlled Random Search. We validate our methodology byconsidering a set of low and high dimensional benchmark problems (i.e.,problems of dimension between 2 and 1000). The results are compared tothose obtained with the core optimization algorithms alone and with twoadditional global optimization methods (Direct Tabu Search and ContinuousGreedy Randomized Adaptive Search). These latter also aim at improvingthe initial condition for the core algorithms. The numerical results seemto indicate that our approach improves the performances of the core optimizationalgorithms and allows to generate algorithms more efficient thanthe other optimization methods studied here. A Matlab optimization packagecalled ”Global Optimization Platform” (GOP), implementing the algorithmspresented here, has been developed and can be downloaded at:http://www.mat.ucm.es/momat/software.ht

Doctor of Philosophy

dissertationThe objective of this dissertation is to estimate possible leakage pathways such as abandoned wells and fault zones in the deep subsurface for CO2 storage using inverse analysis. Leakage pathways through a cap rock may cause CO2 to migrate into the layers above cap rock. An inverse analysis using iTOUGH2 was applied to estimate possible leakage pathways using pressure anomalies in the overlying formation induced by brine and/or CO2 leaks. Prior to applying inverse analysis, sensitivity analysis and forward modeling were conducted. In addition, an inverse model was developed for single-phase flow and it was applied to the leakage pathway estimation in a brine/CO2 system. Migration of brine/CO2 through the leakage pathway was simulated in the generic homogeneous and heterogeneous domains. The increased pressure gradient due to CO2 injection continuously induced brine leaks through the leakage pathway. Capillary pressure was induced by the migration of CO2 along the leakage pathway saturated by brine. Pressure anomalies due to capillary pressures were propagated to the entire overlying formation. The sensitivity analysis was focused on how the hydrogeological properties affect the pressure signals at monitoring wells. Parameter estimation using the iTOUGH2 model was applied to detect locations of leakage pathways in homogeneous and heterogeneous model domains. For homogeneous models, the parameterization of uncertain permeability in an overlying formation could improve location estimation accuracy. Residual analysis illustrated that pressure anomalies in the overlying formation induced by leaks are critical information for the leakage pathway estimation. For heterogeneous models, the calibration of renormalized permeability values could reduce systematic modeling errors and should improve the leakage pathway location estimation accuracy. The weighting factors significantly influenced the accuracy of the leakage pathway estimation. The developed inverse model was applied to estimate the leakage pathway in a brine/CO2 system using pressure anomalies induced by only brine leaks. To estimate a possible leakage pathway, the developed inverse model calibrated each integrated parameter (of both cross-sectional area and vertical hydraulic conductivity) of initial guesses of the leakage pathway. This application can provide warning before the CO2 leaks, and will be useful in mitigating the risk of CO2 leaks

Extended crossover model for human-control of fractional order plants

A data-driven generalization of the crossover model is proposed, characterizing the human control of systems with both integer and fractional-order plant dynamics. The model is developed and validated using data obtained from human subjects operating in compensatory and pursuit tracking tasks. From the model, it is inferred that humans possess a limited but consistent capability to compensate for fractional-order plant dynamics. Further, a review of potential sources of fractionality within such man–machine systems suggests that visual perception, based on visual cues that contain memory, and muscular dynamics are likely sources of fractional-order dynamics within humans themselves. Accordingly, a possible mechanism for fractional-order compensation, operating between visual and muscular sub-systems, is proposed. Deeper analysis of the data shows that human response is more highly correlated to fractional-order representations of visual cues, rather than directly to objective engineering variables, as is commonly proposed in human control models in the literature. These results are expected to underpin future design developments in human-in-the-loop cyber-physical systems, for example, in semi-autonomous highway driving

A Target Coverage Scheduling Scheme Based on Genetic Algorithms in Directional Sensor Networks

As a promising tool for monitoring the physical world, directional sensor networks (DSNs) consisting of a large number of directional sensors are attracting increasing attention. As directional sensors in DSNs have limited battery power and restricted angles of sensing range, maximizing the network lifetime while monitoring all the targets in a given area remains a challenge. A major technique to conserve the energy of directional sensors is to use a node wake-up scheduling protocol by which some sensors remain active to provide sensing services, while the others are inactive to conserve their energy. In this paper, we first address a Maximum Set Covers for DSNs (MSCD) problem, which is known to be NP-complete, and present a greedy algorithm-based target coverage scheduling scheme that can solve this problem by heuristics. This scheme is used as a baseline for comparison. We then propose a target coverage scheduling scheme based on a genetic algorithm that can find the optimal cover sets to extend the network lifetime while monitoring all targets by the evolutionary global search technique. To verify and evaluate these schemes, we conducted simulations and showed that the schemes can contribute to extending the network lifetime. Simulation results indicated that the genetic algorithm-based scheduling scheme had better performance than the greedy algorithm-based scheme in terms of maximizing network lifetime