Finding Optimal Cayley Map Embeddings Using Genetic Algorithms

Genetic algorithms are a commonly used metaheuristic search method aimed at solving complex optimization problems in a variety of fields. These types of algorithms lend themselves to problems that can incorporate stochastic elements, which allows for a wider search across a search space. However, the nature of the genetic algorithm can often cause challenges regarding time-consumption. Although the genetic algorithm may be widely applicable to various domains, it is not guaranteed that the algorithm will outperform other traditional search methods in solving problems specific to particular domains. In this paper, we test the feasibility of genetic algorithms in solving a common optimization problem in topological graph theory. In the study of Cayley maps, one problem that arises is how one can optimally embed a Cayley map of a complete graph onto an orientable surface with the least amount of holes on the surface as possible. One useful application of this optimization problem is in the design of circuit boards since such a process involves minimizing the number of layers that are required to build the circuit while still ensuring that none of the wires will cross. In this paper, we study complete graphs of the form K_12m + 7 for positive integers m and we work on mappings with the finite cyclic group Z_n. We develop several baseline search algorithms to first gain an understanding of the search space and its complexity. Then, we employ two different approaches to building the genetic algorithm and compare their performances in finding optimal Cayley map embeddings

A review on Estimation of Distribution Algorithms in Permutation-based Combinatorial Optimization Problems

Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. Characterized by the use of probabilistic models to represent the solutions and the dependencies between the variables of the problem, these algorithms have been applied to a wide set of academic and real-world optimization problems, achieving competitive results in most scenarios. Nevertheless, there are some optimization problems, whose solutions can be naturally represented as permutations, for which EDAs have not been extensively developed. Although some work has been carried out in this direction, most of the approaches are adaptations of EDAs designed for problems based on integer or real domains, and only a few algorithms have been specifically designed to deal with permutation-based problems. In order to set the basis for a development of EDAs in permutation-based problems similar to that which occurred in other optimization fields (integer and real-value problems), in this paper we carry out a thorough review of state-of-the-art EDAs applied to permutation-based problems. Furthermore, we provide some ideas on probabilistic modeling over permutation spaces that could inspire the researchers of EDAs to design new approaches for these kinds of problems

Metaheuristics for the Minimum Time Cut Path Problem with Different Cutting and Sliding Speeds

The problem of efficiently cutting smaller two-dimensional pieces from a larger surface is recurrent in several manufacturing settings. This problem belongs to the domain of cutting and packing (C&P) problems. This study approached a category of C&P problems called the minimum time cut path (MTCP) problem, which aims to identify a sequence of cutting and sliding movements for the head device to minimize manufacturing time. Both cutting and slide speeds (just moving the head) vary according to equipment, despite their relevance in real-world scenarios. This study applied the MTCP problem on the practical scope and presents two metaheuristics for tackling more significant instances that resemble real-world requirements. The experiments presented in this study utilized parameter values from typical laser-cutting machines to assess the feasibility of the proposed methods compared to existing commercial software. The results show that metaheuristic-based solutions are competitive when addressing practical problems, achieving increased performance regarding the processing time for 94% of the instances

Determining Community Structure and Modularity in Social Network using Genetic Algorithm

 Research on determining community structure in complex networks has attracted a lot of attention in various applications, such as email networks and social networks. The popularity determines the structure of a community because it can analyze the structure.Meanwhile, to determine the structure of the community by maximizing the value of modularity is difficult. Therefore, a lot of research introduces new algorithms to solve problems in determining community structure and maximizing the value of modularity. Genetic Algorithm can provide effective solutions by combining exploration and exploitation.This study focuses on the Genetic Algorithm which added a cleanup feature in the process. The final results of this study are the results of a comparison of modularity values based on the determination of the community structure of the Genetic Algorithm, Girvan and Newman Algorithm, and the Louvain Algorithm. The best modularity values were obtained using the Genetic Algorithm which obtained 0.6833 results for Zachary's karate club dataset, 0.7446 for the Bottlenose dolphins dataset, 0.7242 for the American college football dataset, and 0.5892 for the Books about US politics dataset

Problemas de asignación de recursos humanos a través del problema de asignación multidimensional

149 páginas. Doctorado en Optimización.El problema de asignación de personal aparece en diversas industrias. La asignación eficiente de personal a trabajos, proyectos, herramientas, horarios, entre otros, tiene un impacto directo en términos monetarios para el negocio. El problema de asignación multidimensional (PAM) es la extensión natural del problema de asignación y puede ser utilizado en aplicaciones donde se requiere la asignación de personal. El caso más estudiado de PAM es el problema de asignación en tres dimensiones, sin embargo en años recientes han sido propuestas algunas heurísticas de búsqueda local y algoritmos meméticos para el caso general. En este trabajo de tesis se realiza un estudio profundo de PAM comenzando con un resumen del estado del arte de algoritmos, heurísticas y metaheurísticas para su resolución. Se describen algunos algoritmos y se propone uno nuevo que resuelve instancias de tamaño medio para PAM. Se propone la generalización de las conocidas heurísticas de variación de dimensión como una búsqueda local generalizada que proporciona un nuevo estado del arte de búsquedas locales para PAM. Adicionalmente, se propone un algoritmo memético con una estructura sencilla pero efectiva y que es competitivo con el mejor algoritmo memético conocido para PAM. Finalmente, se presenta un caso particular de problema de asignación de personal: el Problema de Asignación de Horarios (PAH). El PAH considera la asignación de personal a uno, dos o más conjuntos de objetos, por ejemplo puede ser requerida la asignación de profesores a cursos a periodos de tiempo a salones, para determinados grupos de estudiantes. Primero, se presenta el PAH así como una breve descripción de su estado del arte. Luego, se propone una nueva forma de modelar este problema a través de la resolución de PAM y se aplica sobre el PAH en la Universidad Autónoma Metropolitana, unidad Azcapotzalco (UAM-A). Se describen las consideraciones particulares del PAH en la UAM-A y proponemos una nueva solución para éste. Nuestra solución se basa en la resolución de múltiples PA3 a través de los algoritmos y heurísticas propuestos.Personnel assignment problems appear in several industries. The e cient assignment of personnel to jobs, projects, tools, time slots, etcetera, has a direct impact in terms monetary for the business. The Multidimensional Assignment Problem (MAP) is a natural extension of the well-known assignment problem and can be used on applications where the assignment of personnel is required. The most studied case of the MAP is the three dimensional assignment problem, though in recent years some local search heuristics and memetic algorithms have been proposed for the general case. Let X1; : : : ;Xs be a collection of s 3 disjoint sets, consider all combinations that belong to the Cartesian product X = X1 Xs such that each vector x 2 X, where x = (x1; : : : ; xs) with xi 2 Xi 8 1 i s, has associated a weight w(x). A feasible assignment is a collection A = (x1; : : : ; xn) of n vectors if xi k 6= xj k for each i 6= j and 1 k s. The weight of an assignment A is given by w(A) = Pn i=1 w(xi). A MAP in s dimensions is denoted as sAP. The objective of sAP is to nd an assignment of minimal weight. In this thesis we make an in depth study of MAP beginning with the state-ofthe- art algorithms, heuristics, and metaheuristics for solving it. We describe some algorithms and we propose a new one for solving optimally medium size instances of MAP. We propose the generalization of the called dimensionwise variation heuristics for MAP and a new generalized local search heuristic that provides new state-of-theart local searches for MAP. We also propose a new simple memetic algorithm that is competitive against the state-of-the-art memetic algorithm for MAP. In the last part of this thesis, we study a particular case of personnel assignment problem: the School Timetabling Problem (STP). The STP considers the assignment of personnel to other two or more sets, for example the assignment of professors to courses to time slots to rooms can be required. First, we provide a brief description of the state-of-the-art for STP. Then, we introduce a new approach for modeling this problem through the resolution of several MAP and we apply our solution on a real life case of study: STP at the Universidad Autonoma Metropolitana campus Azcapotzalco (UAM-A). We provide the particular aspects for STP at UAM-A and we provide a new solution for this problem. Our approach is based on solving several 3AP considering the introduced model and our proposed techniques.Consejo Mexiquense de Ciencia y Tecnología (Comecyt).Consejo Nacional de Ciencia y Tecnología (México

A Sustainable Autonomic Architecture for Organically Reconfigurable Computing Systems

A Sustainable Autonomic Architecture for Organically Reconfigurable Computing System based on SRAM Field Programmable Gate Arrays (FPGAs) is proposed, modeled analytically, simulated, prototyped, and measured. Low-level organic elements are analyzed and designed to achieve novel self-monitoring, self-diagnosis, and self-repair organic properties. The prototype of a 2-D spatial gradient Sobel video edge-detection organic system use-case developed on a XC4VSX35 Xilinx Virtex-4 Video Starter Kit is presented. Experimental results demonstrate the applicability of the proposed architecture and provide the infrastructure to quantify the performance and overcome fault-handling limitations. Dynamic online autonomous functionality restoration after a malfunction or functionality shift due to changing requirements is achieved at a fine granularity by exploiting dynamic Partial Reconfiguration (PR) techniques. A Genetic Algorithm (GA)-based hardware/software platform for intrinsic evolvable hardware is designed and evaluated for digital circuit repair using a variety of well-accepted benchmarks. Dynamic bitstream compilation for enhanced mutation and crossover operators is achieved by directly manipulating the bitstream using a layered toolset. Experimental results on the edge-detector organic system prototype have shown complete organic online refurbishment after a hard fault. In contrast to previous toolsets requiring many milliseconds or seconds, an average of 0.47 microseconds is required to perform the genetic mutation, 4.2 microseconds to perform the single point conventional crossover, 3.1 microseconds to perform Partial Match Crossover (PMX) as well as Order Crossover (OX), 2.8 microseconds to perform Cycle Crossover (CX), and 1.1 milliseconds for one input pattern intrinsic evaluation. These represent a performance advantage of three orders of magnitude over the JBITS software framework and more than seven orders of magnitude over the Xilinx design flow. Combinatorial Group Testing (CGT) technique was combined with the conventional GA in what is called CGT-pruned GA to reduce repair time and increase system availability. Results have shown up to 37.6% convergence advantage using the pruned technique. Lastly, a quantitative stochastic sustainability model for reparable systems is formulated to evaluate the Sustainability of FPGA-based reparable systems. This model computes at design-time the resources required for refurbishment to meet mission availability and lifetime requirements in a given fault-susceptible missions. By applying this model to MCNC benchmark circuits and the Sobel Edge-Detector in a realistic space mission use-case on Xilinx Virtex-4 FPGA, we demonstrate a comprehensive model encompassing the inter-relationships between system sustainability and fault rates, utilized, and redundant hardware resources, repair policy parameters and decaying reparability