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

Improvements on the bees algorithm for continuous optimisation problems

This work focuses on the improvements of the Bees Algorithm in order to enhance the algorithm’s performance especially in terms of convergence rate. For the first enhancement, a pseudo-gradient Bees Algorithm (PG-BA) compares the fitness as well as the position of previous and current bees so that the best bees in each patch are appropriately guided towards a better search direction after each consecutive cycle. This method eliminates the need to differentiate the objective function which is unlike the typical gradient search method. The improved algorithm is subjected to several numerical benchmark test functions as well as the training of neural network. The results from the experiments are then compared to the standard variant of the Bees Algorithm and other swarm intelligence procedures. The data analysis generally confirmed that the PG-BA is effective at speeding up the convergence time to optimum. Next, an approach to avoid the formation of overlapping patches is proposed. The Patch Overlap Avoidance Bees Algorithm (POA-BA) is designed to avoid redundancy in search area especially if the site is deemed unprofitable. This method is quite similar to Tabu Search (TS) with the POA-BA forbids the exact exploitation of previously visited solutions along with their corresponding neighbourhood. Patches are not allowed to intersect not just in the next generation but also in the current cycle. This reduces the number of patches materialise in the same peak (maximisation) or valley (minimisation) which ensures a thorough search of the problem landscape as bees are distributed around the scaled down area. The same benchmark problems as PG-BA were applied against this modified strategy to a reasonable success. Finally, the Bees Algorithm is revised to have the capability of locating all of the global optimum as well as the substantial local peaks in a single run. These multi-solutions of comparable fitness offers some alternatives for the decision makers to choose from. The patches are formed only if the bees are the fittest from different peaks by using a hill-valley mechanism in this so called Extended Bees Algorithm (EBA). This permits the maintenance of diversified solutions throughout the search process in addition to minimising the chances of getting trap. This version is proven beneficial when tested with numerous multimodal optimisation problems

Swarm intelligence: novel tools for optimization, feature extraction, and multi-agent system modeling

Abstract Animal swarms in nature are able to adapt to dynamic changes in their envi-ronment, and through cooperation they can solve problems that are crucial for their survival. Only by means of local interactions with other members of the swarm and with the environment, they can achieve a common goal more efficiently than it would be done by a single individual. This problem-solving behavior that results from the multiplicity of such interactions is referred to as Swarm Intelligence. The mathematical models of swarming behavior in nature were initially proposed to solve optimization problems. Nevertheless, this decentralized approach can be a valuable tool for a variety of applications, where emerging global patterns represent a solution to the task at hand. Methods for the solution of difficult computational problems based on Swarm Intelligence have been experimentally demonstrated and reported in the literature. However, a general framework that would facilitate their design does not exist yet. In this dissertation, a new general design methodology for Swarm Intelligence tools is proposed. By defining a discrete space in which the members of the swarm can move, and by modifying the rules of local interactions and setting the adequate objective function for solutions evaluation, the proposed methodology is tested in various domains. The dissertation presents a set of case studies, and focuses on two general approaches. One approach is to apply Swarm Intelligence as a tool for optimization and feature extraction, and the other approach is to model multi-agent systems such that they resemble swarms of animals in nature providing them with the ability to autonomously perform a task at hand. Artificial swarms are designed to be autonomous, scalable, robust, and adaptive to the changes in their environment. In this work, the methods that exploit one or more of these features are presented. First, the proposed methodology is validated in a real-world scenario seen as a combinatorial optimization problem. Then a set of novel tools for feature extraction, more precisely the adaptive edge detection and the broken-edge linking in digital images is proposed. A novel data clustering algorithm is also proposed and applied to image segmentation. Finally, a scalable algorithm based on the proposed methodology is developed for distributed task allocation in multi-agent systems, and applied to a swarm of robots. The newly proposed general methodology provides a guideline for future developers of the Swarm Intelligence tools. Los enjambres de animales en la naturaleza son capaces de adaptarse a cambios dinamicos en su entorno y, por medio de la cooperación, pueden resolver problemas ´ cruciales para su supervivencia. Unicamente por medio de interacciones locales con otros miembros del enjambre y con el entorno, pueden lograr un objetivo común de forma más eficiente que lo haría un solo individuo. Este comportamiento problema-resolutivo que es resultado de la multiplicidad de interacciones se denomina Inteligencia de Enjambre. Los modelos matemáticos de comportamiento de enjambres en entornos naturales fueron propuestos inicialmente para resolver problemas de optimización. Sin embargo, esta aproximación descentralizada puede ser una herramienta valiosa en una variedad de aplicaciones donde patrones globales emergentes representan una solución de las tareas actuales. Aunque en la literatura se muestra la utilidad de los métodos de Inteligencia de Enjambre, no existe un entorno de trabajo que facilite su diseño. En esta memoria de tesis proponemos una nueva metodologia general de diseño para herramientas de Inteligencia de Enjambre. Desarrollamos herramientas noveles que representan ejem-plos ilustrativos de su implementación. Probamos la metodología propuesta en varios dominios definiendo un espacio discreto en el que los miembros del enjambre pueden moverse, modificando las reglas de las interacciones locales y fijando la función objetivo adecuada para evaluar las soluciones. La memoria de tesis presenta un conjunto de casos de estudio y se centra en dos aproximaciones generales. Una aproximación es aplicar Inteligencia de Enjambre como herramienta de optimización y extracción de características mientras que la otra es modelar sistemas multi-agente de tal manera que se asemejen a enjambres de animales en la naturaleza a los que se les confiere la habilidad de ejecutar autónomamente la tarea. Los enjambres artificiales están diseñados para ser autónomos, escalables, robustos y adaptables a los cambios en su entorno. En este trabajo, presentamos métodos que explotan una o más de estas características. Primero, validamos la metodología propuesta en un escenario del mundo real visto como un problema de optimización combinatoria. Después, proponemos un conjunto de herramientas noveles para ex-tracción de características, en concreto la detección adaptativa de bordes y el enlazado de bordes rotos en imágenes digitales, y el agrupamiento de datos para segmentación de imágenes. Finalmente, proponemos un algoritmo escalable para la asignación distribuida de tareas en sistemas multi-agente aplicada a enjambres de robots. La metodología general recién propuesta ofrece una guía para futuros desarrolladores deherramientas de Inteligencia de Enjambre

Solving Real-Life Hydroinformatics Problems with Operations Research and Artificial Intelligence

Many real life problems in the hydraulic engineering literature can be modelled as constrained optimisation problems. Often, they are addressed in the literature through genetic algorithms, although other techniques have been proposed. In this thesis, we address two of these real life problems through a variety of techniques taken from the Artificial Intelligence and Operations Research areas, such as mixed-integer linear programming, logic programming, genetic algorithms and path relinking, together with hybridization amongst these technologies and with hydraulic simulators. For the first time, an Answer Set Programming formulation of hydroinformatics problems is proposed. The two real life problems addressed hereby are the optimisation of the response in case of contamination events, and the optimisation of the positioning of the isolation valves. The constraints of the former describe the feasible region of the Multiple Travelling Salesman Problem, while the objective function is computed by a hydraulic simulator. A simulation–optimisation approach based on Genetic Algorithms, mathematical programming, and Path Relinking, and a thorough experimental analysis are discussed hereby. The constraints of the latter problem describe a graph partitioning enriched with a maximum flow, and it is a new variant of the common graph partitioning. A new mathematical model plus a new formalization in logic programming are discussed in this work. In particular, the technologies adopted are mixed-integer linear programming and Answer Set Programming. Addressing these two real applications in hydraulic engineering as constrained optimisation problems has allowed for i) computing applicable solutions to the real case, ii) computing better solutions than the ones proposed in the hydraulic literature, iii) exploiting graph theory for modellization and solving purposes, iv) solving the problems by well suited technologies in Operations Research and Artificial Intelligence, and v) designing new integrated and hybrid architectures for a more effective solving

Advances in Artificial Intelligence: Models, Optimization, and Machine Learning

The present book contains all the articles accepted and published in the Special Issue “Advances in Artificial Intelligence: Models, Optimization, and Machine Learning” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of artificial intelligence and its subfields. These topics include, among others, deep learning and classic machine learning algorithms, neural modelling, architectures and learning algorithms, biologically inspired optimization algorithms, algorithms for autonomous driving, probabilistic models and Bayesian reasoning, intelligent agents and multiagent systems. We hope that the scientific results presented in this book will serve as valuable sources of documentation and inspiration for anyone willing to pursue research in artificial intelligence, machine learning and their widespread applications

Optimisation algorithms inspired from modelling of bacterial foraging patterns and their applications

Research in biologically-inspired optimisation has been fl<;lurishing over the past decades. This approach adopts a bott0!ll-up viewpoint to understand and mimic certain features of a biological system. It has been proved useful in developing nondeterministic algorithms, such as Evolutionary Algorithms (EAs) and Swarm Intelligence (SI). Bacteria, as the simplest creature in nature, are of particular interest in recent studies. In the past thousands of millions of years, bacteria have exhibited a self-organising behaviour to cope with the natural selection. For example, bacteria have developed a number of strategies to search for food sources with a very efficient manner. This thesis explores the potential of understanding of a biological system by modelling the' underlying mechanisms of bacterial foraging patterns and investigates their applicability to engineering optimisation problems. :rvlodelling plays a significant role in understanding bacterial foraging behaviour. Mathematical expressions and experimental observations have been utilised to represent biological systems. However, difficulties arise from the lack of systematic analysis of the developed models and experimental data. Recently, Systems Biology has be,en proposed to overcome this barrier, with the effort from a number of research fields, including Computer Science and Systems Engineering. At the same time, Individual-based Modelling (IbM) has emerged to assist the modelling of a biological system. Starting from a basic model of foraging and proliferation of bacteria, the development of an IbM of bacterial systems of this thesis focuses on a Varying Environment BActerial Model (VEBAM). Simulation results demonstrate that VEBAM is able to provide a new perspective to describe interactions between the bacteria and their food environment. Knowledge transfer from modelling of bacterial systems to solving optimisation problems also composes an important part of this study. Three Bacteriainspired Algorithms (BalAs) have been developed to bridge the gap between modelling and optimisation. These algorithms make use of the. self-adaptability of individual bacteria in the group searching activities described in VEBAM, while incorporating a variety of additional features. In particular, the new bacterial foraging algorithm with varying population (BFAVP) takes bacterial metabolism into consideration. The group behaviour in Particle Swarm Optimiser (PSO) is adopted in Bacterial Swarming Algorithm (BSA) to enhance searching ability. To reduce computational time, another algorithm, a Paired-bacteria Optimiser (PBO) is designed specifically to further explore the capability of BalAs. Simulation studies undertaken against a wide range of benchmark functions demonstrate a satisfying performance with a reasonable convergence speed. To explore the potential of bacterial searching ability in optimisation undertaken in a varying environment, a dynamic bacterial foraging algorithm (DBFA) is developed with the aim of solving optimisation in a time-varying environment. In this case, the balance between its convergence and exploration abilities is investigated, and a new scheme of reproduction is developed which is different froin that used for static optimisation problems. The simulation studies have been undertaken and the results show that the DBFA can adapt to various environmental changes rapidly. One of the challenging large-scale complex optimisation problems is optimal power flow (OPF) computation. BFAVP shows its advantage in solving this problem. A simulation study has been performed on an IEEE 30-bus system, and the results are compared with PSO algorithm and Fast Evolutionary Programming (FEP) algorithm, respectively. Furthermore, the OPF problem is extended for consideration in varying environments, on which DBFA has been evaluated. A simulation study has been undertaken on both the IEEE 30-bus system and the IEEE l1S-bus system, in compariso~ with a number of existing algorithms. The dynamic OPF problem has been tackled for the first time in the area of power systems, and the results obtained are encouraging, with a significant amount of energy could possibly being saved. Another application of BaIA in this thesis is concerned with estimating optimal parameters of a power transformer winding model using BSA. Compared with Genetic Algorithm (GA), BSA is able to obtain a more satisfying result in modelling the transformer winding, which could not be achieved using a theoretical transfer function model

Robust and Constrained Portfolio Optimization using Multiobjective Evolutionary Algorithms

Optimization plays an important role in many areas of science, management,economics and engineering. Many techniques in mathematics and operation research are available to solve such problems. However these techniques have many shortcomings to provide fast and accurate solution particularly when the optimization problem involves many variables and constraints. Investment portfolio optimization is one such important but complex problem in computational finance which needs effective and efficient solutions. In this problem each available asset is judiciously selected in such a way that the total profit is maximized while simultaneously minimizing the total risk. The literature survey reveals that due to non availability of suitable multi objective optimization tools, this problem is mostly being solved by viewing it as a single objective optimization problem

Computational tools for modeling and measuring chromosome structure

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 99-112).DNA conformation within cells has many important biological implications, but there are challenges both in modeling DNA due to the need for specialized techniques, and experimentally since tracing out in vivo conformations is currently impossible. This thesis contributes two computational projects to these efforts. The first project is a set of online and offline calculators of conformational statistics using a variety of published and unpublished methods, addressing the current lack of DNA model-building tools intended for general use. The second project is a reconstructive analysis that could enable in vivo mapping of DNA conformation at high resolution with current experimental technology.by Brian Christopher Ross.Ph.D