On Foundations of Evolutionary Computation: An Evolutionary Automata Approach

On Foundations of Evolutionary Computation: An Evolutionary Automata Approach

Mark Burgin (University of California, USA) and Eugene Eberbach (Rensselaer Polytechnic Institute, USA)
DOI: 10.4018/978-1-60566-310-4.ch016
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Abstract

There are different models of evolutionary computations: genetic algorithms, genetic programming, etc. This chapter presents mathematical foundations of evolutionary computation based on the concept of evolutionary automaton. Different classes of evolutionary automata (evolutionary finite automata, evolutionary Turing machines and evolutionary inductive Turing machines) are introduced and studied. It is demonstrated that evolutionary algorithms are more expressive than conventional recursive algorithms, such as Turing machines. Universal evolutionary algorithms and automata are constructed. It is proved that classes of evolutionary finite automata, evolutionary Turing machines and evolutionary inductive Turing machines have universal automata. As in the case of conventional automata and Turing machines, universal evolutionary algorithms and automata provide means to study many important problems in the area of evolutionary computation, such as complexity, completeness, optimality and search decidability of evolutionary algorithms, as well as such natural phenomena as cooperation and competition. Expressiveness and generality of the introduced classes of evolutionary automata are investigated.
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Background

Evolution by natural selection is one of the most compelling themes of modern science. In evolutionary algorithms, selection operates on population of individuals represented by semiotic chromosomes, which are stored in a computer’s memory. Populations of semiotic chromosomes evolve in a computational process, using mutation and/or crossover in much the same way as natural populations do. This form of computation is called Evolutionary Computation (EC). Evolutionary Computation consists of four main areas: Genetic Algorithms (GA), Genetic Programming (GP), Evolution Strategies (ES) and Evolutionary Programming (EP). Additional areas include: Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), co-evolution, Artificial Immune Systems (AIS), evolutionary robotics, evolvable hardware, Evolutionary Artificial Neural Networks (EANN), evolutionary multiobjective optimization, Artificial Life (A-Life), Classifier Systems, DNA-Based Computing and some fields in bioinformatics. Applications of Evolutionary Computing are vast and diverse. Evolutionary Computing is used for finding solutions of intractable (hard and NP-complete) optimization problems, machine learning, data mining, neural network training, evolution of technology, robotics, control, electronic circuit design, games, economics, network design, pattern recognition, genome and protein analysis, DNA-based computing, evolvable programming languages, reconfigurable hardware and many others (Back, Fogel and Michalewicz 1997; Fogel 2001; Michalewicz and Fogel, 2004).

Key Terms in this Chapter

Super-Turing Models of Computation: Models of computation more expressive than Turing machines.

Expressiveness of an Evolutionary Algorithm: Characterized by the class of problems solvable by an evolutionary algorithm.

Completeness of a Class of Evolutionary Algorithms: The ability to find any solution using algorithms from this class.

Subrecursive Algorithms: Classes of algorithms that cannot solve all problems (compute everything) that Turing machines can solve (compute).

Inductive Turing Machines of the Order n: Inductive Turing machines that have a memory connections in which are constructed by an inductive Turing machine of the order n - 1.

Evolutionary Inductive Turing Machine: An evolutionary automaton that consists of an infinite series of inductive Turing machines each of which computes a generation in evolution.

Decidability of an Evolutionary Algorithm: The ability to find whether the evolutionary algorithm can solve a specific problem or class of problems.

Decidability of a Class of Evolutionary Algorithms: The ability to find whether it is possible solve a specific problem or class of problems using algorithms from this class.

Evolutionary Turing Machine: An evolutionary automaton that consists of an infinite series of Turing machines each of which computes a generation in evolution.

Inductive Turing Machines of the First Order: Inductive Turing machines that have recursive memory.

Completeness of an Evolutionary Algorithm: The ability of an evolutionary algorithm to find any solution.

Recursive Algorithms: Classes of algorithms that can solve the same problems (compute the same fucntions) as Turing machines.

Evolutionary Automata: Class of abstract automata designed to model evolutionary processes.

Inductive Turing Machine: A finite-state machine associated that has an external storage or memory medium and gives its final result only when its output stops changing after a finite number of steps.

Super-Recursive Algorithms: Classes of algorithms that can solve more problems (compute more) than Turing machines.

Expressiveness of a Class of Evolutionary Algorithms: Characterized by the class of problems solvable by evolutionary algorithms from this class.

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Table of Contents
Foreword
Lipo Wang
Preface
Hongwei Mo
Chapter 1
Fabio Freschi, Carlos A. Coello Coello, Maurizio Repetto
This chapter aims to review the state of the art in algorithms of multiobjective optimization with artificial immune systems (MOAIS). As it will be... Sample PDF
Multiobjective Optimization and Artificial Immune Systems: A Review
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Chapter 2
Jun Chen, Mahdi Mahfouf
The primary objective of this chapter is to introduce Artificial Immune Systems (AIS) as a relatively new bio-inspired optimization technique and to... Sample PDF
Artificial Immune Systems as a Bio-Inspired Optimization Technique and Its Engineering Applications
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Chapter 3
Licheng Jiao, Maoguo Gong, Wenping Ma
Many immue-inspired algorithms are based on the abstractions of one or several immunology theories, such as clonal selection, negative selection... Sample PDF
An Artificial Immune Dynamical System for Optimization
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Chapter 4
Malgorzata Lucinska, Slawomir T. Wierzchon
Multi-agent systems (MAS), consist of a number of autonomous agents, which interact with one-another. To make such interactions successful, they... Sample PDF
An Immune Inspired Algorithm for Learning Strategies in a Pursuit-Evasion Game
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Chapter 5
Luis Fernando Niño Vasquez, Fredy Fernando Muñoz Mopan, Camilo Eduardo Prieto Salazar, José Guillermo Guarnizo Marín
Artificial Immune Systems (AIS) have been widely used in different fields such as robotics, computer science, and multi-agent systems with high... Sample PDF
Applications of Artificial Immune Systems in Agents
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Chapter 6
Xingquan Zuo
Inspired from the robust control principle, a robust scheduling method is proposed to solve uncertain scheduling problems. The uncertain scheduling... Sample PDF
An Immune Algorithm Based Robust Scheduling Methods
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Chapter 7
Fabio Freschi, Maurizio Repetto
The increasing cost of energy and the introduction of micro-generation facilities and the changes in energy production systems require new... Sample PDF
Artificial Immune System in the Management of Complex Small Scale Cogeneration Systems
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Chapter 8
Krzysztof Ciesielski, Mieczyslaw A. Klopotek, Slawomir T. Wierzchon
In this chapter the authors discuss an application of an immune-based algorithm for extraction and visualization of clusters structure in large... Sample PDF
Applying the Immunological Network Concept to Clustering Document Collections
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Chapter 9
Xiangrong Zhang, Fang Liu
The problem of feature selection is fundamental in various tasks like classification, data mining, image processing, conceptual learning, and so on.... Sample PDF
Feature Selection Based on Clonal Selection Algorithm: Evaluation and Application
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Chapter 10
Yong-Sheng Ding, Xiang-Feng Zhang, Li-Hong Ren
Future Internet should be capable of extensibility, survivability, mobility, and adaptability to the changes of different users and network... Sample PDF
Immune Based Bio-Network Architecture and its Simulation Platform for Future Internet
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Chapter 11
Tao Gong
Static Web immune system is an important applicatiion of artificial immune system, and it is also a good platform to develop new immune computing... Sample PDF
A Static Web Immune System and Its Robustness Analysis
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Chapter 12
Alexander O. Tarakanov
Based on mathematical models of immunocomputing, this chapter describes an approach to spatio-temporal forecast (STF) by intelligent signal... Sample PDF
Immunocomputing for Spatio-Temporal Forecast
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Chapter 13
Fu Dongmei
In engineering application, the characteristics of the control system are entirely determined by the system controller once the controlled object... Sample PDF
Research of Immune Controllers
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Chapter 14
Xiaojun Bi
In fact, image segmentation can be regarded as a constrained optimization problem, and a series of optimization strategies can be used to complete... Sample PDF
Immune Programming Applications in Image Segmentation
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Chapter 15
Xin Wang, Wenjian Luo, Zhifang Li, Xufa Wang
A hardware immune system for the error detection of MC8051 IP core is designed in this chapter. The binary string to be detected by the hardware... Sample PDF
A Hardware Immune System for MC8051 IP Core
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Chapter 16
Mark Burgin, Eugene Eberbach
There are different models of evolutionary computations: genetic algorithms, genetic programming, etc. This chapter presents mathematical... Sample PDF
On Foundations of Evolutionary Computation: An Evolutionary Automata Approach
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Chapter 17
Terrence P. Fries
Path planning is an essential component in the control software for an autonomous mobile robot. Evolutionary strategies are employed to determine... Sample PDF
Evolutionary Path Planning for Robot Navigation Under Varying Terrain Conditions
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Chapter 18
Konstantinos Konstantinidis, Georgios Ch. Sirakoulis, Ioannis Andreadis
The aim of this chapter is to provide the reader with a Content Based Image Retrieval (CBIR) system which incorporates AI through ant colony... Sample PDF
Ant Colony Optimization for Use in Content Based Image Retrieval
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Chapter 19
Miroslav Bursa, Lenka Lhotska
The chapter concentrates on the use of swarm intelligence in data mining. It focuses on the problem of medical data clustering. Clustering is a... Sample PDF
Ant Colonies and Data Mining
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Chapter 20
Bo-Suk Yang
This chapter describes a hybrid artificial life optimization algorithm (ALRT) based on emergent colonization to compute the solutions of global... Sample PDF
Artificial Life Optimization Algorithm and Applications
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Chapter 21
Martin Macaš, Lenka Lhotská
A novel binary optimization technique is introduced called Social Impact Theory based Optimizer (SITO), which is based on social psychology model of... Sample PDF
Optimizing Society: The Social Impact Theory Based Optimizer
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Chapter 22
James F. Peters, Shabnam Shahfar
The problem considered in this chapter is how to use the observed behavior of organisms as a basis for machine learning. The proposed approach for... Sample PDF
Ethology-Based Approximate Adaptive Learning: A Near Set Approach
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Chapter 23
Dingju Zhu
Parallel computing is more and more important for science and engineering, but it is not used so widely as serial computing. People are used to... Sample PDF
Nature Inspired Parallel Computing
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Chapter 24
Tang Mo, Wang Kejun, Zhang Jianmin, Zheng Liying
An understanding of the human brain’s local function has improved in recent years. But the cognition of human brain’s working process as a whole is... Sample PDF
Fuzzy Chaotic Neural Networks
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