An Artificial Immune Dynamical System for Optimization

An Artificial Immune Dynamical System for Optimization

Licheng Jiao (Xidian University, China), Maoguo Gong (Xidian University, China) and Wenping Ma (Xidian University, China)
DOI: 10.4018/978-1-60566-310-4.ch003
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Abstract

Many immue-inspired algorithms are based on the abstractions of one or several immunology theories, such as clonal selection, negative selection, positive selection, rather than the whole process of immune response to solve computational problems. In order to build a general computational framework by simulating immune response process, this chapter introduces a population-based artificial immune dynamical system, termed as PAIS, and applies it to numerical optimization problems. PAIS models the dynamic process of human immune response as a quaternion (G, I, R, Al), where G denotes exterior stimulus or antigen, I denotes the set of valid antibodies, R denotes the set of reaction rules describing the interactions between antibodies, and Al denotes the dynamic algorithm describing how the reaction rules are applied to antibody population. Some general descriptions of reaction rules, including the set of clonal selection rules and the set of immune memory rules are introduced in PAIS. Based on these reaction rules, a dynamic algorithm, termed as PAISA, is designed for numerical optimization. In order to validate the performance of PAISA, 9 benchmark functions with 20 to 10,000 dimensions and a practical optimization problem, optimal approximation of linear systems are solved by PAISA, successively. The experimental results indicate that PAISA has high performance in optimizing some benchmark functions and practical optimization problems.
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Introduction

Biological inspiration can successfully be transferred into novel computational paradigms, as shown in the development and successful use of concepts such as artificial neural networks, evolutionary algorithms, swarm algorithms, and so on. Many bio-inspired algorithms are based on populations of agents trained to perform some task or optimization. The most obvious one is the area of evolutionary algorithms, based on analogy to populations of organisms breeding and selecting to become “fitter” (Stepney, Smith, Timmis, & Tyrrell, 2004).

In recent years, Artificial Immune Systems (AIS) have received a significant amount of interest from researchers and industrial sponsors. Some of the first work in applying human immune system (HIS) metaphors was undertaken in the area of fault diagnosis (Ishida, 1990). Later work applied HIS metaphors to the field of computer security (Forrest, Perelson, Allen, & Cherukuri, 1994), which seemed to act as a catalyst for further investigation of HIS as a metaphor in such areas as Anomaly Detection (Gonzalez, Dasgupta, & Kozma, 2002), Pattern Recognition (Carter, 2000; Timmis, Neal, & Hunt, 2000; White, & Garrett, 2003), Job shop Scheduling (Hart, & Ross, 1999; Coello Coello, Rivera, & Cortes, 2003), optimization (Jiao &Wang, 2000; de Castro & Von Zuben, 2002) and Engineering Design Optimization (Hajela, Yoo, & Lee, 1997; Gong, Jiao, Du, & Wang, 2005).

In order to build a general computational framework by simulating the whole process of immune response, this chapter introduces a model for population-based Artificial Immune Systems, termed as PAIS. PAIS models the dynamic process of human immune response as a quaternion (G, I, R, Al), where G denotes exterior stimulus or antigen, I denotes the set of valid antibodies, R denotes the set of reaction rules describing the interactions between antibodies, and Al denotes the dynamic algorithm describing how the reaction rules are applied to antibody population. PAIS can be considered as a general architecture of population-based artificial immune systems rather than an immune algorithm. Many immune phenomena, such as clonal selection, immune memory, negative selection, passive selection, can be modeled as corresponding reaction rules and added to the set of reaction rules R. Based on the PAIS, our final aim is to build a self-adaptive dynamical system by simulating all the possible interactions between antibodies during immune response. Then the PAIS can automatically select reaction rules depending on antigen G, and thereby the pending problems could be solved automatically. In order to solve numerical optimization problems, the set of clonal selection rules and the set of immune memory rules are introduced. Consequently, a dynamic algorithm based on these heuristic rules is designed, which can effectively solve numerical optimization problems even when the number of variable parameters is as many as 10 000.

The rest of the paper is organized as follows: Section 2 describes some related background. Section 3 describes the population-based artificial immune dynamical system architecture. Section 4 describes the experimental study on nine benchmark functions. Section 5 describes the experimental study on the optimal approximation of linear systems. Finally, concluding remarks are presented in Section 6.

Key Terms in this Chapter

Clonal Selection: Human immune response relies on the prior formation of an incredibly diverse population of B cells and T cells. The specificity of both the B-cell receptors and T-cell receptors, that is, the epitope to which a given receptor can bind, is created by a remarkable genetic mechanism. Each receptor is created even though the epitope it recognizes may never have been present in the body. If an antigen with that epitope should enter the body, those few lymphocytes able to bind to it will do so. If they also receive a second co-stimulatory signal, they may begin repeated rounds of mitosis. In this way, clones of antigen-specific lymphocytes (B and T) develop providing the basis of the immune response. This phenomenon is called clonal selection

Natural Computation: Natural computation is the study of computational systems that are inspired from natural systems, including biological, ecological, physical, chemical, economical and social systems

Dynamical System: A means of describing how one state develops into another state over the course of time. A dynamical system is a smooth action of the reals or the integers on another object.

Optimization: Find values of the variables that minimize or maximize the objective function while satisfying the constraints.

Evolutionary Algorithms: Evolutionary algorithms are search methods that take their inspiration from natural selection and survival of the fittest in the biological world.

Artificial Immune Systems: Artificial immune systems are adaptive systems inspired by theoretical immunology and observed immune functions, principles and models, which are applied to complex problem domains

Immune Memory: Besides the clonal selection, during the initial expansion of clones, some of the progeny cells neither went on dividing nor developed into plasma cells. Instead, they reverted to small lymphocytes bearing the same B-cell receptor on their surface that their ancestors had. This lays the foundation for a more rapid and massive response the next time the antigen enters the body, i.e. immune memory

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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
$37.50
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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