Genetic Algorithms and Multimodal Search

Genetic Algorithms and Multimodal Search

Marcos Gestal (University of A Coruña, Spain), José Manuel Vázquez Naya (University of A Coruña, Spain) and Norberto Ezquerra (Georgia Institute of Technology, USA)
DOI: 10.4018/978-1-59904-996-0.ch013
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Traditionally, the Evolutionary Computation (EC) techniques, and more specifically the Genetic Algorithms (GAs), have proved to be efficient when solving various problems; however, as a possible lack, the GAs tend to provide a unique solution for the problem on which they are applied. Some non global solutions discarded during the search of the best one could be acceptable under certain circumstances. Most of the problems at the real world involve a search space with one or more global solutions and multiple local solutions; this means that they are multimodal problems and therefore, if it is desired to obtain multiple solutions by using GAs, it would be necessary to modify their classic functioning outline for adapting them correctly to the multimodality of such problems. The present chapter tries to establish, firstly, the characterisation of the multimodal problems will be attempted. A global view of some of the several approaches proposed for adapting the classic functioning of the GAs to the search of mu ltiple solutions will be also offered. Lastly, the contributions of the authors and a brief description of several practical cases of their performance at the real world will be also showed.
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Multimodal Problems

The multimodal problems can be defined as those problems that have either multiple global optima or multiple local optima (Harik, 1995).

For this type of problems, it is interesting to obtain the greatest number of solutions due to several reasons; on one hand, when there is not a total knowledge of the problem, the solution obtained might not be the best one, as it can not be stated that no better solution could be found at the search space not explored yet. On the other hand, although being certain that the best solution has been achieved, there might be other equally fitted or slightly worse solutions that might be preferred due to different factors (easier application, simpler interpretation, etc.) and therefore considered globally better.

One of the most characteristic multimodal functions used in lab problems is the Rastrigin function (see Figure 1) which offers an excellent graphical point of view about what multimodality means.

Figure 1.

Rastrigin function: 3D and 2D representations

Providing multiple optimal (and valid) solutions, and not only a unique global solution, is crucial in multiple environments. Usually, it is very complex to implement in practice the best solution, so it can offer multiple problems: computational cost too high, complex interpretation, difficulty in the acquisition of information, etc.

In these situations it is useful to have a choice of several valid solutions and, although they are not the best solution to the problem, they might offer a level of acceptable adjustment, be simpler to implement, to understand or to distribute than the ideal global one.


Evolutionary Computation And Multimodal Problems

As it has been mentioned, the application of EC techniques to the resolution of multimodal problems sets out the difficulty that this type of techniques shows since they tend to solely provide the best of the found solutions and to discard possible local optima that might have been found throughout the search. Quite many modifications have been included in the traditional performance of the GA in order to achieve good results with multimodal problems.

A crucial aspect when obtaining multiple solutions consists on keeping the diversity of the genetic population, distributing as much as possible the genetic individuals throughout the search space.

Complete Chapter List

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Table of Contents
Alfonso Araque Almendros
Ana B. Porto Pazos, Alejandro Pazos Sierra, Washington Buño Buceta
Chapter 1
Eduardo Malmierca, Nazareth P. Castellanos, Valeri A. Makarov, Angel Nuñez
It is well know the temporal structure of spike discharges is crucial to elicit different types of neuronal plasticity. Also, precise and... Sample PDF
Corticofugal Modulation of Tactile Responses of Neurons in the Spinal Trigeminal Nucleus: A Wavelet Coherence Study
Chapter 2
Didier Le Ray, Morgane Le Bon-Jego, Daniel Cattaert
Computational neuroscience has a lot to gain from invertebrate research. In this chapter focusing on the sensory-motor network that controls leg... Sample PDF
Neural Mechanisms of Leg Motor Control in Crayfish: Insights for Neurobiologically-Inspired Autonomous Systems
Chapter 3
Oscar Herreras, Julia Makarova, José Manuel Ibarz
Neurons send trains of action potentials to communicate each other. Different messages are issued according to varying inputs, but they can also mix... Sample PDF
Forward Dendritic Spikes: A Mechanism for Parallel Processing in Dendritic Subunits and Shifting Output Codes
Chapter 4
Gheorghe Paun, Mario J. Perez-Jimenez
This chapter is a quick survey of spiking neural P systems, a branch of membrane computing which was recently introduced with motivation from neural... Sample PDF
Spiking Neural P Systems: An Overview
Chapter 5
Juan Ramón Rabuñal Dopico, Javier Pereira Loureiro, Mónica Miguélez Rico
In this chapter, we state an evolution of the Recurrent ANN (RANN) to enforce the persistence of activations within the neurons to create activation... Sample PDF
Simulation of the Action Potential in the Neuron's Membrane in Artificial Neural Networks
Chapter 6
Ana B. Porto Pazos, Alberto Alvarellos González, Alejandro Pazos Sierra
The Artificial NeuroGlial Networks, which try to imitate the neuroglial brain networks, appeared in order to process the information by means of... Sample PDF
Recent Methodology in Connectionist Systems
Chapter 7
José A. Fernández-León, Gerardo G. Acosta, Miguel A. Mayosky, Oscar C. Ibáñez
This work is intended to give an overview of technologies, developed from an artificial intelligence standpoint, devised to face the different... Sample PDF
A Biologically Inspired Autonomous Robot Control Based on Behavioural Coordination in Evolutionary Robotics
Chapter 8
Enrique Mérida-Casermeiro, Domingo López-Rodríguez, J.M. Ortiz-de-Lazcano-Lobato
In this chapter, two important issues concerning associative memory by neural networks are studied: a new model of hebbian learning, as well as the... Sample PDF
An Approach to Artificial Concept Learning Based on Human Concept Learning by Using Artificial Neural Networks
Chapter 9
Enrique Fernández-Blanco, Julian Dorado, Nieves Pedreira
The artificial embryogeny term overlaps all the models that try to adapt cellular properties into artificial models. This chapter presents a new... Sample PDF
Artificial Cell Systems Based in Gene Expression Protein Effects
Chapter 10
Computing vs. Genetics  (pages 165-181)
José M. Barreiro, Juan Pazos
This chapter first presents the interrelations between computing and genetics, which both are based on information and, particularly... Sample PDF
Computing vs. Genetics
Chapter 11
Iara Moema Oberg Vilela
This chapter discusses guidelines and models of Mind from Cognitive Sciences in order to generate an integrated architecture for an artificial mind... Sample PDF
Artificial Mind for Virtual Characters
Chapter 12
Zhijun Yang, Felipe M.G. França
As an engine of almost all life phenomena, the motor information generated by the central nervous system (CNS) plays a critical role in the... Sample PDF
A General Rhythmic Pattern Generation Architecture for Legged Locomotion
Chapter 13
Marcos Gestal, José Manuel Vázquez Naya, Norberto Ezquerra
Traditionally, the Evolutionary Computation (EC) techniques, and more specifically the Genetic Algorithms (GAs), have proved to be efficient when... Sample PDF
Genetic Algorithms and Multimodal Search
Chapter 14
Jesús M. Miró, Alfonso Rodríguez-Patón
Synthetic biology and biomolecular computation are disciplines that fuse when it comes to designing and building information processing devices. In... Sample PDF
Biomolecular Computing Devices in Synthetic Biology
Chapter 15
Alejandro Rodríguez, Alexander Grushin, James A. Reggia
Drawing inspiration from social interactions in nature, swarm intelligence has presented a promising approach to the design of complex systems... Sample PDF
Guiding Self-Organization in Systems of Cooperative Mobile Agents
Chapter 16
Agostino Forestiero, Carlo Mastroianni, Fausto Pupo, Giandomenico Spezzano
This chapter proposes a bio-inspired approach for the construction of a self-organizing Grid information system. A dissemination protocol exploits... Sample PDF
Evaluating a Bio-Inspired Approach for the Design of a Grid Information System: The SO-Grid Portal
Chapter 17
Steven M. Corns, Daniel A. Ashlock, Kenneth Mark Bryden
This chapter presents Graph Based Evolutionary Algorithms. Graph Based Evolutionary Algorithms are a generic enhancement and diversity management... Sample PDF
Graph Based Evolutionary Algorithms
Chapter 18
Daniela Danciu
Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call... Sample PDF
Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria
Chapter 19
Jianhua Yang, Evor L. Hines, Ian Guymer, Daciana D. Iliescu, Mark S. Leeson, Gregory P. King, XuQuin Li
In this chapter a novel method, the Genetic Neural Mathematical Method (GNMM), for the prediction of longitudinal dispersion coefficient is... Sample PDF
A Genetic Algorithm-Artificial Neural Network Method for the Prediction of Longitudinal Dispersion Coefficient in Rivers
Chapter 20
Malcolm J. Beynon, Kirsty Park
This chapter employs the fuzzy decision tree classification technique in a series of biological based application problems. With its employment in a... Sample PDF
The Exposition of Fuzzy Decision Trees and Their Application in Biology
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