1. Introduction

Bio-inspired optimization algorithms are based on precise observation of natural systems [1–3]. A relevant characteristic of these algorithms is that the biological process had been tested, validated and proven by means of evolution. The mechanisms of self-adaption, self-organizing and self-learning in natural inspired optimization approaches provide means to address challenging problems that cannot be solved by traditional methods [4].

Thus, bio-inspired algorithms become particularly important to tackle complex optimization problems [6–10]. The outstanding performance of bio-inspired optimization algorithms is attributed

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and eproduction in any medium, provided the original work is properly cited.

to their structures which are closely related to one or other features observed in nature [10]. Accuracy and repeatability are the prime objectives of every optimization algorithm. Therefore, modeling biological mechanisms may impact the outcome of the observed system, designing more accurate and efficient heuristic algorithms [13, 16].

family of computer vision algorithms whose paradigm is based on extracting structures when movement is detected or extracting movement when structures are detected in 2D images. Therefore, in this work, BAM-PSO is tested with several popular and well-established benchmark functions and its performance is compared to well-known evolutionary algorithms in

Particle Swarm Optimization Algorithm with a Bio-Inspired Aging Model

http://dx.doi.org/10.5772/intechopen.71791

11

Aging is the process of becoming older, which consists on the accumulation of changes over time. This process affects all living systems: humans, cells, unicellular organisms, fruit flies and mammals like rodents [12, 32, 42]. Since the particles of the PSO optimizer algorithm can be treated as a living system, aging could represent a relevant mechanism to alleviate the premature convergence problem in heuristic algorithms. Nowadays, we have better understanding of the lifespan of human cells, which is determined by homoeostatic properties of the immune system. Homeostasis refers to the regulation of the lymphocytes pool in an organism. It is assumed that the number of cells is determined by the capacity of the peripheral immune

In the immune system, it is observed that cell death rate accelerates if the immune cells exceed the allocated free space [33]. For instance, in the course of a viral infection, immune system cells can undergo approximately 15–20 divisions. Total proliferative capacity of human T lymphocyte is about 40–45 divisions and depends on the telomere length [41]. Telomeres are the end parts of the chromosomes, which become shorter in every cell division; this can be appreciated in Figure 1. The cell can reach its unresponsiveness state when the telomere length

Telomere dynamics can be interpreted in a mathematical model based on experimental observations. In this work, we consider the mathematical model proposed by [33] to represent the

where T represents the remaining telomere divisions per cell. α defines the telomere consumption rate per iteration. p<sup>∗</sup> represents the length of telomere repeats in naive cells produced at

Eq. (1) is a differential non-ascending equation that defines the derivative in telomere division per cell depending on the consumption rate of the cell α, telomere capacity of the cell (p<sup>∗</sup>) and number of cells (N). Eq. (1) describes the dynamic of average telomere length T in the pool of naive cells. The rate of this process depends on <sup>p</sup>ð Þ <sup>∗</sup> � <sup>T</sup> , where <sup>p</sup><sup>∗</sup> is the telomere length in the cells and p<sup>0</sup> defines the telomere at initial age. This dynamic describes the self-sustaining process of regulation of total concentration of the T cells and how the telomere is affected by

dt <sup>¼</sup> <sup>α</sup> <sup>p</sup><sup>∗</sup> ð Þ � <sup>T</sup> <sup>N</sup> (1)

) and N is the number of cells as defined in [33].

2. Aging mechanisms to alleviate the premature convergence

both low and high dimensional scenarios.

completes about one half of its initial value.

the age <sup>t</sup> (with initial length <sup>p</sup>0= 8:<sup>3</sup> � 103

T cells concentration and iterations [33].

telomere dynamics. This model considers the following equation:

dT

system.

Problem-solving algorithms inspired by one or more biological features have been developed after observing the behavior in humans, animals, and cells [10–13]. For instance, Genetic Algorithms (GA) [4] defined the basis for evolutionary computing using the early works of Darwin [14] and Mendel [15]; or the Ant Colony System (ACS) [6, 7] which considers the traveling behavior model of self-organized argentine ants published by Goss [5], solving in a fashion way travel salesman-type problems; or the Particle Swarm Optimization (PSO) [8] inspired on feeding behavior of bird flocks becoming a very popular optimizer nowadays [17].

Particle-based optimizers, like those described in [8]; or those presented in [18–22, 28] are very popular because instead of working with one candidate solution, they offer a subset of individual candidate solutions (particles), which are explored, exploited and improved. A relevant mechanism related to evolution that could play a central role in optimization algorithms is aging [23, 25]. Aging is a natural characteristic whose inclusion in a particle-based optimizer could give a mean of individual control over the particle without highly increasing the complexity of algorithms [26].

To the authors' best knowledge, previous PSO algorithms did not have a measurement to control individual particle existence within the swarm by evaluating each particle performance. In PSO, because of the very nature of the algorithm, an effect called premature convergence appears when most (or all) of the particles within a swarm compromises their ability to explore and stay close to a local solution. The Particle Swarm Optimization with an Aging Leader and Challengers (ALC-PSO) [24] was the first approach to include aging processes to alleviate this unwanted effect. However, this was only leadership-oriented and not swarm-related; even more important: the aging dynamics were linear and bounded to static predefined values. In [29], it is used to design a high speed symmetric switching CMOS inverter.

Our PSO variant proposal, the Particle Swarm Optimization with Bio-inspired Aging Model (BAM-PSO) is based on a mathematical model that describes the telomeres shortening observed in the immune system cells, this model includes a form of aging effect over all the particles of the swarm; this mechanism provides a mean to control the existence of each particle within the swarm avoiding the premature convergence effect. Therefore, the PSO variant with aging model possesses the potential to outperform current optimization algorithms and have further implications in computational intelligence. Finally, optimization under uncertainty and complex functions is an area of special scientific interest, and many real problems and applications include some form of uncertainty; it is also known that collectiveintelligence algorithms perform excellent in this type of scenarios [11]; BAMPSO has been successfully implemented in several optimization applications: in time-series forecasting [30] it was implemented as a training algorithm for an artificial neural network and in [31] it was used over a Geometric Algebra (GA) framework in order to compute the rigid movement on images to improve the accuracy of Structure from Motion (SfM) algorithms, which comprises a family of computer vision algorithms whose paradigm is based on extracting structures when movement is detected or extracting movement when structures are detected in 2D images. Therefore, in this work, BAM-PSO is tested with several popular and well-established benchmark functions and its performance is compared to well-known evolutionary algorithms in both low and high dimensional scenarios.
