The quasispecies regime for the simple genetic algorithm with ranking selection

Cerf, Raphaël

doi:10.1090/tran/7170

Cited by 5 publications

(5 citation statements)

References 52 publications

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“…Our results have their roots in the quasispecies theory developed by Eigen, McCaskill and Schuster [7]. We refer the reader to the introduction of [3] for a quick summary of the development of these ideas, as well as for pointers to the numerous relevant references in the genetic algorithm literature.…”

Section: Introductionmentioning

confidence: 77%

“…The proof is elementary, in the sense that it relies essentially on two classical exponential inequalities (which are recalled in the appendix). This proof is an adaptation of the proof of proposition 6.7 in [3]. In proposition 5.4, we shall then bound from below the probability of hitting a value larger than m/ √ π before time κ ln m and this will conclude the proof of theorem 3.2.…”

Section: The Quasispecies Regimementioning

confidence: 86%

“…More precisely, we will consider here the case of large populations. This kind of analysis has been previ-ously conducted for the simple genetic algorithm with ranking selection [3]. We try here to extend this analysis to the simple genetic algorithm with roulette-wheel selection.…”

Section: Introductionmentioning

confidence: 99%

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The quasispecies regime for the simple genetic algorithm with roulette wheel selection

Cerf

2017

Adv. Appl. Probab.

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We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best fit chromosomes from one generation to the next. We believe that the genetic algorithm operates best when this parameter is slightly larger than 1 and we prove two results supporting this belief. We consider the case of the simple genetic algorithm with the roulette-wheel selection mechanism. We denote by ℓ the length of the chromosomes, by m the population size, by pC the crossover probability and by pM the mutation probability. We start the genetic algorithm with an initial population whose maximal fitness is equal to f * 0 and whose mean fitness is equal to f0. We show that, in the limit of large populations, the dynamics of the genetic algorithm depends in a critical way on the parameter π = f * 0 /f0 (1 − pC)(1 − pM ) ℓ . If π < 1, then the genetic algorithm might operate in a disordered regime: there exist positive constants β and κ which do not depend on m such that, for some fitness landscapes and some initial populations, with probability larger than 1 − 1/m β , before generation κ ln m, the best fit chromosome will disappear, and until generation κ ln m, the mean fitness will stagnate. If π > 1, then the genetic algorithm operates in a quasispecies regime: there exist positive constants κ, p * which do not depend on m such that, for any fitness landscape and any initial population, with probability larger than p * , until generation κ ln m, the maximal fitness will not decrease and before generation κ ln m, the mean fitness will increase by a factor √ π. These results suggest that the mutation and crossover probabilities should be tuned so that, at each generation, maximal fitness × (1 − pC)(1 − pM ) ℓ > mean fitness.

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Section: Introductionmentioning

confidence: 77%

Section: The Quasispecies Regimementioning

confidence: 86%

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The quasispecies regime for the simple genetic algorithm with roulette wheel selection

Cerf

2017

Adv. Appl. Probab.

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“…In the present work, PSOvm, CCPSO [32], DE (based on DE/rand/1/bin strategy) [37], [38], IWO [39]- [41], and a simple genetic algorithm (GA) [42] are comparatively applied to design LPDAs that concurrently satisfy requirements for low standing wave ratio (SWR), high FG and low GF over the DVB-T band as well as an additional requirement for low FG above 800 MHz to ensure rejection of LTE800 signals and thus improve the quality of signal reception in the DVB-T band. To have precise calculations of the antenna radiation characteristics, each one of the above five methods is combined with a full wave analysis software.…”

Section: Max Minmentioning

confidence: 99%

Optimal LTE-Protected LPDA Design for DVB-T Reception Using Particle Swarm Optimization With Velocity Mutation

Zaharis

Gravas

Lazaridis

et al. 2018

IEEE Trans. Antennas Propagat.

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A near-optimal design of a log-periodic dipole array (LPDA), suitable for DVB-T reception (470-790 MHz), is presented. The LPDA is required to provide low standing wave ratio as well as high-gain radiation pattern with sufficient gain flatness over the entire passband, and concurrently achieve low gain for frequencies above 800 MHz to reject LTE800 signals and thus improve the reception quality in the DVB-T band. All the above requirements are better satisfied by applying a novel particle swarm optimization (PSO) variant, called PSO with velocity mutation (PSOvm). PSOvm induces mutation on the velocities of those particles, which are unable to improve their fitness. As shown in this paper, PSOvm comes closer to the above requirements compared to four well-known optimization methods and outperforms the traditional LPDA design method proposed by Carrel. The LPDA geometry chosen for optimization is not the conventional one and therefore the dipoles are not considered to be included inside a specified angle as proposed by Carrel. Thus, the dipole lengths and distances as well as the boom dimensions are independently optimized. The PSOvm-based LPDA sufficiently meets all the above requirements and thus is suitable for DVB-T reception without the use of an external LTE-band rejection filter.

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“…The use of ordinary differential equations (ODEs) has, to date, been one of the most appropriate techniques for understanding the mechanisms that govern host-guest kinetics [15], assuming, like in this paper, a pathogen guest. In the realm of quasi-species theory [16] (i.e., a theory about Darwinian evolution in self-replicating organisms), ODEs have also been successfully applied, e.g., in the study of HIV (Human Immunodeficiency Virus) virus evolution [17]. Nevertheless, the WHD term generally refers to a host-guest coexistence model in which guest evolution is not included.…”

Section: Introductionmentioning

confidence: 99%

An Evolutionary Computing Model for the Study of Within-Host Evolution

Gómez-Mompeán

Lahoz-Beltrá

2020

Computation

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Evolution of an individual within another individual is known as within-host dynamics (WHD). The most common modeling technique to study WHD involves ordinary differential equations (ODEs). In the field of biology, models of this kind assume, for example, that both the number of viruses and the number of mouse cells susceptible to being infected change according to their interaction as stated in the ODE model. However, viruses can undergo mutations and, consequently, evolve inside the mouse, whereas the mouse, in turn, displays evolutionary mechanisms through its immune system (e.g., clonal selection), defending against the invading virus. In this work, as the main novelty, we propose an evolutionary WHD model simulating the coexistence of an evolving invader within a host. In addition, instead of using ODEs we developed an alternative methodology consisting of the hybridization of a genetic algorithm with an artificial immune system. Aside from the model, interest in biology, and its potential clinical use, the proposed WHD model may be useful in those cases where the invader exhibits evolutionary changes, for instance, in the design of anti-virus software, intrusion detection algorithms in a corporation’s computer systems, etc. The model successfully simulates two intruder detection paradigms (i.e., humoral detection, danger detection) in which the intruder represents an evolving invader or guest (e.g., virus, computer program,) that infects a host (e.g., mouse, computer memory). The obtained results open up the possibility of simulating environments in which two entities (guest versus host) compete evolutionarily with each other when occupying the same space (e.g., organ cells, computer memory, network).

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The quasispecies regime for the simple genetic algorithm with ranking selection

Cited by 5 publications

References 52 publications

The quasispecies regime for the simple genetic algorithm with roulette wheel selection

The quasispecies regime for the simple genetic algorithm with roulette wheel selection

Optimal LTE-Protected LPDA Design for DVB-T Reception Using Particle Swarm Optimization With Velocity Mutation

An Evolutionary Computing Model for the Study of Within-Host Evolution

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