Dualities in population genetics: a fresh look with new dualities

We apply our general method of duality, introduced in [Giardina', Kurchan, Redig, J. Math. Phys. 48, 033301 (2007)], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman's type, as well as for models with finite population size. Next, using SU(1,1) raising and lowering operators, we find new dualities between the Wright-Fisher diffusion with $d$ types and the Moran model, both in presence and absence of mutations. These new dualities relates two forward evolutions. From our general scheme we also identify self-duality of the Moran model.Comment: 36 pages, to appear on Stochastic Processes and their Application

Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

DIFFERENTIAL EVOLUTION FOR OPTIMIZATION OF PID GAIN IN ELECTRICAL DISCHARGE MACHINING CONTROL SYSTEM

ABSTRACT PID controller of servo control system maintains the gap between Electrode and workpiece in Electrical Dis- charge Machining (EDM). Capability of the controller is significant since machining process is a stochastic phenomenon and physical behaviour of the discharge is unpredictable. Therefore, a Proportional Integral Derivative (PID) controller using Differential Evolution (DE) algorithm is designed and applied to an EDM servo actuator system in order to find suitable gain parameters. Simulation results verify the capabilities and effectiveness of the DE algorithm to search the best configuration of PID gain to maintain the electrode position. Keywords: servo control system; electrical discharge machining; proportional integral derivative; con- troller tuning; differential evolution

Paraiso : An Automated Tuning Framework for Explicit Solvers of Partial Differential Equations

We propose Paraiso, a domain specific language embedded in functional programming language Haskell, for automated tuning of explicit solvers of partial differential equations (PDEs) on GPUs as well as multicore CPUs. In Paraiso, one can describe PDE solving algorithms succinctly using tensor equations notation. Hydrodynamic properties, interpolation methods and other building blocks are described in abstract, modular, re-usable and combinable forms, which lets us generate versatile solvers from little set of Paraiso source codes. We demonstrate Paraiso by implementing a compressive hydrodynamics solver. A single source code less than 500 lines can be used to generate solvers of arbitrary dimensions, for both multicore CPUs and GPUs. We demonstrate both manual annotation based tuning and evolutionary computing based automated tuning of the program.Comment: 52 pages, 14 figures, accepted for publications in Computational Science and Discover

Application of differential evolution to power system stabilizer design

Includes synopsis.Includes bibliographical references.In recent years, many Evolutionary Algorithms (EAs) such as Genetic Algorithms (GAs) have been proposed to optimally tune the parameters of the PSS. GAs are population based search methods inspired by the mechanism of evolution and natural genetic. Despite the fact that GAs are robust and have given promising results in many applications, they still have some drawbacks. Some of these drawbacks are related to the problem of genetic drift in GA which restricts the diversity in the population. ... To cope with the above mentioned drawbacks, many variants of GAs have been proposed often tailored to a particular problem. Recently, several simpler and yet effective heuristic algorithms such as Population Based Incremental Learning (PBIL) and Differential Evolution (DE), etc., have received increasing attention

Comparison of Evolutionary Optimization Algorithms for FM-TV Broadcasting Antenna Array Null Filling

Broadcasting antenna array null filling is a very challenging problem for antenna design optimization. This paper compares five antenna design optimization algorithms (Differential Evolution, Particle Swarm, Taguchi, Invasive Weed, Adaptive Invasive Weed) as solutions to the antenna array null filling problem. The algorithms compared are evolutionary algorithms which use mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. The focus of the comparison is given to the algorithm with the best results, nevertheless, it becomes obvious that the algorithm which produces the best fitness (Invasive Weed Optimization) requires very substantial computational resources due to its random search nature

Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies

Differential evolution algorithm aided minimum symbol error rate multi-user detection for multi-user OFDM/SDMA systems

A Differential Evolution (DE) algorithm assisted Minimum Symbol Error Ratio (MSER) Multi-User Detection (MUD) scheme is proposed for multi-user Multiple-Input Multiple-Output (MIMO) aided Orthogonal Frequency-Division Multiplexing / Space Division Multiple Access (OFDM/SDMA) systems. Quadrature Amplitude Modulation (QAM) is employed in most wireless standards by virtue of providing a high throughput. The MSER Cost Function (CF) may be deemed to be the most relevant one for QAM, but finding its minimum is challenging. Hence we propose a sophisticated DE assisted MSER-MUD scheme, which directly minimizes the SER CF of multi-user OFDM/SDMA systems employing QAM. Furthermore, the effects of the DE assisted MSER-MUD’s algorithmic parameters, namely those of the population size Ps, of the scaling factor ? and of the crossover probability Cr on the number of DE generations required for attaining convergence were investigated in our simulations. This allowed us to directly quantify their complexity. The simulation results also demonstrate that the proposed DE assisted MSER-MUD scheme significantly outperforms the conventional MMSE-MUD in term of the system’s overall BER and it is capable of narrowing its BER performance discrepancy with respect to the optimal Maximum Likelihood (ML) MUD to about 4dB, while requiring about 200 times less CF evaluations compared to the optimal ML-MUD scheme