# Particle Swarm Optimization and gravitational wave data analysis: Performance on a binary inspiral testbed 

Department of Astronomy, Nanjing University, Nanjing, 210093, China ∗ 

Yan Wang 

Soumya D. Mohanty 

Center for Gravitational Wave Astronomy, Dept. of Physics and Astronomy, The University of Texas at Brownsville, 80 Fort Brown, Brownsville, TX 78520, U.S.A. † 

The detection and estimation of gravitational wave (GW) signals belonging to a parameterized family of waveforms requires, in general, the numerical maximization of a data-dependent func- tion of the signal parameters. Due to noise in the data, the function to be maximized is often highly multi-modal with numerous local maxima. Searching for the global maximum then becomes computationally expensive, which in turn can limit the scientific scope of the search. Stochastic op- timization is one possible approach to reducing computational costs in such applications. We report results from a first investigation of the Particle Swarm Optimization (PSO) method in this context. The method is applied to a testbed motivated by the problem of detection and estimation of a binary inspiral signal. Our results show that PSO works well in the presence of high multi-modality, making it a viable candidate method for further applications in GW data analysis. 

The detection and estimation of a gravitational wave (GW) signal belonging to a parameterized family of waveforms requires, in general, the numerical maximiza- tion of some data-dependent function over the space of the signal parameters. For example, in the matched fil- tering [1, 2] method, which is the focus of this paper, the function to be maximized is a suitably defined inner product between the data and parameterized signal wave- forms. The global maximum of this function serves as a detection statistic. A point estimate of the signal param- eters is furnished by the location of the global maximum in parameter space. 

The presence of noise in the output of GW detectors leads to a large number of local maxima in this func- tion that are distributed randomly in parameter space. The search for the global maximum in this forest of lo- cal maxima then becomes a computationally expensive task. This can affect the sensitivity of a search by limit- ing either the volume that is searched in parameter space or the integration length of data required for accumulat- ing sufficient signal-to-noise ratio (SNR), or both. The computational efficiency of the search for the global max- imum is, thus, an important issue in GW data analysis. The various search strategies proposed in the GW liter- ature so far can be broadly divided into those based on sampling the function on predetermined grids of points in parameter space [3–5], and those that use stochastic optimization methods (e.g., [8–10]). 

PACS numbers: 95.85.Sz,04.80.Nn, 07.05.Kf, 02.50.Tt, 02.60.Pn 

## I. INTRODUCTION 

In the class of grid-based methods, significant savings in computational costs have been demonstrated with a hierarchy of grids [4, 6, 7]. A nice feature of grid-based methods is that they are easy to characterize statistically and, hence, design variables of the algorithm, such as the spacing of points, can be fixed systematically. 

Stochastic methods do not use pre-determined grids but employ some form of random walk through the pa- rameter space. The probabilistic rules of the random walk are tuned to maximize the chances of its terminating close to the global maximum. There are many algorithms that fall under the class of stochastic methods, a hybrid of simulated annealing and Metropolis-Hastings Markov Chain Monte Carlo (MCMC) being the most widely ex- plored in GW data analysis [8–10]. 

Since the number of points in a grid grows exponen- tially with the dimensionality of the parameter space, stochastic methods tend to outperform grid-based ones with an increase in the number of signal parameters. It is worth noting here that stochastic methods in GW data analysis incur the additional computational cost of generating signal waveforms on the fly. In grid-based methods, on the other hand, waveforms can be computed and stored in advance of processing the data. Stochas- tic methods can, therefore, lose their advantage if the computational cost of generating waveforms becomes too high. 

The performance of a stochastic method may be sensi- tive to the values to which its design variables are tuned. Since the tuning is usually done on simulated data, it is not clear how robust current stochastic methods are against features of real data such as non-stationarity and non-Gaussianity. Additionally, the number of de- sign variables that require careful tuning is fairly large for some of the methods. In such cases, tuning becomes more of an art than a well defined procedure and this may 

