12 The higher cost of PSO is not surprising since grid-based searches are usually more efficient than stochastic meth- ods in low-dimensional problems such as the one consid- ered here. The performance gain of stochastic methods appears due to the slower rise in their computational cost, with increase in dimensionality, compared to the expo- nential one of grid-based searches. Therefore, we expect PSO to be cheaper than grid-based searches in higher dimensional problems. However, a definitive answer re- quires an actual test on problems such as the inspiral of high mass spinning binary components or the LISA Galactic Binary resolution problem [21]. The demonstra- tion in this paper that PSO can handle the more serious challenge of high multi-modality is the first step towards such future investigations. The computational cost of PSO may be significantly reduced by taking into account the physical boundary in parameter space (see Fig. 5). The current implementa- tion of PSO requires the search to extend over a large unphysical region. In fact, as far as the binary inspiral problem goes, we find this to be the most outstanding is- sue. We have tried the invisible walls condition with the curved physical boundary but find that the performance of PSO is negatively affected. Specifically, termination takes a much longer time and the probability of cluster- ing is significantly reduced. This behavior is attributable to the curved shape of the boundary allowing a signif- icantly larger number of particles to escape the search domain. Once outside, particles contribute nothing to the search and keep moving until they are pulled back. To solve this problem, it appears inevitable that the dynamical equations of PSO must be modified. For sig- nals other than binary inspirals, such as Galactic Binaries in the case of LISA, the nature of the boundary problem would be different and it may not be an issue in some applications. Finally, a comment about the use of Gaussian, station- ary noise in the testbed. We emphasize here that PSO is a method for finding the global maximum of a fitness function irrespective of what produces that peak, a gen- uine GW signal or an instrumental transient. Since, the implementation of PSO in this paper uses no prior infor- mation about features of the fitness function, it should find the peak regardless of its source. Thus, there should be no significant difference in the performance of PSO and a grid-based method even for non-stationary, non- Gaussian noise. In future work, we will verify this ex- plicitly by using non-GW signals in our simulations. Acknowledgments This work was supported by Research Corporation award CC6584. YW was supported by NSFC grant 10773005 of China and NSF award HRD-0734800 to the Centre for Gravitational Wave Astronomy at the Univer- sity of Texas at Brownsville. 1. PSO is a viable method for signal detection and estimation in GW data analysis as it can success- fully handle the challenge of high multi-modality presented by such problems. 2. Good performance was achieved by tuning only two out of the nine design variables involved in the method. Thus, PSO is a stochastic method that offers the possibility of having a small number of design variables in practice. 3. The design variables were tuned using a systematic procedure that does not require any prior informa- tion about features of the fitness function. As such, the procedure should be widely applicable to other stochastic methods also. 4. PSO is about 7 times more expensive than a grid- based search in the number of fitness function eval- uations required. For ground-based detectors, the dominant computa- tional cost comes from the pure noise case. Although our tuning procedure produced N$_{p}$ = 81 and N$_{t}$ = 80 as the optimal combination, there is statistical uncertainty in this result due to the finite and somewhat small number of trials used. To make our estimate of the computational cost conservative, we use the combination N$_{p}$ = 121 and N$_{t}$ = 80 instead for which all the performance measures are significantly better. From Table I, the typical number of fitness evaluations required for the testbed considered here is ∼ 7 × 10 4 with a spread of about ± 2 × 10 $^{4}$. Of this, the termination criterion itself accounts for a fixed number, ( N$_{t}$ = 80) × ( N$_{p}$ = 121) = 9680, of evaluations. A grid-based search provides a convenient perspective for evaluating the computational cost of PSO. According to [5], for 2PN waveform and initial LIGO noise PSD, the number of fitness function evaluations required in a single grid with a minimal match of 0.97 ( ⇒ α = 0 . 03) is 1 . 1 × 10 4 if the minimum mass used for constructing the template waveforms is 1 M$_{⊙}$ . In the current testbed, the search region in the mass plane (c.f., Fig. 2) is not the simple one considered in [5] although the minimum masses are similar. Additionally, [5] uses an analytic fit for the noise PSD that differs from the one used here. Ignoring these differences we find that the current imple- mentation of PSO requires about 7 times as many eval- uations, on the average, as a grid-based method. VI. CONCLUSIONS We applied PSO to the binary inspiral testbed where the main challenge was to locate the global maximum of a highly multi-modal fitness function. Such functions, with an unpredictable number of extrema having random locations and sizes, are typical in GW data analysis. In response to the questions posed at the beginning, the results obtained from simulations show clearly that: