alberto godio

francesca pace

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

11 February 2024POLITECNICO DI TORINORepository ISTITUZIONALEThe role of three different metaheuristic methods in geophysical data optimization / Pace, Francesca; Godio, Alberto. -ELETTRONICO. - (2023). (Intervento presentato al  convegno The 41st National Conference of the GNGTS tenutosi aBologna nel 7-9 Febbraio 2023) [10.13120/2tf2-1j75].OriginalThe role of three different metaheuristic methods in geophysical data optimization.Publisher:PublishedDOI:10.13120/2tf2-1j75Terms of use:Publisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2979384 since: 2023-06-15T08:43:57ZGNGTSGruppo Nazionale di Geofisica della Terra SolidaBOOK OF ABSTRACTS  41st NATIONAL CONFERENCE7-9 FEBRUARY 2023BOLOGNA22° CONVEGNO NAZIONAL ESession 3.3 ______ ___ GNGTS 2023The role of three different metaheuristicmethods in geophysical data optimizationF. Pace1, A. Godio11 Department of Environment, Land and Infrastructure Engineering (DIATI), Politecnico di Torino,Torino, ItalyIntroductionThere has been an increasing interest in global search methods for solving the geophysical inverseproblem during the last decades (Sen and Stoffa, 2013). Several metaheuristic methods have beenadopted in the geophysical literature, and ever novel methods are being proposed fromnon-geophysical studies. These methods are the so-called nature-inspired algorithms based onbiological systems and social dynamics of groups of entities such as birds, fish, bats, ants, wolvesand so on (Engelbrecht, 2007). These algorithms are original, sophisticated, and efficient in theoptimization of geophysical data. The most popular metaheuristics are the genetic algorithm (GA)and particle swarm optimization (PSO), which have been largely adopted (Sen and Stoffa, 2013;Pace et al., 2021). An example of an emerging and promising population-based algorithm is thegrey wolf optimizer (GWO) (Mirjalili et al., 2014). Then, the scientific question that arises is if allthese algorithms are efficient and useful.We focused on a comparative analysis among the performances of three metaheuristic methods,that is, GA, PSO and GWO, for the optimization of time-domain electromagnetic (TDEM) data (Paceet al., 2022). The aim of the work is to highlight their advantages and weaknesses because it seemsthat they have been indistinctly applied to geophysical data so far. Moreover, it is rare the threealgorithms are contextually compared.The three metaheuristic algorithms: GA, PSO, GWOThe GA is an Evolutionary Computation paradigm and mimics the inheritance rules in nature,where the individuals with the best chromosomes survive (and the weakest individuals must die)(Sen and Stoffa, 2013). The PSO algorithm is based on the social behavior of agents sharingknowledge to achieve the best objective of the group, such as escaping from a predator orsearching for food (Pace et al., 2019, 2021). The GWO algorithm is based on the social dynamicsadopted by a group of wolves attacking a prey while searching for food (Mirjalili et al., 2014).The comparison among the three methods was performed by setting some common features. Thesame settings of the algorithms were the objective function, the forward modeling code, thenumber of candidate solutions sampled, the stopping criterion, the random initialization, theSession 3.3 ______ ___ GNGTS 2023boundary conditions, and the computational resources. The other settings were specific for eachalgorithm and were chosen following the most recent findings for GA (Pace et al. 2022), PSO (Paceet al. 2019) and GWO (Mirjalili et al., 2014) applied to geophysical data.A field case studyThe methods were first validated on a synthetic example of noise-corrupted data and then appliedto two field surveys located in Italy. One field case study is a TDEM sounding located in Stupinigi(Torino district area) acquired for groundwater prospection over a known stratigraphy (comingfrom a close borehole). The TDEM acquisition was a coincident loop of 50 m length for the loopsize. The time range of acquisition was 10-5 –10-3 s. The 1D model was discretized into 19 layers,whose thickness logarithmically increased with depth. The number of iterations was 500 for PSOand GWO, and 800 for GA since we observed insufficient convergence and minimization. Thenumber of individuals (GA), particles (PSO) and wolves (GWO) were 170, for a proper solutionexploration. The boundary conditions of the search space were 1 and 500 Ωm. Each algorithm wasindependently run 10 times or trials to inspect the variability of the equivalent final solutions andthen highlight the solution with the minimum nRMSE. The outcomes of GA, PSO and GWO areshown in in Figs. 1b, 2b and 3b, respectively. The final data misfit (nRMSE) was 0.0764 for GA,0.0618 for PSO, and 0.0619 for GWO. The lowest runtime and nRMSE were achieved by PSO, whileGA had the worst performance. The data fitting is satisfactory for the three methods. There issimilarity among the solutions of the PSO and GWO trials, while they significantly differ for GA.Figure 3c plots the minimization of the objective function along the iterations for GA (black dots),PSO (blue dots) and GWO (pink dots). The trend of the PSO curve is gradual from the highest to thelowest value, meaning good balance between exploration and exploitation of the search space. GAand GWO show a stepped trend that decreases rapidly and becomes flat earlier than PSO, meaninga possible premature exploitation phase.ConclusionsThe performance of three different and widely adopted metaheuristic algorithms were analyzedfor the optimization of TDEM data. The comparative analysis reveals that PSO and GWO performbetter than GA. GA yields the highest data misfit and an ineffective minimization of the objectivefunction. PSO and GWO provide similar outcomes in terms of both resistivity distribution and datamisfits, possibly because they are based on the same computational principle known as SwarmIntelligence. The results prove compelling evidence that both the emerging GWO and theestablished PSO are highly valid tools for stochastic inverse modeling in geophysics, while GAappears to be less competitive than them.Session 3.3 ______ ___ GNGTS 2023Fig. 1 – The result of GA: a) TDEM observed signal (the red dots with error bars) and GA predicted response (blue line);b) the final resistivity models after 10 trials (the green lines) and the best GA solution highlighted in blueFig. 2 – The result of PSO: a) TDEM observed signal (the red dots with error bars) and PSO predicted response (blueline); b) the final resistivity models after 10 trials (the green lines) and the best PSO solution highlighted in blueSession 3.3 ______ ___ GNGTS 2023Fig. 3 – The result of GWO: a) TDEM observed signal (the red dots with error bars) and GWO predicted response (blueline); b) the final resistivity models after 10 trials (the green lines) and the best GWO solution highlighted in blue; c)The curves of the objective function minimization for the GWO (pink), PSO (blue) and GA (black) algorithms.AcknowledgementsComputational resources were provided by hpc@polito (http://hpc.polito.it).Session 3.3 ______ ___ GNGTS 2023ReferencesEngelbrecht A. P.; 2007: Computational Intelligence: An Introduction. John Wiley and Sons Ltd.Mirjalili S., Mirjalili S. M. and Lewis A.; 2014: Grey wolf optimizer. Advances in EngineeringSoftware, 69, 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007Pace F., Raftogianni A. and Godio A.; 2022: A Comparative Analysis of ThreeComputational-Intelligence Metaheuristic Methods for the Optimization of TDEM Data. Pure andApplied Geophysics, 179(10), 3727-3749.Pace F., Santilano A. and Godio A.; 2019: Particle swarm optimization of 2D magnetotelluric data.Geophysics, 84(3), E125–E141. https://doi.org/10.1190/geo2018-0166.1Pace F., Santilano A. and Godio A.; 2021: A review of geophysical modeling based on particle swarmoptimization. Surveys in Geophysics, 42(3), 505–549. https://doi.org/10.1007/s10712-021-09638-4Sen M. K. and Stoffa P. L.; 2013: Global Optimization Methods in Geophysical Inversion (2nd ed.).Cambridge University Press.Corresponding author: francesca.pace@polito.it

The role of three different metaheuristic methods in geophysical data optimization.

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The role of three different metaheuristic methods in geophysical data optimization.

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