## 5 Conclusions  
The proposed CGO used in this study begins with the application of a local optimization algorithm that requires the use of appropriate regularization parameters incorporated into the DCR and SR objective functions, and it is optimized (using the LOM) to obtain the best model, which will be used as an input model for the combined local-global optimization CGO method. This study applied this concept to obtain the best model parameters for both an individual and joint inversion of the DCR and SR geophysical methods. The CGO algorithm used to overcome the challenges associated with the separate application of LOM and GOM involved the application of the final output (optimum model parameter) of the LOM as the input for the CGO techniques. The global optimization part of the single objective CGO applied the GA to optimize the DCR and SR misfit functions (Equations (13) and (14), respectively) while the NSGA II was used to optimize the resultant misfit from the DCR and SR in the multi-objective optimization algorithm. Apart from the CGO method, which improved the computation run time, we made a part (the misfit function) of the CGO algorithm run on parallel computing. This approach not only contributed to the optimization of the CGO algorithm run time but also provided an opportunity to test the convectional GOM using a computer with 12 logical processor units (six cores). The CGO algorithm was tested with both resistivity and velocity models that had a dyke, two blocks (positive), and two blocks (positive and negative) anomalies. Generally, the CGO algorithm showed an improvement when compared with the local optimization output (Tables 2-4). However, the conventional GOM results showed instability in the delineation of the anomalies in all the tested SR and DCR models, and the model instability was probably due to the use of an unconstraint objective function. However, the CGO method overcame the challenge of model instability since it was linearly constrained by using the LOM's output to define the search space's lower and upper bounds. Additionally, the conventional GOM application remained computationally expensive (especially for the SR method) relative to the CGO techniques. Therefore, this study recommends applying a combined approach (local and global optimization algorithm) when characterizing the subsurface when both DCR and SR data are acquired.  
Figure 17: Effect of population size on DC-resistivity inversion using the genetic algorithm; (**a**) test of optimum population size that produces the most significant misfit and (**b**) test of optimum run time with respect to population size.  
**Author Contributions:** Conceptualization, P.S.; methodology, I.D., I.A., H.A.H., P.S., and E.C.; software, P.E., I.D., I.A., and H.A.H.; validation, I.D., I.A., and H.A.H.; formal analysis, P.E., I.D., I.A., H.A.H., P.S., and E.C.; resources, P.S.; data curation, P.E., I.D., I.A., H.A.H., P.K., and P.S.; writing--original draft preparation, P.E., I.D., I.A., H.A.H., P.K., and P.S.; writing--review and editing, P.E., I.D., I.A., H.A.H., P.K., P.S., E.C., S.H., and A.A.-S.; visualization, P.E., P.K., and P.S.; supervision, P.S.; project administration, P.S.; funding acquisition, A.A.-S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the start-up grant SF18060 from the College of Petroleum Engineering and Geosciences (CPG) at King Fahd University of Petroleum and Minerals (KFUPM).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.