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We have proposed hybrid approaches to solve dynamic provisioning problems in fixed-grid and elastic optical networks (EON). The proposed approaches use the information from the optimization models, which normally are used to solve static problems, to guide the search for a good solution in dynamic networking. We have presented three models, i.e., Route-Model, RouteRes-Model, and RouteEON-Model. Route-Model computes routing information which is integrated with the first-fit algorithm. RouteRes-Model computes routes and a set of wavelengths for each end pair. Both models are utilized for dynamic provisioning of routing and wavelength assignment in fixed-grid networks. Similarly, RouteEON-Model considers the elastic characteristics of flexible networks and computes routing information. This is integrated with the first-fit algorithm for dynamic provisioning. The proposed solutions efficiently reduce the blocking probability (BP) in fixed-grid networks and the bandwidth BP in EON compared to the shortest path first (SPF) routing and alternate (<inline-formula><tex-math notation="LaTeX">$k=2$</tex-math></inline-formula>) routing. Similarly, RouteRes-Model achieved high wavelength utilization compared to other solutions. Finally, the proposed solutions utilized approximately equal number of paths compared to SPF routing. However, compared to SPF routing, Route-Model and RouteRes-Model supported approximately 43&#x0025; and 66&#x0025; more traffic respectively while alternate routing supported 36&#x0025; more traffic for the same values of BPs.