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We propose an algorithmic framework that successfully addresses three vehicle routing problems: the multidepot VRP, the periodic VRP, and the multidepot periodic VRP with capacitated vehicles and constrained route duration. The metaheuristic combines the exploration breadth of population-based evolutionary search, the aggressive-improvement capabilities of neighborhood-based metaheuristics, and advanced population-diversity management schemes. Extensive computational experiments show that the method performs impressively in terms of computational efficiency and solution quality, identifying either the best known solutions, including the optimal ones, or new best solutions for all currently available benchmark instances for the three problem classes. The proposed method also proves extremely competitive for the capacitated VRP.