We propose a new metaheuristic framework embodied in two approaches, Relaxation Adaptive Memory Programming (RAMP) and its primal-dual extension (PD-RAMP). The RAMP method, at the first level, operates by combining fundamental principles of mathematical relaxation with those of adaptive memory programming, as expressed in tabu search. The extended PD-RAMP method, at the second level, integrates the RAMP approach with other more advanced strategies. We identify specific combinations of such

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... egies at both levels, based on Lagrangean and surrogate constraint relaxation on the dual side and on scatter search and path relinking on the primal side, in each instance joined with appropriate guidance from adaptive memory processes. The framework invites the use of alternative procedures for both its primal and dual components, including other forms of relaxations and evolutionary approaches such as genetic algorithms and other procedures based on metaphors of nature.