In this paper, we propose an extended local search framework to solve combinatorial optimization problems with data uncertainty. Our approach represents a major departure from scenario-based or stochastic programming approaches often used to tackle uncertainty. Given a value 0 < ε ≤ 1, we are interested to know what the robust objective value is, i.e. the optimal value if we allow an ε chance of not meeting it, assuming that certain data values are defined on bounded random variables. We show how a standard local search or meta-heuristic routine can be extended to efficiently construct a decision rule with such guarantee, albeit heuristically. We demonstrate its practical applicability on the Resource Constrained Project Scheduling Problem with minimal and maximal time lags (RCPSP/max) taking into consideration activity duration uncertainty. Experiments show that, partial order schedules can be constructed that are robust in our sense without the need for a large planned horizon (due date), which improves upon the work proposed by Policella et al. 2004.