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In the paper we address traffic engineering problems related to optimization of routing in IP networks applying destination-based shortest path routing (SPR) of the OSPF type. An SPR routing pattern is determined by a system of (administrative) weights defined over the set of IP links: the routes for IP forwarding are determined as the shortest paths computed locally at the nodes using the current link weights. When the shortest path from a certain node (node v, say) to a particular destination (destination t, say) is not unique, the traffic routed from node v to destination t is split equally among all links outgoing from v that belong to the shortest paths to destination t, i.e., according to the Equal Cost Multiple-Paths (ECMP) rule. The basic problem considered in this paper consists in finding a resilient link weight system generating a routing scheme that satisfies given traffic demands and does not lead to link overloads both in the normal network state of operation and in all considered failure states when certain IP links are failed. We assume that if a failure occurs then the weight system is modified by assigning infinite weights to the failed links, and not altering the weights of the remaining, operating links. We consider the traffic engineering goal related to minimization, over all failure states, of the maximal link overload. We formulate the considered problem as a mixed integer programme (MIP) and propose a heuristic algorithm based on the tabu search metaheuristic. The efficiency of the proposed weight optimization method is illustrated by means of a numerical study.