In this paper, we present an integer linear programming (ILP) approach, called CoRe-ILP, for finding an optimal time consistent cophylogenetic host-parasite reconciliation under the cophylogenetic event model with the events cospeciation, duplication, sorting, host switch, and failure to diverge. Instead of assuming event costs, a simplified model is used, maximizing primarily for cospeciations and secondarily minimizing host switching events. Duplications, sortings, and failure to diverge events are not explicitly scored. Different from existing event based reconciliation methods, CoRe-ILP can use (approximate) phylogenetic branch lengths for filtering possible ancestral host-parasite interactions. Experimentally, it is shown that CoRe-ILP can successfully use branch length information and performs well for biological and simulated data sets. The results of CoRe-ILP are compared with the results of the reconciliation tools Jane 4, Treemap 3b, NOTUNG 2.8 Beta, and Ranger-DTL. Algorithm CoRe-ILP is implemented using IBM ILOG CPLEX Optimizer 12.6 and is freely available from http://pacosy.informatik.uni-leipzig.de/core-ilp.