In vehicle routing problems with time windows (VRPTW), a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for servicing. The objective is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. As finding a feasible solution to the problem is NP-complete, search methods based upon heuristics are most promising for problems of practical size. In this chapter we describe GIDEON, a Genetic Algorithm for heuristically solving the VRPTW. GIDEON has a global customer clustering method and a local post-optimization method. The global customer clustering method uses an adaptive search strategy based upon population genetics, to assign vehicles to customers. The best solution, obtained from the clustering method is improved by a local post-optimization method. The synergy between a global adaptive clustering method and a local route optimization method produce results superior to those obtained by competing heuristic search methods. The results obtained by GIDEON on a standard set of 56 VRPTW problems obtained from the literature were as good as or better than solutions from known competing heuristics.