A branch-and-bound algorithm for the solution of sequence dependent routing problems
Michael Joseph DeHaemer · Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School) · 1970
A branch-and-bound algorithm, which finds the optimal route through n nodes when a different cost matrix occurs after each arc in the sequence is traversed, is presented. The route may begin at any node and must pass through each of the n nodes exactly once. The objective is to minimize total cost in traversing (n-1) arcs of the route. The cost of traversing each arc is r k/ij which is a function of the distance between nodes i and j and a function of the kth position in the sequence of arcs forming the route. The algorithm is presented in step-by-step detail and illustrated by flow chart and examples. A modification for symmetric (r k/ij) improves the efficiency of the algorithm. A trade-off between computation time and storage requirements may be accomplished by alternate branching policies. Suboptimal solutions may be obtained with reduced computation.