Graph representation of the fixed route dial-a-ride problem

The fixed route dial-a-ride problem (FRDARP) is a variant of the famous dial-a-ride problem, in which all the requests are chosen between terminals that are located along a fixed route. A reduction to the shortest path problem enables finding an optimal solution for FRDARP in polynomial time. However, the basic graph construction ends up with a huge graph, which makes the reduction impractical due to its memory consumption. To this end, we propose several pruning heuristics that enable us to considerably reduce the size of the graph through its dynamic construction. Additionally, we utilize the special features of the problem to apply parallelization to the graph traversal process. Our experiments show that each of the proposed heuristics on its own improves the practical solvability of FRDARP. Moreover, using them together is considerably more efficient than any single heuristic. Finally, the experiments confirm the efficiency of our suggested parallelization policy.