A Bicriterion Optimization Problem on Logistic Networks

Abstract

So many algorithms of the shortest path problem with one objective have been proposed in the field of network theory. For decision making in some complicated systems such as transportation problems and large scale industrial systems, the shortest path for one objective is seldom optimal as a solution. In other words some problems are often with two objective functions or more. This idea is justified by the following example. Let's suppose the shortest path problem in a road network where both toll ways and conventional ways are available. The travel is very rapid but expensive when taking some toll ways while it is slow but inexpensive when not taking them. This problem has two different objectives, i. e., cost and time. Due to such complex systems theories and studies the multiobjective optimization are extensively tackled these days. In our study first the constrained k shortest paths problem is investigated that efficiently finds all feasible paths with their total lengths not violating a given length allowance. Next we propose an extended version of this class of problem, i. e., the constrained k shortest paths problem with two objectives. Two different types of algorithm are developed for each problem. Furthermore the bicriterion shortest path problem, that yields the pareto set of the shortest paths, is studied by using the algorithms for the constrained k shortest paths problem with two objectives. Finally some numerical results for these problems are provided by the algorithms implemented with FORTRAN77.