Constrained Shortest Path by Parameter Searching

Given an undirected graph, one start point and one end point belong to this graph, and nonnegative groups of weights for each edge, we consider the problem of finding a path that has lowest total cost with respect to cost weight and has constrained budget with respect to constrains weight [9]. Different from the traditional Lagrangean relaxation method, we proposed a new parameter space searching method for solving the multi-constrained shortest path problem (MCSP) in this paper. For this newly proposed method all the solutions found are in the original problem's feasible region, there is no need to do the hard work to close the gap between the original problem and its Lagrangean relaxation. The proposed algorithm is very easy to parallelize, and can take full advantage of multi-core multi-thread processors to improve problem solving efficiency. For most optimization algorithms, properly selecting the super parameters is not an easy work. Through multi-rounds computer numerical simulation with different super parameters, we can see that our algorithm is robust to super parameters.