On improving a solution to the ATSP with fixed origin and precedence relationships

Given the directed graph G1 = (N, A1) with a node origin and a penalty matrix C, the ATSP with fixed origin and precedence relationships (hereafter, ASTP-PR) consists of finding the permutation of the nodes from the set N, such that it minimizes a matrix C based function and does not violate the precedence relationships given by the set A1. In this work we present an algorithm for improving a given feasible solution to the problem, by performing a local search that uses 3- and 4-change based procedures. Computational results on a broad set of cases is reported.