This article introduces a new algorithm for finding feasible or makespan-optimal solutions of Traveling Salesman Problems with Time Windows (TSPTWs) and Time-Dependent TSPTWs (TDTSPTWs). The starts from sequence visits the customers involved in problem, uses destroy repair operations to iteratively improve this sequence, applies perturbations diversify search. For phase, are removed current as ...

The traveling salesman problem is a classical NP-hard problem, and also hard to approximate at all under the assumption P 6= NP. Definition 1. A vertex tour of a graph G is a path which visits all vertices and returns to its starting vertex. This is another name for a Hamiltonian cycle on G. Traveling salesman problems involve finding a tour of undirected graph G with edge weights d(·), which w...

different manufacturing enterprises use regularly scheduling algorithms in order to help meeting demands over time and reducing operational costs. nowadays, for a better useofresources and manufacturingin accordance withcustomer needs and given the level ofcompetitionbetweencompanies, employing asuitablescheduling programhasa double importance. conventional productionmethods are constantly subs...

Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...

In this paper we present a fast approach for solving large scale Traveling Salesman Problems (TSPs). The heuristic is based on Delaunay Triangulation and its runtime is therefore bounded by O(n log n). The algorithm starts by construction the convex hull and successively replaces one edge with two new edges of the triangulation, thus inserting a new city. The decision which edge to remove is ba...