Study of the Brand and Bound Algorithm Performance on Traveling Salesman Problem Variants

Abstract

Traveling salesman problem (TSP) can be applied to distribution problems, namely determining the minimum route from the depot to all customers exactly once and back to the depot. Some constraints can be added to the problem such as time constraints, additional salesmen on the route that is passed, the need for an order of delivery, and passing one-way road. This article will discuss TSP variants developed from basic TSP, namely TSPTW, MTSP, TSPPC, and ATSPTW. The differences in formulations of these variants are described and the branch and bound algorithm is used to solve them. There are three main steps to the branch and bound algorithm namely the initialization stage to obtain the initial solution, the process stage and solution improvement, and the determination of the optimum solution. Identification of the similarities and differences in the application of the branch and bound algorithm steps on these variants are discussed in this article. An example is given of the application of the branch and bound algorithm to the four variants of 8 customers and one depot. The results of the application examples are depicted on a graph in order of the minimum total distance, namely ATSPTW, TSPTW, TSPPC, and MTSP.

Design and Implementation of the Shortest Path Navigation in Samosir District using Branch and Bound Algorithm

“…Each subset in the partition is represented by a child of the node. Branch-and bound algorithm procedure repeatedly forms a search tree and a bonding process by determining the upper and lower bound in finding the optimal solution [25]. Comparing exact and approximate methods the conclusion is the exact method performs and has poor worst-case behavior [26].…”