Efficient Approximations for Many-Visits Multiple Traveling Salesman Problems

Abstract

A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of m salesmen jointly visit all cities from a set of n cities. The mTSP models many important real-life applications, in particular for vehicle routing problems. An extensive survey by Bektas (Omega 34(3), 2006) lists a variety of heuristic and exact solution procedures for the mTSP, which quickly solve particular problem instances.In this work we consider a further generalization of mTSP, the many-visits mTSP, where each city v has a request r(v) of how many times it should be visited by the salesmen. This problem opens up new real-life applications such as aircraft sequencing, while at the same time it poses several computational challenges. We provide multiple efficient approximation algorithms for important variants of the many-visits mTSP, which are guaranteed to quickly compute high-quality solutions for all problem instances.

Optimal Scheduling of Rainwater Collection Vehicles: Mixed Integer Programming and Genetic Algorithms

“…In many cases, the sequencing problem can be modeled as a traveling salesman problem (TSP). Some studies investigated multiple TSP where some salesmen visit all the cities [15]. This can be helpful for real-life applications [16].…”

“…Constraint (14) is to guarantee that all the truckloads served by all the trucks are exactly as the truckload found in the street (d j ). Constraint (15) is to enforce the model to assign 1 for w mj whenever A mj is greater than zero. This model contains all types of variables: continuous, integer, and binary, as shown in the last four constraints.…”