Speaker

Kaarthik Sundar, Scientist, Los Alamos National Laboratory

Abstract

The Multiple Traveling Salesman Problem (MTSP) with a single depot is a generalization of the well-known Traveling Salesman Problem (TSP) that involves an additional parameter, namely, the number of salesmen. In the MTSP, several salesmen at the depot need to visit a set of interconnected targets, such that each target is visited precisely once by at most one salesman while minimizing the total length of their tours. An equally important variant of the MTSP, the min-max MTSP, aims to distribute the workload (length of the individual tours) among salesmen by requiring the longest tour of all the salesmen to be as short as possible, i.e., minimizing the maximum tour length among all salesmen. The min-max MTSP appears in real-life applications to ensure a good balance of workloads for the salesmen. It is known in the literature that the min-max MTSP is notoriously difficult to solve to optimality due to the poor lower bounds its linear relaxations provide. In this talk, we shall formulate two novel parametric variants of the MTSP called the "fair-MTSP". One variant is formulated as a Mixed-Integer Second Order Cone Program (MISOCP), and the other as a Mixed Integer Linear Program (MILP). Both focus on enforcing the workloads for the salesmen to be equitable, i.e., the distribution of tour lengths for the salesmen to be fair while minimizing the total cost of their tours. We present algorithms to solve the two variants of the fair-MTSP to global optimality and computational results on benchmark and real-world test instances that make a case for fair-MTSP as a viable alternative to the min-max MTSP.

Bio

Kaarthik received a Ph.D. and M.S. in Mechanical and Electrical Engineering, from Texas A&M University, College Station, TX, USA, in 2016 and 2012, respectively. He is a Scientist in the Information Systems and Modeling Group at Los Alamos National Laboratory, Los Alamos, NM, USA. His research interests include problems pertaining to vehicle routing, path planning, and control for unmanned/autonomous systems; non-linear optimal control, estimation, and large-scale optimization problems in power and gas networks, combinatorial optimization, and global optimization for mixed-integer non-linear programs.