Optimized Fuzzy Market-Based Solution to the Multiple Traveling Salesmen Problem using Particle Swarm Optimization Elad H. Kivelevitch ∗ Kelly Cohen † Manish Kumar ‡ University of Cincinnati, Cincinnati, OH, 45221, USA The Multiple Traveling Salesmen Problem (MTSP) is a well-known com- binatorial optimization problem, in which a set of locations is to be visited exactly once by a collection of traveling agents. The goal is to either mini- mize the sum of all tour lengths or the longest tour. This problem has high sensitivity to the perfect knowledge of city locations; however, in many ap- plications, e.g. military or search missions, locations of the tasks is known only up to some level of accuracy. We solve the MTSP using a market-based solution (MBS) in which agents bid for tasks and trade them amongst them- selves based on the additional cost of traveling to an additional location. By using a fuzzy cost instead of an crisp cost, taking into account the level of uncertainty in the locations, the sensitivity of the problem to task locations can be reduced. Particle Swarm Optimization (PSO) is used for optimizing the membership functions of the fuzzy cost used in the MBS. We show that the results of the optimized fuzzy market are better than using a crisp cost. I. Introduction We consider the problem of allocating a group of mobile autonomous agents to perform a set of tasks defined by location, priority and time constraints. The problem of allocating resources to tasks is a fundamental problem in optimization of a variety of autonomous sys- tems. Some examples include allocating computer resources, 1–3 allocating network resources * Visiting Research Associate, School of Aerospace Systems, AIAA Member. † Associate Professor, School of Aerospace Systems, AIAA Associate Fellow. ‡ Assistant Professor, School of Dynamic Systems. 1 of 12 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 09 - 12 January 2012, Nashville, Tennessee AIAA 2012-0488 Copyright © 2012 by Elad Kivelevitch, Kelly Cohen and Manish Kumar. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Downloaded by UNIVERSITY OF CINCINNATI on December 4, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.2012-488