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Volume 2017, Article ID 3813912, 12 pages
Research Article

The Multiagent Planning Problem

1Department of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Budapest, Hungary
2SPS Italiana Pack Systems, Novara, Italy

Correspondence should be addressed to Tamás Kalmár-Nagy; moc.yganramlak@ytixelpmoc

Received 31 July 2016; Revised 17 December 2016; Accepted 4 January 2017; Published 5 February 2017

Academic Editor: Roberto Natella

Copyright © 2017 Tamás Kalmár-Nagy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The classical Multiple Traveling Salesmen Problem is a well-studied optimization problem. Given a set of goals/targets and agents, the objective is to find round trips, such that each target is visited only once and by only one agent, and the total distance of these round trips is minimal. In this paper we describe the Multiagent Planning Problem, a variant of the classical Multiple Traveling Salesmen Problem: given a set of goals/targets and a team of agents, subtours (simple paths) are sought such that each target is visited only once and by only one agent. We optimize for minimum time rather than minimum total distance; therefore the objective is to find the Team Plan in which the longest subtour is as short as possible (a min–max problem). We propose an easy to implement Genetic Algorithm Inspired Descent (GAID) method which evolves a set of subtours using genetic operators. We benchmarked GAID against other evolutionary algorithms and heuristics. GAID outperformed the Ant Colony Optimization and the Modified Genetic Algorithm. Even though the heuristics specifically developed for Multiple Traveling Salesmen Problem (e.g., -split, bisection) outperformed GAID, these methods cannot solve the Multiagent Planning Problem. GAID proved to be much better than an open-source Matlab Multiple Traveling Salesmen Problem solver.