A distributed simplex algorithm for degenerate linear programs and multi-agent assignments

• Published in: Automatica (Oxford) Vol. 48; no. 9; pp. 2298 - 2304
• Main Authors: Bürger, Mathias, Notarstefano, Giuseppe, Bullo, Francesco, Allgöwer, Frank
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2012; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Asynchronous algorithm; Completion time; Computer science; control theory; systems; Computer simulation; Computer systems and distributed systems. User interface; Distributed linear programming; Distributed simplex; Exact sciences and technology; Graphs; Multi-agent task assignment; Multiagent systems; Networks; Optimization; Running; Software; Distributed linear programming; Asynchronous algorithm; Multi-agent task assignment; Distributed simplex; Network structure; Peer to peer; Degenerate system; Task scheduling; Linear programming; Distributed system; Intelligent agent; Multiagent system; Information network; Simplex method; Optimal solution; Distributed algorithm; Communication graph; Information structure; Artificial intelligence; Diameter; Infeasibility; Execution time; Asynchronous transmission
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.06.040

In this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous peer-to-peer networks with distributed information structures. We propose a distributed version of the well-known simplex algorithm for general degenerate linear programs. A network of agents, running our algorithm, will agree on a common optimal solution, even if the optimal solution is not unique, or will determine infeasibility or unboundedness of the problem. We establish how the multi-agent assignment problem can be efficiently solved by means of our distributed simplex algorithm. We provide simulations supporting the conjecture that the completion time scales linearly with the diameter of the communication graph.