Optimal on-line scheduling in stochastic multi-agent systems in continuous space and time.
Wim Wiegerinck, Bart Broek and Bert Kappen
In: AAMAS, 14-18 May 2007, Hawai.

Abstract

We consider multi-agent systems with stochastic non-linear dynamics in continuous space-time. We focus on systems of agents that aim to visit a number of given target locations at given points in time at minimal control cost. The on- line optimization of which agent has to visit which target requires the solution of the Hamilton-Jacobi-Bellman (HJB) equation, which is a non-linear partial dierential equation (PDE). Under some conditions, the log-transform can be applied to turn the HJB equation into a linear PDE.We then show that the optimal solution in the multi-agent scheduling problem can be expressed in closed form as a sum of single schedule solutions. Categories and Subject Descriptors G.1.6 [Numerical analysis]: Optimization|stochastic pro- gramming; I.2.8 [Articial Intelligence]: Problem Solv- ing, Control Methods, and Search|control theory ,dynamic programming, scheduling; I.2.11 [Articial Intelligence]: Distributed Articial Intelligence|Multiagent systems;

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