Abstract
Many systems like manufacturing systems, biological processes and even stock markets can be seen as networks of coupled decision makers and thus be described as networked discrete event systems (DES) or multi-agent discrete event systems (MADES). Information interchange between agents is usually performed indirectly via competition for shared resources. The problem of trajectory planning for MADES is about finding an optimal sequence of decisions for the particular agents. The planning process can be performed in a distributed manner. To encode the trajectory planning problem, we utilize Petri net models and present a formal way to derive integer linear programs (ILPs) that exhibit a bordered block-diagonal structure. We apply Dantzig’s decomposition method to decompose the LP-relaxed problem into multiple subproblems that can be solved locally by their corresponding agents. In general, the obtained LP solutions are non-integer. Therefore, we ensure feasibility to the original ILP using a superior Branch-and-Bound algorithm. Hence, we end up with a so called Branch-and-Price algorithm, tailored to solve trajectory planning problems for general MADES via distributed optimization.
Zusammenfassung
Vielfältige Systeme, darunter Produktionssysteme, biologische Prozesse und Finanzmärkte, können als Netzwerke interagierender Entscheider und damit als ereignisdiskrete Multi-Agenten-Systeme (MADES) beschrieben werden. Der Informationsaustausch zwischen einzelnen Agenten erfolgt indirekt im Wettstreit um gemeinsame Ressourcen. Das Trajektorienplanungsproblem für MADES fragt nach optimalen Entscheidungssequenzen für die einzelnen Agenten. Der Planungsprozess kann verteilt erfolgen. Zur Kodierung des Trajektorienplanungsproblems werden Petri-Netze verwendet und anschließend ganzzahlige lineare Programme (ILPs) mit berandeter Blockdiagonalstruktur hergeleitet. Um das LP-relaxierte Problem in Subprobleme zu zerlegen, die lokal von ihren korrespondierenden Agenten gelöst werden können, wird die Dantzig-Wolfe-Dekomposition angewendet. Im Allgemeinen ist die so gefundene LP-Lösung nicht ganzzahlig. Ein übergeordneter Branch-and-Bound-Algorithmus sichert deshalb die Zulässigkeit der Lösung. Es resultiert ein Branch-and-Price-Algorithmus, zugeschnitten, um Trajektorienplanungsprobleme für allgemeine MADES verteilt zu lösen.
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