Abstract:
Multi-agent systems for resource allocation (MRAs) have been introduced as a concept for modelling
competitive resource allocation problems in distributed computing. An MRA is composed of a set
of agents and a set of resources. Each agent has goals in terms of allocating certain resources. For
MRAs it is typically of importance that they are designed in a way such that there exists a strategy
that guarantees that all agents will achieve their goals. The corresponding model checking problem
is to determine whether such a winning strategy exists or not, and the synthesis problem is to actually
build the strategy. While winning strategies ensure that all goals will be achieved, following such
strategies does not necessarily involve an optimal use of resources.
In this paper, we present a technique that allows to synthesise cost-optimal solutions to distributed
resource allocation problems. We consider a scenario where system components such as agents and
resources involve costs. A multi-agent system shall be designed that is cost-minimal but still capable
of accomplishing a given set of goals. Our approach synthesises a winning strategy that minimises
the cumulative costs of the components that are required for achieving the goals. The technique is
based on a propositional logic encoding and a reduction of the synthesis problem to the maximum
satisfiability problem (Max-SAT). Hence, a Max-SAT solver can be used to perform the synthesis.
From a truth assignment that maximises the number of satisfied clauses of the encoding a cost-
optimal winning strategy as well as a cost-optimal system can be immediately derived.
