Optimal directed hypergraph traversal with ant-colony optimisation

Abstract

Directed hypergraphs are an extension of directed graphs in which edges connect a set of source nodes to a set of target nodes. Unlike graphs, they can capture complex relations in network structures that go beyond the union of pairwise associations. They are widely applied in a variety of different domains, such as finding pathways in chemical reaction networks or minimising propositional Horn formulas. Calculating optimal paths in hypergraphs in the general case is an NP-hard problem, which can be solved in polynomial time only when utility functions hold specific properties. We present in this paper an approach to search for optimal hypergraph paths in the general case based on ant colony optimisation. Ant colony optimisation is an evolutionary meta-heuristic that is particularly suitable to combinatorial problems, such as optimal graph traversal. We present an experimental evaluation using artificially-generated hypergraphs and discuss innovative applications of the proposed approach in the domains of industrial engineering and chemical informatics