Paving the Royal Road for Complex Systems: On the Influence of Memory on Adaptivity

Abstract

The "Royal Road" objective function was proposed by J. H. Holland in 1993 as a very hard benchmark problem for evolutionary algorithms. Generally, it belongs to the class of combinatorial optimization problems. In our work, we solve the problem in a distributed way by assigning each decision variable to an autonomous agent. The resulting multi-agent system "COHDA" forms a self-organizing complex system, where the global solution emerges from local interactions. By applying the XOR instance generator introduced by S. Yang in 2003, we are able to pertubate the system during runtime by modifying the objective function. This allows us to examine the robustness of COHDA against dynamic objectives. Here, we focus on the influence of runtime memory, which comprises the beliefs of each agent, on the adaptivity capabilities of the agents after an occured pertubation. We show that the final fitness values produced by the system do not suffer from a dynamic objective function, and are not influenced by the availability of an agents’ runtime memory. The time needed by the system to adapt to such a pertubation, however, significantly increases if the agents’ beliefs are being distorted. We conclude that, in terms of solution quality, COHDA is very robust against dynamic objective functions. With respect to adaptation speed, the heuristic benefits from the availability of runtime memory.