Complexity, Patches and Fitness: A Model of Decentralised Problem-Solving

We present a model of decentralisation of organisational search activity in NK fitness landscapes. The degree of decentralisation is expressed as the number of elements within a patch P. We derive analytical results for landscapes of maximum complexity (K = N-1) for the expected number of local optima for different degrees of decentralisation. The ruggedness of a landscape depends on the search strategy applied. We distinguish between conventional adaptive walk that accepts a new string only if mean fitness of elements belonging to a patch is increased, and Pareto search that accepts a new string only if both the mean fitness of elements belonging to a patch is increased and none of the fitness values of individual elements is decreased. We show that, for all values of N and P, adaptive walks encounter much less local optima than Pareto search, which implies that the optimal size of a patch is higher for adaptive walks than for Pareto search. Simulation result on the number and fitness of local optima are discussed for intermediate complexity (0 < K < N-1). Further research questions and empirical implications are elaborated at the end.