The surprising little effectiveness of cooperative algorithms in parallel problem solving

TL;DR

This paper evaluates the effectiveness of cooperative algorithms like imitative learning and evolutionary algorithms in solving NK-fitness landscapes, revealing that they often do not outperform simple blind search, especially in rugged landscapes.

Contribution

It provides a comparative analysis of cooperative algorithms versus blind search in NK landscapes, highlighting their limited advantages and vulnerabilities to local maxima.

Findings

Evolutionary algorithms perform similarly to blind search on smooth landscapes.

Imitative learning is more effective on smooth landscapes but prone to local maxima in rugged landscapes.

Blind search matches or outperforms cooperative algorithms in rugged landscapes with many local maxima.

Abstract

Biological and cultural inspired optimization algorithms are nowadays part of the basic toolkit of a great many research domains. By mimicking processes in nature and animal societies, these general-purpose search algorithms promise to deliver optimal or near-optimal solutions using hardly any information on the optimization problems they are set to tackle. Here we study the performances of a cultural-inspired algorithm -- the imitative learning search -- as well as of asexual and sexual variants of evolutionary algorithms in finding the global maxima of NK-fitness landscapes. The main performance measure is the total number of agent updates required by the algorithms to find those global maxima and the baseline performance, which establishes the effectiveness of the cooperative algorithms, is set by the blind search in which the agents explore the problem space (binary strings) by flipping bits at random. We find that even for smooth landscapes that exhibit a single maximum, the evolutionary algorithms do not perform much better than the blind search due to the stochastic effects of the genetic roulette. The imitative learning is immune to this effect thanks to the deterministic choice of the fittest string in the population, which is used as a model for imitation. The tradeoff is that for rugged landscapes the imitative learning search is more prone to be trapped in local maxima than the evolutionary algorithms. In fact, in the case of rugged landscapes with a mild density of local maxima, the blind search either beats or matches the cooperative algorithms regardless of whether the task is to find the global maximum or to find the fittest state within a given runtime.