Gossiping Differential Evolution: A Decentralized Heuristic for Function Optimization in P2P Networks

Abstract

Abstract-P2P-based optimization has recently gained interest among distributed function optimization scientists. Several wellknown optimization heuristics have been recently re-designed to exploit the peculiarity of such a distributed environment. The final goal is to perform high quality function optimization by means of inexpensive, fully decentralized machines, which may either be purposely organized in a P2P network, or voluntarily join a running P2P optimization task. In this paper we present the GoDE algorithm (Gossip-based Differential Evolution), which obtains remarkable results on several test functions. We describe in detail the algorithm design and the epidemic mechanism that greatly improves the performance. Experimental results in a simulated environment show how GoDE adapts to network scale and how the epidemic communication protocol can make the algorithm achieve good results even in presence of a high churn rate.Keywords-peer-to-peer, function optimization, differential evolution, heuristic, churn I. PROBLEM AND GOALWhen confronted with a function optimization problem, scientists are presented with a large choice space of algorithms and techniques. Recently, a new dimension has been added to this space: distribution. Optimization tasks could be distributed among a collection of independent machines, with the obvious goal of obtaining a speed-up.Most of the existing research in distributed optimization, however, has been focused on tightly-coupled architectures, such as parallel systems [14] or high-performance clusters, usually managed by a central coordinator [15]. These systems either have strict synchronization requirements or rely completely on a central server, which coordinates the work of clients and acts as a state repository.Quite recently, the possibility to perform optimization tasks in a P2P decentralized network of solvers has been investigated and explored. Our target networking environment consists of independent nodes that are connected via an error-free message passing service. All nodes have an identical role running an identical algorithm. Joining and failing nodes are tolerated automatically via the inherent (or explicit) redundancy of the algorithm design. While such a distributed environment sounds like "no big issue" concerning nodes cooperation, communication and connectivity, it is not trivial at all from the point of view of executing a distributed function optimization task.To simplify the discussion, we briefly define some basic terminology. The system we target is composed by a (potentially large) number of solvers, each of them being a running instance of an optimization algorithm. Each solver iteratively evaluates one or more points of an objective function, with the goal of finding a better objective value (minimum or maximum). Solvers may share information with each other about the progress of the optimization process (solution quality). Subsequent iterations of the local instance of the algorithm may depend not only on the objective values that have been found lo...

Designing robust volunteer-based evolutionary algorithms

“…In addition, every single study establishes its own characterization of churn, which prevents to conclude that volunteer-based evolutionary algorithms are viable in general; especially, when a maximum failure rate of 20% is considered in most of the cases (e.g. [Scriven et al(2008a), Biazzini and Montresor(2010), Bánhelyi et al(2009), Scriven et al(2009)]). …”

“…P2P systems, on the other hand, overcome this issue with a decentralized architecture in which ev-ery computing node acts either as a client or as a server, thus limiting the impact a node can have on the system. Following such a decentralized philosophy, many approaches have been tackling the design of P2P meta-heuristics [Arenas et al(2002), Wickramasinghe et al(2007), , Biazzini and Montresor(2010), Scriven et al(2009), Bánhelyi et al(2009), Biazzini and Montresor(2013]. …”

“…Biazzini and Montresor [Biazzini and Montresor(2010)] propose a gossiping differential evolution algorithm where individuals are spread to different sub-populations using an epidemic migration. The proposal considers a similar characterization of churn as the previous work but replacing in turn five and ten percent of the nodes.…”

“…In fact, there is a growing interest of the scientific community in the paradigm and many optimization heuristics have been redesigned recently in order to take advantage of this aggregated source of computational power, e.g. [Desell et al(2008), , Scriven et al(2008b), Biazzini and Montresor(2010), Bánhelyi et al(2009)]. Overall, the purpose is to increase the convergence speed via the massive CPU availability of volunteer systems.…”

Validating a Peer-to-Peer Evolutionary Algorithm

“…In this context and under the term of P2P optimization, many optimization heuristics such as Evolutionary Algorithms (EAs), Particle Swarm (PSO) or Branch-and-bound have been re-designed in order to take advantage of such computing platforms [16,13,5,3]. The key issue here is that gathering a large amount of computational devices pose a whole set of practical problems.…”