Jorge Peña

Heterogeneous particle swarm optimizers

Particle swarm optimization (PSO) is a swarm intelligence technique originally inspired by models of flocking and of social influence that assumed homogeneous individuals. During its evolution to become a practical optimization tool, some heterogeneous variants have been proposed. However, heterogeneity in PSO algorithms has never been explicitly studied and some of its potential effects have therefore been overlooked. In this paper, we identify some of the most relevant types of heterogeneity that can be ascribed to particle swarms. A number of particle swarms are classified according to the type of heterogeneity they exhibit, which allows us to identify some gaps in current knowledge about heterogeneity in PSO algorithms. Motivated by these observations, we carry out an experimental study of two heterogeneous particle swarms each of which is composed of two kinds of particles. Directions for future developments on heterogeneous particle swarms are outlined.

Conformity hinders the evolution of cooperation on scale-free networks.

We study the effects of conformity, the tendency of humans to imitate locally common behaviors, in the evolution of cooperation when individuals occupy the vertices of a graph and engage in the one-shot prisoners dilemma or the snowdrift game with their neighbors. Two different graphs are studied: rings (one-dimensional lattices with cyclic boundary conditions) and scale-free networks of the Barabási-Albert type. The proposed evolutionary-graph model is studied both by means of Monte Carlo simulations and an extended pair-approximation technique. We find improved levels of cooperation when evolution is carried on rings and individuals imitate according to both the traditional payoff bias and a conformist bias. More importantly, we show that scale-free networks are no longer powerful amplifiers of cooperation when fair amounts of conformity are introduced in the imitation rules of the players. Such weakening of the cooperation-promoting abilities of scale-free networks is the result of a less biased flow of information in scale-free topologies, making hubs more susceptible of being influenced by less-connected neighbors.

Group-size diversity in public goods games.

Public goods games are models of social dilemmas where cooperators pay a cost for the production of a public good while defectors free ride on the contributions of cooperators. In the traditional framework of evolutionary game theory, the payoffs of cooperators and defectors result from interactions in groups formed by binomial sampling from an infinite population. Despite empirical evidence showing that group‐size distributions in nature are highly heterogeneous, most models of social evolution assume that the group size is constant. In this article, I remove this assumption and explore the effects of having random group sizes on the evolutionary dynamics of public goods games. By a straightforward application of Jensen’s inequality, I show that the outcome of general nonlinear public goods games depends not only on the average group size but also on the variance of the group‐size distribution. This general result is illustrated with two nonlinear public goods games (the public goods game with discounting or synergy and the N‐person volunteer’s dilemma) and three different group‐size distributions (Poisson, geometric, and Waring). The results suggest that failing to acknowledge the natural variation of group sizes can lead to an underestimation of the actual level of cooperation exhibited in evolving populations.

Particle Swarm Optimization with Discrete Recombination: An Online Optimizer for Evolvable Hardware

Self-reconfigurable adaptive systems have the possibility of adapting their own hardware configuration. This feature provides enhanced performance and flexibility, reflected in computational cost reductions. Self-reconfigurable adaptation requires powerful optimization algorithms in order to search in a space of possible hardware configurations. If such algorithms are to be implemented on chip, they must also be as simple as possible, so the best performance can be achieved with the less cost in terms of logic resources, convergence speed, and power consumption. This paper presents hybrid bio-inspired optimization technique that introduces the concept of discrete recombination in a particle swarm optimizer, obtaining a simple and powerful algorithm, well suited for embedded applications. The proposed algorithm is validated using standard benchmark functions and used for training a neural network-based adaptive equalizer for communications systems

Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

By combining evolutionary game theory and graph theory, “games on graphs” study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner’s dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner’s dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures.

Theoretical and empirical study of particle swarms with additive stochasticity and different recombination operators

Standard particle swarms exhibit both multiplicative and additive stochasticity in their update equations. Recently, a simpler particle swarm with just additive stochasticity has been proposed and studied using a new theoretical approach. In this paper we extend the main results of that study to a large number of existing particle swarm optimisers by defining a general update rule from which actual algorithms can be instantiated via the choice of specific recombination operators. In particular, we derive the stability conditions and the dynamic equations for the first two moments of the sampling distribution during stagnation, and show how they depend on the used recombination operator. Finally, the optimisation efficiency of several particle swarms with additive stochasticity is compared in a suite of 16 benchmark functions.

Participation costs can suppress the evolution of upstream reciprocity

Indirect reciprocity, one of the many mechanisms proposed to explain the evolution of cooperation, is the idea that altruistic actions can be rewarded by third parties. Upstream or generalized reciprocity is one type of indirect reciprocity in which individuals help someone if they have been helped by somebody else in the past. Although empirically found to be at work in humans, the evolution of upstream reciprocity is difficult to explain from a theoretical point of view. A recent model of upstream reciprocity, first proposed by Nowak and Roch (2007) and further analyzed by Iwagami and Masuda (2010), shows that while upstream reciprocity alone does not lead to the evolution of cooperation, it can act in tandem with mechanisms such as network reciprocity and increase the total level of cooperativity in the population. We argue, however, that Nowak and Rochs model systematically leads to non-uniform interaction rates, where more cooperative individuals take part in more games than less cooperative ones. As a result, the critical benefit-to-cost ratios derived under this model in previous studies are not invariant with respect to the addition of participation costs. We show that accounting for these costs can hinder and even suppress the evolution of upstream reciprocity, both for populations with non-random encounters and graph-structured populations.

Evolutionary Graph Models with Dynamic Topologies on the Ubichip

The ubichip is a reconfigurable digital circuit with special reconfiguration mechanisms, such as dynamic routing and self-replication, for supporting the implementation of bio-inspired hardware systems. The dynamic routing mechanism allows to create and destroy interconnections between remote units in a distributed fashion, thus proving useful for implementing cellular systems featuring dynamic topologies. Evolutionary graph theory investigates genetic and cultural evolution processes using the mathematical formalism of both evolutionary game and graph theory. Populations are embedded in graphs representing interaction and imitation links. Payoffs are assigned and successful individuals are imitated with high probability. This paper describes the hardware implementation of a general evolutionary graph model in which the imitation network changes over time by exploiting the dynamic routing capabilities of the ubichip. As a particular example, we analyze the case of a coordination game played by agents arranged in a cycle in which imitation links are randomly created so as to simulate dynamic small-world networks.

Simple Dynamic Particle Swarms without Velocity

The standard particle swarm optimiser uses update rules including both multiplicative randomness and velocity. In this paper, we look into a general particle swarm model that removes these two features, and study it mathematically. We derive the recursions and fixed points for the first four moments of the sampling distribution, and analyse the transient behaviour of the mean and the variance. Then we define actual instances of the algorithm by coupling the general update rule with specific recombination operators, and empirically test their optimisation efficiency.

Conformity and network effects in the Prisoner's Dilemma

We study the evolution of cooperation using the Prisoners Dilemma as a metaphor of the tensions between cooperators and non-cooperators, and evolutionary game theory as the mathematical framework for modeling the cultural evolutionary dynamics of imitation in a population of unrelated individuals. We investigate the interplay between network reciprocity (a mechanism that promotes cooperation in the Prisoners Dilemma by restricting interactions to adjacent sites in spatial structures or neighbors in social networks) and conformity (the tendency of imitating common behaviors). We confirm previous results on the improved levels of cooperation when both network reciprocity and conformity are present in the model and evolution is carried on top of degree-homogeneous graphs, such as rings and grids. However, we also find that scale-free networks are no longer powerful amplifiers of cooperation when fair amounts of conformity are introduced in the imitation rules of the players. Such weakening of the cooperation-promoting abilities of scale-free networks is the result of a less biased flow of information in such topologies, making hubs more susceptible of being influenced by lessconnected neighbors.