Cooperative Coevolution for Non-Separable Large-Scale Black-Box Optimization: Convergence Analyses and Distributed Accelerations

Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer optimization framework, on non-separable functions. First, we reveal empirical reasons of why decomposition-based methods are preferred or not in practice on some non-separable large-scale problems, which have not been clearly pointed out in many previous CC papers. Then, we formalize CC to a continuous game model via simplification, but without losing its essential property. Different from previous evolutionary game theory for CC, our new model provides a much simpler but useful viewpoint to analyze its convergence, since only the pure Nash equilibrium concept is needed and more general fitness landscapes can be explicitly considered. Based on convergence analyses, we propose a hierarchical decomposition strategy for better generalization, as for any decomposition there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally, we use powerful distributed computing to accelerate it under the multi-level learning framework, which combines the fine-tuning ability from decomposition with the invariance property of CMA-ES. Experiments on a set of high-dimensional functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores

Contractually stable networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with his coalition members and with individuals outside his coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concept of contractual stability which requires that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. We show that there always exists a contractually stable coalitional network under the simple majority decision rule and the component-wise egalitarian or majoritarian allocation rules. Moreover, requiring the consent of group members may help to reconcile stability and efficiency.networks, coalition structures, contractual stability, allocation rules.

Identifying influencers in a social network : the value of real referral data

Individuals influence each other through social interactions and marketers aim to leverage this interpersonal influence to attract new customers. It still remains a challenge to identify those customers in a social network that have the most influence on their social connections. A common approach to the influence maximization problem is to simulate influence cascades through the network based on the existence of links in the network using diffusion models. Our study contributes to the literature by evaluating these principles using real-life referral behaviour data. A new ranking metric, called Referral Rank, is introduced that builds on the game theoretic concept of the Shapley value for assigning each individual in the network a value that reflects the likelihood of referring new customers. We also explore whether these methods can be further improved by looking beyond the one-hop neighbourhood of the influencers. Experiments on a large telecommunication data set and referral data set demonstrate that using traditional simulation based methods to identify influencers in a social network can lead to suboptimal decisions as the results overestimate actual referral cascades. We also find that looking at the influence of the two-hop neighbours of the customers improves the influence spread and product adoption. Our findings suggest that companies can take two actions to improve their decision support system for identifying influential customers: (1) improve the data by incorporating data that reflects the actual referral behaviour of the customers or (2) extend the method by looking at the influence of the connections in the two-hop neighbourhood of the customers

The use of multilayer network analysis in animal behaviour

Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as \emph{multilayer network analysis}, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour as connected 'layers' of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population, and evolutionary levels of organisation. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.Comment: Thoroughly revised; title changed slightl