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Pareto-based evolutionary multiobjective approaches are methods that use the Pareto dominance concept to guide the search of evolutionary algorithms towards the Pareto frontier of a problem. To address the challenge of providing an entire set of optimal solutions they use specially designed mechanisms for preserving search diversity and maintaining the non-dominated solutions set. The limitation of the Pareto dominance relation in high-dimensional spaces has rendered these methods inefficient for many-objective optimization. In this paper we aim to exploit existing Pareto-based methods to compute the generalized Nash equilibrium for multi-player games by replacing the Pareto dominance relation with an equilibrium generative relation. The generalized Nash equilibrium extends the Nash equilibrium concept by considering constraints over players’ strategies. Numerical experiments indicate that the selected methods can be employed for equilibria computation even for games with up to twenty players.

Determining the critical nodes in a complex network is an essential computation problem. Several variants of this problem have emerged due to its wide applicability in network analysis. In this article we study the bi-objective critical node detection problem (BOCNDP), which is a new variant of the well-known critical node detection problem, optimizing two objectives at the same time: maximizing the number of connected components and minimizing the variance of their cardinalities. Evolutionary multi-objective algorithms (EMOA) are a straightforward choice to solve this type of problem. We propose three different smart initialization strategies which can be incorporated into any EMOA. These initialization strategies take into account the basic properties of the networks. They are based on the highest degree, random walk (RW) and depth-first search. Numerical experiments were conducted on synthetic and real-world network data. The three different initialization types significantly improve the performance of the EMOA.

The Berge-Zhukovskii equilibrium is an alternate solution concept in non-cooperative game theory that formalizes cooperation in a noncooperative setting. In this paper, the ϵ-Berge-Zhukovskii equilibrium is introduced and characterized by using a generative relation. The generative relation also provides a solution to the problem of computing the ϵ-Berge-Zhukovskii equilibrium for large games, by using evolutionary algorithms. Numerical examples illustrate the approach and provide a possible application for this equilibrium concept.

The aim of this paper is to asses simultaneous spectrum access situations that may occur in Cognitive Radio (CR) environments. The approach is that of one-shot, non-cooperative games describing CR interactions. Open spectrum access scenarios are modelled based on continuous and discrete reformulations of the Cournot game theoretical model. CR interaction situations are described by Nash and Pareto equilibria. Also, the heterogeneity of players is captured by the new concept of joint Nash-Pareto equilibrium, allowing CRs to be biased toward different types of equilibrium. Numerical simulations reveal equilibrium situations that may be reached in simultaneous access scenarios of two and three users.