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This article introduces a new hybrid hyper-heuristic framework that deals with single-objective continuous optimization problems. This approach employs a nested Markov chain on the base level in the search for the best-performing operators and their sequences and simulated annealing on the hyperlevel, which evolves the chain and the operator parameters. The novelty of the approach consists of the upper level of the Markov chain expressing the hybridization of global and local search operators and the lower level automatically selecting the best-performing operator sequences for the problem. Numerical experiments conducted on well-known benchmark functions and the comparison with another hyper-heuristic framework and six state-of-the-art metaheuristics show the effectiveness of the proposed approach.

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.