A hyper-heuristic algorithm is a general solution framework that adaptively selects the optimizer to address complex problems. A classical hyper-heuristic framework consists of two levels, including the high-level heuristic and a set of low-level heuristics. The low-level heuristics to be used in the optimization process are chosen by the high-level tactics in the hyper-heuristic. In this study, a Cooperative Multi-Stage Hyper-Heuristic (CMS-HH) algorithm is proposed to address certain combinatorial optimization problems. In the CMS-HH, a genetic algorithm is introduced to perturb the initial solution to increase the diversity of the solution. In the search phase, an online learning mechanism based on the multi-armed bandits and relay hybridization technology are proposed to improve the quality of the solution. In addition, a multi-point search is introduced to cooperatively search with a single-point search when the state of the solution does not change in continuous time. The performance of the CMS-HH algorithm is assessed in six specific combinatorial optimization problems, including Boolean satisfiability problems, one-dimensional packing problems, permutation flow-shop scheduling problems, personnel scheduling problems, traveling salesman problems, and vehicle routing problems. The experimental results demonstrate the efficiency and significance of the proposed CMS-HH algorithm.

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The influence maximization problem in social networks aims to select a subset of most influential nodes, denoted as seed set, to maximize the influence diffusion of the seed nodes. The majority of existing works on this problem would ignite all the seed nodes simultaneously at the beginning of the diffusion process and let the influence diffuses passively in the network. However, it cannot depict the practical dynamics exactly of viral marketing campaigns in reality and fails to provide driving policies to control over the diffusion. In this paper, we focus on the dynamic influence maximization problem with limited budget to study the scheduling strategies including which influential node is to be seeded during the diffusion process and when to seed it at the right time. A time-dependent seed activating feedback scheme is modeled firstly by considering the time factor and its impact on the influence obligation in diffusion process. Then a scheduling heuristic based on determinate and latent margin is proposed to evaluate the marginal return of candidate nodes and activate the right seed node to promote the viral marketing. Extensive experiments on four social networks show that the proposed algorithm achieves significantly better results than a typical static influence maximization algorithm based on swarm intelligence and can improve the influence propagation under the time-dependent diffusion model comparing with the centrality-based scheduling heuristics.

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