Social networks have increasingly become important and popular in modern times. Moreover, the influence of social networks plays a vital role in various organizations, including government organizations, academic research organizations and corporate organizations. Therefore, strategizing the optimal propagation strategy in social networks has also become more important. Increasing the precision of evaluating the propagation probability of social networks can indirectly influence the investment of cost, manpower and time for information propagation to achieve the best return. This study proposes a new algorithm, which includes a scale-free network, Barabási–Albert model, binary-addition tree (BAT) algorithm, PageRank algorithm, Personalized PageRank algorithm and a new BAT algorithm to calculate the propagation probability of social networks. The results obtained after implementing the simulation experiment of social network models show that the studied model and the proposed algorithm provide an effective method to increase the efficiency of information propagation in social networks. In this way, the maximum propagation efficiency is achieved with the minimum investment.

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With the evolution of the Internet and the introduction of third-party platforms, a diversified supply chain has gradually emerged. In contrast to the traditional single sales channel, companies can also increase their revenue by selling through multiple channels, such as dual-channel sales: adding a sales channel for direct sales through online third-party platforms. However, due to the complexity of the supply chain structure, previous studies have rarely discussed and analyzed the capital-constrained dual-channel supply chain model, which is more relevant to the actual situation. To solve more complex and realistic supply chain decision problems, this paper uses the concept of game theory to describe the pricing negotiation procedures among the capital-constrained manufacturers and other parties in the dual-channel supply chain by applying the Stackelberg game theory to describe the supply chain structure as a hierarchical multi-level mathematical model to solve the optimal pricing strategy for different financing options to achieve the common benefit of the supply chain. In this study, we propose a Multi-level Improved Simplified Swarm Optimization (MLiSSO) method, which uses the improved, simplified swarm optimization (iSSO) for the Multi-level Programming Problem (MLPP). It is applied to this pricing strategy model of the supply chain and experiments with three related MLPPs in the past studies to verify the effectiveness of the method. The results show that the MLiSSO algorithm is effective, qualitative, and stable and can be used to solve the pricing strategy problem for supply chain models; furthermore, the algorithm can also be applied to other MLPPs.

Network systems are commonly used in various fields, such as power grids, Internet of Things, and gas networks. The reliability redundancy allocation problem is a well-known reliability design tool that needs to be developed when the system is extended from a series-parallel structure to a more general network structure. Therefore, this study proposes a novel reliability redundancy allocation problem, referred to as the general reliability redundancy allocation problem, to be applied in network systems. Because the general reliability redundancy allocation problem is NP-hard, a new algorithm referred to as binary-addition simplified swarm optimization is proposed in this study. Binary-addition simplified swarm optimization combines the accuracy of the Binary Addition Tree Algorithm with the efficiency of Simplified Swarm Optimization, which can effectively reduce the solution space and speed up the time required to find high-quality solutions. The experimental results show that binary-addition simplified swarm optimization outperforms three well-known algorithms: the Genetic Algorithm, Particle Swarm Optimization, and Simplified Swarm Optimization in high-quality solutions and high stability on six network benchmarks.

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