This paper investigates a wireless blockchain network with mobile edge computing in which Internet of Things (IoT) devices can behave as blockchain users (BUs). This blockchain network’s ultimate goal is to increase the overall profits of all BUs. Because not all BUs join in the mining process, using traditional swarm and evolution algorithms to solve this problem results in a high level of redundancy in the search space. To solve this problem, a modified chaotic Henry single gas solubility optimization algorithm, called CHSGSO, has been proposed. In CHSGSO, the allocation of resources to BUs who decide to engage in mining as an individual is encoded. This results in a different size for each individual in the entire population, which leads to the elimination of unnecessary search space regions. Because the individual size equals the number of participating BUs, we devise an adaptive strategy to fine-tune each individual size. In addition, a chaotic map was incorporated into the original Henry gas solubility optimization to improve resource allocation and accelerate the convergence rate. Extensive experiments on a set of instances were carried out to validate the superiority of the proposed CHSGSO. Its efficiency is demonstrated by comparing it to four well-known meta-heuristic algorithms.