In order to improve the revenue of attacking mining pools and miners under block withholding attack, we propose the miner revenue optimization algorithm (MROA) based on Pareto artificial bee colony in blockchain network. MROA establishes the revenue optimization model of each attacking mining pool and revenue optimization model of entire attacking mining pools under block withholding attack with the mathematical formulas such as attacking mining pool selection, effective computing power, mining cost and revenue. Then, MROA solves the model by using the modified artificial bee colony algorithm based on the Pareto method. Namely, the employed bee operations include evaluation value calculation, selection probability calculation, crossover operation, mutation operation and Pareto dominance method, and can update each food source. The onlooker bee operations include confirmation probability calculation, crowding degree calculation, neighborhood crossover operation, neighborhood mutation operation and Pareto dominance method, and can find the optimal food source in multidimensional space with smaller distribution density. The scout bee operations delete the local optimal food source that cannot produce new food sources to ensure the diversity of solutions. The simulation results show that no matter how the number of attacking mining pools and the number of miners change, MROA can find a reasonable miner work plan for each attacking mining pool, which increases minimum revenue, average revenue and the evaluation value of optimal solution, and reduces the spacing value and variance of revenue solution set. MROA outperforms the state of the arts such as ABC, NSGA2 and MOPSO.

为了提高在区块扣留攻击下攻击矿池和矿工的收益，我们在区块链网络中提出了基于帕累托人工蜂群的矿工收益优化算法（MROA）。MROA利用攻击矿池选择、有效算力、挖矿成本和收益等数学公式，建立了每个攻击矿池的收益优化模型和区块扣留攻击下整个攻击矿池的收益优化模型。然后，MROA使用基于Pareto方法的改进人工蜂群算法对模型进行求解。即采用的蜜蜂运算包括评价值计算、选择概率计算、交叉运算、变异运算和帕累托​​优势法，可以更新每个食物源。围观蜂操作包括确认概率计算、拥挤度计算、邻域交叉操作、邻域变异操作和帕累托优势法，可以在分布密度较小的多维空间中寻找最优食物源。侦察蜂操作删除不能产生新食物源的局部最优食物源，以确保解决方案的多样性。仿真结果表明，无论攻击矿池数量和矿工数量如何变化，MROA都能为每个攻击矿池找到合理的矿工工作计划，从而增加最小收益、平均收益和最优解的评估值，并减小收益解集的间距值和方差。MROA 的表现优于 ABC、NSGA2 和 MOPSO 等现有技术。