Miner revenue optimization algorithm based on Pareto artificial bee colony in blockchain network

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.