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

Yourong Chen,Banteng Liu,Meng Han,Hao Chen,Zhangquan Wang,Zhenghua Ma,Qiuxia Chen

doi:10.1186/s13638-021-02018-x

Abstract

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.

Highlights

With the continuous development of information technology, information security issues in our daily lives are becoming more and more important [1]
The scout bee operations delete the local optimal food source that cannot produce new food sources to ensure the diversity of solutions
To overcome the fast-changing block withholding attacks among multiple mining pools composed of miners in the blockchain system, we propose a mining pool computing power allocation algorithm, which significantly improves the revenues of mining pools with block withholding attacks [32], but the algorithm does not consider the selection of the miners during the model establishment

Summary

Introduction

With the continuous development of information technology, information security issues in our daily lives are becoming more and more important [1]. 3.2.2 Employed bee operation MROA calculates the total computing power that each attacking mining pool can use for honest mining and block withholding attack by formula (4) and formula (5). Mutation operation can help MROA to reduce that the revenue gap among mining pools, that is, letting that current row is the first row, MROA carries out the following operations for Nw times until the mutation operation of the food source is completed: it randomly generates a mutation factor φ1 ; if the mutation factor φ1 is larger than the threshold φ1thr , it uses the formula (8) to obtain the revenue of each attacking mining pool in the food source and replaces the current row according to formula (14), which makes the mutation result of food source beneficial to the current attacking mining pool of lowest revenue; Otherwise, it does not change; the number of current row adds 1. When the algorithm iteration is completed, it uses the non-dominated solution set QF2 as the solution set for maximum revenue of multiple mining pools, and we take the food source with the largest evaluation value as the optimal solution

Scout bee operation

Results and discussion

Conclusion