In order to improve the revenues of attack mining pools and miners under block withholding attack, we propose the mining revenue optimization algorithm (MROA) of miners in PoW-based blockchain network. MROA establishes the revenue optimization model of each attack mining pool and revenue optimization model of entire mining attack pools under block withholding attack with the mathematical formulas such as attack 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 Pareto. Namely, employed bee operations include evaluation value calculation, selection probability calculation, crossover operation, mutation operation and Pareto domination calculation, 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 domination calculation, and can find the optimal food source in multidimensional space with smaller distribution density. Scout bee operations delete the local optimal food source which cannot produce new food sources to ensure the diversity of solutions. The simulation results show that no matter how the number of attack mining pools and the number of miners change, MROA can find a reasonable miner work plan for each attack mining pool, which improves 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-arts such as ABC, NSGA2 and MOPSO.

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This preprint is available for download as a PDF.

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Posted 13 Nov, 2020

###### No community comments so far

###### Editorial decision:

**Major revision**On 31 Mar, 2021

###### Review #3 received

Received 29 Mar, 2021

###### Reviewer #4 agreed

On 09 Feb, 2021

###### Review #2 received

Received 11 Jan, 2021

###### Reviewer #3 agreed

On 10 Jan, 2021

###### Review #1 received

Received 24 Dec, 2020

###### Reviewer #2 agreed

On 16 Dec, 2020

###### Reviewers invited

Invitations sent on 25 Nov, 2020

###### Reviewer #1 agreed

On 25 Nov, 2020

###### Editor assigned

On 10 Nov, 2020

###### Editor invited

On 10 Nov, 2020

###### Submission checks complete

On 10 Nov, 2020

###### First submitted

On 06 Nov, 2020

Posted 13 Nov, 2020

###### No community comments so far

###### Editorial decision:

**Major revision**On 31 Mar, 2021

###### Review #3 received

Received 29 Mar, 2021

###### Reviewer #4 agreed

On 09 Feb, 2021

###### Review #2 received

Received 11 Jan, 2021

###### Reviewer #3 agreed

On 10 Jan, 2021

###### Review #1 received

Received 24 Dec, 2020

###### Reviewer #2 agreed

On 16 Dec, 2020

###### Reviewers invited

Invitations sent on 25 Nov, 2020

###### Reviewer #1 agreed

On 25 Nov, 2020

###### Editor assigned

On 10 Nov, 2020

###### Editor invited

On 10 Nov, 2020

###### Submission checks complete

On 10 Nov, 2020

###### First submitted

On 06 Nov, 2020

In order to improve the revenues of attack mining pools and miners under block withholding attack, we propose the mining revenue optimization algorithm (MROA) of miners in PoW-based blockchain network. MROA establishes the revenue optimization model of each attack mining pool and revenue optimization model of entire mining attack pools under block withholding attack with the mathematical formulas such as attack 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 Pareto. Namely, employed bee operations include evaluation value calculation, selection probability calculation, crossover operation, mutation operation and Pareto domination calculation, 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 domination calculation, and can find the optimal food source in multidimensional space with smaller distribution density. Scout bee operations delete the local optimal food source which cannot produce new food sources to ensure the diversity of solutions. The simulation results show that no matter how the number of attack mining pools and the number of miners change, MROA can find a reasonable miner work plan for each attack mining pool, which improves 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-arts such as ABC, NSGA2 and MOPSO.

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This preprint is available for download as a PDF.

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