In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal ...In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.展开更多
In order to explore the optimal phosphorus application rate of tobacco in Yongzhou area and provide scientific basis for the rational application of phosphorus fertilizer in tobacco production,field plot experiments w...In order to explore the optimal phosphorus application rate of tobacco in Yongzhou area and provide scientific basis for the rational application of phosphorus fertilizer in tobacco production,field plot experiments with 4 phosphorus application rates were conducted to study the effects of different phosphorus application rate on the growth period,agronomic characters and economic characters of tobacco.The results showed that when the nitrogen fertilizer,phosphorus fertilizer and potassium fertilizer was 135,135 and 418.5 kg/hm2,respectively,namely the ratio of 1∶1∶3.1,the field growth period was the shortest,only 107 d;the agronomic characters and physical indexes showed good results in their performance;the ratio of superior tobacco leaves,average price and output value were 49.36%、26.04 yuan/kg and 56064.12 yuan/hm2 respectively,significantly higher than that of other treatments.Therefore,the suitable phosphorus application in Yongzhou tobacco area was 135 kg/hm2.In conclusion,rational phosphorus application rate was conducive to accelerating the growth and development of tobacco plant and early harvest;it could also effectively increase the output value and yield of tobacco leaves and was more conducive to the formation of high-quality tobacco leaves.展开更多
基金supported in part by the Science and Technology Project of Yunnan Tobacco Industrial Company under Grant JB2022YL02in part by the Natural Science Foundation of Henan Province of China under Grant 242300421413in part by the Henan Province Science and Technology Research Projects under Grants 242102110334 and 242102110375.
文摘In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.
文摘In order to explore the optimal phosphorus application rate of tobacco in Yongzhou area and provide scientific basis for the rational application of phosphorus fertilizer in tobacco production,field plot experiments with 4 phosphorus application rates were conducted to study the effects of different phosphorus application rate on the growth period,agronomic characters and economic characters of tobacco.The results showed that when the nitrogen fertilizer,phosphorus fertilizer and potassium fertilizer was 135,135 and 418.5 kg/hm2,respectively,namely the ratio of 1∶1∶3.1,the field growth period was the shortest,only 107 d;the agronomic characters and physical indexes showed good results in their performance;the ratio of superior tobacco leaves,average price and output value were 49.36%、26.04 yuan/kg and 56064.12 yuan/hm2 respectively,significantly higher than that of other treatments.Therefore,the suitable phosphorus application in Yongzhou tobacco area was 135 kg/hm2.In conclusion,rational phosphorus application rate was conducive to accelerating the growth and development of tobacco plant and early harvest;it could also effectively increase the output value and yield of tobacco leaves and was more conducive to the formation of high-quality tobacco leaves.
