It is unpractical to learn the optimal structure of a big Bayesian network(BN)by exhausting the feasible structures,since the number of feasible structures is super exponential on the number of nodes.This paper propos...It is unpractical to learn the optimal structure of a big Bayesian network(BN)by exhausting the feasible structures,since the number of feasible structures is super exponential on the number of nodes.This paper proposes an approach to layer nodes of a BN by using the conditional independence testing.The parents of a node layer only belong to the layer,or layers who have priority over the layer.When a set of nodes has been layered,the number of feasible structures over the nodes can be remarkably reduced,which makes it possible to learn optimal BN structures for bigger sizes of nodes by accurate algorithms.Integrating the dynamic programming(DP)algorithm with the layering approach,we propose a hybrid algorithm—layered optimal learning(LOL)to learn BN structures.Benefitted by the layering approach,the complexity of the DP algorithm reduces to O(ρ2^n?1)from O(n2^n?1),whereρ<n.Meanwhile,the memory requirements for storing intermediate results are limited to O(C k#/k#^2 )from O(Cn/n^2 ),where k#<n.A case study on learning a standard BN with 50 nodes is conducted.The results demonstrate the superiority of the LOL algorithm,with respect to the Bayesian information criterion(BIC)score criterion,over the hill-climbing,max-min hill-climbing,PC,and three-phrase dependency analysis algorithms.展开更多
针对城市居民区回收箱布局规划和路径优化问题,首先构建居民区回收箱数量与人口、回收频率、回收阈值的线性函数,并构建双层优化模型,回收总利润最大化作为上层目标,运输成本最小化作为下层目标。其次,为求解具有NP-hard特征的新模型,...针对城市居民区回收箱布局规划和路径优化问题,首先构建居民区回收箱数量与人口、回收频率、回收阈值的线性函数,并构建双层优化模型,回收总利润最大化作为上层目标,运输成本最小化作为下层目标。其次,为求解具有NP-hard特征的新模型,设计加入团体学习算子和自适应选择策略的人类学习优化算法,并与禁忌搜索算法嵌套构建混合人类学习算法(hybrid human learning optimization algorithm,HHLO)。再次,采用不同规模算例,并将新算法与基本人类学习算法、遗传算法、自适应粒子群算法、红嘴蓝鹊算法进行对比分析,验证了模型的可行性和算法的有效性。最后,通过上海杨浦区某实例进行灵敏度分析,探讨回收箱容量、分时定价策略和分区定价策略对回收中心总利润与居民满意度的影响。展开更多
基金supported by the National Natural Science Foundation of China(61573285)
文摘It is unpractical to learn the optimal structure of a big Bayesian network(BN)by exhausting the feasible structures,since the number of feasible structures is super exponential on the number of nodes.This paper proposes an approach to layer nodes of a BN by using the conditional independence testing.The parents of a node layer only belong to the layer,or layers who have priority over the layer.When a set of nodes has been layered,the number of feasible structures over the nodes can be remarkably reduced,which makes it possible to learn optimal BN structures for bigger sizes of nodes by accurate algorithms.Integrating the dynamic programming(DP)algorithm with the layering approach,we propose a hybrid algorithm—layered optimal learning(LOL)to learn BN structures.Benefitted by the layering approach,the complexity of the DP algorithm reduces to O(ρ2^n?1)from O(n2^n?1),whereρ<n.Meanwhile,the memory requirements for storing intermediate results are limited to O(C k#/k#^2 )from O(Cn/n^2 ),where k#<n.A case study on learning a standard BN with 50 nodes is conducted.The results demonstrate the superiority of the LOL algorithm,with respect to the Bayesian information criterion(BIC)score criterion,over the hill-climbing,max-min hill-climbing,PC,and three-phrase dependency analysis algorithms.
文摘针对城市居民区回收箱布局规划和路径优化问题,首先构建居民区回收箱数量与人口、回收频率、回收阈值的线性函数,并构建双层优化模型,回收总利润最大化作为上层目标,运输成本最小化作为下层目标。其次,为求解具有NP-hard特征的新模型,设计加入团体学习算子和自适应选择策略的人类学习优化算法,并与禁忌搜索算法嵌套构建混合人类学习算法(hybrid human learning optimization algorithm,HHLO)。再次,采用不同规模算例,并将新算法与基本人类学习算法、遗传算法、自适应粒子群算法、红嘴蓝鹊算法进行对比分析,验证了模型的可行性和算法的有效性。最后,通过上海杨浦区某实例进行灵敏度分析,探讨回收箱容量、分时定价策略和分区定价策略对回收中心总利润与居民满意度的影响。
