WO2022161303A1 - 一种基于复杂网络的关联物品储位优化方法 - Google Patents

一种基于复杂网络的关联物品储位优化方法 Download PDF

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WO2022161303A1
WO2022161303A1 PCT/CN2022/073420 CN2022073420W WO2022161303A1 WO 2022161303 A1 WO2022161303 A1 WO 2022161303A1 CN 2022073420 W CN2022073420 W CN 2022073420W WO 2022161303 A1 WO2022161303 A1 WO 2022161303A1
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community
node
nodes
item
network
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方水良
王思扬
方强
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浙江大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/08—Logistics, e.g. warehousing, loading or distribution; Inventory or stock management
    • G06Q10/087—Inventory or stock management, e.g. order filling, procurement or balancing against orders
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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  • the invention relates to a method for optimizing the storage position of related items based on a complex network, in particular to an optimization method for analyzing the correlation of stored items based on the complex network theory and further distributing the storage positions of the items accordingly.
  • Common storage allocation strategies include positioning storage strategy, random storage strategy, classified storage strategy, near-exit storage strategy, turnover-based storage strategy, association-based storage strategy, and so on.
  • most of the existing technologies are difficult to describe the intricate access correlation between multiple items, and the storage space allocation strategy cannot be well combined with the actual layout characteristics of the warehouse. Therefore, it is necessary to design a storage space allocation method that considers the relevance of items and the frequency of access from a global perspective, so as to meet the needs of efficient warehouse management.
  • the present invention provides a method for optimizing the storage location of related items based on a complex network. Based on the item association network, a storage location optimization method for associated items is proposed.
  • the main contents of the optimization method of the present invention include: 1) building a weighted item association network with each storage item as a network node and the common use frequency of each pair of items as an edge; 2) comprehensively considering the proximity centrality of item nodes and their neighbor node pairs Its importance contribution value, sorts the importance of item nodes, and determines the core node, that is, the starting point of community expansion; 3) Taking the capacity of each shelf as the limit of community volume, and the weighted modularity and dependency as expansion criteria, determine the association of items The community structure of the network; 4) For the community edge nodes, according to the strength of their associations with other communities, determine the storage location of each item.
  • a weighted item association network G (V, E, W), where V is the set of nodes, that is, the set of items to be stored in the warehouse; E is the set of sides e ij (where i, j ⁇ V, e ij ⁇ E), that is, the set of strong and weak associations between items; W is the weight matrix, w ij corresponds to the weight of e ij , and its value is equal to item i ,j
  • the frequency of taking at the same time reflects the strength of the relationship between the item nodes. If an independent node exists, it is removed from the above-mentioned associated network.
  • a community is a set of nodes in a complex network with very close internal connections and sparse connections with other nodes. Aiming at the selection of the core node of the item association network and the initialization of the community structure, the present invention comprehensively considers two factors, the proximity centrality of the node and the contribution value of the importance of the neighbor nodes, to determine the core node of the association network, that is, the community expansion seed node.
  • the specific process includes:
  • the strength si of a node i is equal to the sum of the weights of the edges connected to it:
  • N i represents the set of neighbor nodes of node i, that is, the set of all nodes associated with node i.
  • the shortest path between any two nodes in a weighted network is the most vulnerable branch. which is:
  • h n is the halfway node on each i, j branch, M is a large number, generally take maxw ij +1.
  • each node is equal to the reciprocal of the sum of the shortest paths from the node to all other nodes multiplied by the number of other nodes, namely:
  • n is the total number of nodes in the network.
  • node i For an item association weighted network with n nodes and an average strength of ⁇ s>, node i will assign its own importance to the weighted network. Contribute to its neighbor node j. If the edge weight of node j connected to node i is greater or the strength of node i is greater, then the contribution of node i to the importance of node j is greater. Considering the proximity centrality of a node and the importance contribution of all neighboring nodes to it, the node importance C i (i) can be obtained:
  • ⁇ ij represents the connectivity between two nodes, and the connectivity is 1, otherwise it is 0.
  • the shelf capacity, and the number of network nodes associated with the item are determined.
  • the core node is determined, that is, the starting point of community expansion.
  • the user can set the community size and number of communities according to the specific layout of the warehouse. If there are a total of n shelves, the number of communities can be set to n, or the community size can be determined according to the shelf capacity, which can be set according to needs.
  • the composition of core nodes is determined according to the order of node importance and the number of communities. For example, if the number of shelves is n, the number of communities is determined to be n, and the core node is the node with the top n in importance;
  • the present invention adopts the weighted modularity and the weighted dependency as the community expansion criterion. Specifically, the neighbor nodes of each core node are firstly added to the candidate node set of each community expansion, and the modularity increment ⁇ Q w of each node in the candidate node set joining the corresponding community is calculated:
  • w represents the total weight value of the edges in the weighted network, represents the sum of the edge weights within the community, represents the sum of all edge weights connecting point i and the internal nodes of community C j , Represents the sum of all edge weights associated with the internal nodes of the community. Then select the node with the largest increment from the candidate node set to join the community. If the node has joined other communities, compare the modularity changes when the node belongs to two communities. If the node joins the new community, the modularity increment If it is greater than the modularity increment of keeping the node in the original community, it will be deleted from the original community and added to the new community.
  • the present invention determines the composition of overlapping nodes by comparing and weighting the modularity increments. Specifically, firstly, the nodes at the edge of the community and connected with other communities are added to the potential overlapping node set U, and the modularity increment of each potential overlapping node joining other communities is calculated. Then calculate the modularity increment that keeps the node in the original community and combine it with for comparison, if the difference between the two is less than Then it is considered that the potential overlapping node overlaps with other communities. Finally, the number of nodes that really have overlap between two communities is analyzed, and the degree of overlap between communities is determined by dividing this number by the sum of the number of nodes in the two communities.
  • the present invention proposes a storage allocation strategy that comprehensively considers the community structure of the item association network and the frequency of the item itself. Specifically, the core of this step is to formulate a storage space allocation strategy that matches the current situation of the warehouse according to the warehouse layout and the community structure divided in step (4).
  • the frequency of use of each community divided in step (4) is sorted, and they are allocated to each lane one by one according to the ranking of the community; if a community is allocated, there are still If the number of high-overlapped communities is greater than the number of remaining shelves, the high-overlapped communities with an overlap of more than 10% with the above-mentioned communities will be placed on other shelves in the same lane; if the number of high-overlapped communities is greater than the number of remaining shelves, press
  • the community access frequency determines which high-overlapping community the remaining shelves belong to; if there is no high-overlapping community with an overlap greater than 10%, the remaining shelves are allocated according to the frequency of each community's access; and then the storage spaces in the shelves are allocated.
  • the present invention adopts the evaluation function S i to determine the storage arrangement of items in the community:
  • the storage location optimization method based on the complex network proposed by the present invention fully considers the relationship between each item and all other items, and overcomes the traditional association rule mining.
  • the method is difficult to describe the intricate relationship between multiple items;
  • the present invention uses complex network theory to deal with the relationship between items, which has more advantages in solving efficiency compared with intelligent algorithms such as genetic algorithm and simulated annealing algorithm.
  • the method provided by the present invention can also provide the storage position arrangement faster; (3) the present invention fully combines the community discovery strategy, the storage position allocation strategy and the actual layout mode of the warehouse It makes the storage space allocation result more suitable for the actual operation of the warehouse; (4) the present invention can also be applied to other fields of storage space allocation, such as supermarket distribution system, pharmacy storage system and so on.
  • Fig. 1 The overall process of the storage location optimization method for related items based on a complex network
  • Figure 2 is a schematic diagram of a dual-zone single-channel warehouse
  • Fig. 3 is a schematic diagram of the storage location allocation flow based on the structure of the article community and the frequency of access (taking the dual-zone single-channel warehouse of Fig. 2 as an example);
  • Figure 4 is a schematic diagram of the construction of an item association network
  • Figure 5 Schematic diagram of the distribution result of the association network of the item and the distribution of overlapping nodes.
  • a complex network-based storage location optimization method for associated items includes the following steps:
  • Step (1) Build a weighted item association network.
  • the frequency that i and j are taken at the same time reflects the strength of the relationship between item nodes. If an independent node exists, it is removed from the above-mentioned associated network.
  • Step (2) Rank the importance of item nodes according to the proximity centrality of the node and the importance contribution value of neighbor nodes to it, and determine the core node, that is, the initial node of the community.
  • the strength si of a node i is equal to the sum of the weights of the edges connected to it:
  • N i represents the set of neighbor nodes of node i, that is, the set of all nodes associated with node i.
  • the shortest path between any two nodes in a weighted network is the most vulnerable branch. which is:
  • h n is the halfway node on each i, j branch, and M is a large number.
  • the proximity centrality of each node is equal to the reciprocal of the sum of the shortest paths from the node to all other nodes multiplied by the number of other nodes, namely:
  • n is the total number of nodes in the network.
  • the importance of the item nodes is sorted according to the proximity centrality of the item node and the importance contribution of its neighbor nodes.
  • node i will assign its own importance to the weighted network. Contribute to its neighbor node j. If the edge weight of node j connected to node i is greater or the strength of node i is greater, then the contribution of node i to the importance of node j is greater.
  • the node importance C i (i) can be obtained:
  • ⁇ ij represents the connectivity between two nodes, and the connectivity is 1, otherwise it is 0. Then, according to the total number of shelves in the warehouse, the capacity of the shelves, and the number of network nodes associated with the items, the community body and the number of communities are determined. Finally, the core nodes, that is, the starting point of community expansion, are determined according to the importance of the item nodes and the number of communities.
  • Step (3) Considering the shelf capacity, determine the community structure of the item association network.
  • the neighbor nodes of each core node are added to the candidate node set of each community expansion, and the modularity increment ⁇ Q w of each node in the candidate node set joining the corresponding community is calculated:
  • w represents the total weight value of the edges in the weighted network, represents the sum of the edge weights within the community, represents the sum of all edge weights connecting point i and the internal nodes of community C j , Represents the sum of all edge weights associated with the internal nodes of the community. Then select the node with the largest increment from the set of candidate nodes to join the community. If the node has joined other communities, compare the modularity changes when the node belongs to two communities. If the node joins the new community, the modularity increment If it is greater than the modularity increment of keeping the node in the original community, it will be deleted from the original community and added to the new community.
  • Step (4) Determine overlapping nodes that are strongly related to other communities.
  • the nodes at the edge of the community and connected with other communities are added to the potential overlapping node set U, and the modularity increment of each potential overlapping node joining other communities is calculated. Then calculate the modularity increment that keeps the node in the original community and combine it with for comparison, if the difference between the two is less than Then it is considered that the potential overlapping node overlaps with other communities. Finally, analyze the number of nodes with real overlap between the two communities, and determine the degree of overlap between the communities.
  • Step (5) Determine the storage location of each item based on the community structure of the item association network and the access frequency of the item itself.
  • the core of this step is to formulate a storage space allocation strategy that matches the current situation of the warehouse according to the warehouse layout and the community structure divided in step (4).
  • the frequency of use of each community divided in step (4) is sorted, and they are allocated to each lane one by one according to the ranking of the community; If there are free shelves, consider the degree of overlap between each community, and place the high-overlap community with the above-mentioned community that overlaps more than 10% on other shelves in the same lane; if the number of high-overlap communities is greater than the number of remaining shelves, Then determine which highly overlapping community the remaining shelves belong to according to the frequency of community access; if there is no highly overlapping community with an overlap greater than 10%, the remaining shelves are allocated according to the frequency of each community; and then the storage space in the shelf is allocated.
  • the present invention adopts the evaluation function S i to determine the storage arrangement of items in the community:
  • the number of core nodes is set to 7
  • the number of community bodies is set to 66.
  • community expansion and overlapping node discovery are carried out.
  • the expanded community structure and overlapping nodes The distribution is shown in Figure 5.
  • the number of each community is 66, 65, 63, 58, 57, 54, and 39, which meet the shelf capacity limit.
  • a storage location is allocated for each material.
  • the results of the complex network-based storage location optimization method for related items proposed by the present invention are compared with the results of common storage location allocation methods as shown in Table 2 below.

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Abstract

一种基于复杂网络的关联物品储位优化方法，主要包括以下步骤：1)以仓储物品为网络节点，两两物品的共同取用频率为边，构建加权物品关联网络；2)综合考虑物品节点的接近中心性及其邻居节点对其的重要度贡献值，对物品节点的重要性进行排序，确定社团初始节点；3)以各货架容量为社团体量限制，以加权模块度、依赖度为扩张准则，确定物品关联网络的社团结构；4)对于社团边缘节点，依据其与其他社团关联关系的强弱，判断其是否为重叠节点；5)综合考虑物品关联网络的社团结构和物品自身的取用频率，确定各物品的最佳储位。该方法将复杂网络理论应用到关联物品取用的储位分配问题，减少了物品取用的综合路程及时间，提高了物品取用效率。

Description

一种基于复杂网络的关联物品储位优化方法 技术领域
本发明涉及一种基于复杂网络的关联物品储位优化方法，尤其涉及一种基于复杂网络理论进行仓储物品的关联性分析并据此进一步分配物品储位的优化方法。
背景技术
随着我国经济的高速发展，货架式仓储***已逐步替代陈旧落后的平面仓库，而储位分配问题是影响货架式仓储***出货效率的关键问题；此外，由于物品取用过程往往同时包含两种或多种物品，物品取用存在一定关联性，若能根据关联性优化分配关联物品的储位，将会大大提高物品取用效率。
常见储位分配策略有定位存储策略、随机存储策略、分类存储策略、近出口存储策略、基于周转率的存储策略、基于关联性的存储策略等等。但现有技术大多难以描述多个物品间错综复杂的存取关联性，储位分配策略也未能很好地与仓库实际布局特点结合起来。因此，有必要设计出一种从全局角度考虑物品关联性及取用频率的储位分配方法，以满足高效仓库管理的需要。
发明内容
为克服已有技术的不足，本发明提供一种基于复杂网络的关联物品储位优化方法，该方法是基于复杂网络进行物品关联网络构建与分析，以描述多个物品间错综复杂的关联性，并基于物品关联网络提出关联物品的储位优化方法。
本发明的优化方法主要内容包括：1)以各仓储物品为网络节点，两两物品共同取用频率为边，构建加权物品关联网络；2)综合考虑物品节点的接近中心性及其邻居节点对其的重要度贡献值，对物品节点的重要性进行排序，确定核心节点，即社团扩张起点；3)以各货架容量为社团体量限制，加权模块度、依赖度为扩张准则，确定物品关联网络的社团结构；4)对于社团边缘节点，依据其与其他社团关联关系的强弱，判 确定各物品的储位归属。
具体步骤描述如下：
(1)以仓储物品为网络节点，两两物品共同取用频率为边，构建加权物品关联网络G＝(V,E,W)，其中V是节点集合，即仓库内需要存放的物品集合；E是各边e ij的集合(其中：i,j∈V，e ij∈E)，即物品间的强弱关联集合；W是权重矩阵，w ij对应e ij的权重，其数值等于物品i,j同时取用的频率，反映了物品节点之间关联关系的强弱。若存在独立节点，则将其从上述关联网络中删除。
(2)社团是复杂网络中一组内部联系非常紧密而与其他节点联系较为稀疏的节点集合。针对物品关联网络核心节点选择、社团结构初始化等问题，本发明综合考虑了节点接近中心性、邻居节点重要度贡献值两个因素来确定关联网络的核心节点，即社团扩张种子节点。具体流程包括：
(i)确定节点强度、两两节点间的最短路径
加权物品关联网络中，节点i的强度s i等于与它相连的边的权重之和：
Figure PCTCN2022073420-appb-000001
其中，N i表示节点i的邻居节点集合，即与节点i有关联的所有节点集合。
加权网络中任意两个节点间的最短路径是最容易受到影响的一条支路。即：
Figure PCTCN2022073420-appb-000002
其中，h n为每一条i,j支路上的中途节点，M为一个大数，一般取maxw ij+1。
(ii)根据最短路径计算节点接近中心性
各节点的接近中心性等于节点到其他所有节点最短路径之和的倒数再乘以其他节点个数，即：
Figure PCTCN2022073420-appb-000003
其中，n为网络总节点数。
(iii)在接近中心性的基础上，根据物品节点的接近中心性及其邻居节点对其的重要度贡献值，对物品节点的重要性进行排序
对于一个节点数为n，平均强度为<s>的一个物品关联加权网络，节点i将会把自身重要度的
Figure PCTCN2022073420-appb-000004
贡献给其邻居节点j，若节点j与节点i相连的边权越大或节点i的强度越大，则节点i对节点j的重要度贡献越大。综合考虑节点的接近中心性及其所有邻居节点对其的重要度贡献值，可得到节点重要度C i(i)：
Figure PCTCN2022073420-appb-000005
其中，δ ij表示两节点间的连通情况，连通则取1，否则为0。然后根据仓库内货架总数、货架容量、物品关联网络节点数确定社团体量和社团数，最后根据社团数和物品节点重要度，确定核心节点，即社团扩张起点。使用者可根据仓库具体布局情况设定社团体量和社团数，如总共有n个货架，则可以将社团数设为n，或根据货架容量，确定社团体量，具体可以根据需要进行自行设定；之后按照节点重要度排序及社团数确定核心节点组成，比如：若货架数为n，社团数确定为n，核心节点即为重要度排名前n的节点；
(3)针对物品关联网络的社团结构确定，本发明采用加权模块度和加权依赖度作为社团扩张准则。具体来说，首先将各个核心节点的邻居节点加入各个社团扩张的备选节点集，计算备选节点集中各节点加入对应社团的模块度增量ΔQ w：
Figure PCTCN2022073420-appb-000006
Figure PCTCN2022073420-appb-000007
其中，w表示加权网络中边的总权重值，
Figure PCTCN2022073420-appb-000008
表示社团内部边权重之和，
Figure PCTCN2022073420-appb-000009
表示连接点i和社团C j内部节点的所有边权重之和，
Figure PCTCN2022073420-appb-000010
表示与社团内部节点有关联的所有边权重之和。然后从备选节点集中选取增量最大的节点加入社团，若该节点已加入其它社团，则比较该节点分属于两个社团时的模块度变化情况，若节点加入新社团导致的模块度增量大于将节点保留在原社团的模块度增量，则将其从原社团删除并加入新社团。迭代此过程，直至社团结构不再改变且符合要求或ΔQ w均小于0。若此时仍存在独立节点，则计算该节点对其邻居社团C的依赖度D i,C'，按依赖度排序选择仍未达到社团体量的邻居社团加入。
Figure PCTCN2022073420-appb-000011
(4)针对物品网络中可能出现的社团重叠情况，本发明采用对比加权模块度增量的方式确定重叠节点组成。具体而言，首先将处在社团边缘且与其他社团有连接关系的节点加入潜在重叠节点集合U，计算各潜在重叠节点加入其他社团的模块度增量
Figure PCTCN2022073420-appb-000012
然后计算将节点保留在原社团的模块度增量
Figure PCTCN2022073420-appb-000013
并将其与
Figure PCTCN2022073420-appb-000014
进行对比，若二者差值小于
Figure PCTCN2022073420-appb-000015
则认为该潜在重叠节点与其他社团存在重叠性。最后分析两两社团间真正具备重叠性的节点数，通过将该数除以两社团节点数之和，确定社团间的重叠度。
(5)确定了物品网络的社团结构后，本发明提出综合考虑物品关联网络社团结构和物品自身取用频率的储位分配策略。具体而言，本步骤的核心是根据仓库布局和步骤(4)划分出的社团结构制定与仓库现状匹配的储位分配策略。
以图2所示的双区单通道型仓库为例，首先对步骤(4)划分出的各个社团进行取用频率排序，按社团排名逐个分配至各个巷道；若分配一个社团后巷道内还有空闲货 架，则考虑各个社团间的重叠度，将与上述社团重叠度高于10％的高重叠性社团放置在同巷道内的其他货架上；若高重叠性社团数大于剩余货架数，则按社团取用频率决定剩余货架归属于哪个高重叠性社团；若无重叠度高于10％的高重叠性社团，则按照各社团取用频率分配剩余货架；然后对货架内储位进行分配。由于此种布局下跨巷道拿取均需通过巷道入口，因此无论重叠物品的重叠社团位于哪个巷道，仅需将该物品在原社团内放置得离巷道入口更近，就能减少重叠社团与该物品间的距离。因此本发明采用评价函数S i决定物品在社团内的储位安排：
Figure PCTCN2022073420-appb-000016
其中，COI i代表物品i的取用频率；
Figure PCTCN2022073420-appb-000017
代表该社团内物品的最大取用频率；
Figure PCTCN2022073420-appb-000018
表示重叠物品i与重叠社团C jn相连边权重之和；当i的重叠社团不止一个，为JN个时，
Figure PCTCN2022073420-appb-000019
即表示重叠物品i与其所属的所有外部重叠社团相连边权重之和；
Figure PCTCN2022073420-appb-000020
则表示重叠物品i与其真实所属社团C j相连边的权重之和；δ i是0-1变量，若i是重叠物品，则δ i＝1，否则为0；α，β表示该评价函数两大组成部分的权重，α+β＝1，由于重叠物品与其所属社团内部关系的强弱和它与外部重叠社团关系的强弱较为接近，因此α,β可以均取0.5，若仓库更重视物品本身的取用频率，则α可以适度大于β；然后计算货架内各个储位的到达时间t，在人工拣选仓库中t＝t 步行+t 拿取，即步行时间与站定后垂直拿取时间之和；最后按物品评价函数打分排序和储位到达时间排序完成物品与储位的匹配；若存在独立节点，则按取用频率将其分配至空余货位中。
与现有技术相比，本发明的有益效果主要体现在：(1)本发明提出的基于复杂网络的储位优化方法充分考虑了各个物品与其他所有物品的关联情况，克服了传统关联规则挖掘方法难以描述多个物品间错综复杂的关联关系的问题；(2)本发明采用复杂网络理论处理物品间的关联性，相较于遗传算法、模拟退火算法等智能算法，在求解 效率上更具优势，若一段时间后仓库需要根据需求变动调整储位，本发明提供的方法也能更快给出储位安排；(3)本发明将社团发现策略、储位分配策略与仓库实际布局模式充分结合了起来，使得储位分配结果更切合仓库实际运行情况；(4)本发明还可应用到储位分配的其他领域中，如超市布货***、药房仓储***等。
附图说明
图1基于复杂网络的关联物品储位优化方法整体流程；
图2双区单通道型仓库示意图；
图3基于物品社团结构和取用频率的储位分配流程示意图(以图2的双区单通道型仓库为例)；
图4物品关联网络构建示意图；
图5物品关联网络社团分配结果及重叠节点分布示意图。
具体实施方式
下面结合附图对本发明的技术方案做进一步的说明。
一种基于复杂网络的关联物品储位优化方法，如图1所示，包括以下步骤：
步骤(1)：构建加权物品关联网络。
本发明以各类仓储物品为网络节点，两两物品共同取用频率为边，构建加权物品关联网络G＝(V,E,W)，其中V是节点集合，即仓库内需要存放的物品集合；E是各边e ij的集合(其中：i,j∈V，e ij∈E)，即物品间的强弱关联集合；W是权重矩阵，w ij对应e ij的权重，其数值等于物品i,j同时取用的频率，反映了物品节点之间关联关系的强弱。若存在独立节点，则将其从上述关联网络中删除。
步骤(2)：根据节点的接近中心性和邻居节点对其的重要度贡献值，对物品节点的重要性进行排序，确定核心节点，即社团初始节点。
首先需要确定节点强度、两两节点间的最短路径。加权物品关联网络中，节点i的强度s i等于与它相连的边的权重之和：
Figure PCTCN2022073420-appb-000021
其中，N i表示节点i的邻居节点集合，即与节点i有关联的所有节点集合。
加权网络中任意两个节点间的最短路径是最容易受到影响的一条支路。即：
Figure PCTCN2022073420-appb-000022
其中，h n为每一条i,j支路上的中途节点，M为一个大数。
然后可以根据最短路径计算节点接近中心性，各节点的接近中心性等于节点到其他所有节点最短路径之和的倒数再乘以其他节点个数，即：
Figure PCTCN2022073420-appb-000023
其中，n为网络总节点数。
接着在接近中心性的基础上，根据物品节点的接近中心性及其邻居节点对其的重要度贡献值，对物品节点的重要性进行排序。对于一个节点数为n，平均强度为<s>的一个物品关联加权网络，节点i将会把自身重要度的
Figure PCTCN2022073420-appb-000024
贡献给其邻居节点j，若节点j与节点i相连的边权越大或节点i的强度越大，则节点i对节点j的重要度贡献越大。综合考虑节点的接近中心性及其所有邻居节点对其的重要度贡献值，可得到节点重要度C i(i)：
Figure PCTCN2022073420-appb-000025
其中，δ ij表示两节点间的连通情况，连通则取1，否则为0。然后是根据仓库内货架总数、货架容量、物品关联网络节点数确定社团体量和社团数，最后根据物品节点重要度排序和社团数，确定核心节点，即社团扩张起点。
步骤(3)：考虑货架容量，确定物品关联网络的社团结构。
首先将各个核心节点的邻居节点加入各个社团扩张的备选节点集，计算备选节点集中各节点加入对应社团的模块度增量ΔQ w：
Figure PCTCN2022073420-appb-000026
Figure PCTCN2022073420-appb-000027
其中，w表示加权网络中边的总权重值，
Figure PCTCN2022073420-appb-000028
表示社团内部边权重之和，
Figure PCTCN2022073420-appb-000029
表示连接点i和社团C j内部节点的所有边权重之和，
Figure PCTCN2022073420-appb-000030
表示与社团内部节点有关联的所有边权重之和。然后从备选节点集中选取增量最大的节点加入社团，若该节点已加入其它社团，则比较该节点分属于两个社团时的模块度变化情况，若节点加入新社团导致的模块度增量大于将节点保留在原社团的模块度增量，则将其从原社团删除并加入新社团。迭代此过程，直至社团结构不再改变且符合要求或ΔQ w均小于0。若此时仍存在独立节点，则计算该节点对其邻居社团的依赖度D i,C'，按依赖度排序选择仍未达到社团体量的邻居社团加入。
Figure PCTCN2022073420-appb-000031
步骤(4)：确定与其他社团有较强关联性的重叠节点。
首先将处在社团边缘且与其他社团有连接关系的节点加入潜在重叠节点集合U，计算各潜在重叠节点加入其他社团模块度增量
Figure PCTCN2022073420-appb-000032
然后计算将节点保留在原社团的模块度增量
Figure PCTCN2022073420-appb-000033
并将其与
Figure PCTCN2022073420-appb-000034
进行对比，若二者差值小于
Figure PCTCN2022073420-appb-000035
则认为该潜在重叠节点与其他社团存在重叠性。最后分析两两社团间真正具备重叠性的节点数，确定社团间的重叠度。
步骤(5)：基于物品关联网络的社团结构和物品自身的取用频率，确定各物品的储位归属。
本步骤的核心是根据仓库布局和步骤(4)划分出的社团结构制定与仓库现状匹配的储位分配策略。以双区单通道型仓库(如图2所示)为例，首先对步骤(4)划分出的各个社团进行取用频率排序，按社团排名逐个分配至各个巷道；若分配一个社团后巷道内还有空闲货架，则考虑各个社团间的重叠度，将与上述社团重叠度高于10％的高重叠性社团放置在同巷道内的其他货架上；若高重叠性社团数大于剩余货架数，则按社团取用频率决定剩余货架归属于哪个高重叠性社团；若无重叠度高于10％的高重叠性社团，则按照各社团取用频率分配剩余货架；然后对货架内储位进行分配。由于此种布局下跨巷道拿取均需通过巷道入口，因此无论重叠物品的重叠社团位于哪个巷道，仅需将该物品在原社团内放置得离巷道入口更近，就能减少重叠社团与该物品间的距离。本发明采用评价函数S i决定物品在社团内的储位安排：
Figure PCTCN2022073420-appb-000036
其中，COI i代表物品i的取用频率；
Figure PCTCN2022073420-appb-000037
代表该社团内物品的最大取用频率；
Figure PCTCN2022073420-appb-000038
表示重叠物品i与重叠社团C jn相连边权重之和；当i的重叠社团不止一个，为JN个时，
Figure PCTCN2022073420-appb-000039
即表示重叠物品i与其所属的所有外部重叠社团相连边权重之和；
Figure PCTCN2022073420-appb-000040
则表示重叠物品i与其真实所属社团C j相连边的权重之和；δ i是0-1变量，若i是重叠物品，则δ i＝1，否则为0；α，β表示该评价函数两大组成部分的权重，α+β＝1，由于重叠物品与其所属社团内部关系的强弱和它与外部重叠社团关系的强弱较为接近，因此α,β可以均取0.5，若仓库更重视物品本身的取用频率，则α可以适度大于β；然后计算货架内各个储位的到达时间t，在人工拣选仓库中t＝t 步行+t 拿取，即步行时间与站定后垂直拿取时间之和；最后按物品评价函数打分排序和储位到达时间排序完成物品与储位的匹配；若存在独立节点，则按取用频率将其分配至空余货位中。本步骤具体流程如图3所示。
以下通过一个具体的例子对本实施例中的方法加以进一步说明。
某双区单通道型式仓库布局，现有402种物料存放于7个11列6层的货架上，通过对500余张过往取用出库单分析，可绘制出物料关联网络如图4所示。然后根据式(1)-式(4)计算各物料的重要性如下表1所示。
表1 物料重要度排序
Figure PCTCN2022073420-appb-000041
按照货架容量及物料种类数将核心节点数定为7个，社团体量定为66，然后根据式(5)-式(7)进行社团扩张和重叠节点发现，扩张后的社团结构以及重叠节点分布情况如图5所示，各社团体量为66,65,63,58,57,54,39，符合货架容量限制。最后根据步骤(5)为每种物料分配储位。本发明提出的基于复杂网络的关联物品储位优化方法与常见储位分配方法的结果对比如下表2所示。
表2 各种储位分配方法对比
Figure PCTCN2022073420-appb-000042
以上数据表明，本发明提出的基于复杂网络的关联物品储位优化方法相较于其他常用方法，在缩短拣货时间及减少跨巷道拿取次数方面均有明显成效，能较好地解决关联物品的储位分配优化问题。
以上所述仅为本发明的较佳实施例，仅用于帮助理解本发明，并不用以限制本发明。对于本发明所属技术领域的技术人员，还可依据本发明思想，做出若干简单推演、变形，如根据其他仓库布局模式设计相应货位分配策略等。

Claims (5)

  1. 一种基于复杂网络的关联物品储位优化方法，该方法包括如下步骤：
    步骤1：以仓储物品为网络节点，两两物品共同取用频率为边，构建加权物品关联网络G＝(V,E,W)，其中V是节点集合，即仓库内需要存放的物品集合；E是边e ij的集合，其中：i,j∈V，e ij∈E，即物品间的强弱关联集合；W是权重矩阵，w ij对应e ij的权重，其数值等于物品i,j同时取用的频率，反映物品节点之间关联关系的强弱，若存在独立节点，则将其从上述关联网络中删除；
    步骤2：综合考虑物品节点的接近中心性C c(i)及其邻居节点对其的重要度贡献值
    Figure PCTCN2022073420-appb-100001
    其中s i为节点i的强度，<s>为所有节点的平均强度，对物品节点i的重要性C i(i)进行排序，确定核心节点，作为社团扩张起点；
    步骤3：以各货架容量为社团体量限制，以加权模块度Q w、加权依赖度D i,C'为扩张准则，确定物品关联网络的社团结构；
    步骤4：对于社团边缘节点，依据其与其他社团关联关系的强弱，判断其是否为重叠节点；
    步骤5：综合考虑物品关联网络的社团结构和物品自身的取用频率，确定各物品的储位归属。
  2. 根据权利要求1所述的一种基于复杂网络的关联物品储位优化方法，其特征在于，步骤2具体为：
    (a)分析加权物品关联网络基本结构，计算各物品节点的接近中心性
    在加权物品关联网络中，节点i的强度s i等于与它相连的边的权重之和：
    Figure PCTCN2022073420-appb-100002
    其中，N i表示节点i的邻居节点集合，即与节点i有关联的所有节点集合；
    加权网络中任意两个节点间的最短路径是最容易受到影响的一条支路，即：
    Figure PCTCN2022073420-appb-100003
    其中，h n为每一条i,j支路上的中途节点，M为一个大数；
    此时，各节点的接近中心性等于节点到其他所有节点最短路径之和的倒数再乘以其他节点个数，即：
    Figure PCTCN2022073420-appb-100004
    其中，n为网络总节点数；
    (b)根据物品节点的接近中心性及其邻居节点对其的重要度贡献值，对物品节点的重要性进行排序
    对于一个节点数为n，平均强度为<s>的一个物品关联加权网络，节点i将会把自身重要度的
    Figure PCTCN2022073420-appb-100005
    贡献给其邻居节点j，若节点j与节点i相连的边权越大或节点i的强度越大，则节点i对节点j的重要度贡献越大；综合考虑节点的接近中心性及其所有邻居节点对其的重要度贡献值，得到节点重要度C i(i)：
    Figure PCTCN2022073420-appb-100006
    其中，δ ij表示两节点间的连通情况，连通则取1，否则为0；
    (c)社团是复杂网络中一组内部联系非常紧密而与其他节点联系较为稀疏的节点集合；本步骤将首先根据仓库内货架总数、货架容量、物品关联网络节点数确定社团体量和社团数，然后根据社团数以及物品节点重要度排序，确定核心节点与社团扩张起点组成。
  3. 根据权利要求1所述的一种基于复杂网络的关联物品储位优化方法，其特征在于，步骤3具体为：
    (a)将各个核心节点的邻居节点加入各个社团扩张的备选节点集，计算备选节点集中各节点加入对应社团的模块度增量ΔQ w：
    Figure PCTCN2022073420-appb-100007
    Figure PCTCN2022073420-appb-100008
    其中，w表示加权网络中边的总权重值，
    Figure PCTCN2022073420-appb-100009
    表示社团内部边权重之和，
    Figure PCTCN2022073420-appb-100010
    表示连接点i和社团C j内部节点的所有边权重之和，
    Figure PCTCN2022073420-appb-100011
    表示与社团内部节点有关联的所有边权重之和；
    (b)选取模块度增量最大的节点加入社团，若该节点已加入其它社团，则比较该节点分属于两个社团时的模块度变化情况，若节点加入新社团导致的模块度增量大于将节点保留在原社团的模块度增量，则将其从原社团删除并加入新社团；迭代此过程，直至社团结构不再改变且符合要求或ΔQ w均小于0；若此时仍存在独立节点，则计算该节点对其邻居社团C的依赖度D i,C'，按依赖度排序选择仍未达到社团体量的邻居社团，将该节点加入所述邻居社团，
    Figure PCTCN2022073420-appb-100012
  4. 根据权利要求1所述的一种基于复杂网络的关联物品储位优化方法，其特征在于，步骤4具体为：
    (a)将处在社团边缘且与其他社团有连接关系的节点加入潜在重叠节点集合U，计算各潜在重叠节点加入其他社团的模块度增量
    Figure PCTCN2022073420-appb-100013
    (b)计算将节点保留在原社团的模块度增量
    Figure PCTCN2022073420-appb-100014
    若
    Figure PCTCN2022073420-appb-100015
    和
    Figure PCTCN2022073420-appb-100016
    的差值小于
    Figure PCTCN2022073420-appb-100017
    则认为该潜在重叠节点与其他社团存在重叠性；
    (c)计算两两社团间真正具备重叠性的节点数，通过将该数除以两社团节点数之和，确定社团之间的重叠度。
  5. 根据权利要求1所述的一种基于复杂网络的关联物品储位优化方法，其特征在于，步骤5具体为：
    根据仓库布局情况及所划分出的社团结构，制定储位分配策略；
    首先对划分出的各个社团进行取用频率排序，按社团排名逐个分配至仓库的各个巷道；若分配一个社团后巷道内还有空闲货架，则考虑各个社团间的重叠度，将与上述社团重叠度高于10％的高重叠性社团放置在同巷道内的其他货架上；若高重叠性社团数大于剩余货架数，则按社团取用频率决定剩余货架归属于哪个高重叠性社团；若无重叠度高于10％的高重叠性社团，则按照各社团取用频率分配剩余货架；然后对货架内储位进行分配；单通道布局下跨巷道拿取均需通过巷道入口，因此无论重叠物品的重叠社团位于哪个巷道，仅需将该物品在原社团内放置得离巷道入口更近，就能减少重叠社团与该物品间的距离，因此采用评价函数S i决定物品在社团内的储位安排：
    Figure PCTCN2022073420-appb-100018
    其中，COI i代表物品i的取用频率；
    Figure PCTCN2022073420-appb-100019
    代表该社团内物品的最大取用频率；
    Figure PCTCN2022073420-appb-100020
    表示重叠物品i与重叠社团C jn相连边权重之和；当i的重叠社团不止一个，为 JN个时，
    Figure PCTCN2022073420-appb-100021
    即表示重叠物品i与其所属的所有外部重叠社团相连边权重之和；
    Figure PCTCN2022073420-appb-100022
    则表示重叠物品i与其真实所属社团C j相连边的权重之和；δ i是0-1变量，若i是重叠物品，则δ i＝1，否则为0；α，β表示该评价函数两大组成部分的权重，α+β＝1，然后计算货架内各个储位的到达时间t，在人工拣选仓库中t＝t 步行+t 拿取，即步行时间与站定后垂直拿取时间之和；按物品评价函数打分排序和储位到达时间排序完成物品与储位的匹配；
    最后将可能存在的独立节点，按取用频率将其分配至空余货位中。
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