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Generalized network design problems

Generalized Network Design ProblemsbyCorinne Feremans1,2Martine Labb´e1Gilbert Laporte3March20021Institut de Statistique et de Recherche Op´e rationnelle,Service d’Optimisation,CP210/01, Universit´e Libre de Bruxelles,boulevard du Triomphe,B-1050Bruxelles,Belgium,e-mail: mlabbe@smg.ulb.ac.be2Universiteit Maastricht,Faculty of Economics and Business Administration Depart-ment,Quantitative Economics,P.O.Box616,6200MD Maastricht,The Netherlands,e-mail:C.Feremans@KE.unimaas.nl3Canada Research Chair in Distribution Management,´Ecole des Hautes´Etudes Com-merciales,3000,chemin de la Cˆo te-Sainte-Catherine,Montr´e al,Canada H3T2A7,e-mail: gilbert@crt.umontreal.ca1AbstractNetwork design problems consist of identifying an optimal subgraph ofa graph,subject to side constraints.In generalized network design prob-lems,the vertex set is partitioned into clusters and the feasibility conditionsare expressed in terms of the clusters.Several applications of generalizednetwork design problems arise in theﬁelds of telecommunications,trans-portation and biology.The aim of this review article is to formally deﬁnegeneralized network design problems,to study their properties and to pro-vide some applications.1IntroductionSeveral classical combinatorial optimization problems can be cast as Network Design Problems(NDP).Broadly speaking,an NDP consists of identifying an optimal subgraph F of an undirected graph G subject to feasibility conditions. Well known NDPs are the Minimum Spanning Tree Problem(MSTP),the Trav-eling Salesman Problem(TSP)and the Shortest Path Problem(SPP).We are interested here in Generalized NDPs,i.e.,in problems where the vertex set of G is partitioned into clusters and the feasibility conditions are expressed in terms of the clusters.For example,one may wish to determine a minimum length tree spanning all the clusters,a Hamiltonian cycle through all the clusters,etc.Generalized NDPs are important combinatorial optimization problems in their own right,not all of which have received the same degree of attention by operational researchers.In order to solve them,it is useful to understand their structure and to exploit the relationships that link them.These problems also underlie several important applications areas,namely in theﬁelds of telecommu-nications,transportation and biology.Our aim is to formally deﬁne generalized NDPs,to study their properties and to provide examples of their applications.We willﬁrst deﬁne an uniﬁed notational framework for these problems.This will be followed by complexity results and by the study of seven generalized NDPs.2Deﬁnitions and notationsAn undirected graph G=(V,E)consists of aﬁnite non-empty vertex set V= {1,...,n}and an edge set E⊆{{i,j}:i,j∈V}.Costs c i and c ij are assigned to vertices and edges respectively.Unless otherwise speciﬁed,c i=0for i∈V and c ij≥0for{i,j}∈E.We denote by E(S)={{i,j}∈E:i,j∈S},the subset of edges having their two end vertices in S⊆V.A subgraph F of G is denoted2by F=(V F,E F),V F⊆V,E F⊆E(V F),and its cost c(F)is the sum of its vertex and edge costs.It is convenient to deﬁne an NDP as a problem P associated with a subset of terminal vertices T⊆V.A feasible solution to P is a subgraph F=(V F,E F),where T⊆V F,satisfying some side constraints.If T=V,then the NDP is spanning;if T⊂V,it is non-spanning.Let G(T)=(T,E(T))and denote by F P(T)the subset of feasible solutions to the spanning problem P de-ﬁned on the graph G(T).Let S⊆V be such that S∩T=∅,and denote by F P(T,S)the set of feasible solutions of the non-spanning problem P on graph G(S∪T)that spans T,and possibly some vertices from S.In this framework,feasible NDP solutions correspond to a subset of edges satisfying some constraints.Natural spanning NDPs are the following.1.The Minimum Spanning Tree Problem(MSTP)(see e.g.,Magnanti andWolsey[45]).The MSTP is to determine a minimum cost tree on G that includes all the vertices of V.This problem is polynomially solvable.2.The Traveling Salesman Problem(TSP)(see e.g.,Lawler,Lenstra,RinnooyKan and Shmoys[42]).The TSP consists ofﬁnding a minimum cost cycle that passes through each vertex exactly once.This problem is N P-hard.3.The Minimum Perfect Matching Problem(MPMP)(see e.g.,Cook,Cun-ningham,Pulleyblank and Schrijver[8]).A matching M⊆E is a subset of edges such that each vertex of M is adjacent to at most one edge of M.A perfect matching is a matching that contains all the vertices of G.The problem consists ofﬁnding a perfect matching of minimum cost.This problem is polynomial.4.The Minimum2-Edge-Connected Spanning Network(M2ECN)(see e.g.,Gr¨o tschel,Monma and Stoer[26]and Mahjoub[46].The M2ECN consists ofﬁnding a subgraph with minimal total cost for which there exists two edge-disjoint paths between every pair of vertices.5.The Minimum Clique Problem(MCP).The MCP consists of determining aminimum total cost clique spanning all the vertices.This problem is trivial since the whole graph corresponds to an optimal solution.We also consider the following two non-spanning NDPs.1.The Steiner Tree Problem(STP)(see Winter[61]for an overview).TheSTP is to determine a tree on G that spans a set T of terminal vertices at minimum cost.A Steiner tree may contain vertices other than those of T.These vertices are called the Steiner vertices.This problem is N P-hard.32.The Shortest Path Problem(SPP)(see e.g.,Ahuja,Magnanti and Orlin[1]).Given an origin o and a destination d,o,d∈V,the SPP consists of deter-mining a path of minimum cost from o to d.This problem is polynomially solvable.It can be seen as a particular case of the STP where T={o,d}.In generalized NDPs,V is partitioned into clusters V k,k∈K.We now formally deﬁne spanning and non-spanning generalized NDPs.Deﬁnition1(“Exactly”generalization of spanning problem).Let G= (V,E)be a graph partitioned into clusters V k,k∈K.The“exactly”generaliza-tion of a spanning NDP P on G consists of identifying a subgraph F=(V F,E F) of G yieldingmin{c(F):|V F∩V k|=1,F∈F P( k∈K(V F∩V k))}.In other words,F must contain exactly one vertex per cluster.Two diﬀer-ent generalizations are considered for non-spanning NDPs.Deﬁnition2(“Exactly”generalizations of non-spanning problem).Let G=(V,E)be a graph partitioned into clusters V k,k∈K,and let{K T,K S}be a partition of K.The“exactly”T-generalization of a non-spanning problem NDP P on G consists of identifying a subgraph F=(V F,E F)of G yielding min{c(F):|V F∩V k|=1,k∈K T,F∈F P( k∈K T(V F∩V k), k∈K S V k)}.The“exactly”S-generalization of a non-spanning problem NDP P on G consists of identifying a subgraph F=(V F,E F)of G yieldingmin{c(F):|V F∩V k|=1,k∈K S,F∈F P( k∈K T V k, k∈K S(V F∩V k))}.In other words,in the“exactly”T-generalization,F must contain exactly one vertex per cluster V k with k∈K T,and possibly other vertices in k∈K S V k.In the“exactly”S-generalization,F must contain exactly one vertex per cluster V k with k∈K S,and all vertices of k∈K T V k.We can replace|V F∩V k|=1in the above deﬁnitions by|V F∩V k|≥1 or|V F∩V k|≤1,leading to the“at least”version or“at most”version of the generalization.The“exactly”,“at least”and“at most”versions of a generalized NDP P are denoted by E-P,L-P and M-P,respectively.In the“at most”and in the“exactly”versions,intra-cluster edges are neglected.In this case,we call the graph G,|K|-partite complete.In the“at least”version the intra-cluster edges are taken into account.43Complexity resultsWe provide in Tables1and2the complexity of the generalized versions in their three respective forms(“exactly”,“at least”and“at most”)for the seven NDPs considered.Some of these combinations lead to trivial problems.Obviously,if a classical NDP is N P-hard,its generalization is also N P-hard.The indication“∅is opt”means that the empty set is feasible and is optimal for the correspond-ing problem.References about complexity results for the classical version of the seven problems considered can be found in Garey and Johnson[20].As can be seen from Table2,two cases of the generalized SPP are N P-hard by reduction from the Hamiltonian Path Problem(see Garey and Johnson[20]). Li,Tsao and Ulular[43]show that the“at most”S-generalization is polynomial if the shrunk graph is series-parallel but provide no complexity result for the gen-eral case.A shrunk graph G S=(V S,E S)derived from a graph G partitioned into clusters is deﬁned as follows:V S contains one vertex for each cluster of G, and there exists an edge in E S whenever an edge between the two corresponding clusters exists in G.An undirected graph is series-parallel if it is not contractible to K4,the complete graph on four vertices.A graph G is contractible to an-other graph H if H can be obtained from G by deleting and contracting edges. Contracting an edge means that its two end vertices are shrunk and the edge is deleted.We now provide a short literature review and applications for each of the seven generalized NDPs considered.Table1:Complexity of classical and generalized spanning NDPs Problem MSTP TSP MPMP M2ECN MCP Classical Polynomial N P-hard Polynomial N P-hard Trivial,polynomial Exactly N P-hard[47]N P-hard Polynomial N P-hard N P-hard(with vertexcost)[35]At least N P-hard[31]N P-hard Polynomial N P-hard Equivalent toexactlyAt most∅is opt∅is opt∅is opt∅is opt∅is opt5Table2:Complexity of classical and generalized non-spanning NDPsProblem STP SPPClassical N P-hard PolynomialExactly T-generalization N P-hard PolynomialExactly S-generalization N P-hard N P-hardAt least T-generalization N P-hard PolynomialAt least S-generalization N P-hard N P-hardAt most T-generalization∅is opt∅is optAt most S-generalization N P-hard Polynomial if shrunk graphis series-parallel[43]4The generalized minimum spanning tree prob-lemThe Generalized Minimum Spanning Tree Problem(E-GMSTP)is the problemofﬁnding a minimum cost tree including exactly one vertex from each vertexset from the partition(see Figure1a for a feasible E-GMSTP solution).Thisproblem was introduced by Myung,Lee and Tcha[47].Several formulations areavailable for the E-GMSTP(see Feremans,Labb´e and Laporte[17]).The Generalized Minimum Spanning Tree Problem in its“at least”version(L-GMSTP)is the problem ofﬁnding a minimum cost tree including at least onevertex from each vertex set from the partition(see Figure1b for a feasible solu-tion of L-GMSTP).This problem was introduced by Ihler,Reich and Widmayer[31]as a particular case of the Generalized Steiner Tree Problem(see Section9)under the name“Class Tree Problem”.Dror,Haouari and Chaouachi[11]showthat if the family of clusters covers V without being pairwise disjoint,then theL-GMSTP deﬁned on this family can be transformed into the original L-GMSTPon a graph G′obtained by substituting each vertex v∈ ℓ∈L Vℓ,L⊆K by|L| copies vℓ∈Vℓ,ℓ∈L,and adding edges of weight zero between each pair of thesenew vertices(clique of weight zero between vℓforℓ∈L).This can be done aslong as there is noﬁxed cost on the vertices,and this transformation does nothold for the“exactly”version of the problem.Applications modeled by the E-GMSTP are encountered in telecommuni-cations,where metropolitan and regional networks must be interconnected by atree containing a gateway from each network.For this internetworking,a vertexhas to be chosen in each local network as a hub and the hub vertices must be con-nected via transmission links such as opticalﬁber(see Myung,Lee and Tcha[47]).6Figure 1a: E−GMSTP Figure 1b: L−GMSTPFigure1:Feasible GMSTP solutionsThe L-GMSTP has been used to model and solve an important irrigation network design problem arising in desert environments,where a set of|K|poly-gon shaped parcels share a common source of water.Each parcel is represented by a cluster made up of the polygon vertices.Another cluster corresponds to the water source vertex.The problem consists of designing a minimal length irriga-tion network connecting at least one vertex from each parcel to the water source. This irrigation problem can be modeled as an L-GMSTP as follows.Edges corre-spond to the boundary lines of the parcel.The aim is to construct a minimal cost tree such that each parcel has at least one irrigation source(see Dror,Haouari and Chaouachi[11]).Myung,Lee and Tcha[47]show that the E-GMSTP is strongly N P-hard, using a reduction from the Node Cover Problem(see Garey and Johnson[20]). These authors also provide four integer linear programming formulations.A branch-and-bound method is developed and tested on instances involving up to 100vertices.For instances containing between120and200vertices,the method is stopped before theﬁrst branching.The lower bounding procedure is a heuris-tic method which approximates the linear relaxation associated with the dual of a multicommodityﬂow formulation for the E-GMSTP.A heuristic algorithm ﬁnds a primal feasible solution for the E-GMSTP using the lower bound.The branching strategy performed in this method is described in Noon and Bean[48].A cluster isﬁrst selected and branching is performed on each vertex of this cluster.In Faigle,Kern,Pop and Still[14],another mixed integer formulation for the E-GMSTP is given.The linear relaxation of this formulation is computed for a set of12instances containing up to120vertices.This seems to yield an7optimal E-GMSTP solution for all but one instance.The authors also use the subpacking formulation from Myung,Lee and Tcha[47]in which the integrality constraints are kept and the subtour constraints are added dynamically.Three instances containing up to75vertices are tested.A branch-and-cut algorithm for the same problem is described in Feremans[15].Several families of valid inequalities for the E-GMSTP are introduced and some of these are proved to be facet deﬁputational results show that instances involving up to200vertices can be solved to optimality using this method.A comparison with the computational results obtained in Myung,Lee and Tcha[47]shows that the gap between the lower bound and the upper bound obtained before branching is reduced by10%to20%.Pop,Kern and Still[51]provide a polynomial approximation algorithm for the E-GMSTP.Its worst-case ratio is bounded by2ρif the cluster size is bounded byρ.This algorithm is derived from the method described in Magnanti and Wolsey[45]for the Vertex Weighted Steiner Tree Problem(see Section9).Ihler,Reich,Widmayer[31]show that the decision version of the L-GMSTP is N P-complete even if G is a tree.They also prove that no constant worst-case ratio polynomial-time algorithm for the L-GMSTP exists unless P=N P,even if G is a tree on V with edge lengths1and0.They also develop two polynomial-time heuristics,tested on instances up to250vertices.Finally,Dror,Haouari and Chaouachi[11]provide three integer linear programming formulations for the L-GMSTP,two of which are not valid(see Feremans,Labb´e and Laporte[16]). The authors also describeﬁve heuristics including a genetic algorithm.These heuristics are tested on20instances up to500vertices.The genetic algorithm performs better than the other four heuristics.An exact method is described in Feremans[15]and compared to the genetic algorithm in Dror,Haouari and Chaouachi[11].These results show that the genetic algorithm is time consuming compared to the exact approach of Feremans[15].Moreover the gap between the upper bound obtained by the genetic algorithm and the optimum value increases as the size of the problem becomes larger.5The generalized traveling salesman problem The Generalized Traveling Salesman Problem,denoted by E-GTSP,consists of ﬁnding a least cost cycle passing through each cluster exactly once.The sym-metric E-GTSP was introduced by Henry-Labordere[28],Saskena[56]and Sri-vastava,Kumar,Garg and Sen[60]who proposed dynamic programming formu-lations.Theﬁrst integer linear programming formulation is due to Laporte and Nobert[40]and was later enhanced by Fischetti,Salazar and Toth[18]who in-8troduced a number of facet deﬁning valid inequalities for both the E-GTSP and the L-GTSP.In Fischetti,Salazar and Toth[19],a branch-and-cut algorithm is developed,based on polyhedral results developed in Fischetti,Salazar and Toth [18].This method is tested on instances whose edge costs satisfy the triangular inequality(for which E-GTSP and L-GTSP are equivalent).Moreover heuristics producing feasible E-GTSP solutions are provided.Noon[50]has proposed several heuristics for the GTSP.The most sophis-ticated heuristic published to date is due to Renaud and Boctor[53].It is a generalization of the heuristic proposed in Renaud,Boctor and Laporte[54]for the classical TSP.Snyder and Daskin[59]have developed a genetic algorithm which is compared to the branch-and-cut algorithm of Fischetti,Salazar and Toth[19]and to the heuristics of Noon[50]and of Renaud and Boctor[53].This genetic algorithm is slightly slower than other heuristics,but competitive with the CPU times obtained in Fischetti,Salazar and Toth[19]on small instances, and noticeably faster on the larger instances(containing up to442vertices).Approximation algorithms for the GTSP with cost function satisfying the triangle inequality are described in Slav´ık[58]and in Garg,Konjevod and Ravi [21].A non-polynomial-time approximation heuristic derived from Christoﬁdes heuristic for the TSP[7]is presented in Dror and Haouari[10];it has a worst-case ratio of2.Transformations of the GTSP instances into TSP instances are studied in Dimitrijevi´c and Saric[9],Laporte and Semet[41],Lien,Ma and Wah[44],Noon and Bean[49].According to Laporte and Semet[41],they do not provide any signiﬁcant advantage over a direct approach since the TSP resulting from the transformation is highly degenerate.The GTSP arises in several application contexts,several of which are de-scribed in Laporte,Asef-Vaziri and Sriskandarajah[38].These are encountered in post box location(Labb´e and Laporte[36])and in the design of postal deliv-ery routes(Laporte,Chapleau,Landry,and Mercure[39]).In theﬁrst problem the aim is to select a post box location in each zone of a territory in order to achieve a compromise between user convenience and mail collection costs.In the second application,collection routes must be designed through several post boxes at known locations.Asef-Vaziri,Laporte,and Sriskandarajah[3]study the problem of optimally designing a loop-shaped system for material transportation in a factory.The factory is partitioned into|K|rectilinear zones and the loop must be adjacent to at least one side of each zone,which can be formulated as a GTSP.The GTSP can also be used to model a simple case of the stochastic vehicle routing problem with recourse(Dror,Laporte and Louveaux[12])and some families of arc routing problems(Laporte[37]).In the latter application,a9symmetric arc routing problem is transformed into an equivalent vertex routing problem by replacing edges by vertices.Since the distance from edge e1to edge e2depends on the traversal direction,each edge is represented by two vertices, only one of which is used in the solution.This gives rise to a GTSP.6The generalized minimum perfect matching problemThe E-GMPMP and L-GMPMP are polynomial.Indeed,the E-GMPMP remains a classical MPMP on the shrunk graph,where c kℓ:=min{c ij:i∈V k,j∈Vℓ}for {k,ℓ}∈E S.Moreover the L-GMPMP can be reduced to the E-GMPMP.7The generalized minimum2-edge-connected network problemThe Generalized Minimum Cost2-Edge-Connected Network Problem(E-G2ECN) consists ofﬁnding a minimum cost2-edge-connected subgraph that contains ex-actly one vertex from each cluster(Figure2).Figure2:A feasible E-G2ECN solutionThis problem arises in the context of telecommunications when copper wire is replaced with high capacity opticﬁber.Because of its high capacity,this new technology allows for tree-like networks.However,this new network becomes failure-sensitive:if one edge breaks,all the network is disconnected.To avoid this situation,the network has to be reliable and must fulﬁll survivability condi-tions.Since two failures are not likely to occur simultaneously,it seems reasonable to ask for a2-connected network.10This problem is a generalization of the GMSTP.Local networks have to be interconnected by a global network;in every local network,possible locations for a gate(location where the global network and local networks can be intercon-nected)of the global network are given.This global network has to be connected, survivable and of minimum cost.The E-G2ECNP and the L-G2ECNP are studied in Huygens[29].Even when the edge costs satisfy the triangle inequality,the E-G2ECNP and the L-G2ECNP are not equivalent.These problems are N P-hard.There cannot exist a polynomial-time heuristic with bounded worst-case ratio for E-G2ECNP.In Huy-gens[29],new families of facet-deﬁning inequalities for the polytope associated with L-G2ECNP are provided and heuristic methods are described.8The generalized minimum clique problemIn the Generalized Minimum Clique Problem(GMCP)non-negative costs are associated with vertices and edges and the graph is|K|-partite complete.The GMCP consists ofﬁnding a subset of vertices containing exactly one vertex from each cluster such that the cost of the induced subgraph(the cost of the selected vertices plus the cost of the edges in the induced subgraph)is minimized(see Figure3).Figure3:A feasible GMSCP solutionThe GMCP appears in the formulation of particular Frequency Assignment Problems(FAP)(see Koster[34]).Assume that“...we have to assign a frequency to each transceiver in a mobile telephone network,a vertex corresponds to a transceiver.The domain of a vertex is the set of frequencies that can be assigned to that transceiver.An edge indicates that communication from one transceiver may interfere with communication from the other transceiver.The penalty of an11edge reﬂects the priority with which the interference should be avoided,whereas the penalty of a vertex can be seen as the level of preference for the frequen-cies.”(Koster,Van Hoesel and Kolen[35]).The GMCP can also be used to model the conformations occurring in pro-teins(see Althaus,Kohlbacher,Lenhof and M¨u ller[2]).These conformations can be adequately described by a rather small set of so-called rotamers for each amino-acid.The problem of the prediction of protein complex from the structures of its single components can then be reduced to the search of the set of rotamers, one for each side chain of the protein,with minimum energy.This problem is called the Global Minimum Energy Conformation(GMEC).The GMEC can be formulated as follows.Each residue side chain of the protein can take a number of possible rotameric states.To each side chain is associated a cluster.The vertices of this cluster represent the possible rotameric states for this chain.The weight on the vertices is the energy associated with the chain in this rotameric state. The weight on the edges is the energy coming from the combination of rotameric states for diﬀerent side chains.The GMCP is N P-hard(Koster,Van Hoesel and Kolen[35]).Results of polyhedral study for the GCP were embedded in a cutting plane approach by these authors to solve diﬃcult instances of frequency assignment problems. The structure of the graph in the frequency assignment application is exploited using tree decomposition approach.This method gives good lower bounds for diﬃcult instances.Local search algorithms to solve FAP are also investigated. Two techniques are presented in Althaus,Kohlbacher,Lenhof and M¨u ller[2]to solve the GMEC:a“multi-greedy”heuristic and a branch-and-cut algorithm. Both methods are able to predict the correct complex structure on the instances tested.9The generalized Steiner tree problemThe standard generalization of the STP is the T-Generalized Steiner Tree Prob-lem in its“at least”version(L-GSTP).Let T⊆V be partitioned into clusters. The L-GSTP consists ofﬁnding a minimum cost tree of G containing at least one vertex from each cluster.This problem is also known as the Group Steiner Tree Problem or the Class Steiner Tree Problem.Figure4depicts a feasible L-GSTP solution.The L-GSTP is a generalization of the L-GMSTP since the L-GSTP deﬁned on a family of clusters describing a partition of V is a L-GMSTP.This problem was introduced by Reich and Widmayer[52].The L-GSTP arises in wire-routing with multi-port terminals in physical Very Large Scale Integration(VLSI)design.The traditional model assuming sin-12Figure4:A feasible L-GSTP solutiongle ports for each of the terminals to be connected in a net of minimum length is a case of the classical STP.When the terminal is a collection of diﬀerent pos-sible ports,so that the net can be connected to any one of them,we have an L-GSTP:each terminal is a collection of ports and we seek a minimum length net containing at least one port from each terminal group.The multiple port locations for a single terminal may also model diﬀerent choices of placing a single port by rotating or mirroring the module containing the port in the placement (see Garg,Konjevod and Ravi[21]).More detailed applications of the L-GSTP in VLSI design can be found in Reich and Widmayer[52].The L-GSTP is N P-hard because it is a generalization of an N P-hard problem.When there are no Steiner vertices,the L-GSTP remains N P-hard even if G is a tree(see Section4).This is a major diﬀerence from the classical STP(if we assume that either there is no Steiner vertices or that G is a tree,the complexity of STP becomes polynomial).Ihler,Reich and Widmayer[31]show that the graph G can be transformed(in linear time)into a graph G′(without clusters)such that an optimal Steiner tree on G′can be transformed back into an optimal generalized Steiner tree in G.Therefore,any algorithm for the STP yields an algorithm for the L-GSTP.Even if there exist several contributions on polyhedral aspects(see among others Goemans[24],Goemans and Myung[23],Chopra and Rao[5],[6])and exact methods(see for instance Koch and Martin[33])for the classical problem, only a few are known,as far as we are aware,for the L-GSTP.Polyhedral aspects are studied in Salazar[55]and a lower bounding procedure is described in Gillard and Yang[22].13A number of heuristics for the L-GSTP have been proposed.Early heuris-tics for the L-GSTP are developed in Ihler[30]with an approximation ratio of |K|−1.Two polynomial-time heuristics are tested on instances up to250vertices in Ihler,Reich and Widmayer[31],while a randomized algorithm with polylog-arithmic approximation guarantee is provided in Garg,Konjevod,Ravi[21].A series of polynomial-time heuristics are described in Helvig,Robins,Zelikovsky [27]with worst-case ratio of O(|K|ǫ)forǫ>0.These are proved to empirically outperform one of the heuristic developed in Ihler,Reich and Widmayer[31].In the Vertex Weighted Steiner Tree Problem(VSTP)introduced by Segev [57],weights are associated with the vertices in V.These weights can be negative, in which case they represent proﬁt gained by selecting the vertex.The problem consists ofﬁnding a minimum cost Steiner tree(the sum of the weights of the selected vertices plus the sum of the weights of the selected edges).This problem is a special case of the Directed Steiner Tree Problem(DSP)(see Segev[57]). Given a directed graph G=(V,A)with arc weights,aﬁxed vertex and a subset T⊆V,the DSP requires the identiﬁcation of a minimum weighted directed tree rooted at theﬁxed vertex and spanning T.The VSTP has been extensively studied(see Duin and Volgenant[13],Gorres[25],Goemans and Myung[23], Klein and Ravi[32]).As far as we know,no Generalized Vertex Weighted Steiner Tree Problem has been addressed.An even more general problem would be the Vertex Weighted Directed Steiner Tree Problem.10The generalized shortest path problemLi,Tsao and Ulular[43]describe an S-generalization of the SPP in its“at most”version(M-GSPP).Let o and d be two vertices of G and assume that V\{o,d}is partitioned into clusters.The M-GSPP consists of determining a shortest path from o to d that contains at most one vertex from each cluster.Note that the T-generalization is of no interest since it reduces to computing the shortest paths between all the pairs of vertices belonging to the two diﬀerent clusters.In the problem considered by Li,Tsao and Ulular[43],each vertex is as-signed a non-negative weight.The problem consists ofﬁnding a minimum cost path from o to d such that the total vertex weight on the path in each traversed cluster does not exceed a non-negative integerℓ(see Figure5).This problem with ℓ=1and vertex weights equal to one for each vertex coincides with the M-GSPP.The problem arises in optimizing the layout of private networks embedded in a larger telecommunication network.A vertex in V\{o,d}represents a digital cross connect center(DCS)that treats the information and insures the transmis-sion.A cluster corresponds to a collection of DCS located at the same location14。

Python--深入浅出Apriori关联分析算法（一）

Python--深⼊浅出Apriori关联分析算法（⼀）在美国有这样⼀家奇怪的超市，它将啤酒与尿布这样两个奇怪的东西放在⼀起进⾏销售，并且最终让啤酒与尿布这两个看起来没有关联的东西的销量双双增加。

这家超市的名字叫做沃尔玛。

你会不会觉得有些不可思议？虽然事后证明这个案例确实有根据，美国的太太们常叮嘱她们的丈夫下班后为⼩孩买尿布，⽽丈夫们在买尿布后⼜随⼿带回了他们喜欢的啤酒。

但这毕竟是事后分析，我们更应该关注的，是在这样的场景下，如何找出物品之间的关联规则。

接下来就来介绍下如何使⽤Apriori算法，来找到物品之间的关联规则吧。

⼀. Apriori关联分析概述选择物品间的关联规则也就是要寻找物品之间的潜在关系。

要寻找这种关系，有两步，以超市为例1. 找出频繁⼀起出现的物品集的集合，我们称之为频繁项集。

⽐如⼀个超市的频繁项集可能有{{啤酒,尿布},{鸡蛋,⽜奶},{⾹蕉,苹果}}2. 在频繁项集的基础上，使⽤关联规则算法找出其中物品的关联结果。

简单点说，就是先找频繁项集，再根据关联规则找关联物品。

为什么要先找频繁项集呢？还是以超市为例，你想想啊，我们找物品关联规则的⽬的是什么，是为了提⾼物品的销售额。

如果⼀个物品本⾝购买的⼈就不多，那么你再怎么提升，它也不会⾼到哪去。

所以从效率和价值的⾓度来说，肯定是优先找出那些⼈们频繁购买的物品的关联物品。

既然要找出物品的关联规则有两步，那我们也⼀步⼀步来。

我们会先介绍如何⽤Apriori找出物品的频繁项集，然后下⼀篇会在Apriori处理后的频繁项集的基础上，进⾏物品的关联分析。

⼆. Apriori算法基础概念在介绍Apriori算法之前，我们需要先了解⼏个概念，别担⼼，我们会结合下⾯的例⼦来进⾏说明的。

这些是⼀个超市⾥⾯的⼀部分购买商品记录：2.1 关联分析的⼏个概念⽀持度（Support）：⽀持度可以理解为物品当前流⾏程度。

计算⽅式是：⽀持度 = （包含物品A的记录数量） / （总的记录数量）⽤上⾯的超市记录举例，⼀共有五个交易，⽜奶出现在三个交易中，故⽽{⽜奶}的⽀持度为3/5。

英语跨境电商英语30题

英语跨境电商英语30题1. In cross-border e-commerce, “Fulfillment Center” means _____.A. 销售中心B. 物流中心C. 客服中心D. 采购中心答案：B。

“Fulfillment Center”常见释义为“物流中心”，A 选项“销售中心”常用“Sales Center”；C 选项“客服中心”常用“Customer Service Center”；D 选项“采购中心”常用“Procurement Center”。

2. Which of the following is the correct term for “海关申报” in cross-border e-commerce?A. Custom DeclarationB. Custom ReportC. Custom ApplicationD. Custom Registration答案：A。

“海关申报”常见表达为“Custom Declaration”，B 选项“Custom Report”通常指“海关报告”；C 选项“Custom Application”一般指“海关申请”；D 选项“Custom Registration”常表示“海关登记”。

3. In cross-border e-commerce, “Product Listing” refers to _____.A. 产品清单B. 产品描述C. 产品上架D. 产品评价答案：C。

“Product Listing”常见释义为“产品上架”，A 选项“产品清单”常用“Product List”；B 选项“产品描述”常用“Product Description”；D 选项“产品评价”常用“Product Review”。

4. What does “Drop Shipping” mean in cross-border e-commerce?A. 直接发货B. 代发货C. 批量发货D. 延迟发货答案：B。

apriori用法python

主题：apriori算法在Python中的使用内容：1. 介绍apriori算法- apriori算法是一种经典的关联规则挖掘算法，用于发现数据集中项与项之间的关联关系。

该算法基于Apriori原理，即如果一个项集是频繁的，则它的所有子集都是频繁的。

- apriori算法主要用于市场篮分析、推荐系统和数据挖掘等领域，能够帮助我们发现数据中隐藏的规律和关联性。

2. apriori算法的实现- 在Python中，可以使用mlxtend库中的apriori模块来实现apriori算法。

mlxtend是一个用于提供数据挖掘和机器学习工具的Python库，它包含了许多常用的数据挖掘算法的实现，包括apriori 算法。

3. 安装mlxtend库- 若要使用mlxtend库中的apriori模块，首先需要在Python环境中安装mlxtend库。

可以通过pip命令来进行安装，具体命令如下：```bashpip install mlxtend4. 导入apriori模块- 安装完成mlxtend库后，可以使用import语句将apriori模块导入到Python程序中，具体代码如下：```pythonfrom mlxtend.frequent_patterns import apriori```5. 准备数据集- 在使用apriori算法前，需要准备好待挖掘的数据集。

数据集通常以DataFrame的形式呈现，每一行代表一个样本，每一列表示一个特征。

6. 使用apriori算法- 在准备好数据集后，可以使用apriori函数来进行关联规则挖掘。

apriori函数的参数主要包括数据集、最小支持度和最小置信度等。

```pythonfrequent_itemsets = apriori(df, min_support=0.5,use_colnames=True)```其中，df代表数据集，min_support表示最小支持度，use_colnames表示是否使用列名作为itemsets。

UANTA COMPUTER INC. Quanta LB4M系列二层、三层和IPv6加QoS管理交

4.1
Overview...........................................................................................................49
4.2
How to log in.....................................................................................................49
2.5.6 Quick Start up Downloading from Out-of-Band PC to Switch (Only XMODEM) 44
2.5.7 Quick Start up Downloading from TFTP Server ............................................45
3.3
Set Up your Switch Using Telnet Access...........................................................48
4 Web-Based Management Interface..........................................................................49
6.1.3 show eventlog ..............................................................................................59

OpenText ALM Octane商业发布说明说明书

ALM/Quality Center to ALM Octane Migration Safely and quickly migrate from ALM/Quality Center to ALM OctaneExecutive SummaryIT has a unique opportunity to become theengine that drives innovation, differentiationand business success. As organizations drivetowards the digitization of everything, balanc-ing speed, quality and scale is a key successfactor, but also a challenge for those teamsresponsible for building, testing, and deliveringthe increasingly complex software necessaryto compete in today’s digital marketplace. Manysuch teams are adopting DevOps, Agile devel-opment, Continuous Integration, T esting andDelivery and require a platform to help themestablish and evolve these capabilities.OpenT ext™ Application Lifecycle Management (ALM) Oc t ane is a rich, unified, open platform for your application teams to plan, define, build, test, track, and accelerate the delivery of high-quality applications. It helps teams drive innovation and enhance customer satisfaction with real-time visibility across enterprise proj-ects, Agile release trains, and management of the complete end-to-end pipeline of applica-tion delivery.OpenT ext™ ALM/Quality Center to ALM Octane Migration service from OpenT ext Professional Servi c es helps you transition from traditional delivery to a new way of working. This service not only helps you migrate safely and reliably from ALM/Quality Center with our automated tool, we assist you to decide what you will mi-grate, how to adapt to a new way of working and modernize your application delivery capability. About ALM OctaneALM Octane is a unified platform for defining, managing, and automating activities, gaining in-sight, and sharing assets to deliver applications Figure 1. Capabilities of ALM Octanefrom ideation to production. It manages theprocess and assets from requirements defi-nition through software development, manualand automated testing, defect tracking all theway to the application readiness assessmentfor delivery.ALM Octane integrates with upstream projectportfolio management software and downstreamapplication release automation, continuous de-ployment, monitoring, and incident managementsoftware to drive complete visibility and man-agement of applications from inception to retire-ment. By its nature ALM Octane is your applicationlifecycle platform for the digital revolution.ALM Octane fits within your environment notas a standalone solution but as a convergencepoint for all your application lifecycle solutions.It seamlessly over-arches your ContinuousIntegration and T esting tools, and drives truecollaboration, shift-left quality, innovation andagile delivery.Service OverviewThe ALM/Quality Center to ALM Octane Mi-gration Service is designed to accelerate yourtime to value and get you up and running withALM Octane quickly.Figure 2. ALM/Quality Center to ALM Octane Migration processServices FlyerIt includes the following activities:■Analyze yourALM/Quality Center site and project setup■Planning the migration, understanding what should be migrated and how it canbe migrated■A workshop with your team to understand the differences in working with ALM/Quality Center and ALM Octane and plan for the new way of working■Agile coaching■Prepare environments for testing & production■Preparation of the ALM Octane instances ■Installation of the ALM/Quality Center to A LM Octane migration tool■T est & validate the ALM/Quality Center to ALM Octane migration process■Walkthrough tested migration resultswith stakeholders■Confirm migrated data with stakeholders: Requirements, Manual T ests, T est Runs, Defects, Relationships, User-Defined Fields ■Confirm manually configured items: Workflows, Rules, Forms, Reports and Dashboards■Run the production migration process■Once all projects in scope have been migrated, finalize migration results and confirm that migration is completed BenefitsOur service provides real and tangible benefits:■Expertise, knowledge & insight neededto plan a successful ALM Octane rollout■A reliable, fast and smooth migration using our automated migration tool■Coaching and recommended practices for ALM Octane for a seamless transition, evolving your practices and adopting new capabilitiesThe Professional Services Difference OpenT ext™ provides unmatched capabilities with a comprehensive set of consulting and im-plementation services and unique intellectual property that help you drive innovation through streamlined and efficient software delivery:■Proven OpenT ext software solution implementation expertise■More than 20 years of experience helping large, complex, global organizations realize value from their OpenT ext software investments■Rich intellectual property and unparalleled reach into product engineering■T echnology-agnostic implementation approach with no vendor lock-in, no rip- and-replace■Education and support services to ensure adoptionLearn more atOpenT ext Professional ServicesOpenT ext Application Lifecycle Management Services/opentext261-000176-001 | O | 04/23 | © 2023 Open T ext。

2016沃尔沃经销商大会策划案

19:00-19:30 19:30-19:35 19:35-19:40 19:40-19:50 19:45-19:50 19:50-19:55 19:55-20:05 20:05-20:35 20:35-20:40 20:40-20:45 20:45-20:55 20:55-21:00 21:00-21:05 21:05-21:10 21:10-21:30
Scott Zhu—现场经销商协调 Meky Chi—会场/颁奖/晚宴支持
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Oracle Exadata商品说明书

5 Reasons to run your business on Exadata Oracle Exadata is the only platform that delivers optimum database performance and efficiency for mixed data, analytics, and OL TP workloads. With a full range of deployment options, itallows you to run your Oracle Database and data workloads where you want, how youwant —on-premises, in the Oracle Cloud,Cloud at Customer in your data center , or any combination of these models.Here are five top reasons to chooseExadata to run your business.“ ”We chose Oracle Exadata for its integrated hardware and software platform. It costs 31 percent less than products from other vendors, such as IBM and SAP . By running Oracle’s JD Edwards ERP system on Oracle Exadata, we’ve gained a high-performing, reliable, and scalable database platform that enabled us to create daily sales reports 60x faster,introduce products 36x f a ster, enhanceuser satisfaction, increase IT productivity by 40 percent, and reduce operating costs. D. V. Jachak, General Manager, IT, Sai Prasad GroupZheng Tao, Head of IT, Wumart Stores, Inc.By consolidating 92 percent of our IBM servers and four databases onto a single Oracle Exadata Database Machine, we gained an integrated, high-performing private cloudplatform to support e-business growth. We can process online orders 8x faster, and havereduced operating costs by over 100,000 USD per year. “ ”By consolidating 40 disparate databases on Oracle Exadata Database Machine, we boosted sales and production system performance up to 60 percent and cut initial installation costs by 60 percent. We also enhanced IT governance across the organization, and supported 10 billion USD in turnover via business expansion. Akio Yoshizawa, Senior Manager, IT Infrastructure Solutions Department, NSK Network and Systems Co. Ltd.“ “ Ziraat Bank was alwaysunder pressure to optimizeperformance, because anysmall addition to end-of-dayprocessing could negativelyimpact revenue and the bank’sreputation. Oracle Exadata took all the steam off. We decreased the overnight batch window by more than 60 percent, reduced disk usage by 8x and overallsystem utilization from 70percent to 30 percent, whileimproving uptime for our corebanking online transactionprocessing system. Serdar Mutlu, Manager, Database Systems, T.C. Ziraat Bankasi A.Ş.”Anantha Spirama, VP , Systems and Technology, Macy’s“ Applications, databases,and infrastructure all haveto work together in harmony.When we looked at othercloud providers, they offeredthese in pieces. It was up tous to craft a solution. Oracleoffered an integrated solutionfor me. It was a natural choice. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. Oracle and Java are registered trademarks of Oracle and/or its affiliates. Other names may be trademarks of their respective owners.。

Promotion of Access to Information Manual

ENGINEERING COUNCIL OF SOUTH AFRICAPROMOTION OF ACCESS TO INFORMATION MANUAL Compiled in terms of Section 14 of the Promotion of Access to Information Act, 2 of 2000(“PAIA”)ECSA’S CONTACT DETAILSPostal: Private Bag X691, Bruma, 2026Physical: 1st Floor, Waterview Corner, 2 Ernest Oppenheimer AvenueBruma, 2198Telephone: (011) 607-9500Facsimile: (011) 622-9295Email: ****************.zaWeb: www.ecsa.co.zaCONTENTS1. INTRODUCTION 33 2. THE HUMAN RIGHTS COMMISSION GUIDE AND HOWTO ACCESS IT3. THE STRUCTURE AND FUNCTIONS OF ECSA 44. THE INFORMATION OFFICER OF ECSA 45. RECORDS OF ECSA 56. REQUEST PROCEDURE 66 7. INFORMATION THAT IS READILY AVAILABLE –REQUIRING NO ACCESS REQUEST (SECTION 15 –VOLUNTARY DISCLOSURE NOTICE)6 8. MANDATORY PROTECTION OF CERTAINCONFIDENTIAL INFORMATION INTERMS OF SECTION37 OF PAIA7 9. SERVICES AVAILABLE TO MEMBERS OF THE PUBLICAND HOW TO GAIN ACCESS TO THOSE SERVICES7 10. APPEAL AGAINST REFUSAL OF INFORMATION BY THEINFORMATION OFFICER OF ECSA11. SCHEDULES 8SCHEDULE 1 9 SCHEDULE 2 111. INTRODUCTION1.1 Section 32 of the Constitution of the Republic of South Africa Act, 1996 (Act No. 108 of1996), stipulates that everyone has the right of access to any information held by theState or any another person provided the information is required for the exercise orprotection of any rights. The Act further stipulates that national legislation must beenacted to give effect to this right.1.2 The Promotion of Access to Information Act, 2000 (Act No. 2 of 2000) hereinafterreferred to as “the Act” gives effect to the constitutional right of access to informationheld by any public or private body and required for the exercise or protection of anyrights. The Act details the procedures to be followed when making such request forinformation held either by a public body or private body.1.3 Section 9 of the Act, however, recognizes that such right to access to information issubject to certain justifiable limitations including, but not restricted to:1.3.1 The reasonable protection of privacy;1.3.2 Commercial confidentiality; and1.3.3 Effective, efficient and good governance.1.4 Section 14 of the Act obliges public bodies to compile a Manual to assist a person toobtain access to information held by the public body. The Act also stipulates theminimum requirements with which such a Manual has to comply.1.5 The purpose of this Manual is therefore to inform a person on how to obtain access torecords held by the Engineering Council of South Africa, hereafter referred to as “ECSA”thus giving effect to section 14 of the Act.2. THE HUMAN RIGHTS COMMISSION GUIDE AND HOW TO ACCESS IT2.1 Section 10 of PAIA, requires the Human Rights Commission to compile in each officiallanguage, a guide containing such information, in an easily comprehensible form andmanner, as may reasonably be required by a person who wishes to exercise any rightcontemplated in the Act. The guide must be made available by the Human RightsCommission by 31 August 2003.2.2 The South African Human Rights Commission2.2.1 Address:PAIA UnitThe Research and Documentation DepartmentPrivate Bag 2700Houghton, 20412.2.2 Contact details:Telephone number: (011) 484-8300Telefax number: (011) 484-0582Email address: *************.zaWeb-site address: .za3. THE STRUCTURE AND FUNCTIONS OF ECSA3.1 VISIONEngineering excellence, transforming the nation.3.2 VALUESProfessional – Conduct beyond reproach to the highest ethical standards underpinnedby quality, timeliness, trust and respect.Accountable – Doing what we commit to do in an environment of trust and respect andbeing answerable for our failures to meet our committed obligations.Collaborative – Working as a team to achieve exceptional results.Transparent –Honest and open communication and sharing of information betweenstakeholders.3.3 STRUCTUREThe Engineering Council of South Africa (ECSA) is a statutory body established by theEngineering Profession Act, 46 of 2000 (the EPA). ECSA is one of six Built EnvironmentCouncils. The Council consists of 50 members appointed by the Minister of PublicWorks and is constituted as follows:3.3.1 Thirty registered persons;3.3.2 Ten persons in the service of the State; and3.3.3 Ten members of the public nominated through an open process of publicparticipation.4. THE INFORMATION OFFICER OF ECSAMr Edmund NxumaloExecutive: Regulatory Functions2nd Floor, Waterview Corner2 Ernest Oppenheimer AvenueBruma, 2198.Email: ****************.za5. RECORDS OF ECSAECSA has records on the following (the list is not exhaustive):5.1 Registrations, Continuing Professional Development and Related Forms:5.1.1 Register of all persons registered in terms of the EPA.5.1.2 Registration requirements and Procedures.5.1.3 Personal files of all registered persons.5.1.4 Prescribed forms.5.2 Finance:5.2.1 Copies of cheques and orders.5.2.2 Audited financial statements.5.2.3 Cash books and reconciliation statements.5.2.4 General Ledgers.5.2.5 Trial Balances.5.2.6 Bank Statements.5.2.7 EFT files for transfers.5.2.8 Deposit slips, where applicable.5.2.9 Registered Persons statements of account.5.2.10 Statutory returns.5.2.11 Contracts.5.2.12 Receipt Books.5.2.13 Payment vouchers.5.2.14 Budgets.5.2.15 Minutes of the Audit Committee and Finance and Staff Committee.5.3 Governance and Administration:5.3.1 Agendas and Minutes of Council and Committee Meetings.5.3.2 Operational procedures.5.3.3 Contracts between ECSA and third parties.5.3.4 Memoranda of Understanding between ECSA and third parties.5.3.5 Correspondence between ECSA and third parties.5.4 Support Services:5.4.1 Tender submissions.5.5 Communication and Marketing:5.5.1 Annual Reports.5.5.2 Media Statements.5.5.3 Newsletters.5.5.4 E-Bulletin.5.5.5 Documentation on Engenius.5.6 Human Resources (ECSA Personnel):5.6.1 Human resource policies.5.6.3 Personnel files.5.7 Regulation of the Profession:5.7.1 Information gathered in the investigation of complaints.5.7.2 Investigation reports.5.7.3 Records of all investigations of alleged unprofessional conduct.5.7.4 Code of Conduct.5.7.5 Method of Inquiry.5.7.6 Charge Sheets.5.7.7 Sanctions published in the Government Gazette.6. REQUEST PROCEDURE6.1 Access to the records of ECSA may be requested by:6.1.1 Completing the prescribed request form contained in Schedule 1 to this Manual;6.1.2 Paying the prescribed fee as stated in Schedule 2 to this Manual; and6.1.3 Delivering the request form and applicable payment to the Information Officer ofECSA.6.2 Any requester who is aggrieved by the decision of the Information Officer to refuseaccess to a record may appeal in writing against the decision to the Chief ExecutiveOfficer of ECSA within 60 (sixty) days of the Information O fficer’s decision.6.3 Any requester who is aggrieved by the decision of the Chief Executive Officer (CEO) onappeal may apply to a competent court for appropriate relief as contemplated in Section78 of the Promotion of Access to Information Act, 2 of 2000.RMATION THAT IS READILY AVAILABLEAll information on the ECSA website is freely available.8.MANDATORY PROTECTION OF CERTAIN CONFIDENTIAL INFORMATION IN TERMS OFSECTION 37 OF PAIA AND CLASSIFIED AS SUCH.8.1 Reports produced by registered persons appointed to investigate cases of potentialimproper conduct by a registered person.8.2 Referee reports for purposes of registration.8.3 Council and Committee minutes and records.8.4 Information held in the Registration, Continuous Professional Education (CPD),Educational Qualifications, Investigations and related files in respect of personsregistered with ECSA.8.5 Any other information which in Council’s view is confidential.9.SERVICES AVAILABLE TO MEMBERS OF THE PUBLIC (and how to gain access tothose services)ECSA is a statutory body and does not offer general services to the public. However a member of the public may at any time:9.1 Ascertain the registration status, category and engineering discipline of registeredpersons.9.2 Lodge a complaint against registered persons for investigation of potential breach of theCode of Conduct.10. APPEAL AGAINST REFUSAL OF INFORMATION BY THE INFORMATION OFFICER10.1 If a request for information in terms of PAIA had been refused by the InformationOfficer, the requester may, within 60 days and in the prescribed form and againstpayment of the prescribed appeal fee, lodge an internal appeal against the decision ofthe Information Officer in accordance with the provisions of Section 75 of PAIA. If aninternal appeal is lodged after expiry of the prescribed period, the CEO may, subjectto good and reasonable cause being shown, condone such late lodging subject tosubmission of an affidavit containing reasons for late submission. Such an appeal willbe heard by the CEO.10.2 When deciding on an internal appeal, the CEO may confirm the original decision beingappealed, or substitute a new decision in its place. This decision will be made within30 days of receipt by the CEO of the appeal and notice will be given to all partiesconcerned. The notice will state reasons for the decision, but will exclude anyreference to the content of the record being requested. It will also state that theappellant, third party or requester, as the case may be, may lodge an application witha court against the decision on this internal appeal within 30 days of such a decision.The application to court procedure is set out in the Promotion of Access to InformationAct under Part 4, Chapter 2.10.3 If the internal appeal is upheld, the CEO will immediately give the requester access tothe record concerned.10.4 If the CEO fails to give notice of a decision on an internal appeal to the appellantwithin the 30-day period, then, for purposes of PAIA, this appeal is regarded as havingbeen dismissed.11.SCHEDULESThe following schedules form part of this Manual:Schedule 1: Application for Access to Information.Schedule 2: Prescribed Fee Scales.Schedule 1Application for Access to InformationENGINEERING COUNCIL OF SOUTH AFRICA (ECSA)Please note that ECSA has policies governing routine requests and you should first approach ECSA’s Information Officer if your request is routine, (see Item 7 of ECSA’s manual). The privacy of Council and Committee members and personnel will be protected. You may be requested to complete this form which may be directed to the Information Officer if the request is considered non-routine.PLEASE RETURN THIS FORM TO THE INFORMATION OFFICERThe following information will be needed by ECSA to process your request and you are requested to provide as much information as you can to facilitate our processing of your application. Please provide contact details within the Republic of South Africa.1. Contact detailsName: IdentityNumber:Postal Address: CodeFax number:E-mail address:Date of request:2. Access request (please use a separate sheet if required. – all additional sheets must besigned):2.1 Description of the information required. Please provide enough information, includingreference number if known to you, so that we are able to identify the particular record towhich you are requesting access.2.2 Please specify the nature of the access you require. Note that where necessary we willcharge for the service and for copies.2.3 Fees2.4 Please specify the right you want to exercise or protect by requesting this access andexplain why access to this information will enable you to exercise or protect that right.2.5 We will notify you of the outcome of our decision as soon as we are able to do so – wewill send the notification to the above postal address. Please stipulate with reasons ifyou require the outcome of our decision to be communicated in any other way.Signature: __________________________________________(In accordance with Government Gazette Notice No. R187 of 15 February 2002)Schedule 2Prescribed Fee ScalesENGINEERING COUNCIL OF SOUTH AFRICA (ECSA)Part II of Notice 187 in the Government Gazette on the 15th February 2002 Fees in respect of Public Bodies.1. The fee for a copy of the manual as contemplated in regulation 5(c) is R0, 60 for everyphotocopy of an A4-size page or part thereof.2. The fees for reproduction referred to in regulation 7(1) are as follows:R(a) For every photocopy of an A4-sized page or part thereof 0,60(b) For every printed copy of an A4-size page or part thereof heldon a computer or in an electronic or machine-readable form 0,40(c) For a copy in a computer-readable form on:(i) Stiffy disc 5,00(ii) compact disc 40,00(d) (i) For a transcription of visual images, for an A4-sizepage or part thereof 22,00 (ii) For a copy of visual images 60,00(e) (i) For a transcription of an audio record, for an A4-size page or part thereof 12,00 (ii) For a copy of an audio record 17,003. The request fee payable by every requester, other than a personal requester, referred to inregulation 7(2) is R35, 00.4. The access fees payable by a requester referred to in regulation 7(3) are as follows:R1 (a) For every photocopy of an A4-sized page or part thereof 0,60(b) For every printed copy of an A4-size page or part thereof0,40held on a computer or in an electronic or machine-readableform(c) For a copy in a computer-readable form on:(i) Stiffy disc 5,00(ii) compact disc 40,00(d) (i) For a transcription of visual images, for an A4-size pageor part thereof 22,00 (ii) For a copy of visual images 60,00(e) (i) For a transcription of an audio record, for an A4-size page or part thereof 12,00(ii) For a copy of an audio record 17,00(f) To search for and prepare the record for disclosure, R15.00 for each hour orpart of an hour or part of an hour, excluding the first hour, reasonably required5. The actual postage is payable when a copy of a record must be posted to a requester.。

林青霞电影

CLAMP

专利名称：CLAMP发明人：DAI, ALEX,戴健郎申请号：CN2014/089985申请日：20141031公开号：WO2015/070710A1公开日：20150521专利内容由知识产权出版社提供专利附图：摘要：A clamp (1), comprising a first clamp body (10), a second clamp body (20), a first elastic piece (30) and a bridge mechanism (40); the first clamp body (10) has a conductive first jaw portion (11); the second clamp body (20) is pivotally connected to the first clamp body (10); two ends of the first elastic piece (30) respectively and flexibly press betweenthe first clamp body (10) and the second clamp body (20); the bridge mechanism (40) comprises a reciprocating assembly (41), a stop assembly (42) and an operating piece (43) movably disposed on the first clamp body (10); the stop assembly (42) is disposed between the reciprocating assembly (41) and the operating piece (43), and the stop assembly (42) and the reciprocating assembly (41) are mutually independent and separated; the reciprocating assembly (41) is movable between a first position and a second position; the stop assembly (42) is movable between a third position and a fourth position; the operating piece (43) is movable between a fifth position and a sixth position; when the operating piece (43) is located at the fifth position, and the stop assembly (42) is located at the third position, the reciprocating assembly (41) is stopped by the stop assembly (42) and is located at the second position, and enables electrical conductivity between the first jaw portion (11) and an electrode via the reciprocating assembly (41); and when the operating piece (43) is located at the sixth position, the reciprocating assembly (41) is not stopped by the stop assembly (42) and can be located at the first position and is not connected to the first jaw portion (11).申请人：DAI, Alex,戴健郎地址：432 CN,432 CN国籍：CN,CN代理人：BEIJING BEIXIN-ZHICHENG INTELLECTUAL PROPERTY AGENT CO., LTD.,北京北新智诚知识产权代理有限公司更多信息请下载全文后查看。

Python与Hootsuite自动化社交媒体管理

Python与Hootsuite自动化社交媒体管理在当今数字化的时代，社交媒体已经成为企业和个人推广品牌、与受众互动以及获取信息的重要渠道。

然而，管理多个社交媒体平台可能是一项繁琐且耗时的任务。

这就是为什么自动化工具变得如此重要，而 Python 和 Hootsuite 的结合为我们提供了强大的解决方案。

Python 作为一种强大的编程语言，具有广泛的应用领域，包括数据科学、机器学习、Web 开发等等。

在社交媒体管理方面，Python 可以发挥其优势，帮助我们实现各种自动化任务。

首先，Python 可以用于数据收集和分析。

通过使用相关的库，如｀requests` 和｀BeautifulSoup`，我们能够从社交媒体平台上抓取数据，例如用户的评论、点赞数、分享数等。

这些数据可以为我们提供有关受众行为和兴趣的有价值洞察，从而帮助我们制定更有效的社交媒体策略。

其次，Python 能够实现内容的自动化生成。

借助自然语言处理库，如｀NLTK` 和｀SpaCy`，我们可以根据给定的主题或关键词生成吸引人的文案。

这不仅节省了时间，还确保了内容的一致性和质量。

再者，Python 可以用于自动化的社交媒体发布。

我们可以编写脚本，将预先准备好的内容按照预定的时间和频率发布到不同的社交媒体平台上，确保我们的信息能够及时传达给受众。

Hootsuite 则是一款知名的社交媒体管理平台，它集成了多个社交媒体渠道，如 Facebook、Twitter、Instagram 等，为用户提供了一个集中管理的界面。

Hootsuite 的主要优势之一是其强大的调度功能。

用户可以轻松安排帖子的发布时间，确保在最佳的时间段与受众互动。

此外，它还提供了监控和分析工具，让我们能够实时跟踪帖子的表现，了解哪些内容最受欢迎，哪些需要改进。

当 Python 与 Hootsuite 结合使用时，其效果更是显著。

我们可以使用 Python 编写脚本来与 Hootsuite 的 API 进行交互，实现更高级的自动化功能。

Python商业应用案例分享

Python商业应用案例分享Python是一种流行的开源编程语言，用于各种各样的应用程序开发。

它是一种通用性强、简单易学、高效的编程语言，拥有大量的库和模块，使得开发人员能够快速创建高质量的应用程序。

Python不仅被广泛用于科学计算、机器学习和Web开发，还可以用于商业应用程序的开发。

在本文中，我们将分享一些Python商业应用案例，希望给您带来一些启示和灵感。

财务分析众所周知，财务分析是企业管理中至关重要的一环。

Python可以轻松地处理和分析大规模数据集，使其成为一项理想的工具来进行财务分析。

Python在财务分析方面的应用案例很多，其中之一是公司中点（Point72）。

他们开发了一个名为“公式一”的系统，能够将数千种基于API的金融数据源和机器学习算法结合起来。

这个系统具有规模化、可扩展性和反应速度快的特点，帮助他们进行了大量的量化分析，有效提高了决策效率。

另一个例子是Bloomberg终端。

Bloomberg终端是一个广泛使用的金融新闻和数据平台，拥有大量的数据分析工具。

Python成为Bloomberg平台的关键工具之一，许多Python库和模块被用于解决金融数据分析和预测问题，帮助从业者快速制定策略。

Python在金融领域的应用不止于此，还有Algorithmia、Eveoh、Quandl等等许多公司都在不断探索Python在财务分析方面的应用。

可以看到，Python在财务分析方面的应用非常广泛，成为企业决策的重要工具。

物流管理Python可以帮助企业管理物流和库存。

例如，一个名为Kuehne + Nagel的公司，他们在全球范围内提供优质的物流服务。

他们开发了一个名为“KN Login”的Web应用程序，使用Python实现核心算法，帮助他们优化了物流计划和库存管理。

另一个例子是NTT数据，他们开发了一个名为“Nysle”的物流管理软件。

这个软件使用Python作为主要编程语言，并使用大量库和模块，以便快速分析、构建图表和生成报告。

python航空公司的超额售票策略

python航空公司的超额售票策略
超额售票策略是指航空公司为了避免因乘客取消或改签航班而导致座位空缺，会在预售每个航班的座位数量时留出一定的空缺率，然后在航班起飞前不断地售票，超过实际座位数量，以确保每个座位都能被占用。

这种策略在名为“双倍坐骑”（Double Booking）的情况下实现。

Python航空公司超额售票策略的实现方式如下：
1. 在预售每个航班的座位数量时留出一定的空缺率，例如预售座位数量是100个，留出10%的空缺率，即为90个座位。

2. 在航班起飞前，不断地售票，超过实际座位数量，以确保每个座位都能被占用。

例如，如果航班实际座位数量是100个，那么我们可以售出110张机票。

3. 在乘客取消或改签航班时，及时安排其他乘客填补空缺的座位。

在这种情况下，航空公司需要在保持超额售票策略的同时确保不会超售太多。

4. 航空公司需要通过不断地优化算法和技术手段，以最小的代价和风险来实现超额售票策略。

例如，可以通过机器学习和数据分析来预测乘客改签和取消情况，以及根据乘客的历史乘坐数据等信息来确定超售数量。

超额售票策略对航空公司来说是一种风险管理的策略，可以在保证收益最大化的
同时提高每个航班的利用率。

但是，过度的超售可能会影响乘客体验和信任度，影响航空公司的品牌形象和声誉。

因此，航空公司需要在超售数量和风险之间找到平衡点，以提高乘客满意度和忠诚度。

Python与Hootsuite自动化社交媒体管理

Python与Hootsuite自动化社交媒体管理在当今数字化的时代，社交媒体已经成为企业和个人进行品牌推广、沟通交流和获取信息的重要渠道。

然而，随着社交媒体平台的不断增加和用户需求的日益多样化，手动管理社交媒体变得越来越困难和耗时。

这时候，自动化工具就成为了提高社交媒体管理效率和效果的关键。

Python 和 Hootsuite 就是两个在自动化社交媒体管理方面表现出色的工具。

Python 作为一种强大的编程语言，具有丰富的库和工具，使其非常适合用于社交媒体管理的自动化任务。

无论是数据收集、分析、内容生成还是发布，Python 都能提供高效的解决方案。

首先，Python 可以用于收集社交媒体数据。

通过使用像｀requests` 和｀beautifulsoup` 这样的库，我们可以从各种社交媒体平台获取有价值的信息，例如用户评论、点赞数、分享数等。

这些数据可以帮助我们了解用户的行为和偏好，从而优化我们的社交媒体策略。

其次，Python 能够进行数据分析。

收集到的数据需要进行分析才能得出有意义的结论。

使用｀pandas` 和｀numpy` 等库，我们可以对数据进行清洗、处理和可视化，发现趋势、模式和异常值。

例如，我们可以分析不同时间段的帖子互动情况，找出最佳的发布时间。

再者，Python 还能用于内容生成。

利用自然语言处理技术和机器学习算法，我们可以使用 Python 生成吸引人的社交媒体文案、标题和描述。

这不仅节省了时间，还能确保内容的质量和一致性。

Hootsuite 则是一款专门为社交媒体管理设计的综合性平台。

它支持多个社交媒体平台的集成，包括 Facebook、Twitter、Instagram 等，让用户可以在一个界面上管理所有的社交媒体账号。

Hootsuite 的一个重要功能是排程发布。

用户可以提前准备好帖子内容，并设置在特定的时间自动发布。

这对于保持社交媒体账号的活跃度和一致性非常有帮助，尤其是对于那些在不同时区有受众的企业。

基于果蝇优化算法的超临界机组主蒸汽温度控制

基于果蝇优化算法的超临界机组主蒸汽温度控制发布时间：2021-05-11T03:09:25.136Z 来源：《中国电业》（发电）》2021年第1期作者：罗家运[导读] 主汽温调节扰动因素过多，影响过程复杂多变，控制过程的可控程度很低，被控对象变量有很多[6]。

广东粤电花都天然气热电有限公司广东广州 510000摘要：主蒸汽温度控制是超临界机组控制系统的重要控制环节。

主蒸汽温度是超临界机组的主要参数，主蒸汽温度过高过低，都将会损坏机组重要设备甚至危及火电机组运行的安全经济性。

由于被控对象具有大惯性、迟延大、干扰因素多等特点[1]，传统的的常规串级PID控制器很难实现最佳的控制效果。

果蝇优化算法具有简单容易理解、寻优效率高、收敛可靠性稳定的特点，将其应用于主汽温控制系统PID参数优化中[2]。

通过MATLAB仿真，对主汽温跟踪性能分析。

仿真结果表明，基于果蝇优化算法的FOA-PID控制比传统PID控制响应更快，抗干扰性能和鲁棒性性能更好。

关键词: 超临界机组；主汽温控制；果蝇优化算法；PID参数优化Abstract：Main steam temperature control is an important part of supercritical unit control system. The main steam temperature is the main parameter of supercritical unit. If the main steam temperature is too high or too low, it will damage the important equipment of unit, even endanger the safety and economy of thermal power unit. The controlled object has the characteristics of large inertia, large delay and many interference factors, the traditional cascade PID controller is difficult to achieve the best control effect.Drosophila optimization algorithm has the characteristics of simple and easy to understand, high optimization efficiency and stable convergence reliability. It is applied to PID parameter optimization of main steam temperature control system.To use the MATLAB to analysis the main steam temperature performance. Simulation results show that the FOA-PID control based on fruit fly optimization algorithm response faster than traditional PID control, and has better anti-jamming performance and robustness performance.Key words: Supercritical unit;Main steam temperature control;Fruit fly optimization algorithm; PID parameter optimization0 前言主汽温调节扰动因素过多，影响过程复杂多变，控制过程的可控程度很低，被控对象变量有很多[6]。

python企业案例

python企业案例Python是一种广泛使用的高级编程语言，它简单易学、开发效率高，因此在众多企业中得到了广泛应用。

下面我将列举出10个Python 企业案例，以展示Python在不同行业中的应用。

1. AirbnbAirbnb是一家知名的共享经济平台，它使用Python开发了自己的后端服务，包括网站和移动应用程序。

Python的简洁和高效使得Airbnb能够快速迭代和扩展其平台，满足不断增长的用户需求。

2. DropboxDropbox是一家云存储服务提供商，它的后端基础设施主要使用Python构建。

Python的扩展性和灵活性使得Dropbox能够高效地处理大量的文件上传、下载和同步操作，为用户提供可靠的云存储服务。

3. InstagramInstagram是一家全球知名的社交媒体平台，它的后端服务主要使用Python编写。

Python的简洁和易用性使得Instagram能够快速开发和部署新功能，同时保持高性能和可靠性。

4. SpotifySpotify是一家流媒体音乐平台，它的后端服务主要使用Python开发。

Python的丰富的第三方库和框架使得Spotify能够高效地处理大量的音乐数据，并向用户提供个性化的音乐推荐服务。

5. NetflixNetflix是一家全球知名的在线视频平台，它的后端服务主要使用Python编写。

Python的高效和可扩展性使得Netflix能够处理大量的视频流并实时推送给用户，同时提供个性化的视频推荐服务。

6. NASANASA（美国国家航空航天局）在航天探索和科学研究中广泛使用Python。

Python的易学性和强大的科学计算库使得NASA的科学家能够高效地处理和分析大量的数据，并进行模拟和预测。

7. GoogleGoogle是全球最大的搜索引擎和互联网技术公司，它在很多项目中使用Python。

Python的简洁和高效使得Google能够快速开发和部署新功能，同时保持高性能和可扩展性。

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