CN101261654A - Recursion optimization algorithm for drainpipe network - Google Patents

Abstract

The invention relates to a drainpipe network recursion optimizing arithmetic. The arithmetic adopts a graphic matrix to manage a drainpipe network system, and the serial numbers of a pipe network system of a fixed drainpipe network arrangement graph are adopted to define a pipe network relation matrix M (i, j), as shown in the graph, wherein, i represents a node row variable and j represents a pipe section line variable; the nodes in the pipe network are taken as objects, an optional initial calculation node is appointed, and a node recursion arithmetic is adopted to traverse all the nodes and the pipe sections of the pipe network. In the invention, the serial number sequences of the nodes and the pipe sections in the pipe network are not needed to be defined strictly and are free from the impact of node positions, thus leading the arrangement of the pipe network to be more flexible. Just one-time circulation can solve the problem of the optimization of the whole pipe network system so as to maximally optimize and reduce project investment and enhance the feasibility and the reliability of project design.

Description

Recursion optimization algorithm for drainpipe network

Technical field

The present invention relates to the optimal design and the calculating of drainage pipeline networks in the municipal works, comprise sewage, Storm Sewer Network engineering, combined system pipe-networks engineering etc., be specifically related to the recursive optimization algorithm of a kind of drainage pipeline networks flow, waterpower calculating.

Background technology

Urban drainage pipe network is one of important city foundation works facility, is undertaking sewage such as collecting urban life and commercial production, is in time getting rid of and drop in the city proper and the task of the rainwater in the urban district of flowing through.The quality of drainage system facilities design and construction and science are directly determining the development level in city to affect urban look and hygienic conditions, affect the investment environment in city, even are related to the safety in city.Therefore, scientific and reasonable design sewerage pipeline network is an important ring of city foundation works Facilities Construction, and the investment of job facilities and the reliability of operational management are played key effect.Since the sixties in 20th century, on the basis of summary of experience and mathematical analysis, progressively set up the mathematic(al) mode of various water supply and sewerage systems or process in the world; From the seventies so far, the U.S., Japan and some European developed countries, at water supply and drainage pipeline and treatment project system aspects, various achievements in research not only on methodology and computer program, have been obtained, and the increasingly extensive various calculation procedure software application that it is developed are managed remarkable benefit in the computer-aided design (CAD) and the automatic operating of Water and Waste Water Engineering; China is the optimization expert with the famous professor Yang Qinwei of environmental engineering institute of Tongji University representative in the seventies, has opened up the frontier of Water and Waste Water Engineering optimal design, lays a good foundation for carry out optimal design comprehensively.

The sewerage system optimal design under the fixed tube line mainly is the design parameter optimization problem that solves between caliber and buried depth (gradient) and different pipe sections.For a certain design pipeline section, after flow was determined, the caliber and other hydraulic parameters that satisfy the design specifications requirement had multiple combination, but always have the combination of one group of caliber and other hydraulic parameters, made its investment minimum, and effect is best.For the sewerage pipeline network of being made up of some pipeline sections, the design calculation result of upstream pipeline section will directly have influence on the design parameter of downstream pipeline section, and this can not guarantee the devise optimum of total system with regard to the combination of every pipeline section devise optimum in the illustrative system.Therefore, in order to make whole engineering system devise optimum, just must be whole with the whole drainage system, proceed from the situation as a whole to be optimized design.

Aspect the sewerage system Optimal design and calculation, mainly contain linear programming technique, mixed integer programming method, Nonlinear Programming Method, penalty function discrete optimization method, dynamic programming and unfavourable balance dynamic programming, direct optimization, genetic algorithm etc.From research in the past, use the several problems that mainly face when common optimization method carries out sewerage system Optimal design and calculation under the fixed tube line and be: (1) pipe diameter is not continuous, but discrete specification caliber; (2) objective function of calculation model for design and constraint condition are non-linear mostly, therefore calculate relative complex; (3) optimizing process long operational time, committed memory amount are big; (4) do not satisfy " without aftereffect " between the design of pipeline section and pipeline section; (5) the human intervention factor is more, can not transfer to computing machine fully and finish.(6) more crucial be its result of calculation only at specific pipe network, algorithm also is to determine according to the shape of pipe network, is not suitable for the calculating of other pipe network.If realize the management and the computation optimization of pipe network, must a kind of brand-new pipe network computing method of exploitation.

Summary of the invention

The invention discloses a kind of recursion optimization algorithm for drainpipe network, its purpose is to overcome existing sewerage system Optimal design and calculation only at specific pipe network, and does not have promotional value; Computation model complicated calculations workload is big; Optimizing process long operational time, committed memory amount are big; Do not satisfy " without aftereffect " between pipeline section and the pipeline section design; And the human intervention factor is more, can not transfer to computing machine fully and drawback such as finish.The present invention proposes the node recursive algorithm of pipe network graphics management and computation optimization, genetic manipulations such as the coding that uses in the employing genetic technique field, selection, finally try to achieve optimum solution, genetic algorithm is not only applicable to the optimization problem of pure mathematics, and be applicable to sewer system Optimal design and calculation under the fixed tube line, can be used for solving the optimal design problem of other sewerage pipeline network such as Storm Sewer Network system and combined system pipe network system etc. equally.

Recursion optimization algorithm for drainpipe network is characterized in that: adopt pattern matrix management sewerage pipeline network, by the numbering of the pipe network system of deciding the drainage pipeline networks arranging graphic, determine pipe network relational matrix M (i, j), described pipe network relational matrix M (i, j)

Be expressed as follows:

Wherein i is the capable variable of node, and j is pipeline section row variablees; With the node in the pipe network is object, specifies the arbitrary initial computing node, adopts node recursive algorithm traversal all nodes of pipe network and pipeline section, can once solve the design problem of drainage pipeline networks.

Described numbering comprises node serial number and pipeline section numbering, and node is meant the joint between water entry in the pipe network, EXIT POINT or the pipeline section, and described pipeline section is two pipelines between the node.

The step of node recursive algorithm is as follows:

(1) certain node is the calculating start node in the appointment pipe network;

(2) judge whether starting point, if change (3) into certain pipeline section; If not change (5);

(3) if the starting point of certain pipeline section is then calculated this pipeline section and is labeled as and calculates, and adopt the traversal mode of node → downstream pipeline section → node, find out the downstream node of this pipeline section;

(4) judge whether to be finish node,, stop search if then finish; If not change (5);

(5) check whether these all pipeline sections of node upstream all are labeled as and calculate,, find out the downstream node of this pipeline section, and calculate current pipe section, carry out mark, change (4) if then adopt the traversal mode of node → downstream pipeline section → node; If not change (6);

(6) adopt the search of node → upstream pipeline section → node to travel through mode, find out upstream node, change (5);

Advantage of the present invention and good effect are: adopting with the node is the node recursive algorithm of object, need not the numeral order of node and pipeline section in the strict regulations pipe network, be not subjected to the influence of the node location of pipe net arrangement yet, be convenient to node serial number and actual the use, make the layout of pipe network have greater flexibility, through once calculating the optimal design problem that just can solve whole pipe network system, reach the hydraulic parameters of design of pipe networks of global optimization sewage network engineering, Storm Sewer Network engineering, combined system pipe-networks engineering and the purpose of construction costs.

Utilize optimized Algorithm theory and technologies such as node recursive algorithm and genetic algorithm, can optimize and reduce construction investment to greatest extent, improve the feasibility and the reliability of engineering design.

Description of drawings

Fig. 1 is the sewage network layout of the embodiment of the invention;

Fig. 2 is the recursion optimization algorithm for drainpipe network flow chart.

Numeral 1,2,3 ... 16 are the pipeline section numbering, 1., and 2., 3.

Be node serial number.

Embodiment

The drainage pipeline networks of the statement example that the present invention adopts is made up of 16 drainpipes, 17 nodes as shown in Figure 1, and to the downstream, the node serial number of each pipeline section is a water outlet node behind elder generation's water inlet node to the pipeline section numbering in proper order from the upstream; Drainage pipeline networks can be considered digraph, presses sewage, rainwater or the combined sewage flow direction in pipe, and water is flowed into by the water inlet node of each design pipeline section, and the water outlet node flows out, and the process main compiles gradually and flows to main pipe, flow to the pipe network downstream termination point at last.Whole drainage pipeline networks is just as one tree, and behind the drainage pipeline networks alignment, the joining relation of all pipeline sections and node is just decided fully in the whole pipe network.

According to graph theory, for the drainage pipeline networks digraph, available matrix M is represented the joining relation of its node and pipeline section, and Metzler matrix is expressed as follows:

By graph theory as can be known, after the pipe network figure was determined, the pipe network relational matrix just was determined, otherwise, when known pipe network relational matrix, then can the unique net of fixed tube really figure.

For sewage network figure shown in Figure 1, then pipe network relational matrix M is:

$M=\left[\begin{array}{cccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ -1& 1& 0& 0& 0& -1& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& -1& 1& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& -1& 1& 0& 0& 0& 0& -1& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -1& 1& 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 1\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& -1& -1& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0\end{array}\right]$

The flow direction that designs pipeline section (limit), node (inspection chamber) and water in the pipe network of having gathered the drainage pipeline networks relational matrix waits the placement information and the hydraulic performance information of all pipe networks, determine starting point and flow process that drainage pipeline networks waterpower is calculated, fixed node (inspection chamber) and the relation of design pipeline section and the inflow and the outflow relation of water.This matrix is a sparse matrix, and along with the increase of pipe network system, the sparse property of matrix is just big more.In order to save calculator memory, when practical programs design and establishment, can adopt variable bandwidth compressed storage method.

Node is the bridge of pipeline section contact in the pipe network; In the drainage pipeline networks actual arrangement, can think that node location has determined the arrangement form of pipeline section in the pipe network.Therefore, can begin to travel through whole pipe network system from arbitrary node.For each node, data have determined to be connected in the pipeline section number of this node uniquely in the pipe network connection matrix, and divide into node upstream pipeline section and node downstream pipeline section respectively, and especially, for the starting point of drainage pipeline networks, its upstream tube hop count is zero; For terminal point, its downstream tube hop count is zero.

For a drainage pipeline networks digraph, all nodes all are labeled as " not visit " (unvisited), simultaneously all pipeline sections are labeled as " not calculating " (uncalculated), the mark of pipeline section is a calculated case of representing its all pipeline sections of upstream, if all calculating, the upstream pipeline section finishes, then be labeled as " calculating " (calculated), like this when searching for by node, when having access to certain node, the upstream pipeline section that judgement links to each other with this node mark whether for " calculating " (calculated), if then, conduct interviews according to the visit situation of node, if not, then node must be shifted to upstream node, search for and judge, and do corresponding calculated and processing.In search procedure, any node begins from pipe network, check the whole nodes adjacent successively with present node, with the vertex ticks of visiting for " visiting " (visited), utilize node → downstream pipeline section → node then, or the recursive search of node → upstream pipeline section → node traversal mode, the node that visit had not been visited, until complete pipe network of traversal, its essence is a kind of mathematics recursive algorithm.This method is not only applicable to the design of newly-built pipe network, more can be applicable to the extension project of urban drainage pipe network, and to a certain extent, also compatibly the underground pipelines intersection is many, the drainage pipeline networks engineering design that pipeline layout is difficult etc.

The step of node recursive algorithm is seen Fig. 2 program design computing block diagram.

(1) certain node is the calculating start node in the appointment pipe network;

(2) judge whether starting point, if change (3) into certain pipeline section; If not change (5);

(3) if the starting point of certain pipeline section is then calculated this pipeline section and is labeled as and calculates, and adopt the traversal mode of node → downstream pipeline section → node, find out the downstream node of this pipeline section;

(4) judge whether to be finish node,, stop search if then finish; If not change (5);

(5) check whether these all pipeline sections of node upstream all are labeled as and calculate,, find out the downstream node of this pipeline section, and calculate current pipe section, carry out mark, change (4) if then adopt the traversal mode of node → downstream pipeline section → node; If not change (6);

(6) adopt the search of node → upstream pipeline section → node to travel through mode, find out upstream node, change (5);

The present invention is fit to the designing and calculating of large, medium and small sewerage pipeline network, utilize the node recursive algorithm, in conjunction with the mathematical optimization algorithm, the direction of calculating from upstream node to downstream node carried out, traversal all nodes of pipe network and pipeline section, obtain comparatively ideal results, satisfied under the situation of hydraulics, can optimize pipe network investment about 8～21%.

Claims (3)

1. recursion optimization algorithm for drainpipe network is characterized in that: adopt pattern matrix management sewerage pipeline network, by the numbering of the pipe network system of deciding the drainage pipeline networks arranging graphic, determine pipe network relational matrix M (i, j), described pipe network relational matrix M (i j) is expressed as follows:

Wherein i is the capable variable of node, and j is pipeline section row variablees; With the node in the pipe network is object, specifies the arbitrary initial computing node, adopts node recursive algorithm traversal all nodes of pipe network and pipeline section.

2. recursion optimization algorithm for drainpipe network according to claim 1, it is characterized in that: described numbering comprises node serial number and pipeline section numbering, node is meant the joint between water entry in the pipe network, EXIT POINT or the pipeline section, and described pipeline section is two pipelines between the node.

3. recursion optimization algorithm for drainpipe network according to claim 1 is characterized in that: the step of node recursive algorithm is as follows:

(1) arbitrary node is the calculating start node in the appointment pipe network;

(2) judge whether starting point, if change (3) into certain pipeline section; If not change (5);

(3) if the starting point of certain pipeline section is then calculated this pipeline section and is labeled as and calculates, and adopt the traversal mode of node → downstream pipeline section → node, find out the downstream node of this pipeline section;

(4) judge whether to be finish node,, stop search if then finish; If not change (5);

(5) check whether these all pipeline sections of node upstream all are labeled as and calculate,, find out the downstream node of this pipeline section, and calculate current pipe section, carry out mark, change (4) if then adopt the traversal mode of node → downstream pipeline section → node; If not change (6);

(6) adopt the search of node → upstream pipeline section → node to travel through mode, find out upstream node, change (5).

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