CN104462714A - Calculation method for optimizing municipal drainage network plane layout design - Google Patents

Abstract

The invention discloses a calculation method for optimizing a municipal drainage network plane layout design. The calculation method is characterized by mainly comprising three steps that firstly, a construction cost fitness function which has high matching degree with drainage network assessment is constructed; secondly, an initialized population is obtained from a tree structure genetic algorithm initializing scheme based on the divide-and-conquer method; thirdly, an expanded variable population is obtained by utilizing a line-adding and circle-breaking method. The calculation method for optimizing the municipal drainage network plane layout design has the advantages that the matching degree between the constructed construction cost fitness function and the drainage network assessment is high, so a drainage network can be well planned; the tree structure genetic algorithm initializing scheme based on the divide-and-conquer method enables an initialized scheme of a tree structure to be completed rapidly, and large-scale initialization of the large-scale pipe network can be achieved; a variation algorithm of the drainage network is simpler by utilizing the line-adding and circle-breaking method, a novel pipe network planning map can be generated after each line is cut out in a circle with added lines, and variation diversity is guaranteed.

Description

A kind of municipal drain network plane layout design optimized calculation method

Technical field

The present invention relates to a kind of computing method, be specifically related to a kind of municipal drain network plane layout design optimized calculation method.

Background technology

Urban drainage pipe network is the indispensable important infrastructure in modern city, is also the major project of water prevention and cure of pollution and water drainage mitigation.The limited fund that utilizes that governments at all levels can be helped scientific and reasonable by planning and the design of science realizes the maximization of returns of investment.

The optimal design of drainage pipeline networks comprises the content of two aspects: one is the optimum choice of pipeline floor plan; Two is the optimal design of carrying out pipe parameter and pipeline section caliber and buried depth when pipeline floor plan is determined.Wherein, the optimization of drainage pipeline networks floor plan occupies very important status in urban drainage pipe network planning, and it is related to rationality and the construction costs of whole pipe network system, is the basis that pipe parameter is optimized.

In traditional THE OPTIMIZATION OF DRAINAGE NETWORK, designer is after having grasped comparatively complete reliable design basis data, general elder generation is according to the principle of pipe alignment and system layout, determine one comparatively reasonably pipeline floor plan by rule of thumb, it is random that this makes the decision-making of route selection have very large subjectivity, lacks rationale, often make design relatively conservative, causing the setting that pipe network is unnecessary, add the construction amount of engineering, is economically irrational.

In pipeline floor plan, have scholar abstract for the floor plan of the urban drainage pipe network figure for being made up of Points And lines, the ultimate principle according to graph theory finds shortest path.

Due to drainage pipeline networks run by gravity, shortest path first does not often represent minimum investment, therefore, is necessary to select to consider the factor of other influences pipe network cost while consideration path at this.

Scholar is such as had to propose respectively with the mode Solve problems of three kinds of weights, be minimum pipe range respectively, the amount of excavation that designs according to minimum grade of the Reciprocals sums of minimum grade to be to ask optimal planar arrangement, then the mode determined according to floor plan respectively three kinds of schemes asks minimum investment cost, finally does preferably again.The one that this scheme is actually when shortest path can not represent minimum investment is flexible, since but obviously only consider that shortest path can not represent minimum investment, so only consider the inverse of minimum grade or minimum investment optimization can not be represented according to the amount of excavation of minimum grade design.

The bright grade of Capital Normal University Luo Li in 2008 employs partheno genetic algorithm in based on the pipe network optimization of partheno genetic algorithm and have studied the optimization of pipe network floor plan, but do not consider the relation of caliber and buried depth etc. in the algorithm, meanwhile, owing to not doing rational solution to the algorithm complex problem interpretation of algorithm, its drainage pipeline networks prioritization scheme does not possess practical feasibility.

Summary of the invention

For solving the deficiencies in the prior art, the object of the present invention is to provide a kind of municipal drain network plane layout design optimized calculation method, this algorithm is a kind of new modified partheno genetic algorithm, it not only can make the optimization of pipe network floor plan obtain better effect, and the initialization scheme of tree structure can be completed comparatively fast, the diversity made a variation can also be ensured simultaneously.

In order to realize above-mentioned target, the present invention adopts following technical scheme:

A kind of municipal drain network plane layout design optimized calculation method, is characterized in that, comprise the following steps:

(1), cost fitness function is built:

First, the cost fitness function of single pipeline section is built:

$\mathrm{fitness}=\left\{\begin{array}{cc}(\frac{11113*{(q/1000)}^{0.52}}{i^{0.2}}+15093)*l& i>0\\ 50000*l& i\≤0\end{array}\right.$

In formula, l is the length of single pipeline section, and q is the drain discharge of single pipeline section, and i is the gradient on ground residing for pipeline section;

Then, the cost fitness function of every root pipeline section is superposed, obtains the cost fitness function of drainage pipeline networks:

(2) initialization population is obtained:

1., by an array be divided into m son point array, by two ends all same height count group line be divided into sub-line array;

2., according to sub-line array judge the connectedness of son point array, adjustment point array, every height all points in group of counting all are communicated with;

3., obtain respectively in every height counts group and sub-line array and be communicated with tree at random;

4., with sub-point array be point, son point array between line for be communicated with line formed connected graph, connected graph produces and is communicated with tree at random;

5., by the random connection tree on all connected graphs merge, thus obtain initialization population;

(3) the variation population after, being expanded:

1., get and to be divided and ruled the tree that formula initialization obtains by partheno genetic algorithm;

2. get the limit that does not belong to this tree, at random, this limit is merged with tree and obtains the connected graph that has p bar line;

3., according to broken circle algorithm find corresponding circle, and remove a limit in this circle, thus obtain a newly tree, complete and once make a variation;

4., utilize the population that elitist selection algorithms selection cost fitness function is minimum, proceed to make a variation to this population, until obtain final calculation result next time.

Aforesaid municipal drain network plane layout design optimized calculation method, is characterized in that, in step (2), the process of adjustment point array is:

1., in a son point array, for disconnected point, this point is rejected from book point array, and will reject from corresponding sub-line array to the line that this point connects;

2., disallowable point is communicated with line according to it is inserted into another height that can be communicated with and counts in group, and will be communicated with accordingly in the corresponding sub-line array of line insertion.

Usefulness of the present invention is:

1, build cost fitness function and drainage pipeline networks evaluate between the goodness of fit higher, can be good at planning drainage pipeline networks;

2, based on the tree structure genetic algorithm initialization scheme of divide and conquer, the initialization scheme of tree structure can be completed comparatively fast, the extensive initialization of fairly large pipe network (more than 200 pipeline sections) is achieved;

3, utilize " ledger line Circle-Analysis " to make the mutation algorithm of drainage pipeline networks more simple, a new pipe network planning chart can be generated to deleting each line in enclosing after finding the circle after " ledger line ", ensure that the diversity of variation.

Accompanying drawing explanation

Fig. 1 is the probability statistics figure that different number of vertex n forms tree when getting n-1 bar limit at random;

Fig. 2 is the process flow diagram obtaining initialization population;

Fig. 3 is Yangyuan County floor plan;

Fig. 4 is the alternative wiring diagram of Yangyuan County floor plan;

Fig. 5 is divide and conquer subregion schematic diagram;

Fig. 6 is the schematic diagram that each subregion forms separately random tree;

Fig. 7 is the connection diagram between subregion;

Fig. 8 is the tree schematic diagram that divide and conquer initialization is finally formed;

Fig. 9 is partheno genetic algorithm " Circle-Analysis " mutation operator demonstration graph;

Figure 10 is average fitness value curve;

Figure 11 is minimum fitness value curve;

The floor plan that Figure 12 obtains after being through the hereditary variation of 91 generations.

Embodiment

Municipal drain of the present invention network plane layout design optimized calculation method, it mainly comprises three large steps, that is:

One, structure and drainage pipeline networks have the cost fitness function of the higher goodness of fit between evaluating;

Two, the tree structure genetic algorithm initialization scheme based on divide and conquer obtains initialization population;

Three, the variation population after utilizing " ledger line Circle-Analysis " to be expanded.

Below in conjunction with specific embodiment, concrete introduction is done to the present invention.

One, fitness function is built

In genetic algorithm, determine individual survival probability due to fitness function and determine the solution of last problem, therefore fitness function be determined to become the emphasis studied in genetic algorithm.

Current research shows, cost fitness function F is the function of caliber D and duct length L, and caliber D is derived by pipeline flow Q (variable), and therefore, cost fitness function F is determined by flow Q and length L, i.e. F=f (Q, L).

In the cost estimate function of drainage pipeline networks, cost is the function about buried depth h, caliber d and pipe range l, and the essence of Cost Optimization is exactly under firm discharge, seek less buried depth, compared with pipe with small pipe diameter and the process compared with short path, i.e. fitness function F=f (d, h, l).

In drainage pipeline networks parameter optimization, by the research carried out pipe network cost estimate function, the present invention finally constructs new cost fitness function, this new cost fitness function is not only relevant with the length l of single pipeline section, and it is relevant with the drain discharge q of single pipeline section, simultaneously also relevant with the gradient i on ground residing for pipeline section, the cost fitness function of this single pipeline section is specific as follows:

$\mathrm{fitness}=\left\{\begin{array}{cc}(\frac{11113*{(q/1000)}^{0.52}}{i^{0.2}}+15093)*l& i>0\\ 50000*l& i\≤0\end{array}\right..$

The cost fitness function of whole drainage pipeline networks is superposed by the cost fitness function of every root pipeline section, that is:

This cost fitness function is while effective matching unit price, the ground inclination adopting penalty that pipeline is arranged is greater than 0 as far as possible, pipe network floor plan Cost Optimization can be made to obtain less buried depth by this cost fitness function, compared with pipe with small pipe diameter and the result compared with short path, and finally make the optimization of pipe network floor plan obtain better effect.

Two, initialization population is obtained

In existing tree structure genetic algorithm initialization scheme, when getting n-1 bar limit at random, when then judging that it is connective, along with the increase of n, the probability decline rate forming tree is exceedingly fast, and sees Fig. 1.

As seen from Figure 1: when number of vertex n increases, the probability forming tree during n-1 bar limit can decline rapidly, when number of vertex reaches 30 time, in 10000 circulations, all cannot obtain 1 tree, because the probability forming tree is extremely low, therefore which produces random number will be no longer feasible.

For this reason, the present invention proposes the tree structure genetic algorithm initialization scheme based on divide and conquer, obtain initialization population with this.

In computer science, divide and conquer is a kind of very important algorithm, literal explanation is " dividing and rule ", exactly a complicated problem is divided into two or more same or analogous subproblem, again subproblem is divided into less subproblem ... to the last subproblem can simple direct solution, the merging of the solution of former problem and the solution of subproblem.

Any one can with computing time needed for problem of computer solving all with its scale about: the scale of problem is less, easier direct solution, and required computing time of solving a problem is also fewer; Otherwise required computing time of solving a problem is more.

The comparatively small mode of the subproblem produced by divide and conquer former problem often, this is just for using recursive technique to provide conveniently.In this case, application is divided and ruled means repeatedly, and can make that subproblem is consistent with former problem types and its scale constantly reduces, finally make subproblem narrow down to be easy to directly obtain its solution, this causes the generation of recursive procedure naturally.

Introduce the tree structure genetic algorithm initialization scheme based on divide and conquer that the present invention proposes below in detail.

With reference to Fig. 2, the tree structure genetic algorithm initialization procedure based on divide and conquer is as follows:

1., by an array be divided into m son point array, by two ends all same height count group line be divided into sub-line array.

2., according to sub-line array judge the connectedness of son point array, adjustment point array, every height all points in group of counting all are communicated with.

In a son point array, only need to adjust disconnected point, concrete adjustment process is:

First, this point is rejected from book point array, and reject to the line that this point connects from corresponding sub-line array.

Then, disallowable point is inserted into another height that can be communicated with according to its connection line and counts in group, and will be communicated with accordingly in the corresponding sub-line array of line insertion.

3., adjust all after son point array, obtain respectively in every height counts group and sub-line array and be communicated with tree at random.

4., with sub-point array be point, son point array between line for be communicated with line formed connected graph, connected graph produces and is communicated with tree at random.

5., by the random connection tree on all connected graphs merge, thus obtain initialization population.

With regard to practical problems, this process is demonstrated below.

City overview: Yangyuan County county town belongs in recent years the micropolis grown up, city builds to get up on the basis in original villages and small towns, therefore its urban pipe network very imperfection, along with the fast development of urban economy, is badly in need of carrying out reorganization and expansion to original unwatering system.

Principle of design: 1. run-off system adopts rain, dirty separate system; 2. caliber, flow are by the year two thousand twenty design at a specified future date, and laying of pipe network scope is considered by recent service area; 3. wastewater quantity prediction consideration is pressed in each district of the design discharge of sewer line, calculates sewage design discharge in district by itself service area and average area unit rate of flow; 4. sewer line is by non-flowing full design with no pressure, the degree of filling of pipeline in conjunction with the gradient, design discharge, non-silting velocity, the combined factors such as landform are considered; 5. strict implement country and local relevant specification, standard.

Fig. 3 is shown in by topomap.

This project has 62 draining nodes (n=62), 174 alternative circuits, as shown in Figure 4, when initialization does not use divide and conquer, fails to generate random tree in 5 minutes.

In divide and conquer calculates, first subregion has been carried out, after according to connectedness adjustment subregion, the block plan obtained as shown in Figure 5, as seen from Figure 5: pass through subregion, figure divides in order to six subregions (m=6), and the point in each subregion is communicated with, and the point in maximum subregion is no more than 20.

Then, in each subregion, random tree is formed separately, as shown in Figure 6.

Next, formed between subregion and connect, as shown in Figure 7.If each subregion is thought a point, then this connection is in fact also a random tree connecting each point.

Finally, all random trees (comprising: the random tree that the random tree of by stages and each subregion are independently formed) are combined, obtains the random tree of whole connected graph, as shown in Figure 8.

Facts have proved, utilize divide and conquer initialize flow can at the random spanning tree less than stochastic generation 60 similar Fig. 8 in the time of one minute.

Three, the variation population after being expanded

As can be seen from above to the judgement of the probability of random spanning tree, when node is more time, be difficult to when getting n-1 bar line at random ensure that it remains a tree, namely tree structure is difficult to continue to obtain tree structure after intersecting, and replace operator and single parent's inver-over operator of single parent all can not ensure that the figure after variation remains a tree, therefore, be necessary to study a kind of mutagenic factor remaining tree after heredity.

Algorithm of the present invention is difficult to the feature applied in drainage pipeline networks for original mutation algorithm, propose new " ledger line Circle-Analysis ", obtain rapidly the variation population after new expansion with this.

Broken circle algorithm is a kind of method asking optimal tree proposed by China mathematician Guan Meigu for 1975, the method refers to and in weighted graph, to search out the limit that then a circle remove maximum weight in this circle obtain subgraph, in subgraph, find a circle removing a limit again, and so forth, know remaining subgraph no longer containing till circle, the subgraph of gained is exactly required optimal tree.

Introduce the process that employing " ledger line Circle-Analysis " obtains rapidly the variation population after expanding below in detail.

1., get and to be divided and ruled the tree that formula initialization obtains by partheno genetic algorithm.

2. get the limit that does not belong to this tree, at random, this limit is merged with tree and obtains the connected graph that has p bar line.

3., according to broken circle algorithm find corresponding circle, and remove a limit in this circle, thus obtain a newly tree, complete and once make a variation.

4., utilize the population that elitist selection algorithms selection cost fitness function is minimum, proceed to make a variation to this population, until obtain final calculation result next time.

Being described as establishing certain connected graph to have 5 points, 10 limits 0101100001 to be a random tree wherein from the angle of mathematics, obtaining 0101100 to adding arbitrarily a limit in this tree 101, then this figure encloses to obtain connected graph for there being one, if circle is by figure 010 1100 1the limit of 01 band underscore is formed, then obviously will wherein remove and can obtain broken enclosing to obtain result in any limit, thus acquisition three trees (comprising original tree) 010 0100 101,010 1000 101,010 1100 001.

Demonstrate as shown in Figure 9 in the mode of pictorial diagram.If certain figure is just like the overall situation shown in Fig. 9 (a), produce dendrogram as shown in Fig. 9 (b), then after generation one random line 9,10 line as shown in Fig. 9 (c), obvious 8,9,10 3 form a circle, by 8,9, be referred to as " broken circle " after 10 formed circles remove any one side, therefore, line segment 8-10 or line segment 8-9 removed and can produce the new tree as shown in Fig. 9 (d) He Fig. 9 (e).

When the individuality that all fitness that certain selection mode can ensure in previous generation colony are greater than zero all has an opportunity to be chosen to the next generation, partheno genetic algorithm is global convergence after employing elitist selection.Therefore, on selection strategy, when selecting, the elitist selection method adopting partheno genetic algorithm to recommend, further improves above-mentioned strategy simultaneously, has both ensured that the individuality that fitness is high can evolve to the next generation at every turn, also ensures the diversity of colony simultaneously.

Concrete selection strategy is:

First, adopt Circle-Analysis to utilize broken circle operator to make a variation to the individuality selected, a tree can be formed because Circle-Analysis removes any limit in circle, therefore, it is possible to form the new individuality of some, form population of new generation, calculate the fitness of each individuality.

Then, adopt the method for elitist selection, the fitness assignment method based on sequence will be adopted in parent population, by parent individuality by the ascending sequence of pipe network Cost Function value, judge whether each individuality can enter population of new generation successively, criterion is: if individuality occurs in new population, then no longer select, otherwise individuality is directly saved in new population, repeat said process, until number of individuals reaches population size, so both can ensure that the individuality that fitness is high entered into the next generation, in turn ensure that individual diversity simultaneously, namely do not allow have same individual to occur in colony, the individuality that in population, pipe network Cost Function value is large will be eliminated.

Method of the present invention is divided into child node group draining node in initialization procedure, then random spanning tree is asked respectively, recombinant generates final random tree, and node grouping determined by the coordinate of node itself, therefore the nearer point of coordinate can be made in initialization procedure to have more chance to be communicated with, make average fitness value during initialization lower.

In addition, method of the present invention is owing to selecting elite's genetic algorithm, population of new generation is obtained by sequence, therefore fitness in roulette algorithm can be no longer confined to higher and obtain the larger restriction of population chance of future generation, fitness can be arranged from low to high and choose the minimum population genetic of fitness function to of future generation, thus directly can replace fitness function with cost estimate function, thus the cost estimate function of every generation individuality can be obtained intuitively.

For above-mentioned example, in initialization procedure, connected graph is divided into 6 districts, getting population size is 60, the ideal adaptation degree function data obtained within hereditary 91 generations is successively decreased gradually, often for average fitness value curve as Figure 10, often for minimum fitness value curve as Figure 11, can find out that its average fitness and minimum fitness have different decline by graph curve.

At partheno genetic algorithm after the hereditary variation of 91 generations, obtain floor plan as shown in figure 12, the data of acquisition are in table 1.

Table 1 is drainage pipeline networks floor-plan data after the hereditary variation of 91 generations

Known by data in table, adverse grade pipeline section is less than 10% of house steward's hop count amount, substantially can reach along slope draining, pipeline total length 25619.3938 meters is compared with former pipeline total length 33834.923 meters, pipeline total length reduces about 25%, the project investment in the optimizing process of Yangyuan County drainage pipeline programme of this project achievement reduces 12.6%, achieves good effect.

Facts have proved: algorithm of the present invention not only calculates simply, fast operation, and can reach better plan optimization effect, has good application value.

Method of the present invention can be applicable to sewage network design, also can be applied in the optimization of other tree-like pipe networks to fitness function after suitably revising, such as Storm Sewer Network design and combined system design of pipe networks.

It should be noted that, above-described embodiment does not limit the present invention in any form, the technical scheme that the mode that all employings are equal to replacement or equivalent transformation obtains, and all drops in protection scope of the present invention.

Claims (2)

1. a municipal drain network plane layout design optimized calculation method, is characterized in that, comprise the following steps:

(1), cost fitness function is built:

First, the cost fitness function of single pipeline section is built:

$\mathrm{fitness}=\left\{\begin{array}{cc}(\frac{11113*{(q/1000)}^{0.52}}{i^{0.2}}+15093)*l& i>0\\ 50000*l& i\≤0\end{array}\right.$

In formula, l is the length of single pipeline section, and q is the drain discharge of single pipeline section, and i is the gradient on ground residing for pipeline section;

Then, the cost fitness function of every root pipeline section is superposed, obtains the cost fitness function of drainage pipeline networks:

(2) initialization population is obtained:

1., by an array be divided into m son point array, by two ends all same height count group line be divided into sub-line array;

2., according to sub-line array judge the connectedness of son point array, adjustment point array, every height all points in group of counting all are communicated with;

3., obtain respectively in every height counts group and sub-line array and be communicated with tree at random;

4., with sub-point array be point, son point array between line for be communicated with line formed connected graph, connected graph produces and is communicated with tree at random;

5., by the random connection tree on all connected graphs merge, thus obtain initialization population;

(3) the variation population after, being expanded:

1., get and to be divided and ruled the tree that formula initialization obtains by partheno genetic algorithm;

2. get the limit that does not belong to this tree, at random, this limit is merged with tree and obtains the connected graph that has p bar line;

3., according to broken circle algorithm find corresponding circle, and remove a limit in this circle, thus obtain a newly tree, complete and once make a variation;

4., utilize the population that elitist selection algorithms selection cost fitness function is minimum, proceed to make a variation to this population, until obtain final calculation result next time.

2. municipal drain according to claim 1 network plane layout design optimized calculation method, is characterized in that, in step (2), the process of adjustment point array is:

1., in a son point array, for disconnected point, this point is rejected from book point array, and will reject from corresponding sub-line array to the line that this point connects;

2., disallowable point is communicated with line according to it is inserted into another height that can be communicated with and counts in group, and will be communicated with accordingly in the corresponding sub-line array of line insertion.