CN104462714B - A kind of municipal drain network plane layout design optimized calculation method - Google Patents
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Abstract
The invention discloses a kind of municipal drain network plane layout design optimized calculation method, it is characterised in that mainly includes three big steps：First, the cost fitness function between drainage pipeline networks appraisal with the higher goodness of fit is built；2nd, the tree structure genetic algorithm initialization scheme based on divide and conquer obtains initializing population；3rd, the variation population after utilization " ledger line Circle- Analysis " is expanded.The present invention is advantageous in that：The goodness of fit between cost fitness function and the drainage pipeline networks appraisal of structure is higher, can be good at planning drainage pipeline networks；Tree structure genetic algorithm initialization scheme based on divide and conquer, can more quickly finish the initialization scheme of tree structure so that the extensive initialization of fairly large pipe network is achieved；Cause that the mutation algorithm of drainage pipeline networks is more simple using ledger line Circle- Analysis, a new pipe network planning chart can be generated after the circle after ledger line to deleting each line in circle by finding, it is ensured that the diversity of variation.
Description
Technical field
The present invention relates to a kind of computational methods, and in particular to a kind of municipal drain network plane layout design optimizes calculating side
Method.
Background technology
Urban drainage pipe network is the indispensable important infrastructure of modern city, is also that water prevention and cure of pollution and water drainage subtract
The major project of calamity.By the planning and design of science the limited fund of the scientific and reasonable utilization of governments at all levels can be helped to realize
The maximization of returns of investment.
The optimization design of drainage pipeline networks includes the content of two aspects：One is the optimum choice of pipeline horizontal layout；Two are
The optimization design that pipe parameter is pipeline section caliber and buried depth is carried out in the case where pipeline horizontal layout is fixed.Wherein, drainpipe
Network plane layout optimization occupies very important status in urban drainage pipe network planning, and it is related to whole pipe network system
Reasonability and construction costs, be pipe parameter optimization basis.
In traditional THE OPTIMIZATION OF DRAINAGE NETWORK, designer is grasping more complete reliable design basis data
Afterwards, the general principle first arranged according to pipe alignment and system, empirically determines out a kind of relatively reasonable pipeline horizontal layout
Figure, this makes the decision-making of route selection have very big subjectivity random, lacks rationale, design is partial to conservative, cause pipe
The unnecessary setting of net, adds the construction amount of engineering, is economically irrational.
There is scholar to be made up of Points And lines the horizontal layout of urban drainage pipe network is abstract in terms of pipeline horizontal layout
Figure, shortest path is found according to the general principle of graph theory.
The characteristics of due to drainage pipeline networks gravity stream, shortest path first does not often represent minimum investment, therefore, has herein
Necessary choice is accounted for while path is considered to the factor of other influences pipe network cost.
For example there is scholar to propose the Solve problems in the way of three kinds of weights respectively, be minimum pipe range, minimum grade respectively
The reciprocal and amount of excavation that is designed according to minimum grade seeks optimal planar arrangement, then to three kinds of schemes respectively according to plane
The mode that arrangement is determined seeks minimum investment cost, finally does again preferably.This scheme is actually that can not be represented in shortest path
One kind in the case of minimum investment is flexible, since it is apparent that only considering that shortest path can not represent minimum investment, then only
The amount of excavation for only considering the inverse of minimum grade or being designed according to minimum grade can not represent minimum investment optimization.
The bright grades of Capital Normal University Luo Li in 2008 have used single parent's something lost in the pipe network optimization based on partheno genetic algorithm
Propagation algorithm have studied the optimization of pipe network horizontal layout, but not account for the relation of caliber and buried depth etc. in the algorithm, at the same time, by
Rational solution is not made in the algorithm complex problem interpretation to algorithm, its drainage pipeline networks prioritization scheme does not possess pratical and feasible
Property.
The content of the invention
To solve the deficiencies in the prior art, it is an object of the invention to provide a kind of municipal drain network plane layout design
Optimized calculation method, the algorithm is a kind of new modified partheno genetic algorithm, and it not only can optimize pipe network horizontal layout
More preferable effect is obtained, and can more quickly finish the initialization scheme of tree structure, while variation can also be ensured
Diversity.
In order to realize above-mentioned target, the present invention is adopted the following technical scheme that：
A kind of municipal drain network plane layout design optimized calculation method, it is characterised in that comprise the following steps：
(1) cost fitness function, is built：
First, the cost fitness function of single pipeline section is built：
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 pipeline section is superimposed, obtains the cost fitness function of drainage pipeline networks：
(2) obtain initializing population：
1. an array, is divided into m son point array, two ends are all divided into sub-line number in the line of same height points group
Group；
2. the connectedness of son point array, adjustment point array so that institute in per height points group, are judged according to sub-line array
Some points are all connected；
3., every height points group with sub-line array respectively obtain connect tree at random；
4., the line by point of sub- point array, between sub- point array is that communication line is constituted connected graph, produced on connected graph with
Machine connection tree；
5., the random connection tree on all connected graphs is merged, so as to obtain initialization population；
(3) the variation population after, being expanded：
1., take and divided and ruled obtain one tree of formula initialization by partheno genetic algorithm；
2. a side for being not belonging to the tree, is taken at random, and the side is merged with tree and obtains a connected graph for there are p bar lines；
3. corresponding circle, is found according to broken circle algorithm, and removes a line in the circle, is newly set so as to obtain one, it is complete
Into once making a variation；
4., using the minimum population of elitist selection algorithms selection cost fitness function, the population is proceeded next
Secondary variation, until obtaining final calculation result.
Foregoing municipal drain network plane layout design optimized calculation method, it is characterised in that in step (2), is adjusted
The process of integral point array is：
1., in a son point array, for disconnected point, the point is rejected from book point array, and will be with this
The line of point connection is rejected from corresponding sub-line array；
2., the point being removed is inserted into according to its communication line in another height points group that can be connected, and will be corresponding
Communication line is inserted in corresponding sub-line array.
The present invention is advantageous in that：
1st, the goodness of fit between cost fitness function and the drainage pipeline networks appraisal built is higher, can be good at planning row
Grid；
2nd, the tree structure genetic algorithm initialization scheme based on divide and conquer, can more quickly finish tree structure
Initialization scheme so that the extensive initialization of fairly large pipe network (more than 200 pipeline sections) is achieved；
3rd, utilize " ledger line Circle- Analysis " such that the mutation algorithm of drainage pipeline networks is more simple, it is right after the circle after " ledger line " to find
Each line is deleted in circle can generate a new pipe network planning chart, it is ensured that the diversity of variation.
Brief description of the drawings
Fig. 1 is the probability statistics figure that tree is constituted when different number of vertex n takes n-1 bar sides at random；
Fig. 2 is the flow chart for obtaining initialization population；
Fig. 3 is Yangyuan County floor plan；
Fig. 4 is the alternative line map of Yangyuan County horizontal layout；
Fig. 5 is divide and conquer subregion schematic diagram；
Fig. 6 is the schematic diagram that each subregion independently forms random tree；
Fig. 7 is the connection diagram between subregion；
Fig. 8 is the tree schematic diagram that divide and conquer initialization is ultimately 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；
Figure 12 is the floor plan obtained after the hereditary variation of 91 generations.
Embodiment
The municipal drain network plane layout design optimized calculation method of the present invention, it mainly includes three big step, i.e.,：
First, the cost fitness function between drainage pipeline networks appraisal with the higher goodness of fit is built；
2nd, the tree structure genetic algorithm initialization scheme based on divide and conquer obtains initializing population；
3rd, the variation population after utilization " ledger line Circle- Analysis " is expanded.
Make specific introduce to the present invention below in conjunction with specific embodiment.
First, fitness function is built
In genetic algorithm, because fitness function determines the survival probability of individual and determines the solution of last problem, because
This fitness function is determined to become the emphasis studied in genetic algorithm.
Current research shows that cost fitness function F is caliber D and duct length L function, and caliber D is by pipeline
Flow Q (variable) is exported, 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 on buried depth h, caliber d and pipe range l, and expense is excellent
The essence of change is exactly to seek smaller buried depth, the process compared with pipe with small pipe diameter and shorter path, i.e. fitness function F=under firm discharge
f(d,h,l)。
In drainage pipeline networks parameter optimization, by the research carried out to pipe network cost estimate function, the present invention is final to be built
New cost fitness function, the new cost fitness function is not only relevant with the length l of single pipeline section, and with it is single
The drain discharge q of pipeline section is relevant, while, the cost fitness letter of the single pipeline section relevant also with the gradient i on ground residing for pipeline section
Number is specific as follows：
The cost fitness function of whole drainage pipeline networks is to be superimposed the cost fitness function of every pipeline section, i.e.,：
The cost fitness function makes the ground that pipeline is arranged while effectively fitting unit price using penalty
The face gradient as far as possible be more than 0, by the cost fitness function enable to pipe network horizontal layout Cost Optimization obtain smaller buried depth,
Compared with pipe with small pipe diameter and the result of shorter path, and the optimization of pipe network horizontal layout is finally caused to obtain more preferable effect.
2nd, obtain initializing population
In existing tree structure genetic algorithm initialization scheme, when taking n-1 bars side at random, then judge that it is connective
When, with n increase, the probability decrease speed for constituting tree is exceedingly fast, and sees Fig. 1.
As seen from Figure 1：When number of vertex n increases, the probability of tree is constituted during n-1 bar sides to be declined rapidly, work as summit
When number reaches 30,1 tree can not be all obtained in being circulated at 10000 times, because the probability for constituting tree is extremely low, therefore which
Producing random number will be no longer feasible.
Therefore, the present invention proposes the tree structure genetic algorithm initialization scheme based on divide and conquer, obtained with this just
Beginningization population.
In computer science, divide and conquer is a kind of critically important algorithm, and literal explanation is " dividing and rule ", is exactly
The problem of a complexity, is divided into two or more same or analogous subproblems, then subproblem is divided into smaller son asked
Topic ... to the last subproblem can simple direct solution, the solution of former problem is the merging of the solution of subproblem.
The problem of any one can the use computer solving required calculating time is all relevant with its scale：The scale of problem
Smaller, easier direct solution, the calculating time needed for solving a problem is also fewer；Conversely, the calculating time needed for solving a problem is more.
The subproblem produced by divide and conquer is often the relatively small mode of former problem, and this is just the use recursive technique side of providing
Just.In this case, application is divided and ruled means repeatedly, can make that subproblem is consistent with original problem types and its scale constantly contracts
It is small, finally narrow down to subproblem and be easy to directly obtain its solution, this causes the generation of recursive procedure naturally.
The tree structure genetic algorithm initialization scheme proposed by the present invention based on divide and conquer is described in detail below.
Reference picture 2, the tree structure genetic algorithm initialization procedure based on divide and conquer is as follows：
1. an array, is divided into m son point array, two ends are all divided into sub-line array in the line of same height points group.
2. the connectedness of son point array, adjustment point array so that institute in per height points group, are judged according to sub-line array
Some points are all connected.
In a son point array, it is only necessary to adjust disconnected point, specific adjustment process is：
First, the point is rejected from book point array, and will be rejected with the line that the point is connected from corresponding sub-line array.
Then, the point being removed is inserted into according to its communication line in another height points group that can be connected, and will be corresponding
Communication line insert in corresponding sub-line array.
3., adjust all son point arrays after, every height points group with sub-line array respectively obtain connect tree at random.
4., the line by point of sub- point array, between sub- point array is that communication line is constituted connected graph, and random connection tree is produced on connected graph.
5., the random connection tree on all connected graphs is merged, so as to obtain initialization population.
Practical problem is demonstrated the process below.
City overview：Yangyuan County county town belongs to the micropolis grown up interior in recent years, and city is in original villages and small towns
On the basis of build what is got up, therefore its urban pipe network very imperfection, with the fast development of urban economy, is badly in need of to original draining
System carries out reorganization and expansion.
Design principle：1. run-off system is using rain, dirty separate system；2. caliber, flow press the year two thousand twenty design at a specified future date, laying of pipe network
Scope is considered by recent service area；3. each area of the design discharge of sewage conduct is considered by wastewater quantity prediction, by itself clothes in area
Business area and average area specific discharge calculate sewage design discharge；4. sewage conduct is pressed without pressing the design of non-flowing full, and pipeline is full of
Degree combines the gradient, design discharge, non-silting velocity, and the combined factors such as landform consider；5. strict implement country and place are about specification, standard.
Topographic map is shown in Fig. 3.
The engineering has 62 draining nodes (n=62), 174 alternative circuits, as shown in figure 4, being not used in initialization
During divide and conquer, failed to generate random tree in 5 minutes.
In divide and conquer calculating, subregion has been carried out first, and after according to connectedness adjustment subregion, obtained block plan is as schemed
Shown in 5, as seen from Figure 5：By subregion, the point that figure has been divided into six subregions (m=6), each subregion is connection,
And the point in maximum subregion is no more than 20.
Then, random tree is independently formed in each subregion, as shown in Figure 6.
Next, forming connection between subregion, as shown in Figure 7.If each subregion is considered a point, the company
It is actually also a random tree for connecting each point to connect.
Finally, by all random tree (including：The random tree that the random tree of by stages and each subregion are individually formed) enter
Row combination, obtains the random tree of whole connected graph, as shown in Figure 8.
It was verified that using divide and conquer initialization flow can at random be generated within the time less than one minute 60 it is similar
Fig. 8 random spanning tree.
3rd, the variation population after being expanded
It can be seen from judgement above to the probability of random spanning tree when node is more, n-1 bar lines are taken at random
When it is difficult to ensure that it is still a tree, i.e., tree structure intersect after be difficult to continue to obtain tree structure, and single parent's transposition operator
It is still a tree that the figure after variation can not be all ensured with single parent's inver-over operator, therefore, it is necessary to study a kind of process
It is still the mutagenic factor of tree after heredity.
The characteristics of algorithm of the present invention is difficult to apply for original mutation algorithm in drainage pipeline networks, it is proposed that new " plus
Line Circle- Analysis ", the variation population after new extension is obtained rapidly with this.
Broken circle algorithm is a kind of method for seeking optimal tree proposed by China mathematician Guan Meigu for 1975, and this method is referred to
The side that a circle is searched out in weighted graph and then removes maximum weight in this circle obtains subgraph, finds a circle again in subgraph
Removing a line, and so on, it is known that untill remaining subgraph is no longer containing circle, the subgraph of gained is exactly required optimal tree.
The process of the variation population after use " ledger line Circle- Analysis " is extended rapidly is described in detail below.
1., take and divided and ruled obtain one tree of formula initialization by partheno genetic algorithm.
2. a side for being not belonging to the tree, is taken at random, and the side is merged with tree and obtains a connected graph for there are p bar lines.
3. corresponding circle, is found according to broken circle algorithm, and removes a line in the circle, is newly set so as to obtain one, it is complete
Into once making a variation.
4., using the minimum population of elitist selection algorithms selection cost fitness function, the population is proceeded next
Secondary variation, until obtaining final calculation result.
Being described as setting certain connected graph from the angle of mathematics has 5 points, 10 sides 0101100001 to be one therein random
Tree, 0101100 is obtained to any addition a line in the tree101, then the figure is has one to enclose to obtain connected graph, if circle is by figure
In 0101100101 side with underscore is constituted, then obviously removes and can obtain brokenly enclosing to obtain result wherein any a line, from
And obtain three tree (including original trees) 0100100101,0101000101,0101100001。
The mode for being graphically illustrated figure is demonstrated as shown in Figure 9.If certain figure is just like the overall situation shown in Fig. 9 (a), the tree of generation
Shown in shape figure such as Fig. 9 (b), then after a random line of line 9,10 is produced as shown in Fig. 9 (c), it is clear that 8,9,10 three structures
Into a circle, 8,9,10 formed circles are removed and are referred to as " broken circle " behind any one side, therefore, by line segment 8-10 or line segment 8-
9 remove and can produce new tree such as Fig. 9 (d) and shown in Fig. 9 (e).
When the individual that all fitness that certain selection mode can guarantee that in previous generation colonies are more than zero has the opportunity to be chosen
When selecting the next generation, partheno genetic algorithm is global convergence after using elitist selection.Therefore, on selection strategy, often
During secondary selection, the elitist selection method recommended using partheno genetic algorithm, while above-mentioned strategy is further improved, was both protected
The high individual of card fitness can evolve to the next generation, while also ensureing the diversity of colony.
Specifically selection strategy is：
First, row variation is entered using broken circle operator to the individual of selection using Circle- Analysis, appointed because Circle- Analysis removes in circle
Meaning a line can form a tree, and therefore, it is possible to form a number of new individual, composition population of new generation calculates each
The fitness of individual.
Then, using the method for elitist selection, the fitness assignment method based on sequence will be used in parent population, by parent
Body presses the ascending sequence of pipe network Cost Function value, judges whether each individual can enter population of new generation, criterion successively
For：If individual occurs in new population, individual, is not otherwise saved directly in new population by reselection, repeats above-mentioned mistake
Journey, until number of individuals reaches population size, so can both ensure that the high individual of fitness entered the next generation, in turn ensure that simultaneously
The diversity of individual, i.e., do not allow to have in colony the big individual of pipe network Cost Function value in same individual appearance, population will be eliminated.
Draining node is divided into child node group by the method for the present invention in initialization procedure, and random generation is then asked respectively
Tree, recombinant generates final random tree, and node packet is determined by the coordinate of node in itself, therefore in initialization procedure
The point for enabling to coordinate nearer has more chances to connect so that average fitness value during initialization is relatively low.
In addition, the method for the present invention is due to selection elite genetic algorithm, population of new generation is obtained by sorting, therefore can be with
Be no longer limited to fitness in roulette algorithm higher and obtain the bigger limitation of population chance of future generation, can by fitness by
It is low to high to arrange and choose the minimum population genetic of fitness function to the next generation, so as to directly with cost estimate function generation
For fitness function, so as to intuitively obtain the cost estimate function of every generation individual.
For above-mentioned example, connected graph is divided into 6 areas in initialization procedure, it is 60 to take population size,
The individual adaptation degree function data obtained in hereditary 91 generations is gradually successively decreased, often for average fitness value curve such as Figure 10, and per generation is minimum
Fitness value curve such as Figure 11, by graph curve it can be seen that its average fitness and minimum fitness have different declines.
In partheno genetic algorithm after the hereditary variation of 91 generations, floor plan is obtained as shown in figure 12, the data of acquisition are shown in Table 1.
The drainage pipeline networks floor-plan data after the hereditary variation of 91 generations of table 1
By data in table, adverse grade pipeline section can be reached less than the 10% of house steward's segment number, substantially along slope draining, pipe
25619.3938 meters of line total length is compared with former 33834.923 meters of pipeline total length, and pipeline total length reduces by about 25%, the project
Achievement project investment in the optimization process of Yangyuan County drainage pipeline programme reduces 12.6%, achieves good effect.
It facts have proved：The algorithm of the present invention not only calculate simply, arithmetic speed soon, and better planning can be reached
Effect of optimization, with preferable application value.
The method of the present invention can be applied to sewage network design, can also be applied after being appropriately modified to fitness function
In the optimization of other tree-like pipe networks, such as Storm Sewer Network design and combined system design of pipe networks.
It should be noted that the invention is not limited in any way for above-described embodiment, all use equivalent substitutions or equivalent change
The technical scheme that the mode changed is obtained, all falls within protection scope of the present invention.
Claims (4)
1. a kind of municipal drain network plane layout design optimized calculation method, it is characterised in that comprise the following steps：
Build and estimate identical cost fitness function with drainage pipeline networks；
Tree structure genetic algorithm initialization scheme based on divide and conquer obtains initializing population；
Utilize " ledger line Circle- Analysis " be expanded after variation population；
Wherein, build and estimate that identical cost fitness function includes with drainage pipeline networks：
First, the cost fitness function of single pipeline section is built：
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Then, the cost fitness function of every pipeline section is superimposed, obtains the cost fitness function of drainage pipeline networks：
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.
2. optimized calculation method as claimed in claim 1, wherein obtaining initialization population includes：
1. an array, is divided into m son point array, two ends are all divided into sub-line array in the line of same height points group；
2. the connectedness of son point array, adjustment point array so that all in per height points group, are judged according to sub-line array
Point is all connected；
3., every height points group with sub-line array respectively obtain connect tree at random；
4., the line by point of sub- point array, between sub- point array is that communication line is constituted connected graph, produces and connects at random on connected graph
Logical tree；
5., the random connection tree on all connected graphs is merged, so as to obtain initialization population.
3. optimized calculation method as claimed in claim 1, wherein the variation population after being expanded includes：
1., take and divided and ruled obtain one tree of formula initialization by partheno genetic algorithm；
2. a side for being not belonging to the tree, is taken at random, and the side is merged with tree and obtains a connected graph for there are p bar lines；
3. corresponding circle, is found according to broken circle algorithm, and removes a line in the circle, so as to obtain a new tree, one is completed
Secondary variation；
4., using the minimum population of elitist selection algorithms selection cost fitness function, the population is proceeded next time to become
It is different, until obtaining final calculation result.
4. optimized calculation method according to claim 2, wherein the process of adjustment point array is：
1., in a son point array, for disconnected point, the point is rejected from book point array, and will connect with the point
The line connect is rejected from corresponding sub-line array；
2., the point being removed is inserted into according to its communication line in another height points group that can be connected, and will connected accordingly
Line is inserted in corresponding sub-line array.
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| CN108316442B (en) * | 2018-02-06 | 2023-03-17 | 安徽工业大学 | Method for calculating quantity of sewage in inter-well pipe sections of urban sewage pipe network section by section |
| CN108717584B (en) * | 2018-05-11 | 2022-08-16 | 同济大学 | Multi-target partition method for water supply pipe network |
| CN110147574B (en) * | 2019-04-16 | 2022-12-13 | 吉林大学珠海学院 | Auxiliary design method and system for roof siphon rainwater system and storage medium |
| CN111651544A (en) * | 2020-06-02 | 2020-09-11 | 山东工业职业学院 | Pipe network design system based on GIS positioning |
| CN113158384B (en) * | 2021-03-03 | 2021-10-08 | 东北石油大学 | Oil and gas pipeline route planning method and system |
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