CN108038575A - Waypoint location planing method based on modified NSGA II - Google Patents
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Abstract
With the fashionable whole world of shared bicycle, the problem of it is showed, also getting worse, bicycle disorderly stopped to leave about, take the places such as pavement, car lane, many local congestions, or even the generation of traffic accident are caused, therefore an effective bicycle stop planning is particularly important.In order to solve the problems, such as this, the present invention is on the basis of traditional genetic algorithm, propose a kind of waypoint location planing method based on modified NSGA II, create new site selection model, multi-objective optimization question is solved using the non-dominant quicksort method with elitism strategy, solve the problems, such as that traditional multiple-objection optimization linear weighted function weight distribution inequality causes optimal solution deviation big, the shortcomings that overcoming traditional operator ability of searching optimum difference using improved SBX crossover operators and mutation operator at the same time and population diversity cannot be kept, realize that all stops are minimum to the total distance of its demand point serviced and the total cost of all stops.
Description
Technical field
The present invention relates to computer and electronic field, the waypoint location planning more particularly to based on modified NSGA II
Method.
Background technology
With the fashionable whole world of shared bicycle, shared electric car is also unwilling to be lag behind, and adds shared ranks, but no matter share
Bicycle still shares electric car, and all unsatisfactory in management aspect, the unrest of bicycle stops leaving about, and takes pavement, car lane etc.
Place, causes many local congestions, or even the generation of traffic accident, therefore an effective bicycle stop planning seems particularly
It is important.
Traditional parking lot typically rule of thumb plans that error is big, lacks reasonability.Also have at this stage and pass through mathematics
Model plans that but traditional simulated target is single, and method for solving error is big, cannot all be applied to well physical planning it
In.
The content of the invention
The technical problem to be solved in the present invention is to provide a kind of waypoint location planning side based on modified NSGA II
Method, suitable for the position of planning stop or charging pile, solving traditional multiple-objection optimization linear weighted function weight distribution inequality causes
The problem of optimal solution deviation is big, while traditional operator global search is overcome using improved SBX crossover operators and mutation operator
Energy force difference and the shortcomings that population diversity cannot be kept, all stops are realized to the total distance of its demand point serviced and are owned
The total cost of stop is minimum, while ensures the reasonability and harmony of stop.
The present invention adopts the following technical scheme that solution above-mentioned technical problem：
It is as follows based on the waypoint location planing method of modified NSGA II, step：
(1) initialize：Demand point, the quantity of stop are set respectively, and initial reguirements point coordinates, sets population number respectively
Amount, evolutionary generation, stop spacing distance, and generation parking point coordinates forms initial population at random；
(2) quick non-dominated ranking generation first generation subgroup：Total distance with all stops to its demand point serviced
Totle drilling cost with all stops is optimization aim, builds site selection model；The data that step (1) initializes are passed through into the addressing
All stops described in model solution are to the total distance of its demand point serviced and the total cost of all stops；With obtained
Total distance and totle drilling cost are layered population by quick non-dominated ranking for standard, and assign non-dominant sequence value for all individuals
Rank, the distance most short and minimum individual of cost come first layer, i.e., the layer of non-dominant sequence value rank minimums, and so on, most
Population C after being layered afterwardsi, the individual in same layer has identical non-dominant sequence value rank；
(3) binary algorithm of tournament selection：To the population after layering, two individuals of random selection are compared, non-dominant sequence value
Rank is smaller to represent that individual is more outstanding；If non-dominant sequence value rank is identical, compare their crowding distance, prioritizing selection is gathered around
Squeeze individual in larger distance；All individuals choose excellent individual using the match system of selection of above-mentioned binary brocade bar；
(4) excellent individual that step (3) chooses is carried out intersecting successively as parent population and mutation operation generates
Progeny population Di；
(5) population after layering and progeny population are merged into a new interim population；
(6) the new interim population obtained to step (5) re-starts layering by quick non-dominated ranking, obtains one
The interim population R of layeringi, and calculate each individual crowding distance；
(7) to population Ci, progeny population DiWith interim population RiElitism strategy selection is carried out to form new population Ci+1, it is first
First eliminate population CiIn infeasible individual, then all populations are filled according to non-dominant sequence value rank orders from low to high
Ci+1, until reaching a certain layer FiWhen the Population Size of step (1) setting is occurred more than during filling, to FiAccording to crowding distance by big
To the full population C of small fillingi+1, obtain a new population consistent with initial population quantity；
(8) the straight step (7) of above-mentioned steps (3) is circulated to all evolutionary generations are completed, and obtains optimal solution.
The site selection model of the step (2) is：
Assuming that planning region has m user demand point, wherein the coordinate of i-th of demand point is (xi,yi), which needs
The amount of asking is Ei, i ∈ [1, m], now plan in n stop of the regional construction, wherein the position coordinates of j-th of stop is (x 'j,
y′j), j ∈ [1, n]；
In above formula, S is total distance of the stop to its demand point serviced, and Z builds total cost for all stops；x0With
y0Represent the limitation coordinate in the region, Z (X, Y) represents that the position coordinates set in parking lot, K cannot be builtjRepresent soil charge system
Number；QjRepresent the injected volume of j-th of stop, g represents each car floor space coefficient, and is constant；LijRepresent i-th of demand
O'clock to j-th of stop walking distance, ljkRepresent that j-th of stop represents two parkings to the distance of the k stops, L
The limiting distance of point；TijRepresent whether i-th of demand point removes j-th of stop, restrictive condition is to work as LijIt is critical more than setting
Distance L and represent that user does not remove this stop when random chance p is more than critical probability p ', on the contrary then expression is gone.
The crossover operation of the step (4) is first to carry out differential evolution algorithm, is then introduced just in former SBX crossover operators
State is distributed and discrete recombination operation, forms modified SBX crossover operators；
The formula of the differential evolution algorithm is as follows：
X in above formulabestIt is the excellent individual in parent population, F is scale factor, NPi,jRepresent the jth of i-th of new parent
A variable；
Original SBX crossover operators formula is as follows：
c1/2,j=(x1,j+x2,j)/2±β×(x1,j-x2,j)/2
SBX crossover operator formula after being just distributed very much are introduced to be changed into：
c1/2,j=(x1,j+x2,j)/2±A×|N(0,1)|×(x1,j-x2,j)/2
SBX crossover operator formula are changed into after being re-introduced into reorganization operation：
X in above-mentioned each formula1,jAnd x2,jRepresent corresponding j-th of variable on two parent chromosomes, c1/2,jRepresent filial generation
Corresponding j-th of the variable of chromosome, N (0,1) is just too distribution variables, parameter A represent step-size in search and (x1,j-x2,j)/2
Between proportionality coefficient.
The mutation operation of the step (4) uses Cauchy function operator, and formula is as follows:
In formula, Cauchyj(1) and Cauchy (1) be standard Cauchy distribution random number, δijFor scale parameter, xijTable
Show j-th of variable of i-th of individual, τ1And τ2It is operator collection parameter, generally takes：
It is additionally included in the variable for performing and intersecting or during mutation operation to cross the border processing, is crossed the border using equation below progress variable
Processing：
Wherein, vkFor former variable, v 'kFor the variable after processing of crossing the border, [lk,uk] be variable value range, rand (1)
It is the random number between 0 to 1.
It is an advantage of the invention that：
1st, method of the invention, creates new site selection model, and the limitation of stop interval, parking are with the addition of in site selection model
The condition limitation of the quantity of service of point served distance and stop, avoids stop and is distributed excessively intensive or diverging, ensure
Waypoint location be reasonably distributed, realize all stops to the total distance of its demand point serviced and always making for all stops
Valency is minimum.
2nd, method of the invention, for the deficiency of SBX crossover operators in traditional NSGAII algorithms, first introduces differential evolution and calculates
Son, is adjusted current excellent individual, to obtain more excellent individual, accelerates the search speed of operator.Then in former SBX
Normal distribution and discrete recombination operation are introduced in crossover operator, forms modified SBX crossover operators.Just it is distributed very much crossover operator one
Aspect has suitable development ability with SBX, on the other hand also extends the search space of disaggregation.Biography is abandoned in terms of mutation operation
The multinomial variation of system, the Cauchy function operator used has larger variation step-length, can be quickly jump out regional area, have
There is good ability of searching optimum.
3rd, method of the invention, intersects or variable that when mutation operation uses crosses the border processing method performing, overcomes
The shortcomings that conventional method takes boundary value and reduces population diversity, improved boundary processing method can keep the more of population very well
Sample, while accelerate convergence speed of the algorithm.
Brief description of the drawings
Fig. 1 is the flow chart of the method for the present invention.
Fig. 2 is the disaggregation distribution schematic diagram after the embodiment of the present invention is solved by the method for the present invention.
Fig. 3 is the stop distribution plots solved using conventional model, each unit length is 0.01km in figure.
Fig. 4 is the parking lot distribution plots solved using the method for the present invention, each unit length is 0.01km in figure.
Embodiment
As shown in Figure 1, the step of the present invention is as follows：
1st, initialize.Demand point and the quantity of stop are set, and initialize coordinate, demand point coordinates gives, parking
Point coordinates generates at random.Initial population quantity, evolutionary generation, website spacing distance etc. are set.Control loop variable i=1.
2nd, fitness function.All stops are selected to the total distance of its demand point serviced and the assembly of all stops
This is fitness function, for evaluating data quality.First, all data that step 1 is set site selection model is substituted into try to achieve often
Individual total distance and total cost, are then layered population by non-dominated ranking, total distance most short and the lowest cost
In first layer, and so on, the sequence value of layer is represented with non-dominant sequence value rank, initial population is converted into the population of a layering
Ci, CiSubscript i cyclic variables in order to control.
Assuming that planning region has m user demand point, wherein the coordinate of i-th of demand point is (xi,yi), which needs
The amount of asking is Ei, i ∈ [1, m], now plan in n stop of the regional construction, wherein the position coordinates of j-th of stop is (x 'j,
y′j), j ∈ [1, n]；The site selection model is as follows：
Min [Z]=min [Kj×(Qj×g)]
In formula, S is total distance of the stop to its demand point serviced, and Z builds total cost for all stops；x0And y0
Represent the limitation coordinate in the region, Z (X, Y) represents that the position coordinates set in parking lot, K cannot be builtjRepresent soil charge system
Number；QjRepresent the injected volume of the stop, g represents each bicycle floor space coefficient, and is constant；LijRepresent to need for i-th
Ask o'clock the walking distance to j-th of stop, ljkRepresent that j-th of stop represents two and stop to the distance of the k stops, L
The limiting distance of car point；TijRepresent whether i-th of demand point removes j-th of stop, restrictive condition is to work as LijMore than facing for setting
Boundary distance L and represent that user does not remove this stop when random chance p is more than critical probability p ', on the contrary then expression is gone.
3rd, binary algorithm of tournament selection.Two individuals are randomly choosed from the population after step 2 layering, compare their non-branch
With sequence value rank, non-dominant sequence value rank is smaller to represent that individual is more outstanding, if non-dominant sequence value rank is identical, compares them
Crowding distance, select the big individual of crowding distance, can so keep the diversity of population.K (the size of k is selected altogether
The generally half of initial population quantity) and ensure that all individuals for choosing do not repeat, it is finally a what is chosen
Body is as parent population, the intersection and mutation operation of progress step 4.
4th, intersection and mutation operation.The effect of intersection is that the chromosome segment of defect individual is entailed offspring, is produced new
Excellent individual.The effect of variation is to produce the new individual for being suitable for environment, keeps the diversity of species.Step 3 is selected
The parent population gone out passes through differential evolution operator computing, obtains more outstanding individual, and then individual is just being distributed very much again
Intersect.Finally allow individual to go to make a variation by Cauchy function operator according to random variation probability, obtain progeny population Di, DiSubscript i
Cyclic variable in order to control.The parent population that the progeny population and step 4 are selected finally is merged into an interim population.
Differential evolution algorithm is a kind of adaptive global optimization algorithm based on colony, and distinctive memory capability can be intelligent
The features such as adjusting search strategy, making it have fast convergence rate, strong robustness.The mutation operator that DE is used has many kinds, this hair
It is bright to use DE/best/1 operators.Formula is as follows：
X in above formulabestIt is the excellent individual in parent population, F is scale factor, NPi,jRepresent the jth of i-th of new parent
A variable；The operator is that current excellent individual is adjusted, and to obtain more excellent individual, accelerates the search speed of operator
Degree.
The present invention is using the introducing normal distribution on the basis of original SBX crossover operators and discrete recombination operation, Ran Houjie
Differential evolution operator is closed, forms the crossover operator that whole algorithm needs.
Original SBX operators formula is as follows：
c1/2,j=(x1,j+x2,j)/2±β×(x1,j-x2,j)/2
It is as follows to introduce formula after being just distributed very much：
c1/2,j=(x1,j+x2,j)/2±A×|N(0,1)|×(x1,j-x2,j)/2
The formula introduced after discrete recombination operation is as follows：
X in formula1,jAnd x2,jRepresent corresponding j-th of variable on two parent chromosomes, c1/2,jRepresent child chromosome pair
J-th of the variable answered, N (0,1) is just too distribution variables, parameter A represent step-size in search and (x1,j-x2,jRatio between)/2
Example coefficient.Here the probability that it is developed and explores can be set consistent with SBX, i.e. P=0.5 can be in the hope of A=1.481.
The present invention gives up original multinomial variation, uses Cauchy function operator instead.
Cauchy function operator has larger variation step-length relative to Gaussian mutation operator, can be quickly jump out partial zones
Domain, has good ability of searching optimum.Cauchy function operator formula is as follows:
In formula, Cauchyj(1) and Cauchy (1) be standard Cauchy distribution random number, δijFor scale parameter, xijTable
Show j-th of variable of i-th of individual, τ1And τ2It is operator collection parameter, generally takes：
Intersecting new processing method of crossing the border is used with during mutation operation：
NSGA II algorithms situation about crossing the border more or less can all occur when performing intersection or mutation operation, conventional
Method is that the change crossed the border is measured maximum or minimum value, but passes through verification and find this treating method there is certain to lack
Fall into, amended formula is as follows：
Wherein, vkFor former variable, v 'kFor the variable after processing of crossing the border, [lk,uk] be variable value range, rand (1)
It is the random number between 0 to 1.
5th, non-dominated ranking and crowding distance.The key of multiple-objection optimization is to ask for Paroet optimal solution sets, above-mentioned step
Rapid 4 obtained interim populations are layered interim population by quick non-dominated ranking, and calculate each individual gather around
Distance is squeezed, obtains the interim population R of a layeringi, RiSubscript i cyclic variables in order to control.
6th, elitism strategy.To population Ci, progeny population DiWith interim population RiElitism strategy selection is carried out to form new kind
Group Ci+1, population C is eliminated firstiIn infeasible individual, then all populations according to non-dominant sequence value rank from low to high
Order filling Ci+1, until reaching a certain layer FiWhen the Population Size of step 1 setting is occurred more than during filling, to FiAccording to it is crowded away from
Population C full from descending fillingi+1, thus obtain a new population C consistent with initial population quantityi+1；Ci+1Under
Mark i cyclic variables in order to control.
7th, control loop variable i=i+1, circulation step 3~6, until completing all evolutionary generations, end operation.
Embodiment 1：
Assuming that there are 4 parking lots in certain region, demand point has 21, and the coordinate and demand of demand point are as shown in table 1, parking
Point coordinates generates at random.It is 50 to set Population Size, and stop spacing distance is 2.5km, and maximum evolution number is 200.Specifically
Parameter setting can be changed according to actual conditions.
1 demand point coordinates of table (relative to the position of coordinate origin, unit is 0.01km)
By that can draw a series of solutions after NSGA II Algorithm for Solving, a portion solves for forward position, and a part is feasible
Solution, the solution that forward position solution is 1 for non-dominant sequence value, feasible solution are more than 1 solution for non-dominant sequence value, and forward position is solved all better than feasible
Solution, as shown in Figure 2.
2 forward position of table solution parameter (unit of S is 0.01km, and the unit of Z is member)
Table 2 is the partial parameters of forward position solution, because the non-dominant sequence value of all forward positions solution is all 1, they do not have branch
With relation, but optimal output can be found by crowding distance, crowding distance can be excluded directly for infinite individual, because
They are all a target function value minimums in all forward position solutions, another is maximum as a result, can not meet us will
Ask.As long as the last individual that crowding distance maximum is found in remaining forward position solution is exactly optimal solution.
As shown in figure 3, the parking point coordinates solved using conventional model, due to not accounting for stop spacing and stop
Demand for services point quantity so that the result for causing to solve is likely to occur the situation of skewness.
As shown in figure 4, the parking lot coordinate that the method for the present invention solves is reasonably distributed, parking point coordinates distribution considers
Many aspects, including the requirement such as stop spacing, quantity of service, beeline, least cost.
Patent of the present invention is not limited to a certain hardware requirement or environment, is also not necessarily limited to above-mentioned embodiment, every right
The modification and application of the present invention is all in protection scope of the present invention.
Claims (5)
1. the waypoint location planing method based on modified NSGA II, it is characterised in that step is as follows：
(1) initialize：Respectively set demand point, the quantity of stop, initial reguirements point coordinates, respectively set population quantity,
Evolutionary generation, stop spacing distance, and generation parking point coordinates forms initial population at random；
(2) quick non-dominated ranking generation first generation subgroup：With all stops to the total distance of its demand point serviced and institute
The totle drilling cost for having stop is optimization aim, builds site selection model；The data that step (1) initializes are passed through into the site selection model
All stops are solved to the total distance of its demand point serviced and the total cost of all stops；With it is obtained always away from
Population is layered by quick non-dominated ranking for standard from totle drilling cost, and non-dominant sequence value rank is assigned for all individuals,
The distance most short and minimum individual of cost comes first layer, i.e., the layer of non-dominant sequence value rank minimums, and so on, finally obtain
Population C after layeringi, the individual in same layer has identical non-dominant sequence value rank；
(3) binary algorithm of tournament selection：To the population after layering, two individuals of random selection are compared, non-dominant sequence value rank
It is smaller to represent that individual is more outstanding；If non-dominant sequence value rank is identical, compare their crowding distance, prioritizing selection it is crowded away from
From larger individual；All individuals choose excellent individual using the match system of selection of above-mentioned binary brocade bar；
(4) excellent individual that step (3) chooses is carried out intersecting successively as parent population and mutation operation generates filial generation
Population Di；
(5) population after layering and progeny population are merged into a new interim population；
(6) the new interim population obtained to step (5) re-starts layering by quick non-dominated ranking, obtains a layering
Interim population Ri, and calculate each individual crowding distance；
(7) to population Ci, progeny population DiWith interim population RiElitism strategy selection is carried out to form new population Ci+1, wash in a pan first
Eliminate population CiIn infeasible individual, all populations are then filled C according to non-dominant sequence value rank orders from low to highi+1,
Until reaching a certain layer FiWhen the Population Size of step (1) setting is occurred more than during filling, to FiIt is descending according to crowding distance
The full population C of fillingi+1, obtain a new population consistent with initial population quantity；
(8) the straight step (7) of above-mentioned steps (3) is circulated to all evolutionary generations are completed, and obtains optimal solution.
2. the waypoint location planing method according to claim 1 based on modified NSGA II, it is characterised in that institute
The site selection model for stating step (2) is：
Assuming that planning region has m user demand point, wherein the coordinate of i-th of demand point is (xi,yi), this bicycle demand
For Ei, i ∈ [1, m], now plan in n stop of the regional construction, wherein the position coordinates of j-th of stop is (xj′,
yj'), j ∈ [1, n]；
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<mi>i</mi>
</msub>
<mo>-</mo>
<msup>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
<mo>&prime;</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
</msqrt>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&le;</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>></mo>
<mi>L</mi>
<mo>&cap;</mo>
<mi>p</mi>
<mo><</mo>
<msup>
<mi>p</mi>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>L</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>></mo>
<mi>L</mi>
<mo>&cap;</mo>
<mi>p</mi>
<mo>></mo>
<msup>
<mi>p</mi>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>l</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<msqrt>
<mrow>
<mo>(</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>&prime;</mo>
</msup>
<mo>-</mo>
<msup>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>&prime;</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
<mo>&prime;</mo>
</msup>
<mo>-</mo>
<msup>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>&prime;</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
</msqrt>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>K</mi>
<mi>j</mi>
</msub>
<mo>&Proportional;</mo>
<mrow>
<mo>(</mo>
<msup>
<msub>
<mi>x</mi>
<mi>j</mi>
</msub>
<mo>&prime;</mo>
</msup>
<mo>,</mo>
<msup>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>&NotElement;</mo>
<mi>Z</mi>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>,</mo>
<mi>Y</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>l</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>></mo>
<mi>L</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>{</mo>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>x</mi>
<mo>&le;</mo>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>y</mi>
<mo>&le;</mo>
<msub>
<mi>y</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>}</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In above formula, S is total distance of the stop to its demand point serviced, and Z builds total cost for all stops；x0And y0Table
Show the limitation coordinate in the region, Z (X, Y) represents that the position coordinates set in parking lot, K cannot be builtjRepresent soil charge coefficient；
QjRepresent the injected volume of j-th of stop, g represents each car floor space coefficient, and is constant；LijRepresent i-th of demand point
To the walking distance of j-th of stop, ljkRepresent that j-th of stop represents two stops to the distance of the k stops, L
Limiting distance；TijRepresent whether i-th of demand point removes j-th of stop, restrictive condition is to work as LijMore than setting it is critical away from
Represent that user does not remove this stop when being more than critical probability p ' from L and random chance p, on the contrary then expression is gone.
3. the waypoint location planing method according to claim 1 based on modified NSGA II, it is characterised in that institute
The crossover operation for stating step (4) is first to carry out differential evolution algorithm, then in former SBX crossover operators introduce normal distribution and from
Reorganization operation is dissipated, forms modified SBX crossover operators；
The formula of the differential evolution algorithm is as follows：
X in above formulabestIt is the excellent individual in parent population, F is scale factor, NPi,jRepresent j-th of change of i-th of new parent
Amount；
Original SBX crossover operators formula is as follows：
c1/2,j=(x1,j+x2,j)/2±β×(x1,j-x2,j)/2
SBX crossover operator formula after being just distributed very much are introduced to be changed into：
c12,j=(x1,j+x2,j)/2±A×|N(0,1)|×(x1,j-x2,j)/2
SBX crossover operator formula are changed into after being re-introduced into reorganization operation：
X in above-mentioned each formula1,jAnd x2,jRepresent corresponding j-th of variable on two parent chromosomes, c1/2,jRepresent filial generation dyeing
Corresponding j-th of the variable of body, N (0,1) is just too distribution variables, parameter A represent step-size in search and (x1,j-x2,jBetween)/2
Proportionality coefficient.
4. the waypoint location planing method according to claim 1 based on modified NSGA II, it is characterised in that institute
The mutation operation for stating step (4) uses Cauchy function operator, and formula is as follows:
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<msub>
<mi>&delta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<msub>
<mi>&delta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&times;</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&tau;</mi>
<mn>1</mn>
</msub>
<mo>&times;</mo>
<mi>C</mi>
<mi>a</mi>
<mi>y</mi>
<mi>c</mi>
<mi>g</mi>
<mi>y</mi>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
<mo>+</mo>
<msub>
<mi>&tau;</mi>
<mn>2</mn>
</msub>
<mo>&times;</mo>
<msub>
<mi>Cauchy</mi>
<mi>j</mi>
</msub>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msup>
<msub>
<mi>&delta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&prime;</mo>
</msup>
<mo>&times;</mo>
<msub>
<mi>Cauchy</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mi>n</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, Cauchyj(1) and Cauchy (1) be standard Cauchy distribution random number, δijFor scale parameter, xijRepresent i-th
J-th individual of variable, τ1And τ2It is operator collection parameter, generally takes：
<mrow>
<msub>
<mi>&tau;</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<mn>2</mn>
<msqrt>
<mi>n</mi>
</msqrt>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>,</mo>
<msub>
<mi>&tau;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>.</mo>
</mrow>
5. the waypoint location planing method according to claim 1 based on modified NSGA II, it is characterised in that also
It is included in the variable for performing and intersecting or during mutation operation to cross the border processing, is crossed the border processing using equation below progress variable：
<mrow>
<msubsup>
<mi>v</mi>
<mi>k</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>l</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
<mo>&times;</mo>
<mi>r</mi>
<mi>a</mi>
<mi>n</mi>
<mi>d</mi>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
<mo>+</mo>
<msub>
<mi>l</mi>
<mi>k</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>v</mi>
<mi>k</mi>
</msub>
<mo><</mo>
<msub>
<mi>l</mi>
<mi>k</mi>
</msub>
<mi>o</mi>
<mi>r</mi>
<mi> </mi>
<msub>
<mi>v</mi>
<mi>k</mi>
</msub>
<mo>></mo>
<msub>
<mi>u</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>v</mi>
<mi>k</mi>
</msub>
</mtd>
<mtd>
<mrow>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
<mi>e</mi>
<mi>r</mi>
<mi>w</mi>
<mi>i</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein, vkFor former variable, v 'kFor the variable after processing of crossing the border, [lk,uk] be variable value range, rand (1) is 0 to 1
Between random number.
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|---|---|---|---|---|
| CN108764555A (en) * | 2018-05-22 | 2018-11-06 | 浙江大学城市学院 | A kind of shared bicycle based on Hadoop parks a site selecting method |
| CN109035750A (en) * | 2018-08-30 | 2018-12-18 | 江苏大学 | A kind of shared bicycle disorderly stops the allocation and transportation method left about |
| CN109919485A (en) * | 2019-03-06 | 2019-06-21 | 桂林理工大学 | A kind of Multipurpose Optimal Method of the Water Resources Allocation based on NSGA-II |
| CN110147885A (en) * | 2019-05-07 | 2019-08-20 | 浙江大学城市学院 | A kind of shared bicycle of improved adaptive GA-IAGA parks point distribution method |
| CN111310625A (en) * | 2020-02-06 | 2020-06-19 | 上海智幻软件科技有限公司 | Multi-person posture detection method and system based on openposition |
| CN111582552A (en) * | 2020-04-16 | 2020-08-25 | 浙江大学城市学院 | Shared bicycle parking point distribution method based on multi-target genetic algorithm |
| CN112462803A (en) * | 2020-11-27 | 2021-03-09 | 北京工商大学 | Unmanned aerial vehicle path planning method based on improved NSGA-II |
| CN112487622A (en) * | 2020-11-23 | 2021-03-12 | 国网河北省电力有限公司经济技术研究院 | Method and device for locating and sizing electric vehicle charging pile and terminal equipment |
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| CN108764555A (en) * | 2018-05-22 | 2018-11-06 | 浙江大学城市学院 | A kind of shared bicycle based on Hadoop parks a site selecting method |
| CN108764555B (en) * | 2018-05-22 | 2021-08-31 | 浙江大学城市学院 | Shared bicycle parking point site selection method based on Hadoop |
| CN109035750B (en) * | 2018-08-30 | 2021-02-12 | 江苏大学 | Dispatching method for disorderly parking and disorderly placing shared single vehicles |
| CN109035750A (en) * | 2018-08-30 | 2018-12-18 | 江苏大学 | A kind of shared bicycle disorderly stops the allocation and transportation method left about |
| CN109919485A (en) * | 2019-03-06 | 2019-06-21 | 桂林理工大学 | A kind of Multipurpose Optimal Method of the Water Resources Allocation based on NSGA-II |
| CN110147885A (en) * | 2019-05-07 | 2019-08-20 | 浙江大学城市学院 | A kind of shared bicycle of improved adaptive GA-IAGA parks point distribution method |
| CN111310625A (en) * | 2020-02-06 | 2020-06-19 | 上海智幻软件科技有限公司 | Multi-person posture detection method and system based on openposition |
| CN111582552A (en) * | 2020-04-16 | 2020-08-25 | 浙江大学城市学院 | Shared bicycle parking point distribution method based on multi-target genetic algorithm |
| CN111582552B (en) * | 2020-04-16 | 2023-04-25 | 浙江大学城市学院 | Shared bicycle parking point distribution method based on multi-target genetic algorithm |
| CN112487622A (en) * | 2020-11-23 | 2021-03-12 | 国网河北省电力有限公司经济技术研究院 | Method and device for locating and sizing electric vehicle charging pile and terminal equipment |
| CN112487622B (en) * | 2020-11-23 | 2023-03-21 | 国网河北省电力有限公司经济技术研究院 | Method and device for locating and sizing electric vehicle charging pile and terminal equipment |
| CN112462803A (en) * | 2020-11-27 | 2021-03-09 | 北京工商大学 | Unmanned aerial vehicle path planning method based on improved NSGA-II |
| CN113095943A (en) * | 2021-05-10 | 2021-07-09 | 中国工商银行股份有限公司 | Position determining method, position determining device, electronic equipment and readable storage medium |
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