CN109862573B - LTE hybrid networking self-planning method based on multi-target particle swarm - Google Patents

LTE hybrid networking self-planning method based on multi-target particle swarm Download PDF

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CN109862573B
CN109862573B CN201910168161.4A CN201910168161A CN109862573B CN 109862573 B CN109862573 B CN 109862573B CN 201910168161 A CN201910168161 A CN 201910168161A CN 109862573 B CN109862573 B CN 109862573B
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CN109862573A (en
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董宏成
王腾云
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Chongqing University of Post and Telecommunications
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Abstract

The invention requests to protect an LTE hybrid networking self-planning method based on multi-target particle swarm. Firstly, acquiring service information of a target area user; secondly, reconstructing a plurality of target optimization functions by combining the characteristics of ideal backhaul of the LTE hybrid networking; then, inputting user service information into a multi-objective optimization function, and selecting a better solution from Pareto solution set fuzzy compromise to optimize the model by using an improved discrete multi-objective particle swarm algorithm; and finally, obtaining the base station site selection coordinate of the LTE hybrid networking. The invention improves the planning efficiency of the LTE hybrid networking.

Description

LTE hybrid networking self-planning method based on multi-target particle swarm
Technical Field
The invention belongs to the technical field of communication LTE (Long term evolution) hybrid networking, and particularly relates to an LTE hybrid networking self-planning method based on multi-target particle swarm.
Background
With the continuous development of mobile communication networks, spectrum resources are more and more scarce, single-mode base station independent networking is controlled by capacity limitation and cannot adapt to network requirements, and an operator gradually promotes LTE (long term evolution) mixed networking in various regions in order to meet the gradually-increased throughput requirements and reasonably utilize resources. The LTE hybrid networking is that the existing high-frequency TDD LTE and the low-frequency FDD LTE with replanted frequency are deployed to a certain area at the same time, the interference between the same layers is greatly reduced by the base station with different frequencies through hybrid networking, the advantages of each system can be exerted to the maximum extent, the defects are compensated, the investment cost is reduced, and high-quality network service is provided for users. The LTE hybrid networking is receiving more and more attention, and the demand for site selection and self-planning of the base station of the LTE hybrid networking is becoming higher and higher at present.
The base station site selection plan is used as an important parameter for base station deployment, and has great influence on the coverage and capacity of a network. Nowadays, mobile communication networks are increasingly complex, multi-system base stations coexist in many scenes, an optimal solution is difficult to find in a manual site selection planning mode, operators demand cost reduction and planning efficiency improvement, and a traditional manual network planning mode using drive test information is difficult to adapt to requirements, so site selection self-planning of communication base stations is very important. The existing network self-planning method is not always considered in a complete target, the improved algorithm is too complex, the practical value is not high, and the method cannot be applied to network self-planning under LTE (Long term evolution) hybrid networking. The LTE hybrid networking base station self-planning is different from the traditional base station networking self-planning, and a plurality of targets need to be considered simultaneously when planning FDD and TDD base stations, so that a LTE hybrid networking base station self-planning scheme needs to be researched urgently at present, and an efficient base station deployment scheme is provided for operators.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. The LTE hybrid networking self-planning method based on the multi-target particle swarm is capable of reducing cost and improving LTE network performance. The technical scheme of the invention is as follows:
an LTE hybrid networking self-planning method based on multi-target particle swarm comprises the following steps:
the method comprises the following steps: acquiring service information of a target area user to obtain service distribution of a target area;
step two: combining the characteristics of ideal backhaul of LTE hybrid networking, namely FDD is used as a macro base station to mainly provide wide coverage, TDD is used as a small base station to be deployed to mainly absorb capacity, and a target optimization function including the maximized coverage rate, the maximum network energy efficiency ratio, the maximum network load and the minimum cost is reconstructed;
step three: and (3) optimizing the model by using a discrete multi-target particle swarm algorithm for improving Pareto solution centralized congestion distance sequencing and selecting a better solution from Pareto solution centralized fuzzy compromise, and finally obtaining the base station site selection coordinate of the LTE hybrid networking.
Further, the first step: acquiring service information of a target area user to obtain service distribution of a target area, specifically comprising:
firstly, gridding a target network P into N pixel points, and dividing N test points into common test points N according to service demand prediction1Individual sum hot spot area test point N2Any point on P can be calibrated in a grid by Cartesian coordinates, and any point is represented as riThe coordinate is (x)i，yi)。
Further, the second step combines the characteristics of the LTE hybrid networking ideal backhaul to reconstruct a multi-objective optimization model, and specifically includes:
firstly, k-layer networks are deployed on M candidate subsets, and there are 2-layer networks in total, namely a TDD network and an FDD network respectively, wherein k is equal to 2 to representA total number of network layers, with two options for each base station, akmRepresenting the deployment situation of the base station at the position of the K layer M, wherein '1' represents that the base station at the K layer is built at the position of the M, and '0' represents that the base station at the K layer is not built at the position of the M, and K multiplied by M represents the size of an address selection matrix space, so that the address selection matrix of the base station of the hybrid networking can be obtained:
Figure GDA0003504606160000021
based on the characteristics of dual connection of the LTE hybrid networking, namely, a test point can be simultaneously connected with a TDD base station and an FDD base station, and only whether the service rate of the test point is met or not is considered, so that a base station access indication function and a signal-to-noise ratio are respectively obtained;
Figure GDA0003504606160000031
and Rk,n,m＝Bk,n×log(1+SINRk,n,m)
Wherein Δk,n,mRepresents the situation that the k layer m position covers the test point n, Rk,n,mThe service rate that the base station at the position of k layers m can reach when the test point n receives the test point n is represented, the service rate of the hot test point is higher than the requirement of the common test point, Rmin,nRepresenting the minimum rate for meeting the access requirement of the test point n, and '1' representing that the test point n is covered by the position of k layers m, and R is at the momentk,n,m≥Rmin,nAnd 0 indicates that no k-layer base station is built at the m position, and R is in the timek,n,m≤Rmin,n，Bk,nThe bandwidth of a test point n connected with a k-layer base station;
obtaining a site selection matrix H of the test point finally accessed to the base station according to the site selection matrix of the base station and the test point access indication function:
Figure GDA0003504606160000032
wherein b isnmThe situation that the test point n is covered by the base station at the position m is represented, a TDD base station or an FDD base station may be built at the position m, or the base station is not built, and the test point n is covered by any base station, so that the test point n is represented to be covered;
finally, the four planning targets of the LTE hybrid networking are respectively as follows:
1) maximizing coverage
Figure GDA0003504606160000033
Wherein N is1Number of common test points, N2The number of hot spot test points is determined;
2) maximum network energy efficiency ratio
Figure GDA0003504606160000034
Wherein P isk,mExpressed as the transmit power of a k-tier m base station;
3) maximum network load
Figure GDA0003504606160000035
Wherein P isth,mAnd the load blocking threshold is expressed as the load blocking threshold which should be reached when the base station m is deployed, and is used for limiting the access number of the access test points of the base station. Ψk,n,mRepresenting the percentage of the load in the base station m to the base station demand load, when the value exceeds the threshold P in the practical engineeringth,mThen, the load limiting factor exp (P) may be usedth,m-Ψk,n,m) The load of the access base station m is adjusted and reduced;
4) minimum cost
Figure GDA0003504606160000041
Wherein C iskThe unit cost of the kth base station.
Further, in the third step, an improved discrete multi-objective particle swarm algorithm is utilized, a better solution is selected from a Pareto solution set through fuzzy compromise to optimize the model, and finally the base station site selection coordinate of the LTE hybrid networking is obtained, wherein the method comprises the following steps: first, dynamic crowding distance is improved
Figure GDA0003504606160000042
J is the total number of self-planned targets, fj(i +1) and fj(i-1) j' th target value of the particle before and after the particle i; f. ofjmaxAnd fjminMaximum and minimum values of the jth objective function for all particles in the external document;
calculating the congestion of an individual with an adjacent individual in an external profileThe extrusion degree is sorted according to the new crowding distance, the solution with the minimum dense distance is removed, the dense distances of the rest Pareto solutions are calculated, and the calculation is circulated until the number of the rest Pareto solutions is the external capacity S which is set in an expected mode; finally according to the formula
Figure GDA0003504606160000043
Calculating a standard membership function for particle i, wherein uijRepresenting a standard membership function;
in the iterative formula of the discrete particle swarm, the iterative formulas of the speed and the position are respectively as follows:
Figure GDA0003504606160000044
Figure GDA0003504606160000045
and
Figure GDA0003504606160000046
respectively representing the speed and the position of the particle i in the d-dimensional space of the t +1 generation;
Figure GDA0003504606160000047
and
Figure GDA0003504606160000048
the individual extreme value and the global extreme value of the particle i in the generation t are respectively; r is1And r2Is a random number between 0 and 1; c. C1And c1Is a learning factor, usually taken 2 at the same time; ω is the inertial weight, which is used herein for the adaptive transform, and ω is expressed as:
Figure GDA0003504606160000049
t is the number of current iterations, tmaxIs the maximum number of iterations, ωmaxAnd ωminThe inertial weights, ω max and min, respectively, are usually taken to be ωmax＝0.9，ωmin＝0.4。
Further, in the third step, the improved discrete multi-target particle swarm algorithm specifically comprises the following steps:
step 1, inputting data, and inputting the number of candidate base stations, test point information, access rate, function boundary and dimensionality;
step 2, initializing a particle population: setting the population number and the maximum iteration number, and randomly generating the initial position of 0 moment according to the constraint relation
Figure GDA0003504606160000051
And initial velocity at time 0
Figure GDA0003504606160000052
Calculating an objective function for each particle, initializing the local optimum position of the particle to
Figure GDA0003504606160000053
Setting the maximum crowding distance of the boundary as d when the external file is empty;
step 3, initializing an external file: will be provided with
Figure GDA0003504606160000054
Adding the dominant solution into the external archive at one time and retaining the dominant solution, wherein the dominant solution is represented as an initial solution in the external archive;
step 4, starting iteration, wherein t is 1; according to the above formula
Figure GDA0003504606160000055
Calculating the crowdedness of all individuals in the external profile, and selecting one individual as the global optimal solution by adopting the roulette method described above
Figure GDA0003504606160000056
Step 5, updating the position x and the speed v of the particles according to the particle swarm iterative formula and recalculating the fitness of the individual;
step 6, updating an external file: sequentially adding the particles subjected to position updating into an external file, judging a domination relationship according to the crowding distance, and if the newly added individuals dominate the individuals in the external file, adding the new individuals and deleting the domination individuals; if the new individual does not dominate the individuals in the external file, not adding; if the comparison is impossible, comparing the current external capacity S 'with the expected set external capacity S, if S' is less than or equal to S, adding a new individual into an external file, and adding 1 to S, and when the solution in the external file is greater than a specified value, updating a non-inferior solution set by using the cyclic deletion method;
step 7, updating P of the particlebest. And if the maximum iteration times are met, stopping searching, outputting a Pareto optimal front edge according to an external elite solution set, finding a compromise solution by using the fuzzy decision method, and otherwise, turning to the step 4 when t is t + 1.
Further, the roulette method in step 4 specifically includes: the basic idea is as follows: the probability of each individual being selected is in direct proportion to the fitness function value, the group size is set to be N, and the individual xiHas a fitness of f (x)i) Then the individual xiThe probability of selection of (a) is:
Figure GDA0003504606160000061
and P (x)1)+P(x2)+…+P(xN) When 1, the cumulative distribution probability is:
Figure GDA0003504606160000062
the method comprises the following specific operation steps: calculating the selection probability and cumulative distribution probability of each individual according to the above formula, and generating a [0,1 ] by using rand ()]R is a random number r between, if r is less than or equal to q1Then the individual x1And (6) selecting. If q isk-1＜r＜qk(2. ltoreq. k. ltoreq.N), then the individual xkAnd (6) selecting.
The invention has the following advantages and beneficial effects:
the invention provides an LTE (Long term evolution) hybrid networking self-planning method, which has the following innovation points;
1. and establishing an LTE hybrid networking optimization model. According to the method, an LTE hybrid networking layered multi-target base station planning model is reconstructed by taking coverage rate, load rate, energy efficiency ratio and cost as optimization targets. The model comprehensively considers the characteristics of LTE hybrid networking from four aspects, only considers the cost and coverage rate of networking compared with the conventional planning model, and has certain superiority.
2. The method for sequencing the crowding distances in the multi-target particle algorithm is improved. The conventional congestion sorting is only sorting by the geometric distance between particles, which results in that the particles with excellent fitness value are sorted out later. The invention improves the sorting method of the crowding distance of the particles, adopts the dynamic crowding distance sorting of the particles and is beneficial to that excellent particles are selected in front.
In the invention, the characteristics of the LTE hybrid networking are fully considered, a more perfect model is established, and the improved discrete multi-target particle swarm algorithm is adopted to search the site selection combination of the base station with high coverage rate, low cost, multiple loads and small energy efficiency ratio as far as possible, thereby improving the site selection efficiency and having certain value.
Drawings
Fig. 1 is a schematic flow chart of an LTE hybrid networking self-planning method based on multi-objective particle swarm in the preferred embodiment of the present invention;
fig. 2 is an overall framework diagram of the preferred embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
as shown in fig. 1 and 2: firstly, service prediction is carried out on the area to obtain the capacity conditions of a hot spot area and a common area, the obtained area is represented by a central test point of an area square, and the coverage and capacity conditions of the test point represent the coverage and capacity conditions of the area square; secondly, reconstructing a plurality of target optimization functions by combining the characteristics of ideal backhaul of the LTE hybrid networking; then, inputting user service information into a multi-objective optimization function, and selecting a better solution from Pareto solution set fuzzy compromise to optimize the model by using an improved discrete multi-objective particle swarm algorithm; and finally, obtaining the base station site selection coordinate of the LTE hybrid networking.
The method comprises the following steps: acquiring service information of a target area user to obtain service distribution of a target area:
firstly, gridding a target network P into N pixel points, and dividing N test points into common test points N according to service demand prediction1Individual sum hot spot area test point N2And (4) respectively. Any point on P can be calibrated in a grid in Cartesian coordinates, and any point is represented as riThe coordinate is (x)i,yi)。
Step two: and reconstructing a plurality of target optimization functions by combining the characteristics of ideal backhaul of the LTE hybrid networking.
Firstly, deploying a k-layer network on M candidate subsets, wherein each base station has two choices, and analyzing to obtain a base station site selection matrix of the hybrid networking:
Figure GDA0003504606160000071
based on the characteristic of dual connection of the LTE hybrid networking, the test point can be accessed to any layer network, the number and the type of the test point accessed to the base station are not limited, only whether the service rate of the test point is met or not is considered, and the indication function of base station access and the signal-to-noise ratio can be obtained.
Figure GDA0003504606160000072
And Rk,n,m＝Bk,n×log(1+SINRk,n,m)
Obtaining a site selection matrix H of the test point finally accessed to the base station according to the site selection matrix of the base station and the test point access indication function:
Figure GDA0003504606160000081
finally, four target targets of the LTE hybrid networking are obtained as follows:
1) maximizing coverage
Figure GDA0003504606160000082
2) Maximum network energy efficiency ratio
Figure GDA0003504606160000083
3) Maximum network load
Figure GDA0003504606160000084
4) Minimum cost
Figure GDA0003504606160000085
Finally, obtaining an LTE hybrid networking self-planning model:
Figure GDA0003504606160000086
3. step three: and (3) optimizing the model by utilizing an improved discrete multi-target particle swarm algorithm and selecting a better solution from the Pareto solution set fuzzy compromise, and finally obtaining the base station site selection coordinate of the LTE hybrid networking. Further, the reconstructing a plurality of objective optimization functions by using the ideal backhaul characteristics of the LTE hybrid networking in the second step specifically includes: and selecting a better solution from the Pareto solution set by fuzzy compromise to optimize the model, and finally obtaining the base station site selection coordinate of the LTE hybrid networking. First, dynamic congestion distance is improved
Figure GDA0003504606160000087
And calculating the crowding degree of the individual and the adjacent individual in the external file, then removing the solution with the minimum dense distance after sorting the crowding degree with the new crowding distance, then calculating the dense distance of the rest Pareto solutions, and circularly calculating until the number of the rest Pareto solutions is the external capacity S expected to be set. Finally according to the formula
Figure GDA0003504606160000091
And calculating a standard membership function of the particle i. The solving process is as follows:
step 1, inputting data, and inputting the number of candidate base stations, test point information, access rate, function boundary and dimensionality;
step 2, initializing a particle population: setting the population number and the maximum iteration number, and randomly generating the initial position of 0 moment according to the constraint relation
Figure GDA0003504606160000092
And initial velocity at time 0
Figure GDA0003504606160000093
Calculating an objective function for each particle, initializing the local optimum position of the particle to
Figure GDA0003504606160000094
Setting the maximum crowding distance of the boundary as d when the external file is empty;
step 3, initializing an external file: will be provided with
Figure GDA0003504606160000095
Adding the dominant solution into the external archive at one time and retaining the dominant solution, wherein the dominant solution is represented as an initial solution in the external archive;
step 4, starting iteration, wherein t is 1; according to the above formula
Figure GDA0003504606160000096
Calculating the crowdedness of all individuals in the external profile, and selecting one individual as the global optimal solution by adopting the roulette method described above
Figure GDA0003504606160000097
Step 5, updating the position x and the speed v of the particles according to the particle swarm iterative formula and recalculating the fitness of the individual;
step 6, updating an external file: sequentially adding the particles subjected to position updating into an external file, judging a domination relationship according to the crowding distance, and if the newly added individuals dominate the individuals in the external file, adding the new individuals and deleting the domination individuals; if the new individual does not dominate the individuals in the external file, not adding; if the comparison is impossible, comparing the current external capacity S 'with the expected set external capacity S, if S' is less than or equal to S, adding a new individual into an external file, and adding 1 to S, and when the solution in the external file is greater than a specified value, updating a non-inferior solution set by using the cyclic deletion method;
step 7, updating P of the particlebest. And if the maximum iteration times are met, stopping searching, outputting a Pareto optimal front edge according to an external elite solution set, finding a compromise solution by using the fuzzy decision method, and otherwise, turning to the step 4 when t is t + 1.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.

Claims (1)

1. An LTE hybrid networking self-planning method based on multi-target particle swarm is characterized by comprising the following steps:
the method comprises the following steps: acquiring service information of a target area user to obtain service distribution of a target area;
step two: combining the characteristics of ideal backhaul of LTE hybrid networking, namely FDD is used as a macro base station to mainly provide wide coverage, TDD is used as a small base station to be deployed to mainly absorb capacity, and a target optimization function including the maximized coverage rate, the maximum network energy efficiency ratio, the maximum network load and the minimum cost is reconstructed;
step three: selecting a better solution from Pareto solution centralized fuzzy compromise to optimize a model by utilizing a discrete multi-target particle swarm algorithm for improving Pareto solution centralized congestion distance sequencing, and finally obtaining a base station site selection coordinate of the LTE hybrid networking;
the first step is as follows: acquiring service information of a target area user to obtain service distribution of a target area, specifically comprising:
firstly, gridding a target network P into N pixel points, and dividing N test points into common tests according to service demand predictionPoint N1Individual sum hot spot area test point N2Any point on P can be calibrated in a grid by Cartesian coordinates, and any point is represented as riThe coordinate is (x)i，yi)；
The second step combines the characteristics of the ideal backhaul of the LTE hybrid networking to reconstruct a multi-objective optimization model, and specifically comprises the following steps:
firstly, deploying k-layer networks on M candidate subsets, wherein the total number of the k-layer networks is 2, namely a TDD network and an FDD network, k is equal to 2 and represents the total number of the network layers, each base station has two choices, akmRepresenting the deployment situation of the base station at the position of the K layer M, wherein '1' represents that the base station at the K layer is built at the position of the M, and '0' represents that the base station at the K layer is not built at the position of the M, and K multiplied by M represents the size of an address selection matrix space, so that the address selection matrix of the base station of the hybrid networking can be obtained:
Figure FDA0003504606150000011
based on the characteristics of dual connection of the LTE hybrid networking, namely, a test point can be simultaneously connected with a TDD base station and an FDD base station, and only whether the service rate of the test point is met or not is considered, so that a base station access indication function and a signal-to-noise ratio are respectively obtained;
Figure FDA0003504606150000021
and Rk,n,m＝Bk,n×log(1+SINRk,n,m)
Wherein Δk,n,mRepresents the situation that the k layer m position covers the test point n, Rk,n,mThe service rate that the base station at the position of k layers m can reach when the test point n receives the test point n is represented, the service rate of the hot test point is higher than the requirement of the common test point, Rmin,nRepresenting the minimum rate for meeting the access requirement of the test point n, and '1' representing that the test point n is covered by the position of k layers m, and R is at the momentk,n,m≥Rmin,nAnd 0 indicates that no k-layer base station is built at the m position, and R is in the timek,n,m≤Rmin,n，Bk,nThe bandwidth of a test point n connected with a k-layer base station;
obtaining the test point according to the base station site selection matrix and the test point access indication functionAnd the final access base station site selection matrix H is as follows:
Figure FDA0003504606150000022
wherein b isnmThe situation that the test point n is covered by the base station at the position m is represented, a TDD base station or an FDD base station may be built at the position m, or the base station is not built, and the test point n is covered by any base station, so that the test point n is represented to be covered;
finally, the four planning targets of the LTE hybrid networking are respectively as follows:
1) maximizing coverage
Figure FDA0003504606150000023
Wherein N is1Number of common test points, N2The number of hot spot test points is determined;
2) maximum network energy efficiency ratio
Figure FDA0003504606150000024
Wherein P isk,mExpressed as the transmit power of a k-tier m base station;
3) maximum network load
Figure FDA0003504606150000025
Wherein P isth,mExpressed as the load blocking threshold to be reached at the time of deployment of base station m, for limiting the number of access test points, Ψ, of base stationsk,n,mRepresenting the percentage of the load in the base station m to the base station demand load, when the value exceeds the threshold P in the practical engineeringth,mThen, the load limiting factor exp (P) may be usedth,m-Ψk,n,m) The load of the access base station m is adjusted and reduced;
4) minimum cost
Figure FDA0003504606150000031
Wherein C iskThe cost unit price of the kth base station;
in the third step, an improved discrete multi-target particle swarm algorithm is utilized, and a better solution is selected from a Pareto solution set fuzzy compromise to optimize the modelFinally, obtaining a base station site selection coordinate of the LTE hybrid networking, comprising: first, dynamic crowding distance is improved
Figure FDA0003504606150000032
J is the total number of self-planned targets, fj(i +1) and fj(i-1) j' th target value of the particle before and after the particle i; f. ofjmaxAnd fjminMaximum and minimum values of the jth objective function for all particles in the external document;
calculating the crowding degree of the individual and the adjacent individual in the external file, then removing the solution with the minimum dense distance after sorting the crowding degree with the new crowding distance, then calculating the dense distance of the remaining Pareto solutions, and circularly calculating until the number of the remaining Pareto solutions is the external capacity S expected to be set; finally according to the formula
Figure FDA0003504606150000033
Calculating a standard membership function for particle i, wherein uijRepresenting a standard membership function;
in the iterative formula of the discrete particle swarm, the iterative formulas of the speed and the position are respectively as follows:
Figure FDA0003504606150000034
Figure FDA0003504606150000035
and
Figure FDA0003504606150000036
respectively representing the speed and the position of the particle i in the d-dimensional space of the t +1 generation;
Figure FDA0003504606150000037
and
Figure FDA0003504606150000038
the individual extreme value and the global extreme value of the particle i in the generation t are respectively; r is1And r2Is a random number between 0 and 1; c. C1And c1Is a learning factor, usually taken 2 at the same time; ω is the inertial weight, using the inertial weight of the adaptive transform, and ω is expressed as:
Figure FDA0003504606150000039
t is the number of current iterations, tmaxIs the maximum number of iterations, ωmaxAnd ωminThe inertial weights, ω max and min, respectively, are usually taken to be ωmax＝0.9，ωmin＝0.4；
In the third step, the improved discrete multi-target particle swarm algorithm specifically comprises the following steps:
step 1, inputting data, and inputting the number of candidate base stations, test point information, access rate, function boundary and dimensionality;
step 2, initializing a particle population: setting the population number and the maximum iteration number, and randomly generating the initial position of 0 moment according to the constraint relation
Figure FDA0003504606150000041
And initial velocity at time 0
Figure FDA0003504606150000042
Calculating an objective function for each particle, initializing the local optimum position of the particle to
Figure FDA0003504606150000043
Setting the maximum crowding distance of the boundary as d when the external file is empty;
step 3, initializing an external file: will be provided with
Figure FDA0003504606150000044
Adding the dominant solution into the external archive at one time and retaining the dominant solution, wherein the dominant solution is represented as an initial solution in the external archive;
step 4, starting iteration, wherein t is 1; according to the above formula
Figure FDA0003504606150000045
Calculating the crowdedness of all individuals in the external file, and selecting one individual as a global optimal solution by adopting a roulette method
Figure FDA0003504606150000046
Step 5, updating the position x and the speed v of the particles according to the particle swarm iterative formula and recalculating the fitness of the individual;
step 6, updating an external file: sequentially adding the particles subjected to position updating into an external file, judging a domination relationship according to the crowding distance, and if the newly added individuals dominate the individuals in the external file, adding the new individuals and deleting the domination individuals; if the new individual does not dominate the individuals in the external file, not adding; if the comparison is impossible, comparing the current external capacity S 'with the expected set external capacity S, if S' is less than or equal to S, adding a new individual into an external file, and adding 1 to S, and when the solution in the external file is greater than a specified value, updating a non-inferior solution set by using a cyclic deletion method;
step 7, updating P of the particlebest(ii) a If the maximum iteration times are met, stopping searching, outputting a Pareto optimal front edge according to an external elite solution set, finding a compromise solution by using a fuzzy decision method, otherwise, turning to the step 4 if t is t + 1;
the roulette method in the step 4 specifically includes: the probability of each individual being selected is in direct proportion to the fitness function value, the group size is set to be N, and the individual xiHas a fitness of f (x)i) Then the individual xiThe probability of selection of (a) is:
Figure FDA0003504606150000047
and P (x)1)+P(x2)+…+P(xN) When 1, the cumulative distribution probability is:
Figure FDA0003504606150000051
the method comprises the following specific operation steps: calculating the selection probability and cumulative distribution probability of each individual according to the above formula, and generating a probability by using rand ()[0,1]R is a random number r between, if r is less than or equal to q1Then the individual x1Selecting the selected plants; if q isk-1＜r＜qk(2. ltoreq. k. ltoreq.N), then the individual xkAnd (6) selecting.
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