CN114638145A - Particle swarm algorithm-based multi-objective optimization guarantee equipment reservation algorithm - Google Patents

Particle swarm algorithm-based multi-objective optimization guarantee equipment reservation algorithm Download PDF

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CN114638145A
CN114638145A CN202210286687.4A CN202210286687A CN114638145A CN 114638145 A CN114638145 A CN 114638145A CN 202210286687 A CN202210286687 A CN 202210286687A CN 114638145 A CN114638145 A CN 114638145A
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王治宇
姜坤
张蓉
赵辉
管中庆
韩勇
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Air Force Engineering University of PLA Aircraft Maintenace Management Sergeant School
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Abstract

The invention provides a particle swarm optimization-based multi-objective optimization guarantee equipment reservation algorithm, which comprises the following steps: s1, establishing a mathematical model algorithm; s2, quantizing the preset indexes in a grading and weighting mode; s3, arrangement of preset points of the equipment and distribution of preset quantity are guaranteed, and a graph algorithm is utilized to simplify the arrangement, so that preset storage is localized or approximately localized; s4, dividing the simplified local vertex clusters into a plurality of independent areas, and performing multi-objective optimization in each independent area by the algorithm through the particle swarm optimization. The invention can improve the quick response capability of the maintenance service of the engineering, optimize the algorithm execution efficiency if necessary, properly consider the influence of climate factors, and generate the number of the maintenance equipment required to be configured in each preset place according to the shortest response time.

Description

Particle swarm algorithm-based multi-objective optimization guarantee equipment reservation algorithm
Technical Field
The invention relates to the technical field of aviation maintenance equipment guarantee, in particular to a particle swarm optimization-based multi-objective optimization guarantee equipment reservation algorithm.
Background
In order to improve the response speed of the support service, firstly, considering that support resource stations are optimally arranged according to a traffic network, and starting from the resource arrival time, the station construction cost and the function positioning of lines, a multi-target optimal arrangement model of the support resource stations which is more in line with the requirements of regulations and actual needs is constructed.
Existing models focus mainly on the discussion of related problems using conventional optimization techniques:
advantages and disadvantages of the P-center model, the P-median model, the set coverage model and the maximum coverage model in the layout;
from multiple angles of response time, shortest distance, minimum cost and the like, the guarantee sites are optimally laid by multiple targets;
discretizing time and establishing a time-based dynamic planning model, and considering the multiple distribution of the guarantee facilities;
on the basis that a plurality of fault points exist and the demand is known, the problem of site selection suitable for large-scale emergency is considered;
taking the covered guarantee equipment as a target to maximize, and performing multi-target linear programming of the guarantee resources;
and solving a traffic network guarantee station layout model by utilizing a random simulation genetic algorithm so as to obtain the distribution of the optimal stations.
Whether the various models are in computing performance or in implementability, the models have proper differences from the preset model of the currently required aviation maintenance equipment, and a new method needs to be explored to construct an optimized preset scheme of the aviation maintenance equipment as quickly as possible.
Disclosure of Invention
In view of the above, the present invention provides a particle swarm optimization-based multi-objective optimization security equipment reservation algorithm to solve the above problems.
In order to solve the technical problems, the invention provides a particle swarm optimization-based multi-objective optimization guarantee equipment reservation algorithm, which comprises the following steps:
s1, establishing a mathematical model algorithm;
s2, quantizing the preset indexes in a grading and weighting mode;
s3, arrangement of preset points of the equipment and distribution of preset quantity are guaranteed, and a graph algorithm is utilized to simplify the arrangement, so that preset storage is localized or approximately localized;
s4, dividing the simplified local vertex clusters into a plurality of independent areas, and performing multi-objective optimization in each independent area by the algorithm through the particle swarm optimization.
Further, the mathematical model algorithm is as follows:
the input planning task J relates to m airports, and the set of the airports is A ═ a1,a2,…,amIn which airport akThe model P ═ P needs to be ensured1,p2,…,ptThe respective numbers are Np＝{n1,n2,…,nt}；
When the planned strategic task level is GxThen, the airport a can be calculated according to the quota standard for guaranteeing the preset equipmentkDevice type T ═ T needs to be guaranteed1,T2,…,TyThe numbers of which are nk1,nk2,…nkyH, the total space occupied by each equipment is Ck＝{ck1,ck2,…,cky}；
Let set S ═ S for all preset points1,s2,…,srEach preset point can be used for storing space for ensuring the preset equipment, and V is equal to { V ═ V }1,v2,…,vrIn cubic meters, a preset point i is a straight-through path distance d from airport jijKilometers, the maximum mean transport capacity per unit of the straight-through path is fijCubic meter/hour, the maximum containable volume in single transportation is B cubic meters, and the maximum transportable weight in single transportation is W kilograms;
after the guarantee task occurs, the point is preseti time consumption for delivery to airport j is tijAnd the total time limit standard of finishing all the maintenance equipment transportation is not more than R hours;
the total number of preset points i for presetting the security equipment types u is set as xiuPiece, each preset point storage quantity set X ═ X1u,x2u,…,xruN, the number of j to be sent to the airport after the future guarantee task occurs is njuPieces of equipment, each piece occupying space cuWeight is respectively wuKilogram;
for the preset point i, the shortest total response time allowed on the premise of not delaying equipment scheduling is
The objective function is:
Figure BDA0003559375120000031
the main constraints to be met are:
and (3) limiting the storage capacity:
Figure BDA0003559375120000032
and (3) capacity limitation:
Figure BDA0003559375120000033
space limitation of transportation equipment: c. Cu≤B,wu≤W；
When considering other more optimization objectives, the dimensionality of the objective function is correspondingly increased, becoming:
min[F(X)]＝[f1(x),f2(x),...,fn(x)]Tand n is the optimization target number.
Further, in step S2, the preset indexes are classified into high, medium and low levels, and in the process of performing the algorithm, the requirement of the high level index is preferentially met, and the low level index is accepted.
Furthermore, in order to ensure that all levels of indexes are sequentially and rapidly processed according to high and low levels, three fixed weights are given to the three indexes; when there are multiple sibling indices at the same time, the average of each sibling index is used for normalization for final processing ranking.
Furthermore, the weight given to the high-level, medium-level and low-level indexes is calculated by taking the low-level index as a unit 1, the medium-level index is at least larger than 10, and the high-level index is at least larger than 50.
Further, the direct correlation factors of the preset indexes are a preset place, a preset equipment type and a preset equipment number.
Further, in order to fully utilize the grading of evaluation indexes to optimize the operation of the algorithm, after the data are preprocessed and simplified according to the graph algorithm and before the particle swarm algorithm is completely implemented, the indexes are firstly sorted in a descending manner according to the priority, after the preset requirements of the highest-level index are sequentially met, the scale of the data to be processed in the problem can be greatly reduced, and then the optimized calculation of common indexes is carried out on the data with the reduced scale.
Furthermore, the implementation of the algorithm of the problem is simplified by using a graph algorithm, and the starting point of the algorithm simplification is based on removing a bottleneck and presetting storage localization or approximate localization;
the process is as follows:
according to the minimum guaranteed equipment dispatching time of the points, connection among certain vertexes is cancelled;
searching for joint points in the feasible preset points, and if a path exists between the joint points, directly cutting off the joint points;
removing all joint points in the graph, and searching the maximum connected node in each divided subgraph;
taking all the maximum connected nodes of each subgraph as a center, calculating the maximum flow among the maximum connected nodes, and if the flow of a certain path among the nodes is smaller than a preset value, continuing to cut off the path;
and repeating the previous step until the process cannot be continued.
Furthermore, when the particle swarm optimization algorithm is used for solving the site multi-objective optimization preset model, the particles need to be coded, information carried by the particles is the solution of the optimization preset model, and in the site multi-objective optimization preset problem, the value of each point in the guaranteed resource site selection point set needs to be solved, so that the number and the position of the guaranteed resource sites are determined;
the position of the ith particle in the n-dimensional space is Si＝(si1,si2,…,sin) I is 1,2, …, m is the number of particles in the particle group, and the best position where it travels, i.e. the best fitness value is Spi＝(spi1,spi2,…,spin) The corresponding individual optimum value is denoted as Pi；
The best position of all particles in the population is denoted Sg＝(sg1,sg2,…,sgn) The corresponding global optimum value is marked as Pg；
The velocity of the particles is denoted Vi＝(vi1,vi2,…,vin)；
At the t +1 iteration, the speed of the d-th particle is:
Figure BDA0003559375120000041
the positions are as follows:
Figure BDA0003559375120000042
in the formula:
c1and c2Is a learning factor, and c1 ═ c2 ∈ [1,2.5 ]]；
r1And r2Is uniformly distributed in [0,1 ]]The random number of (2);
gamma is an inertia weight, the value size determines the inherited quantity of the particles to the current speed, and the global and local optimizing capability of the particle swarm algorithm can be improved by adjusting the value size;
the inertia weight is great and beneficial to global search, the inertia weight is small and beneficial to local search, and the calculation formula is as follows:
Figure BDA0003559375120000051
in the formula:
γ0and gammaendRespectively an initial inertia weight and a termination inertia weight;
t is the current iteration number, tmaxIs the maximum number of iterations.
Further, the model solving steps based on the particle swarm algorithm are as follows:
1. setting the total particle group size m and the learning factor c of the particle swarm algorithm1And c2Maximum number of evolutionary iterations tmaxCalculating parameters and the like;
2. randomly generating the position s and the speed v of initial population particles;
3. converting codes and judging whether the particles accord with the constraint of an optimal preset model of a guarantee resource site or not, and calculating the adaptive value of the particles after reinitializing the particles which do not accord with the constraint;
4. after t +1 times of iteration, if the current adaptive value P of the particlei t+1Is superior to the previous adaptation value Pi tIf the current value is the individual optimal value of the particle, the position s of the current particlei t+1The optimal position Spi; further, an individual optimum value of the particle is obtained, and the number and position P of the particle are recordedi；
5. Iteratively optimizing the speed and the position of the initialized particle under the constraint condition, wherein if a particle variable exists in the particle speed variable in the iterative process
Figure BDA0003559375120000061
Greater than the maximum particle velocity vmaxThen set up
Figure BDA0003559375120000062
If there is a particle variable in the particle velocity variable
Figure BDA0003559375120000063
Less than the minimum velocity v of the particlesminThen set up
Figure BDA0003559375120000064
6. Repeating the step 4 to search the positions Pi of other particles under the optimal adaptive value of the particle; then, carrying out an iterative formula, and repeating the steps 4, 5 and 6; if the global optimal adaptive value of the population particles after iteration is smaller than the global optimal adaptive value after last iteration, updating the global optimal adaptive value to the minimum adaptive value, otherwise, not updating; the local optimal updating method and the steps of each particle are the same;
7. and when the iteration result is converged and the iteration times reach the preset maximum iteration times, stopping the iteration, thereby obtaining the optimal preset scheme for guaranteeing the resource site.
And further, evaluating the multi-objective optimization, wherein n evaluation indexes are set, and after the 3 rd step of evaluation of the existing preset scheme is finished, directly entering a link of outputting an evaluation conclusion:
1. calculating the optimal value OPT of each evaluation index independently by ignoring other targetsi；
2. Respectively calculating VAL (value of variable) of each target in optimization schemei；
3. Calculating the relative percentage P of each individual evaluation targeti；
4. Calculating model score PM；
Wherein, the normalized score of the single index is calculated as follows:
Figure BDA0003559375120000065
and the model scoring summarizes each single index and gives a weight:
Figure BDA0003559375120000066
wherein wiThe weight value assigned to the single item score,
Figure BDA0003559375120000071
when the weights of the indexes are equal, the model score degenerates into the indexesMean value of scores.
The technical scheme of the invention has the following beneficial effects:
the invention is according to the configuration requirement of the aircraft security scheme to the aircraft security equipment, according to a plurality of preset optimization targets, the suitable preset stored aircraft security equipment is generated (1) each preset place scheme and (2) each preset place needs to preset the more reasonable scheme of the type and the number of the detailed equipment on the premise of avoiding the delay caused by temporary shortage of the security equipment due to emergency as much as possible, thereby improving the quick response capability of the aircraft security service, optimizing the algorithm execution efficiency if necessary, properly considering the influence of climate factors, and generating the number of the security equipment required to be configured in each preset place according to the shortest (or nearly shortest) response time.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the description of the embodiments of the invention given above, are within the scope of protection of the invention.
Example one
The embodiment provides a multi-objective optimization guarantee equipment reservation algorithm based on a particle swarm algorithm, which comprises the following steps:
s1, establishing a mathematical model algorithm;
s2, quantizing the preset indexes in a grading and weighting mode;
s3, arrangement of preset points of the equipment and distribution of preset quantity are guaranteed, and a graph algorithm is utilized to simplify the arrangement, so that preset storage is localized or approximately localized;
s4, dividing the simplified local vertex clusters into a plurality of independent areas, and performing multi-objective optimization in each independent area by the algorithm through the particle swarm optimization.
Further, the mathematical model algorithm is as follows:
the input planning task J relates to m airports, and the set of the airports is A ═ a1,a2,…,amIn which airport akThe model P ═ P needs to be ensured1,p2,…,ptAre respectively Np＝{n1,n2,…,nt}；
When the planned strategic task level is GxThen, the airport a can be calculated according to the quota standard for guaranteeing the preset equipmentkDevice type T ═ T needs to be guaranteed1,T2,…,TyThe numbers of which are nk1,nk2,…nkyC, total space capacity occupied by various devices isk＝{ck1,ck2,…,cky}；
Let set S ═ S of all preset points1,s2,…,srEach preset point can be used for storing space for ensuring the preset equipment, and V is equal to { V ═ V }1,v2,…,vrCubic meter, and the distance between a preset point i and a straight-through path of an airport j is dijKilometer, maximum average unit transport capacity of the straight-through path fijCubic meter/hour, the maximum containable volume in single transportation is B cubic meters, and the maximum transportable weight in single transportation is W kilograms;
when the guarantee task occurs, the time consumption for the preset point i to be transported to the airport j is tijAnd the total time limit standard of finishing all the maintenance equipment transportation is not more than R hours;
the total number of preset points i for presetting the security equipment types u is set as xiuPiece, each preset point storage quantity set X ═ X1u,x2u,…,xruN, the number of j to be sent to the airport after the future guarantee task occurs is njuPiece of equipment, each piece of space occupied cuRespectively weight is wuKilogram;
for the preset point i, the shortest total response time allowed on the premise of not delaying equipment scheduling is
The objective function is:
Figure BDA0003559375120000081
the main constraints to be met are:
and (3) limiting the storage capacity:
Figure BDA0003559375120000082
and (3) capacity limitation:
Figure BDA0003559375120000091
space limitation of transportation equipment: c. Cu≤B,wu≤W；
When considering other more optimization objectives, the dimensionality of the objective function is correspondingly increased, becoming:
min[F(X)]＝[f1(x),f2(x),...,fn(x)]Tand n is the optimization target number.
As far as individual time optimization goals are concerned, it is clear that the smaller the total time of delivery the better. If all the preset points are near the mission airport and the space of the preset points for storing the guarantee equipment has no upper limit, the optimal conclusion of in-situ presetting can be directly obtained. Although this conclusion is not necessarily feasible in reality and is an important constraint for the optimization goal, some heuristics can be provided for the optimization implementation of the algorithm based on this idea: each preset requirement is localized as much as possible and is divided into a plurality of independent small areas to be processed independently.
To reduce the response time of the preset system, the process can be simplified as follows:
when the time consumed by single transportation between a certain preset point and an airport to be transported exceeds a certain preset time limit, the connection between the two points is directly disconnected.
Obviously, except for extreme occasions such as resource exhaustion in wartime, the general situation can not cause wrong conclusion of the algorithm.
Further, in step S2, the preset indexes are classified into high, medium and low levels, and in the process of performing the algorithm, the requirement of the high level index is preferentially met, and the low level index is accepted.
Furthermore, in order to ensure that all levels of indexes are sequentially and rapidly processed according to high and low levels, three fixed weights are given to the three indexes; when there are multiple sibling indices at the same time, the average of each sibling index is used for normalization for final processing ranking.
Furthermore, the weight given to the high-level, medium-level and low-level indexes is calculated by taking the low-level index as a unit 1, the medium-level index is at least larger than 10, and the high-level index is at least larger than 50.
Further, the direct correlation factors of the preset indexes are a preset place, a preset equipment type and a preset equipment number.
Further, in order to fully utilize the grading of the evaluation indexes to optimize the operation of the algorithm, after the data are preprocessed and simplified according to the graph algorithm and before the particle swarm algorithm is completely implemented, the indexes are sequentially sorted in a descending manner according to the priority, after the preset requirements of the highest-level index are sequentially met, the scale of the data to be processed in the problem can be greatly reduced, and then the optimization calculation of common indexes is carried out on the data with the reduced scale.
Furthermore, the implementation of the algorithm of the problem is simplified by using a graph algorithm, and the starting point of the algorithm simplification is based on removing a bottleneck and presetting storage localization or approximate localization; and therefore from the aspects of the joint point, the minimum cost and maximum flow of the network, the pivot point and the like.
1. Joint point
The joint points are also called cutting points, and the removal of the joint points in the figure can cause the disconnection of the figure, and the regulation and transportation of substances through the joint points can cause congestion; if there is a path between two nodes, the path is known as a bridge.
2. Network maximum flow
The maximum network flow is the maximum flow from a source point to a sink point, and the maximum material carrying capacity which is feasible among the areas on the graph can be determined by calculating the cut amount of the subgraph.
3. Pivot point
As with the central city in life, in order to reduce the total cost of material distribution and transportation, except that part of the oversized overweight equipment is directly preset in a using airport due to the difficulty of transportation, the preset equipment is considered to be concentrated to the central city or the periphery of the central city radiated at a short distance as much as possible, so that the timely response can be ensured when in demand.
The process is as follows:
according to the minimum guaranteed equipment dispatching time of the points, connection among certain vertexes is cancelled;
searching for joint points in the feasible preset points, and if a path exists between the joint points, directly cutting off the joint points;
removing all joint points in the graph, and searching the maximum connected node in each divided subgraph;
calculating the maximum flow among the maximum connected nodes by taking all the maximum connected nodes of each subgraph as the center, and if the flow of a certain path among the nodes is less than a preset value, continuing to cut off the path;
and repeating the previous step until the process cannot be continued.
Furthermore, when the particle swarm optimization algorithm is used for solving the site multi-objective optimization preset model, the particles need to be coded, information carried by the particles is the solution of the optimization preset model, and in the site multi-objective optimization preset problem, the value of each point in the guaranteed resource site address point set needs to be solved, so that the number and the positions of the guaranteed resource sites are determined;
the position of the ith particle in the n-dimensional space is Si＝(si1,si2,…,sin) I is 1,2, …, m is the number of particles in the particle group, and the best position where it travels, i.e. the best fitness value is Spi＝(spi1,spi2,…,spin) The corresponding individual optimum value is denoted as Pi；
The best position of all particles in the population is denoted Sg＝(sg1,sg2,…,sgn) The corresponding global optimum is denoted as Pg；
The velocity of the particles is denoted Vi＝(vi1,vi2,…,vin)；
At the t +1 th iteration, the speed of the d-th particle is:
Figure BDA0003559375120000111
the positions are as follows:
Figure BDA0003559375120000112
in the formula:
c1and c2Is a learning factor, and c1 ═ c2 ∈ [1,2.5 ]]；
r1And r2Is uniformly distributed in [0,1 ]]The random number of (2);
gamma is an inertia weight, the value size determines the inherited quantity of the particles to the current speed, and the global and local optimizing capability of the particle swarm algorithm can be improved by adjusting the value size;
the inertia weight is great to be beneficial to global search, the inertia weight is small to be beneficial to local search, and the calculation formula is as follows:
Figure BDA0003559375120000113
in the formula:
γ0and gammaendRespectively an initial inertia weight and a termination inertia weight;
t is the current iteration number, tmaxIs the maximum number of iterations.
Further, the model solving steps based on the particle swarm algorithm are as follows:
1. setting the total particle group size m and the learning factor c of the particle swarm algorithm1And c2Maximum number of evolutionary iterations tmaxCalculating parameters and the like;
2. randomly generating the position s and the speed v of initial population particles;
3. converting codes and judging whether the particles conform to the constraint of the optimal preset model of the guarantee resource site or not, and calculating the adaptive value of the particles after the particles which do not conform to the constraint are reinitialized;
4. through a processAfter t +1 iterations, if the current adaptive value P of the particlei t+1Is superior to the previous adaptation value Pi tIf the current value is the individual optimal value of the particle and the position of the current particle
Figure BDA0003559375120000121
The optimal position Spi; further, an individual optimum value of the particle is obtained, and the number and position P of the particle are recordedi；
5. Iteratively optimizing the speed and the position of the initialized particle under the constraint condition, wherein if a particle variable exists in the particle speed variable in the iterative process
Figure BDA0003559375120000122
Greater than the maximum particle velocity vmaxThen set up
Figure BDA0003559375120000123
If there is a particle variable in the particle velocity variables
Figure BDA0003559375120000124
Less than the minimum velocity v of the particlesminThen set up
Figure BDA0003559375120000125
6. Repeating the step 4 to search the positions Pi of other particles under the optimal adaptive value of the particle; then, an iterative formula is substituted, and the steps 4, 5 and 6 are repeated; if the global optimal adaptation value of the population particles after iteration is smaller than the global optimal adaptation value after last iteration, updating the global optimal adaptation value to the minimum adaptation value, otherwise, not updating; the local optimal updating method and the steps of each particle are the same;
7. and when the iteration result is converged and the iteration times reach the preset maximum iteration times, stopping the iteration, thereby obtaining the optimal preset scheme for guaranteeing the resource site. Compared with a single-objective optimization problem, the advantages and disadvantages of any two feasible solutions are directly determined by comparing values of an objective function, and the maximum difference of the multi-objective optimization problem is that the objective function is a multi-dimensional vector, in principle, the advantages and disadvantages need to be determined by comparing the sizes of components of the vector, or the modulus of a multi-dimensional space needs to be compared by mathematically discarding the characteristics of the components. However, due to the multi-dimensionality of the objective function of the multi-objective optimization problem, each optimization target is generally not consistent even if the simplest dimension unit is, so that the theoretical methods are difficult to implement in actual use, all the optimization targets are difficult to balance, and each feasible solution, even if the feasible solution is a local optimal solution, is not convenient to directly compare the advantages and disadvantages of the feasible solutions.
Theoretically, each target of the multi-target optimization problem is an optimal solution which is generally called an absolute optimal solution, but the actual problem often does not exist, a plurality of targets are more or less contradicted, it is common that the better target of a certain target may cause the worse of another target, and even there may be contradictory opposition among the optimization targets, for example, pursuing the shortest response time generally causes the larger redundancy of local preset storage capacity, and the like. And finally evaluating the balance multi-objective optimization problem.
The invention evaluates the multi-target optimization, n evaluation indexes are set, and for the evaluation of the existing preset scheme, the method directly enters a link of outputting an evaluation conclusion after the step 3 is finished:
1. calculating the optimal value OPT of each evaluation index independently by ignoring other targetsi；
2. Respectively calculating VAL (value of variable) of each target in optimization schemei；
3. Calculating the relative percentage P of each individual evaluation targeti；
4. Calculating model score PM；
Wherein, the normalized score of the single index is calculated as follows:
Figure BDA0003559375120000131
and the model scoring summarizes each single index and gives a weight:
Figure BDA0003559375120000141
wherein wiThe weight value assigned to the single item score,
Figure BDA0003559375120000142
when the weights of the indices are equal, the model score degenerates to the average of the index scores.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (10)

1. A multi-objective optimization guarantee equipment reservation algorithm based on a particle swarm algorithm is characterized in that: the method comprises the following steps:
s1, establishing a mathematical model algorithm;
s2, quantizing the preset indexes in a grading and weighting mode;
s3, ensuring the arrangement of the preset points of the equipment and the distribution of the preset amount, simplifying by using a graph algorithm, and making the preset storage localized or approximately localized;
s4, dividing the simplified local vertex clusters into independent areas, and performing multi-objective optimization by the aid of particle swarm optimization in each independent area.
2. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 1, wherein: the mathematical model algorithm is as follows:
the input planning task J relates to m airports, and the set of the airports is A ═ a1,a2,…,amIn which airport akThe model P ═ P needs to be ensured1,p2,…,ptAre respectively Np＝{n1,n2,…,nt}；
When the planned strategic task level is GxWhen it is, according to the guarantorRating standard of barrier presetting equipment can be used for calculating airport akDevice type T ═ T needs to be guaranteed1,T2,…,TyThe numbers of which are nk1,nk2,…nkyC, total space capacity occupied by various devices isk＝{ck1,ck2,…,cky}；
Let set S ═ S for all preset points1,s2,…,srEach preset point can be used for storing space for ensuring the preset equipment, and V is equal to { V ═ V }1,v2,…,vrCubic meter, and the distance between a preset point i and a straight-through path of an airport j is dijKilometer, maximum average unit transport capacity of the straight-through path fijCubic meter/hour, the maximum containable volume in single transportation is B cubic meters, and the maximum transportable weight in single transportation is W kilograms;
when the safeguard task occurs, the time consumption for the preset point i to be transported to the airport j is tijAnd the total time limit standard of finishing all the maintenance equipment transportation is not more than R hours;
the total number of preset points i for presetting the security equipment types u is set as xiuPiece, each preset point storage quantity set X ═ X1u,x2u,…,xruN, the number of j to be sent to the airport after the future guarantee task occurs is njuPiece of equipment, each piece of space occupied cuRespectively weight is wuKilogram;
for the preset point i, the shortest total response time allowed on the premise of not delaying equipment scheduling is
The objective function is:
Figure FDA0003559375110000021
the main constraints to be met are:
and (3) limiting the storage capacity:
Figure FDA0003559375110000022
and (3) capacity limitation:
Figure FDA0003559375110000023
space limitation of transportation equipment: c. Cu≤B,wu≤W；
When considering other more optimization objectives, the dimensionality of the objective function is correspondingly increased, becoming:
min[F(X)]＝[f1(x),f2(x),...,fn(x)]Tand n is the optimization target number.
3. The particle swarm algorithm-based multi-objective optimization safeguard equipment reservation algorithm of claim 2, characterized in that: in step S2, the preset indexes are classified into high, medium and low levels, and in the process of performing the algorithm, the requirements of the high level indexes are preferentially met, and the low level indexes are accepted or rejected.
4. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 3, wherein: in order to ensure that indexes at all levels are sequentially and rapidly processed according to high and low levels, three fixed weights are given to the three indexes; when there are multiple sibling indices at the same time, the average of each sibling index is used for normalization for final processing ranking.
5. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 4, wherein: the weight given to the high-level, middle-level and low-level indexes is calculated by taking the low-level indexes as a unit 1, the middle-level indexes are at least larger than 10, and the high-level indexes are at least larger than 50.
6. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 5, wherein: the direct correlation factors of the preset indexes are the preset place, the type of the preset equipment and the number of the preset equipment.
7. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 6, wherein: in order to fully utilize the grading of evaluation indexes to optimize the operation of the algorithm, after the data is preprocessed and simplified according to the graph algorithm and before the particle swarm algorithm is completely implemented, the indexes are sorted in a descending manner according to the priority, after the preset requirements of indexes at the highest level are met in sequence, the scale of the data to be processed in the problem can be greatly reduced, and then the optimized calculation of common indexes is carried out on the data with the reduced scale.
8. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 7, wherein: the implementation of the algorithm of the problem is simplified by using a graph algorithm, and the starting point of the algorithm simplification is based on removing a bottleneck and presetting storage localization or approximate localization;
the process is as follows:
according to the minimum guaranteed equipment dispatching time of the points, connection among certain vertexes is cancelled;
searching for joint points in the feasible preset points, and if a path exists between the joint points, directly cutting off the joint points;
removing all joint points in the graph, and searching the maximum connected node in each divided subgraph;
taking all the maximum connected nodes of each subgraph as a center, calculating the maximum flow among the maximum connected nodes, and if the flow of a certain path among the nodes is smaller than a preset value, continuing to cut off the path;
and repeating the previous step until the process cannot be continued.
9. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 8, wherein: when the particle swarm optimization algorithm is used for solving the site multi-objective optimization preset model, the particles need to be coded, information carried by the particles is the solution of the optimization preset model, and in the site multi-objective optimization preset problem, the value of each point in the guaranteed resource site address point set needs to be solved, so that the number and the positions of the guaranteed resource sites are determined;
the position of the ith particle in the n-dimensional space is Si＝(si1,si2,…,sin) Where i is 1,2, …, m is the number of particles in the population, and the best position where it travels, i.e., the most suitable value, is Spi＝(spi1,spi2,…,spin) The corresponding individual optimum value is denoted as Pi；
The best position of all particles in the population is denoted Sg＝(sg1,sg2,…,sgn) The corresponding global optimum value is marked as Pg；
The velocity of the particles is denoted Vi＝(vi1,vi2,…,vin)；
At the t +1 th iteration, the speed of the d-th particle is:
Figure FDA0003559375110000041
the positions are as follows:
Figure FDA0003559375110000042
in the formula:
c1and c2Is a learning factor, and c1 ═ c2 ∈ [1,2.5 ]]；
r1And r2Is uniformly distributed in [0,1 ]]The random number of (2);
gamma is an inertia weight value, the value size determines the inheritance of the particles to the current speed,
the global and local optimizing capability of the particle swarm algorithm can be improved by adjusting the size of the particle swarm algorithm;
the inertia weight is great and beneficial to global search, the inertia weight is small and beneficial to local search, and the calculation formula is as follows:
Figure FDA0003559375110000043
in the formula:
γ0and gammaendAre respectively a preliminary testAn inertial weight and a termination inertial weight;
t is the current iteration number, tmaxIs the maximum number of iterations.
10. The particle swarm optimization-based multi-objective optimization security equipment reservation algorithm of claim 9, wherein: the model solving steps based on the particle swarm algorithm are as follows:
1. setting the total particle group size m and the learning factor c of the particle swarm algorithm1And c2Maximum number of evolutionary iterations tmaxCalculating parameters and the like;
2. randomly generating the position s and the speed v of initial population particles;
3. converting codes and judging whether the particles conform to the constraint of the optimal preset model of the guarantee resource site or not, and calculating the adaptive value of the particles after the particles which do not conform to the constraint are reinitialized;
4. after t +1 iterations, if the current adaptive value P of the particlei t+1Is superior to the previous adaptation value Pi tIf the current value is the individual optimal value of the particle and the position of the current particle
Figure FDA0003559375110000051
The optimal position Spi; further, an individual optimum value of the particle is obtained, and the number and position P of the particle are recordedi；
5. Iteratively optimizing the speed and the position of the initialized particle under the constraint condition, wherein if a particle variable exists in the particle speed variable in the iterative process
Figure FDA0003559375110000052
Greater than the maximum particle velocity vmaxThen set up
Figure FDA0003559375110000053
If there is a particle variable in the particle velocity variable
Figure FDA0003559375110000054
Less than the minimum velocity v of the particlesminThen set up
Figure FDA0003559375110000055
6. Repeating the step 4 to search the positions Pi of other particles under the optimal adaptive value of the particle; then, carrying out an iterative formula, and repeating the steps 4, 5 and 6; if the global optimal adaptation value of the population particles after iteration is smaller than the global optimal adaptation value after last iteration, updating the global optimal adaptation value to the minimum adaptation value, otherwise, not updating; the local optimal updating method and the steps of each particle are the same;
7. and when the iteration result is converged and the iteration times reach the preset maximum iteration times, stopping the iteration, thereby obtaining the optimal preset scheme for guaranteeing the resource site.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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