CN113158549B - Diversified task oriented ship formation grade repair plan compilation method - Google Patents

Diversified task oriented ship formation grade repair plan compilation method Download PDF

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CN113158549B
CN113158549B CN202110309407.2A CN202110309407A CN113158549B CN 113158549 B CN113158549 B CN 113158549B CN 202110309407 A CN202110309407 A CN 202110309407A CN 113158549 B CN113158549 B CN 113158549B
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蒋铁军
周成杰
张怀强
于淳
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Abstract

The invention discloses a diversified task oriented ship formation grade repair plan compilation method, which comprises the following steps of: step 1: establishing a task demand model of a ship formation; step 2: establishing a ship formation grade repair plan basic database facing diversified tasks; and step 3: establishing a ship formation efficiency evaluation model; and 4, step 4: establishing a diversified task oriented ship formation grade repair plan optimization model; and 5: and obtaining a task configuration plan and a grade repair plan of the ship formation. The invention can provide powerful technical support for the use plan and the grade repair plan of the scientific planned ship formation to ensure the effective fulfillment of the mission task of the ship mission.

Description

Diversified task oriented ship formation grade repair plan compilation method
Technical Field
The invention relates to the technical field of ship maintenance support, in particular to a diversified task oriented ship formation grade repair plan compilation method.
Background
The naval vessel grade repair has long maintenance period, high expense requirement, high resource consumption and large influence on use, and the scientific establishment of the naval vessel grade repair plan is always a key concern in the technical field of naval vessel maintenance and guarantee. Particularly, with the expansion of naval mission tasks, the increase of the use strength of the naval vessels and the improvement of capacity requirements, how to ensure that each capacity of the naval vessels effectively meets the requirement of executing the tasks and scientifically harmonizes the relationship between the use and the repair of the naval vessels is a technical problem to be solved urgently in the field.
Currently, the basic method of planning vessel-level repairs is to schedule specific repair activities at a given financial budget specification in a well-defined repair structure, wherein the repair structure includes a repair level, a repair interval time range, a repair period range, etc. Related research works are also mostly developed under the framework, such as a planning method based on reliability and cost and a planning method based on minimum risk, which take a single ship as an object, a planning method based on fluctuation range of the number of available ships in a service period, a planning method based on maximum deployment time of the ship formation as an object, a planning method based on deployment capacity of a plurality of ships of the same type, and the like.
From the actual work and research condition of the current ship grade repair plan, the method mainly focuses on the arrangement of the ship grade repair plan, and less considers the objective requirements of the ships for executing specific tasks, especially the influence of diversified task requirements on the grade repair plan. In fact, ships exist for completing a given mission task, specifically including training, performing, convoying, fighting and the like, mission tasks of different types of ships are different, capacity requirements of different tasks on the ships are different, and formation of ship formation during task execution is essentially represented as rational configuration of various capacities of the ships. Due to different capability distributions of a single ship and different requirements of different tasks on the capabilities, the selection emphasis of each type of naval vessel is different when the tasks are executed. Therefore, when a vessel level repair plan is arranged, the diversified task requirements and the repair requirements of the vessel need to be fully considered, and the relationship between the two needs to be coordinated and processed.
Disclosure of Invention
The invention aims to provide a diversified task-oriented ship formation grade repair plan compiling method, which is characterized in that under the existing ship grade repair mode frame, on the premise of meeting diversified task requirements, on the basis of establishing a ship formation task requirement model and a ship formation efficiency evaluation model, the method further takes the minimum number of ships for executing tasks and the maximum ship formation efficiency as targets, takes the ship repair, the repair starting time and the ship number required by each task as decision variables, considers the task requirement constraint, the task time overlapping constraint, the repair period constraint, the cross-period repair expense constraint, the repair total expense constraint, the capability constraint and the aircraft rate constraint to establish a ship formation grade repair plan optimization model, adopts a particle swarm optimization algorithm based on a hierarchical sequence to solve the model, and obtains a task configuration plan and a grade repair plan of the ship formation, the coordination problem of the use and the repair of the ship formation is solved. The method can provide powerful technical support for the use plan and the grade repair plan of the scientific planned ship formation to ensure the effective fulfillment of the mission task of the ship mission.
In order to achieve the purpose, the invention designs a diversified task oriented naval vessel formation grade repair plan compilation method, which comprises the following steps:
step 1: establishing a task demand model of the ship formation according to diversified tasks, time demands of different tasks and capacity demands of the ship formation faced by the ships, wherein the time demands are that all the ships in the ship formation are in a usable state in a task time period and cannot be subjected to grade repair; the capacity requirements are that the command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value of the naval vessel formation are all larger than the minimum required value of the task corresponding capacity;
step 2: establishing a ship formation grade repair plan base database facing to diversified tasks according to ship diversified task requirements, ship actual technical states and current ship grade repair regulations, wherein the ship formation grade repair plan base database facing to diversified tasks comprises diversified task data parameters, an initial item division capability value of a ship at a decision starting time point and ship repair data parameters;
and step 3: establishing a ship formation efficiency evaluation model according to the characteristic that the command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value of the ships are attenuated along with time, the weight of the single ship to formation itemizing capacity, the expectation and risk preference degree of a decision maker to the ship formation itemizing capacity and the weight of the contribution degree of each itemizing capacity of the ship formation to the overall efficiency;
and 4, step 4: the method comprises the steps that a ship formation grade repair plan optimization model facing diversified tasks is established by taking the goals of minimum number of ships in ship formation for executing tasks and maximum efficiency of the ship formation, taking the condition whether the ships are repaired, repair starting time and ship number required by each task as decision variables, and considering task demand constraint, task time overlapping constraint, repair period constraint, over-period repair expense constraint, repair total expense constraint, capacity constraint and air rate constraint;
and 5: solving the ship formation grade repair plan optimization model of the orientation diversified tasks by using a particle swarm optimization algorithm based on a hierarchical sequence to obtain a decision variable of the ship formation grade repair plan optimization model, wherein the decision variable comprises whether a ship is repaired, the repair starting time and the ship number required by each task, and further obtaining a task configuration plan and a grade repair plan of the ship formation.
The invention has the beneficial effects that:
the method fully considers the obvious influence of various actual combat training tasks on the scientific arrangement of the ship grade repair plan, establishes a task demand model of the ship formation, fully reflects the essential requirements of various tasks on the ships, establishes a ship formation efficiency evaluation model, reflects the development change rule of the ship efficiency, establishes the double targets of minimum number of ships and maximum efficiency in the ship formation, ensures the optimal utilization of ship resources and meets the mission requirement, solves the model by using a hierarchical sequence-based particle swarm optimization algorithm, can simultaneously determine the task configuration plan and the grade repair plan of the ship formation, effectively solves the problem of ship repair in the plan formulation level, and provides powerful guarantee for the contradiction between scientific management and installation.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 illustrates the vessel number and type of the present invention;
FIG. 3 is a diagram of task time requirements and itemized capacity requirements for fleet vessels in accordance with the present invention;
FIG. 4 is an initial itemized capability value of the vessel of the present invention;
FIG. 5 illustrates vessel repair data parameters in accordance with the present invention;
FIG. 6 is a naval vessel capability decay function according to the present invention;
FIG. 7 is a plan arrangement for configuring the fleet of vessels to perform a mission in accordance with the present invention;
FIG. 8 is a vessel formation level repair scheduling arrangement according to the present invention;
FIG. 9 illustrates the availability of a fleet of vessels according to the present invention;
FIG. 10 is a vessel level repair planning arrangement for two cases of the present invention, whether mission considerations are taken into account.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
as shown in fig. 1, the method for planning the repair of the vessel formation level facing to the diversified tasks is characterized by comprising the following steps:
step 1: according to diversified tasks, time requirements of different tasks and capability requirements for ship formation faced by ships, establishing a task requirement model (the task requirement model comprises the time requirements and the capability requirements) of the ship formation, wherein the time requirements are that all ships in the ship formation are in a usable state in a task time period and cannot be subjected to level repair; the capacity requirements are that the command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value of the naval vessel formation are all larger than the minimum required value of the task corresponding capacity;
step 2: establishing a ship formation grade repair plan base database facing diversified tasks according to ship diversified task requirements, ship actual technical states and current ship grade repair regulations, wherein the ship formation grade repair plan base database facing diversified tasks comprises diversified task data parameters, an initial itemizing capacity value of a ship at a decision starting time point and ship repair data parameters (directly corresponding to the diversified task data parameters in the database according to the diversified task requirements; evaluating the initial itemizing capacity value of the ship at the decision starting time point according to the ship actual technical states to obtain the ship repair data parameters directly corresponding to the ship repair data parameters according to the current ship grade repair regulations);
and step 3: establishing a ship formation efficiency evaluation model (the ship formation efficiency is one of optimization targets in an optimization model, namely the ship formation efficiency required to execute a task is as good as possible) according to the characteristic that the ship command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value are attenuated along with time, the weights of the individual ship formation item capacities of a single ship, the expectation and risk preference degrees of a decision maker to the ship formation item capacities and the weights of the contribution degrees of the individual ship formation item capacities to the overall efficiency;
and 4, step 4: the method comprises the steps that a ship formation grade repair plan optimization model facing diversified tasks is established by taking the goals of minimum number of ships in ship formation for executing tasks and maximum efficiency of the ship formation, taking the condition whether the ships are repaired, repair starting time and ship number required by each task as decision variables, and considering task demand constraint, task time overlapping constraint, repair period constraint, over-period repair expense constraint, repair total expense constraint, capacity constraint and air rate constraint;
and 5: solving the ship formation grade repair plan optimization model of the orientation diversified tasks by using a particle swarm optimization algorithm based on a hierarchical sequence to obtain a decision variable of the ship formation grade repair plan optimization model, wherein the decision variable comprises whether a ship is repaired or not, repair starting time and the ship number required by each task, and further obtains a task configuration plan and a grade repair plan of the ship formation (the task configuration plan is determined by determining the ship number required by each task and the task time, and the repair plan of the ship is determined by determining whether the ship is repaired or not and the repair starting time).
In the technical scheme, the diversified task data parameters are used for describing the requirements of diversified tasks on scale, time and capacity, the initial itemized capacity value of the naval vessel at the decision starting time point is used for describing the capacity performance of the naval vessel at the time point, and the naval vessel repair data parameters are used as basic data of a naval vessel formation level repair plan optimization model.
In step 1 of the above technical scheme, the specific method for establishing the ship formation task demand model comprises the following steps:
firstly, the existing naval vessel set is obtained by considering the naval vessel types and the number of different types of naval vessels:
S＝{{Si},type,ntype}，i＝1,2…,n，type＝1,2,…,k
in the formula, S represents the set of all vessels, SiRepresenting the i-th vessel co-existing with the n vessels S1,S2,…,Si,…SnType denotes the vessel type, there are k types of vessels, ntypeRepresenting the number of various types of vessels, ntype1,ntype2,…,ntypekA step of;
then, considering the specific task to be executed and the number of the vessels required by the task, a task vessel set is established, namely, the vessel formation comprises:
Figure GDA0003523310250000061
in the formula (I), the compound is shown in the specification,
Figure GDA0003523310250000062
indicating the execution of task RjOf a fleet of vessels, comprising
Figure GDA0003523310250000063
A vessel for a vessel, the vessel having a plurality of channels,
Figure GDA0003523310250000064
is a subset of the set S of all vessels;
further, considering the starting time of different tasks and the requirements of the different tasks on the ship formation itemizing capacity, a diversified task model and a task demand model are established;
for the diversified tasks, the following are specifically expressed:
Figure GDA0003523310250000065
wherein R represents a period of time [ T1,T2]Set of tasks, R, facing n vesselsjIt represents the j-th task that is,
Figure GDA0003523310250000066
and
Figure GDA0003523310250000067
respectively represent tasks RjThe start time and the end time of (c),
Figure GDA0003523310250000068
respectively represent tasks RjThe minimum requirements on command control capability value, maneuverability capability value, defense capability value, attack capability value and guarantee capability value of the naval vessel formation are met;
for the requirement of the task time, the task naval vessel is required to be incapable of performing level repair within the task duration, which is specifically expressed as follows:
when in use
Figure GDA0003523310250000069
When the temperature of the water is higher than the set temperature,
Figure GDA00035233102500000610
in the formula (I), the compound is shown in the specification,
Figure GDA00035233102500000611
for task RjThe execution period of (1), i.e. the interval from the start time to the end time of the task;
Figure GDA00035233102500000612
for vessels SiThe repair cycle of (1), i.e., the interval from the repair start time to the repair end time; phi represents an empty set;
for the task capacity requirement, the command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value of the naval vessel formation are required to be greater than the minimum required value of the task corresponding capacity, and the specific expression is as follows:
Figure GDA0003523310250000071
in the formula (I);
Figure GDA0003523310250000072
respectively representing the execution of tasks RjCommand control ability value and maneuvering ability value of naval vessel formationDefense ability value, attack ability value and guarantee ability value;
Figure GDA0003523310250000073
is shown in task RjWithin the execution period of (c);
Figure GDA0003523310250000074
respectively represent tasks RjThe minimum requirement values of command control capability, maneuverability, defense capability, attack capability and guarantee capability of the ship formation.
In step 2 of the above technical scheme, the diversified task data parameters include the number of tasks, the execution times of different tasks, and the minimum required value of the task for the ship formation itemizing capability; the initial itemized capacity value of the naval vessel at the decision starting time point comprises a command control capacity value, a maneuvering capacity value, a defense capacity value, an attack capacity value and a guarantee capacity value, wherein the capacity value represents the size of each itemized capacity and is obtained by comprehensively evaluating the technical state of equipment; the vessel repair data parameters comprise a vessel number, a repair level preliminarily drawn according to the current vessel level repair rule, a budget index, a repair period, a recovery capacity, a time length from the last level repair or the last service guarantee to a decision starting point, and a lowest requirement value of the aviation state capacity.
In step 3 of the above technical scheme, the specific method for establishing the ship formation efficiency evaluation model comprises the following steps:
firstly, aiming at the characteristic that the capability of a naval vessel can be attenuated along with time, a reverse logistic function is adopted to establish a subentry capability evaluation model of naval vessel formation:
Figure GDA0003523310250000075
in the formula (I), the compound is shown in the specification,
Figure GDA0003523310250000081
indicating the execution of task RjThe partial capability values of the ship formation, X, M, F, J and L respectively correspond to the command control capability, the maneuvering capability and the prevention capability of the shipsImperial ability, offensive ability and guarantee ability;
Figure GDA0003523310250000082
representing participation in task RjOf the ith vessel
Figure GDA0003523310250000083
Weighting the grouping capacity of the ship formation;
Figure GDA0003523310250000084
to represent
Figure GDA0003523310250000085
The initial value of the item capability of (2), namely the value of the item capability at the decision starting time point;
Figure GDA0003523310250000086
the capability decay rate is related to the characteristics and the use strength of the naval vessel;
Figure GDA0003523310250000087
the capacity attenuation length is expressed, the time length of slow attenuation of the capacity of the naval vessel formation in the initial use stage is reflected, and the time length is related to the inherent characteristics and the use strength of the naval vessel; t represents time and the completion time of the previous level repair or the service warranty is taken as the origin, and when t takes a certain specific time as the origin, the capacity attenuation length
Figure GDA0003523310250000088
Should be that
Figure GDA0003523310250000089
Wherein
Figure GDA00035233102500000810
Indicating vessels
Figure GDA00035233102500000811
The time length from the completion of the last grade repair or the service warranty to the decision starting time point; e is a natural constant;
Figure GDA00035233102500000812
indicating the execution of task RjNumber of vessels.
Then, considering the expectation and risk preference of a decision maker on the ship formation itemized capacity value, establishing a task ship formation itemized capacity value function by applying a prospect theory:
Figure GDA00035233102500000813
in the formula (I), the compound is shown in the specification,
Figure GDA00035233102500000814
indicating the execution of task RjThe value function of a certain subentry ability of the ship formation,
Figure GDA00035233102500000815
an actual value representing the ability of the vessel to form the itemization,
Figure GDA00035233102500000816
expected value, lambda, representing the ability of the vessel to form the subentryiAnd beta i0 representing the risk aversion coefficients for actual values above and below expectations, respectively<λi<1<βi；
Further, obtaining a ship formation efficiency evaluation model:
Figure GDA00035233102500000817
in the formula (I), the compound is shown in the specification,
Figure GDA0003523310250000091
indicating the execution of task RjShip formation efficiency, wc1～wc5Representing the contribution degree weight of each subentry ability (vessel command and control ability, maneuverability, defense ability, attack ability and guarantee ability) to the overall efficiency,
Figure GDA0003523310250000092
Figure GDA0003523310250000093
respectively representing the execution of tasks RjThe command control capability, the maneuvering capability, the defense capability, the attack capability and the guarantee capability of the ship formation.
The specific method of step 4 in the above technical scheme is as follows:
firstly, establishing two optimization targets of a diversified task oriented ship formation grade repair plan optimization model;
the first objective is to perform the task with the least number of vessels in the fleet of vessels, expressed as:
Figure GDA0003523310250000094
in the formula, nRRepresenting the sum of the number of vessels performing v tasks;
Figure GDA0003523310250000095
indicating the execution of task RjThe number of vessels;
Figure GDA0003523310250000096
indicating the execution of task RjNumber of u-type vessels; k represents the number of types of vessels,
Figure GDA0003523310250000097
respectively representing the number of each type of naval vessel;
the second objective is to maximize the effectiveness of the formation of the vessels performing the mission, expressed as:
Figure GDA0003523310250000098
wherein f (U) is a planning period [ T ]1,T2]The ship formation efficiency sum of the internal execution v tasks;
Figure GDA0003523310250000099
indicating the execution of task RjThe efficiency of the ship formation at the time t; when the task has started before the planning cycle
Figure GDA00035233102500000910
Then, it is ordered
Figure GDA00035233102500000913
When the task is not finished after the planning period
Figure GDA00035233102500000911
Then, it is ordered
Figure GDA00035233102500000912
Then, determining decision variables and value ranges of the optimization model: for naval vessels SiWhether or not to repair xi，xi1 denotes repair, xi0 means no repair; for naval vessels SiRepair start time of
Figure GDA0003523310250000101
For executing task RjShip and ship
Figure GDA0003523310250000102
Figure GDA0003523310250000103
Further, the constraint conditions for determining the optimization model are as follows:
for task demand constraints including task time constraints and task capacity constraints, directly adopting the ship formation task demand model established in the step 1;
for the constraint of overlapping of task time, the same naval vessel is required not to execute two tasks simultaneously, and for the naval vessel SiSpecifically, it is represented as:
when in use
Figure GDA0003523310250000104
When the temperature of the water is higher than the set temperature,
Figure GDA0003523310250000105
in the formula (I), the compound is shown in the specification,
Figure GDA0003523310250000106
and
Figure GDA0003523310250000107
respectively represent tasks RlThe start time and the end time of (c);
Figure GDA0003523310250000108
and
Figure GDA0003523310250000109
respectively represent tasks RjThe start time and the end time of (c),
Figure GDA00035233102500001010
indicating the execution of task RlIn the formation of the pre-formed pre-formed pre-formed pre,
Figure GDA00035233102500001011
indicating the execution of task RjFormation of (1);
for repair time period constraints, according to current repair work regulations, for vessels SiComprises the following steps:
Ti e-Ti s＝ti
in the formula, Ti eIndicating the end of repair time, Ti sIndicating the repair start time, tiIndicating a well-defined repair period according to the regulations;
for the midspan repair cost constraint, when the vessel has a cross-over [ T ]1,T2]Time period of repair, current period [ T ]1,T2]The repair cost is the repair budget index and the current period [ T ]1,T2]Product of repair time fraction, naval vessel SiThe interim repair expenses are:
Figure GDA00035233102500001012
in the formula, ciIndicating vessels SiCurrent stage [ T ]1,T2]Cost of repair, CiRepresenting a repair budget indicator, t'iIndicates the current period [ T1,T2]Repair time;
for the total cost constraint of repair, the total cost of the warship to be repaired is not more than the total cost budget index, which is specifically expressed as:
Figure GDA0003523310250000111
in the formula, xiWhen 0, it represents the vessel SiNo repair is needed; x is the number ofiWhen 1, it represents a vessel SiNeed to be repaired; c. CiIndicating vessels SiCurrent stage [ T ]1,T2]Cost of repair, CzRepresenting a total budget expenditure indicator;
for capacity constraints, repairs, without modification, result in only limited recovery of capacity, and do not achieve the initial capacity at the end of the last level repair or commissioning, when:
Figure GDA0003523310250000112
in the formula (I), the compound is shown in the specification,
Figure GDA0003523310250000113
represents the initial value of a certain subentry capacity of the naval vessel at the end of the last level repair or the service guarantee,
Figure GDA0003523310250000114
representing the value of the vessel before a certain itemized capacity is repaired,
Figure GDA0003523310250000115
a numerical value which represents the recoverable numerical value of the naval vessel after the repair of a certain subentry capacity;
for the overall airspeed constraint, it is specifically expressed as:
Figure GDA0003523310250000116
wherein N represents the total number of vessels, NrIndicating the number of vessels in repair, NuRepresenting the number of ships in a damaged state, and r representing the specified lowest underway rate requirement;
for different types of naval vessels, the airspeed constraint is specifically expressed as:
Figure GDA0003523310250000117
in the formula, NrtypeIndicating the number of repairs under way, N, of each type of vesselutypeIndicating the number of repairs, r, of each type of vesseltypeRepresenting the minimum airspeed requirement, n, for different types of vesselstypeRepresenting the number of various types of vessels.
In step 5 of the above technical scheme, the specific steps of solving the ship formation level repair plan optimization model for the orientation diversified tasks by applying the particle swarm optimization algorithm based on the hierarchical sequence are as follows:
the method comprises the first step of taking the minimum number of ships executing tasks as a primary target to obtain the minimum number of ships required by each task under the condition of meeting all constraint conditions in order to ensure the maintenance of the combat readiness capacity of the ships and prevent resource waste caused by too many ships executing the tasks
Figure GDA0003523310250000121
And the number of vessels of each type, e.g. mission RjThe number of the vessels in the middle and various types is
Figure GDA0003523310250000122
The optimization model is now expressed as:
Figure GDA0003523310250000123
Figure GDA0003523310250000124
secondly, on the basis of the result of the first step, considering the maximum target of the formation efficiency of the ships for executing the tasks, and optimizing and solving to obtain whether the ships are repaired or not, the repair starting time and the ship number required by each task;
the types and the number of the ships required by the task are solved in the first step and are used as additional constraint conditions of the second target to be solved, and at the moment, the optimization model can be expressed as:
Figure GDA0003523310250000131
Figure GDA0003523310250000132
aiming at the optimization model in the second step, the concrete steps of solving by applying the particle swarm optimization algorithm are as follows:
firstly, coding, considering decision variables of a model as whether a naval vessel is repaired or not, the repair starting time and the naval vessel number required by each task, wherein the decision variables are discrete variables and continuous variables, and the decision variables are 0-1 variable and integer variable, and adopting a segmented mixed coding mode, specifically adopting a segmented mixed coding mode
Figure GDA0003523310250000133
Figure GDA0003523310250000134
Wherein, [ x ]1,x2,…,xn]Adopting binary coding, and taking 0 or 1 to represent whether the 1 st to the nth naval vessels are repaired or not;
Figure GDA0003523310250000135
real number coding is adopted, and the value range is [ T ]1,T2]Indicating the initial time of repairing the 1 st to the n th vessels;
Figure GDA0003523310250000136
Figure GDA0003523310250000137
integer coding is adopted, 1,2, …, n is taken as the expression to execute the task R1To RvThe naval vessel number of (a);
at this time, for a population consisting of N particles (a particle is a specific expression in the particle swarm optimization algorithm, and the position of a particle represents a solution given according to a predetermined encoding rule), the current position of a particle m (m is 1,2, …, N) is represented as
Figure GDA0003523310250000138
Figure GDA0003523310250000139
Wherein x ism1,xm2,…,xmnFor the m-th particle corresponds to the decision variable [ x ]1,x2,…,xn]A set of solutions representing whether the vessel is repaired;
Figure GDA00035233102500001310
corresponding decision variables for the m-th particle
Figure GDA00035233102500001311
Represents the starting time of the vessel repair;
Figure GDA00035233102500001312
Figure GDA0003523310250000141
representing decision variables corresponding to the m-th particle
Figure GDA0003523310250000142
Represents the execution of task R1To RvThe naval vessel number of (a); current flight speed (flight speed indicates particle position)The tendency of one-step change) is expressed as
Figure GDA0003523310250000143
Figure GDA0003523310250000144
Particle position is a multidimensional variable, the flight velocity is not the same for each dimension, and therefore the flight velocity is also multidimensional, VmRespectively represent corresponding particle positions XmFlight speeds, Vx, of different dimensionsm1,Vxm2,…,VxmnDenotes xm1,xm2,…,xmnThe flying speed of the aircraft is controlled by the flight control system,
Figure GDA0003523310250000145
to represent
Figure GDA0003523310250000146
The flying speed of the aircraft is controlled by the flight control system,
Figure GDA0003523310250000147
Figure GDA0003523310250000148
to represent
Figure GDA0003523310250000149
Figure GDA00035233102500001410
The flying speed of (2).
Subsequently, the particle group is initialized, i.e., the initial position Q of the particle m is randomly setm(1) And an initial velocity Vm(1)；
Then, calculating the fitness, and directly taking a second objective function f (U) in the ship formation level repair plan optimization model as a fitness function in the particle swarm optimization algorithm to calculate the fitness value of each particle;
when iterating to the k generation, the position of the particle m is Qm(k) Velocity of Vm(k) Record PmThe best effect is found for the particles m in the first k-1 generationThe position of the adaptive value is called an individual optimal position; if Qm(k) Corresponding fitness value is better than PmCorresponding fitness value, then Pm＝Qm(k) Else PmKeeping the same; note PgThe position with the best fitness for all the particles in the particle group in the first k-1 generation is called as a global optimal position; if the corresponding fitness value of a certain particle position is better than PgCorresponding fitness value, then PgUpdated to the position of the particle, otherwise PgKeeping the same;
finally, the flight speed and position of each particle are updated synchronously:
one is the flight speed update, specifically expressed as:
Vm(k+1)＝w(k)*Vm(k)+c1*rand()*(Pm-Qm(k))+c2*rand()*(Pg-Qm(k))
wherein, Vm(k +1) represents the velocity of the (k +1) th generation particle m, Vm(k) Denotes the velocity of the kth generation of particles m, c1For a preset optimum position P relative to the particle mmC learning factor of2Is a preset position P relative to the global optimumgThe learning factor of (1); rand () is at [0, 1 ]]Random number within a range, w (k) is an inertial weight used to control the search range; qm(k) Represents the position of the kth generation particle m; for preventing the particles from jumping out of the optimized interval directly due to excessive speed, the speed of each dimension of the particles is limited to [ V ]min，Vmax]And when the particle exceeds the speed range, the speed of the particle is initialized again.
During the flight speed updating, for the inertia weight w (k), a linear decreasing weight strategy is adopted:
Figure GDA0003523310250000151
wherein, wmaxRepresenting the maximum inertial weight, wminRepresents the minimum inertial weight, K represents the current iteration number, TmaxThe maximum number of iterations is indicated.
Second is particle location update (i.e. generating a set of solutions for the model):
for binary discrete coding, the specific expression is:
Figure GDA0003523310250000152
for continuous coding, it is specifically expressed as:
Qm(k+1)＝Qm(k)+Vm(k+1)
for integer coding, the specific expression is:
Qm(k+1)＝round(Qm(k)+Vm(k+1))
in the formula, Qm(k +1) represents the position of the (k +1) th generation particle m, Qm(k) The position of the k-th generation particle m is shown, and s represents a particle flight speed conversion function; round is an integer function according to a rounding criterion;
for integer coding, since the integer coding is used to describe a naval vessel number (1, 2, …, n), for particles exceeding a position range, an asynchronous process is performed, that is, a position dimension which does not satisfy a constraint is initialized to ensure that the position dimension does not exceed a value range, which is specifically expressed as:
when Q ism(k+1)<1 or Qm(k+1)>When n is, Qm(k+1)＝round(rand()*n)
Iterative optimization, which is to iterate according to the steps, record and update the optimal fitness value and the corresponding particle position of the particle group in the past iteration, synchronously update the flight speed and the position of the particles, and when the preset maximum iteration time T is reachedmaxAnd then, obtaining the particle position with the optimal fitness value, wherein the particle position corresponds to the optimal decision variable in the ship formation grade repair plan model, namely whether the ship is repaired, the repair starting time and the ship number required by each task, so that the ship formation grade repair plan is compiled.
In the embodiment, a certain unit of naval vessel is taken as an object, and the annual naval vessel grade repair plan is compiled under the condition of giving annual task requirements.
According to the step 1, the numbers and types of all vessels are shown in fig. 2, and the time requirements of each task and the requirements on the ship formation itemizing capacity are shown in fig. 3.
According to the step 2, the initial itemized capability values of the vessels at the decision starting time point are shown in fig. 4, and the repair data parameters of each vessel are shown in fig. 5.
According to step 3, the contribution degree weight of the individual ship itemized capacity to the overall efficiency is comprehensively determined by a planning builder according to strategic objectives, mission tasks, relevant regulation instructions and basic unit opinions, (w)c1,wc2,wc3,wc4,wc5) (0.2,0.15,0.25,0.25, 0.15); the vessel capability attenuation function is obtained by curve fitting according to the evaluation data of various capabilities of the vessel at different time points, as shown in fig. 6; the weight of a single ship in formation is determined according to the importance degree of the ship and the army and mission task of the ship in formation, (w)1,w2,w3,w4,w5,w6,w7) (0.17,0.17,0.14,0.14,0.14,0.12, 0.12); the expected value of the formation ability of the naval vessel is determined according to strategic targets, mission tasks, superior instructions and basic unit opinions, (E)X,EM,EF,EJ,EL) (25,40,25,25, 30); risk aversion coefficient lambdaiAnd betaiAnd 0.6 and 1.2 respectively according to the preference of a decision maker for risks.
According to the step 4, the budget index of the ship grade repair expenditure is 7000 ten thousand yuan, and the overall lowest rate of flight of the ship is comprehensively determined to be r 60% according to the army type and the current regulation; the ships are divided into three types of destroyer De, guard ship Fr and supply ship Au, the lowest flight rate of each type of ships is obtained by statistical evaluation according to the flight rate data of the unit in the past year, and the minimum flight rate is determined as rDe＝50％，rFr＝60％，rAu＝50％。
According to the step 5, obtaining the target through the first step of a hierarchical sequence particle swarm optimization algorithm
Figure GDA0003523310250000171
Figure GDA0003523310250000172
That is, task 1 needs 1 expelling warships and 1 replenishing warships; task 2 needs 2 protective warships and 1 replenishment warship.
Setting the parameters of the particle swarm optimization algorithm as follows: n100, T200, c1＝1.5，c2＝1.5，wmax＝0.9，wmin＝0.4，Vmax＝2，VminThe configuration plan for the ship formation to perform the task is shown in fig. 7, the level repair plan is shown in fig. 8, and the available state of the ship is shown in fig. 9.
For comparative analysis, the planned repair plan for the vessel class in both cases of considering the mission factors in the established repair mode is shown in fig. 10.
Compared with the situation without considering tasks, the diversified-task-oriented ship formation grade repair plan considers the influence of the task requirements on the ship formation grade repair plan except for the influence factors and constraints such as the conventional aviation rate, the repair period and the repair expense, brings the task capacity requirement constraint and the task time constraint into consideration, can obtain the task use configuration arrangement and the grade repair plan arrangement of the ships at the same time, can effectively make the use and repair uniform, and solves the problem of the currently ubiquitous use and repair contradiction.
The invention provides a diversified task oriented ship formation grade repair plan compiling method, which can fully consider the influence of diversified tasks on a grade repair plan and the influence of ship use and repair on capacity change, scientifically plans a ship formation grade repair plan based on the existing repair mode framework, coordinates and processes the ship repair relation, and simultaneously meets the diversified task requirements and the repair requirements of ships.
Details not described in this specification are within the skill of the art that are well known to those skilled in the art.

Claims (6)

1. A diversified task-oriented ship formation grade repair plan compilation method is characterized by comprising the following steps:
step 1: establishing a task demand model of the ship formation according to diversified tasks, time demands of different tasks and capacity demands of the ship formation faced by the ships, wherein the time demands are that all the ships in the ship formation are in a usable state in a task time period and cannot be subjected to grade repair; the capacity requirements are that the command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value of the naval vessel formation are all larger than the minimum required value of the task corresponding capacity;
step 2: establishing a ship formation grade repair plan base database facing to diversified tasks according to ship diversified task requirements, ship actual technical states and current ship grade repair regulations, wherein the ship formation grade repair plan base database facing to diversified tasks comprises diversified task data parameters, an initial item division capability value of a ship at a decision starting time point and ship repair data parameters;
and step 3: establishing a ship formation efficiency evaluation model according to the characteristic that the command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value of the ships are attenuated along with time, the weight of the single ship to formation itemizing capacity, the expectation and risk preference degree of a decision maker to the ship formation itemizing capacity and the weight of the contribution degree of each itemizing capacity of the ship formation to the overall efficiency;
and 4, step 4: the method comprises the steps that a ship formation grade repair plan optimization model facing diversified tasks is established by taking the goals of minimum number of ships in ship formation for executing tasks and maximum efficiency of the ship formation, taking the condition whether the ships are repaired, repair starting time and ship number required by each task as decision variables, and considering task demand constraint, task time overlapping constraint, repair period constraint, over-period repair expense constraint, repair total expense constraint, capacity constraint and air rate constraint;
and 5: solving the ship formation grade repair plan optimization model of the orientation diversified tasks by using a particle swarm optimization algorithm based on a hierarchical sequence to obtain a decision variable of the ship formation grade repair plan optimization model, wherein the decision variable comprises whether a ship is repaired, the repair starting time and the ship number required by each task, and further obtains a task configuration plan and a grade repair plan of the ship formation;
in the step 1, the specific method for establishing the ship formation task demand model comprises the following steps:
firstly, the existing naval vessel set is obtained by considering the naval vessel types and the number of different types of naval vessels:
S＝{{Si},type,ntype}，i＝1,2…,n，type＝1,2,…,k
in the formula, S represents the set of all vessels, SiRepresenting the i-th vessel co-existing with the n vessels S1,S2,…,Si,…SnType denotes the vessel type, there are k types of vessels, ntypeRepresenting the number of various types of vessels, ntype1,ntype2,…,ntypekA step of;
then, considering the specific task to be executed and the number of the vessels required by the task, a task vessel set is established, namely, the vessel formation comprises:
Figure FDA0003529548330000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003529548330000022
indicating the execution of task RjOf a fleet of vessels, comprising
Figure FDA0003529548330000023
A vessel for a vessel, the vessel having a plurality of channels,
Figure FDA0003529548330000024
is a subset of the set S of all vessels;
further, considering the starting time of different tasks and the requirements of the different tasks on the ship formation itemizing capacity, a diversified task model and a task demand model are established;
for the diversified tasks, the following are specifically expressed:
Figure FDA0003529548330000025
wherein R represents a period of time [ T1,T2]Set of tasks, R, facing n vesselsjIt represents the j-th task that is,
Figure FDA0003529548330000026
and
Figure FDA0003529548330000027
respectively represent tasks RjThe start time and the end time of (c),
Figure FDA0003529548330000028
respectively represent tasks RjThe minimum requirements on command control capability value, maneuverability capability value, defense capability value, attack capability value and guarantee capability value of the naval vessel formation are met;
for the requirement of the task time, the task naval vessel is required to be incapable of performing level repair within the task duration, which is specifically expressed as follows:
when in use
Figure FDA0003529548330000029
When the temperature of the water is higher than the set temperature,
Figure FDA00035295483300000210
in the formula (I), the compound is shown in the specification,
Figure FDA0003529548330000031
for task RjThe execution period of (a);
Figure FDA0003529548330000032
for vessels SiA grade repair cycle of; phi represents an empty set;
for the task capacity requirement, the command control capacity value, the maneuvering capacity value, the defense capacity value, the attack capacity value and the guarantee capacity value of the naval vessel formation are required to be greater than the minimum required value of the task corresponding capacity, and the specific expression is as follows:
Figure FDA0003529548330000033
in the formula (I);
Figure FDA0003529548330000034
respectively representing the execution of tasks RjThe command control capability value, the maneuvering capability value, the defense capability value, the attack capability value and the guarantee capability value of the naval vessel formation;
Figure FDA0003529548330000035
is shown in task RjWithin the execution period of (c);
Figure FDA0003529548330000036
respectively represent tasks RjThe minimum requirement values of command control capability, maneuverability, defense capability, attack capability and guarantee capability of the ship formation.
2. The diversified mission-oriented vessel fleet level repair planning method according to claim 1, wherein: the diversified task data parameters are used for describing the requirements of diversified tasks on scale, time and capacity, the initial itemized capacity value of the naval vessel at the decision starting time point is used for describing the capacity performance of the naval vessel at the time point, and the naval vessel repair data parameters are used as basic data of a naval vessel formation level repair plan optimization model.
3. The diversified mission-oriented vessel fleet level repair planning method according to claim 1, wherein: in the step 2, the diversified task data parameters comprise the number of tasks, the execution time of different tasks and the minimum required value of the task for the ship formation itemizing capacity; the initial itemized capacity value of the naval vessel at the decision starting time point comprises a command control capacity value, a maneuvering capacity value, a defense capacity value, an attack capacity value and a guarantee capacity value, wherein the capacity value represents the size of each itemized capacity and is obtained by comprehensively evaluating the technical state of equipment; the vessel repair data parameters comprise a vessel number, a repair level preliminarily drawn according to the current vessel level repair rule, a budget index, a repair period, a recovery capacity, a time length from the last level repair or the last service guarantee to a decision starting point, and a lowest requirement value of the aviation state capacity.
4. The diversified mission-oriented vessel fleet level repair planning method according to claim 1, wherein: in step 3, the specific method for establishing the ship formation efficiency evaluation model comprises the following steps:
firstly, aiming at the characteristic that the capability of a naval vessel can be attenuated along with time, a reverse logistic function is adopted to establish a subentry capability evaluation model of naval vessel formation:
Figure FDA0003529548330000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003529548330000042
Z-X, M, F, J, L denotes the execution of task RjThe method comprises the following steps that (1) certain subentry capacity values of a ship formation, X, M, F, J and L respectively correspond to ship command and control capacity, maneuvering capacity, defense capacity, attack capacity and guarantee capacity;
Figure FDA0003529548330000043
representing participation in task RjOf the ith vessel
Figure FDA0003529548330000044
Weighting the grouping capacity of the ship formation;
Figure FDA0003529548330000045
z ═ X, M, F, J, and L represent
Figure FDA0003529548330000046
The initial value of the item capability;
Figure FDA0003529548330000047
is the rate of capacity decay;
Figure FDA0003529548330000048
representing a capacity fade length; t represents time and the completion time of the previous level repair or the service warranty is taken as the origin, and when t takes a certain specific time as the origin, the capacity attenuation length
Figure FDA0003529548330000049
Should be that
Figure FDA00035295483300000410
Wherein
Figure FDA00035295483300000411
Indicating vessels
Figure FDA00035295483300000412
The time length from the completion of the last grade repair or the service warranty to the decision starting time point; e is a natural constant;
Figure FDA00035295483300000413
indicating the execution of task RjThe number of vessels;
then, considering the expectation and risk preference of a decision maker on the ship formation itemized capacity value, establishing a task ship formation itemized capacity value function by applying a prospect theory:
Figure FDA00035295483300000414
in the formula (I), the compound is shown in the specification,
Figure FDA00035295483300000415
Z-X, M, F, J, L denotes the execution of task RjThe value function of a certain subentry ability of the ship formation,
Figure FDA0003529548330000051
z is X, M, F, J and L which represent the actual value of the ability of the vessel to form the itemized items,
Figure FDA0003529548330000052
z is X, M, F, J, L represents the expected value of the ability of the naval vessel to form the itemized items, and lambdaiAnd betai0 < lambda, representing the risk aversion coefficients for actual values above and below expectations, respectivelyi＜1＜βi；
Further, obtaining a ship formation efficiency evaluation model:
Figure FDA0003529548330000053
in the formula (I), the compound is shown in the specification,
Figure FDA0003529548330000054
indicating the execution of task RjShip formation efficiency, wc1～wc5Represents the weight of the contribution degree of each subentry ability to the overall efficiency,
Figure FDA0003529548330000055
respectively representing the execution of tasks RjThe command control capability, the maneuvering capability, the defense capability, the attack capability and the guarantee capability of the ship formation.
5. The diversified mission-oriented vessel fleet level repair planning method according to claim 1, wherein: the specific method of the step 4 comprises the following steps:
firstly, establishing two optimization targets of a diversified task oriented ship formation grade repair plan optimization model;
the first objective is to perform the task with the least number of vessels in the fleet of vessels, expressed as:
Figure FDA0003529548330000056
in the formula, nRRepresenting the sum of the number of vessels performing v tasks;
Figure FDA0003529548330000057
indicating the execution of task RjThe number of vessels;
Figure FDA0003529548330000058
indicating the execution of task RjNumber of u-type vessels; k represents the number of types of vessels,
Figure FDA0003529548330000059
respectively representing the number of each type of naval vessel;
the second objective is to maximize the effectiveness of the formation of the vessels performing the mission, expressed as:
Figure FDA00035295483300000510
wherein f (U) is a planning period [ T ]1,T2]The ship formation efficiency sum of the internal execution v tasks;
Figure FDA00035295483300000620
indicating the execution of task RjThe efficiency of the ship formation at the time t; when the task has started before the planning cycle
Figure FDA0003529548330000061
Then, it is ordered
Figure FDA0003529548330000062
When the task is not finished after the planning period
Figure FDA0003529548330000063
Then, it is ordered
Figure FDA0003529548330000064
Then, determining decision variables and value ranges of the optimization model: for naval vessels SiWhether or not to repair xi，xi1 denotes repair, xi0 means no repair; for naval vessels SiRepair start time of
Figure FDA0003529548330000065
Figure FDA0003529548330000066
For executing task RjShip and ship
Figure FDA0003529548330000067
Figure FDA0003529548330000068
Further, the constraint conditions for determining the optimization model are as follows:
for task demand constraints including task time constraints and task capacity constraints, directly adopting the ship formation task demand model established in the step 1;
for the constraint of overlapping of task time, the same naval vessel is required not to execute two tasks simultaneously, and for the naval vessel SiSpecifically, it is represented as:
when in use
Figure FDA0003529548330000069
When the temperature of the water is higher than the set temperature,
Figure FDA00035295483300000610
in the formula (I), the compound is shown in the specification,
Figure FDA00035295483300000611
and
Figure FDA00035295483300000612
respectively represent tasks RlThe start time and the end time of (c);
Figure FDA00035295483300000613
and
Figure FDA00035295483300000614
respectively represent tasks RjThe start time and the end time of (c),
Figure FDA00035295483300000615
indicating the execution of task RlIn the formation of the pre-formed pre-formed pre-formed pre,
Figure FDA00035295483300000616
indicating the execution of task RjFormation of (1);
for repair time period constraints, according to current repair work regulations, for vessels SiComprises the following steps:
Figure FDA00035295483300000617
in the formula (I), the compound is shown in the specification,
Figure FDA00035295483300000618
the time at which the repair is to be ended is indicated,
Figure FDA00035295483300000619
indicating the repair start time, tiIndicating a well-defined repair period according to the regulations;
for the midspan repair cost constraint, when the vessel has a cross-over [ T ]1,T2]Time periodAt the time of repair, current period [ T ]1,T2]The repair cost is the repair budget index and the current period [ T ]1,T2]Product of repair time fraction, naval vessel SiThe interim repair expenses are:
Figure FDA0003529548330000071
in the formula, ciIndicating vessels SiCurrent stage [ T ]1,T2]Cost of repair, CiRepresenting a repair budget index, ti' indicates the current period [ T1,T2]Repair time;
for the total cost constraint of repair, the total cost of the warship to be repaired is not more than the total cost budget index, which is specifically expressed as:
Figure FDA0003529548330000072
in the formula, xiWhen 0, it represents the vessel SiNo repair is needed; x is the number ofiWhen 1, it represents a vessel SiNeed to be repaired; c. CiIndicating vessels SiCurrent stage [ T ]1,T2]Cost of repair, CzRepresenting a total budget expenditure indicator;
for capacity constraints, repairs, without modification, result in only limited recovery of capacity, and do not achieve the initial capacity at the end of the last level repair or commissioning, when:
Figure FDA0003529548330000073
in the formula (I), the compound is shown in the specification,
Figure FDA0003529548330000074
z is X, M, F, J and L represents the initial value of some partial capacity of the naval vessel at the end of the last level repair or the service guarantee,
Figure FDA0003529548330000075
z is X, M, F, J and L which represent the numerical value before the repair of certain division capacity of the naval vessel,
Figure FDA0003529548330000076
z is X, M, F, J and L which represent the values that can be recovered after the repair of a certain division capacity of the naval vessel;
for the overall airspeed constraint, it is specifically expressed as:
Figure FDA0003529548330000077
wherein N represents the total number of vessels, NrIndicating the number of vessels in repair, NuRepresenting the number of ships in a damaged state, and r representing the specified lowest underway rate requirement;
for different types of naval vessels, the airspeed constraint is specifically expressed as:
Figure FDA0003529548330000078
in the formula, NrtypeIndicating the number of repairs under way, N, of each type of vesselutypeIndicating the number of repairs, r, of each type of vesseltypeRepresenting the minimum airspeed requirement, n, for different types of vesselstypeRepresenting the number of various types of vessels.
6. The diversified mission-oriented vessel fleet level repair planning method according to claim 5, wherein:
in the step 5, solving the ship formation level repair plan optimization model of the orientation diversified tasks by using a particle swarm optimization algorithm based on a hierarchical sequence comprises the following specific steps:
the first step is that the minimum number of ships executing the task is taken as a primary target under the condition that all constraint conditions are met, and the minimum number of ships required by each task is obtained
Figure FDA0003529548330000081
And the number of vessels of each type, e.g. mission RjThe number of the vessels in the middle and various types is
Figure FDA0003529548330000082
The optimization model is now expressed as:
Figure FDA0003529548330000083
Figure FDA0003529548330000091
secondly, on the basis of the result of the first step, considering the maximum target of the formation efficiency of the ships for executing the tasks, and optimizing and solving to obtain whether the ships are repaired or not, the repair starting time and the ship number required by each task;
the type and the number of the ships required by the task are solved in the first step and are used as additional constraint conditions of the second target to be solved, and at the moment, the optimization model can be expressed as:
Figure FDA0003529548330000092
Figure FDA0003529548330000093
aiming at the optimization model in the second step, the concrete steps of solving by applying the particle swarm optimization algorithm are as follows:
firstly, coding, considering decision variables of a model as whether a naval vessel is repaired or not, the initial time of the repair and the naval vessel number required by each task, wherein the decision variables have discrete variables and continuous variables, and have 0-1 variable and integer variable, and adopting a segmented mixed coding mode,in particular to
Figure FDA0003529548330000101
Figure FDA0003529548330000102
Wherein, [ x ]1,x2,…,xn]Adopting binary coding to represent whether the 1 st to the nth ships are repaired or not;
Figure FDA0003529548330000103
real number coding is adopted to represent the repair starting time of the 1 st to the nth naval vessels;
Figure FDA0003529548330000104
Figure FDA0003529548330000105
using integer coding to represent the execution task R1To RvThe naval vessel number of (a);
at this time, for a population consisting of N particles, the current position of the particle m (m ═ 1,2, …, N) is represented as
Figure FDA0003529548330000106
Figure FDA0003529548330000107
Wherein x ism1,xm2,…,xmnFor the m-th particle corresponds to the decision variable [ x ]1,x2,…,xn]A set of solutions representing whether the vessel is repaired;
Figure FDA0003529548330000108
Figure FDA0003529548330000109
corresponding decision variables for the m-th particle
Figure FDA00035295483300001010
Represents the starting time of the vessel repair;
Figure FDA00035295483300001011
Figure FDA00035295483300001012
representing decision variables corresponding to the m-th particle
Figure FDA00035295483300001013
Figure FDA00035295483300001014
Represents the execution of task R1To RvThe naval vessel number of (a); the current flight speed is expressed as
Figure FDA00035295483300001015
Figure FDA00035295483300001016
VmRespectively represent corresponding particle positions XmFlight speeds, Vx, of different dimensionsm1,Vxm2,…,VxmnDenotes xm1,xm2,…,xmnThe flying speed of the aircraft is controlled by the flight control system,
Figure FDA00035295483300001017
to represent
Figure FDA00035295483300001018
The flying speed of the aircraft is controlled by the flight control system,
Figure FDA00035295483300001019
to represent
Figure FDA0003529548330000111
The flying speed of (d);
subsequently, the particle group is initialized, i.e. the initial of the particles m is set randomlyStarting position Qm(1) And an initial velocity Vm(1)；
Then, calculating the fitness, and directly taking a second objective function f (U) in the ship formation level repair plan optimization model as a fitness function in the particle swarm optimization algorithm to calculate the fitness value of each particle;
when iterating to the K generation, the position of the particle m is Qm(K) Velocity of Vm(K) Record PmThe position where the particle m has the best fitness value in the first K-1 generation is called the individual optimal position; if Qm(K) Corresponding fitness value is better than PmCorresponding fitness value, then Pm＝Qm(K) Else PmKeeping the same; note PgThe position with the best fitness for all the particles in the particle group in the first K-1 generation is called as a global optimal position; if the corresponding fitness value of a certain particle position is better than PgCorresponding fitness value, then PgUpdated to the position of the particle, otherwise PgKeeping the same;
finally, the flight speed and position of each particle are updated synchronously:
one is the flight speed update, specifically expressed as:
Vm(K+1)＝w(K)*Vm(K)+c1*rand()*(Pm-Qm(K))+c2*rand()*(Pg-Qm(K))
wherein, Vm(K +1) represents the velocity of the K +1 th generation of particles m, Vm(K) Denotes the velocity of the K-th generation particle m, c1For a preset optimum position P relative to the particle mmC learning factor of2Is a preset position P relative to the global optimumgThe learning factor of (1); rand () is at [0, 1 ]]Random number within a range, w (k) is an inertial weight used to control the search range; qm(K) Represents the position of the K-th generation particle m; for preventing the particles from jumping out of the optimized interval directly due to excessive speed, the speed of each dimension of the particles is limited to [ V ]min,Vmax]If the particle exceeds the speed range, the speed of the particle is initialized again;
during the flight speed updating, for the inertia weight w (K), a linear decreasing weight strategy is adopted:
Figure FDA0003529548330000112
wherein, wmaxRepresenting the maximum inertial weight, wminRepresents the minimum inertial weight, K represents the current iteration number, TmaxRepresenting the maximum number of iterations;
secondly, particle position updating:
for binary discrete coding, the specific expression is:
Figure FDA0003529548330000121
for continuous coding, it is specifically expressed as:
Qm(K+1)＝Qm(K)+Vm(K+1)
for integer coding, the specific expression is:
Qm(K+1)＝round(Qm(K)+Vm(K+1))
in the formula, Qm(K +1) represents the position of the K +1 th generation particle m, Qm(K) The position of the K-th generation particle m is shown, and s represents a particle flight speed conversion function; round is an integer function according to a rounding criterion;
for integer coding, because the integer coding is used to describe a naval vessel number, 1,2, …, n is taken, and therefore, for particles exceeding a position range, asynchronous processing is performed, that is, a position dimension which does not satisfy a constraint is initialized, and it is ensured that the position dimension does not exceed a value range, which is specifically expressed as:
when Q ism(K +1) < 1 or Qm(K+1)>When n is, Qm(K+1)＝round(rand()*n)
Iterative optimization, which is to iterate according to the steps, record and update the optimal fitness value and the corresponding particle position of the particle group in the past iteration, synchronously update the flight speed and the position of the particles, and when the preset maximum iteration time T is reachedmaxThen obtainAnd when the particle position with the optimal fitness value is reached, the optimal decision variables in the ship formation grade repair plan model correspond to the particle position with the optimal fitness value, namely whether the ship is repaired or not, the repair starting time and the ship number required by each task, so that the establishment of the ship formation grade repair plan is realized.
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