CN108428004A - Flying object conflict Resolution paths planning method based on ant group algorithm - Google Patents
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Abstract
The present invention relates to a kind of flying object conflict Resolution paths planning method based on ant group algorithm, includes the following steps：Step S1：Initialize iterations, ant number m, cumulative information significance level factor-alpha, heuristic function significance level factor-beta, multiple track points between departure place and destination and the initial information element concentration between each track points；Step S2：Every ant repeatedly from origin to destination between through different track points cover whole process, complete successive ignition, and then select optimal route, wherein when carrying out state transfer, Discontinuous Factors successively decrease with iterations；When being updated to pheromones, only with overall situation update, also, only pheromones on global optimum path are evaporated and are discharged, and increase pheromones, the pheromones on global most minor path are evaporated and discharged, intermediate path is not processed.The present invention has precocious ability of jumping out when planning flying object path, and convergence rate is accelerated.
Description
Technical field
The present invention relates to unmanned plane low latitude domain hedging technical fields, and in particular to a kind of flying object punching based on ant group algorithm
It is prominent to free paths planning method.
Background technology
In recent years, under the guidance of ICAO new navigation system development plans, global aerial tissue is to ADS-B (broadcast types
Automatic dependent surveillance) it as one of communication and navigation surveillance technology of new generation carried out fruitful research, experiment, popularization, answered
With, and obtain rapid development.ADS-B is a kind of technology hand providing autonomic monitoring information with ground-air monitoring for air-air monitoring
Section, unmanned plane broadcasts the position of its own and other state of flight information by data-link automatically, and obtains aerial ADS-B in real time
Information and ground service information, reach the mutual perception between unmanned plane, and ADS-B is full-featured, and installation is simple and convenient, and expense is
/ 10th or so of radar system, developed country are just gradually replacing primary, secondary radar with ADS-B at present, are applying in military affairs
Field, can improve Battle Space Perception ability, and the automaticity of ADS-B makes it be highly suitable for unmanned plane.
Multiple no-manned plane is total to spatial domain and executes the important trend that task has become Development of UAV.Along with answering extensively for unmanned plane
With, low-latitude flying spatial domain increasingly congestion, the implementation of free flight can improve the utilization rate of spatial domain resource, solve that spatial domain is crowded to ask
Topic, but free flight faces the safety accidents such as unmanned plane damage, crash again and again, unmanned plane and unmanned plane, unmanned plane with have it is man-machine
The collision conflict that spatial domain is flown faced altogether has become the outstanding problem for influencing the autonomous free flight of unmanned plane, therefore, unmanned plane
Very eager is become for the demand of avoiding system.
Unmanned plane avoiding system improves spatial domain flow, efficiently completes task all to ensuring unmanned plane autonomous flight safely
It has practical significance, unmanned plane autonomous flight hedging algorithm is the core of unmanned plane avoiding system, and hedging algorithm is to work as
When detecting unmanned plane will clash with other aircraft, quickly and effectively cooks up and free the hair that flight path avoids conflict
It is raw, it is also and not perfect to the research of unmanned plane hedging model and algorithm both at home and abroad at present, how in the shortest time, consume minimum
In the case of realize unmanned plane conflict Resolution, need further study and improve.
Ant colony optimization algorithm (ACO) is a kind of simulative optimization algorithm of simulation Food Recruiment In Ants behavior, and ant is in motion process
In, a kind of substance being referred to as pheromone can be left in its paths traversed and is transmitted into row information, and ant is being transported
The ant colony collection that can be perceived this substance during dynamic, and instruct the direction of motion of oneself with this, therefore be made of a large amount of ants
Body behavior just shows a kind of information positive feedback phenomenon：The ant passed by a certain path is more, then late comer selects the path
Probability it is bigger.
Positive feedback mechanism in ant group algorithm can enable it to optimize preferable solution, find out solution rapidly, have simultaneously
There is strong robustness, global search, Parallel distributed computing, easily combined with other problems, in aircraft conflict Resolution problem
In be a kind of common method.Article is based on ant group algorithm, in conjunction with elitism strategy, Discontinuous Factors is added, to existing both at home and abroad
Achievement in research carries out algorithm improvement, propose it is a kind of can quickly cook up the optimal algorithm for freeing path, while algorithm has and avoids
Precocious ability.Pass through MATLAB simulating, verifyings, it was demonstrated that algorithm validity.
Ant group algorithm (Ant Colony Optimization, abbreviation ACO) is existed by Marco Dorigo et al. earliest
It is put forward for the first time within 1991, ant mainly exchanges information by a kind of substance being called pheromones, according to pheromones
It is how many to be selected and updated, optimal solution is generated by iteration for several times.The exchange of pheromones is that ant searching shortest path is most heavy
The medium and means wanted, ant are blind, their activity is carried out by pheromones, they have towards the ground more than pheromones
The trend of Fang Yundong, and new pheromones are left, this is a kind of positive feedback mechanism.By being not aspectant direct friendship
Stream, but indirect communication is carried out by pheromones, the information that individual is collected is shared with entire community information, and information is in internal system
Exchange study is carried out, system, i.e. Adaptable System are continued to optimize.Ant group algorithm is used for the solution of optimization problem, is based on true
The similitude of real Food Recruiment In Ants behavior and optimization problem solving process, is shown in Table 1.
Table 1：Optimization problem solving process is compared with Food Recruiment In Ants behavior
Simple individual is utilized in ACO --- ant, the candidate solution of tectonic association optimization problem constantly iteratively.Ant
The construction of solution is instructed by pheromones and heuristic information.It can be used in principle by the component ant group algorithm of definition solution various
Combinatorial problem.One ant starts with an empty solution, then repeats the component of increase solution until generating a complete time
Choosing solution, constructs candidate solution in this way.On each selected element, the component which solution ant has to decide on will be added to the current of it
Part solves.After the construction complete of solution, ant gives the solution that they construct to positive feedback, by launching pheromones to the solution used
Component on.
Although the positive feedback mechanism in ACO can be such that preferable solution is continued to optimize, since algorithm initial stage pheromones are accumulated
Tired difference unobvious, cause ant group algorithm initial stage convergence rate slower, when accelerating convergence rate, although with the progress of search
Search speed is accelerated but is not to rapidly converge to globally optimal solution, it is likely that is absorbed in earliness, in order to solve these problems
Ant group algorithm founder Dorigo has also been proposed a kind of improved ant group algorithm --- ACS algorithm (ACS).
However, in the article of all ACS algorithms all using the local updating of pheromones as the feature of its algorithm it
One, but be found through experiments that, effect is limited.Due to the global regeneration function of pheromones, after searching for several times,
All sides for belonging to optimal path, pheromones level are significantly larger than other sides, differ an order of magnitude.Therefore, pheromones
Local updating effect not can effectively stop search and be absorbed in suboptimization.In addition, since the local updating of pheromones is each
It will be carried out after step search, therefore, consume a large amount of calculating time.
Accordingly, it is desirable to provide a kind of new ant group algorithm.
Invention content
To solve the shortcomings of the prior art, the flying object conflict Resolution based on ant group algorithm that the present invention provides a kind of
Paths planning method includes the following steps：
Step S1：Initialize iterations, ant number m, cumulative information significance level factor-alpha, heuristic function significance level
Factor-beta, multiple track points between departure place and destination and the initial information element concentration between each track points；
Step S2：Every ant repeatedly from origin to destination between through different track points cover whole process, complete more
Secondary iteration, and then select optimal route；
Wherein, ant is when selecting track points, it then follows following rules：
Wherein, pp represents the mode in ant selection path, and q is in the equally distributed random number in [0,1] section, and ant is every
A i points, can randomly generate a q value；Also, different ants have different q values at different track points i；
I indicates that the track points that ant is presently in, j indicate the track points that ant subsequent time may move towards；
τijIt indicates in the current iteration period, the pheromone concentration on path (i, j), ηijIt indicates in the current iteration period
In, ant goes to the expected degree of track points j, and η from track points iij=1/dij；
dijIndicate the distance of ij point-to-point transmissions；
allowedkIndicate that ant k allows the set for accessing track points in next step；
q0=1/et/b；T is current iterations, and b is constant；
pij kIt indicates to be more than q as q0When, ant randomly chooses a paths from possible path (i, j) group.
Wherein, in different iteration cycles, the initial information element concentration update rule between each track points is only with complete
Office's update rule.
Wherein, in different iteration cycles, the global update rule of the pheromone concentration on path (i, j) is：
τij(t=1)=(1- ρ) τij(t)+ρ ﹒ n ﹒ Δs τij(t)
Wherein, τij(t+1) it is the pheromone concentration on path (i, j) in the following iteration period；ρ is the volatilization of pheromones
Parameter, value is between [0,1]；N is the ant sum in all paths (i, j) of passing by a upper iteration cycle, n≤m；Δτij(t)
It is every ant to the pheromones contribution margin of respective path.
Wherein, in different iteration cycles, pheromones increment is determined using following formula：
If path (i, j) is current globally optimal solution, Δ τij(t)=1/Cgb；
If path (i, j) is current global most inferior solution, Δ τij(t)=- 1/Cgb；
Path if (i, j) between current globally optimal solution and current global most inferior solution, Δ τij(t)=0；
Wherein, CgbFor the path length in current global optimum path.
Wherein, in the successive ignition period, pheromone concentration on path (i, j) between a maximum value and minimum value it
Between.
Wherein, in the successive ignition period, the pheromone concentration bounded on optimal path component part is 2 points adjacent.
Wherein, in the successive ignition period, the Ant ColonySystem can with arbitrarily level off to 1 probability close to optimal path.
Wherein, all optimal by fully big iterations after finding optimal path in the successive ignition period
Pheromone concentration on path is above the pheromone concentration on non-optimal path.
Flying object conflict Resolution paths planning method provided by the invention based on ant group algorithm, in planning flying object path
When, have precocious ability of jumping out, convergence rate is accelerated.
Description of the drawings
Fig. 1：The initialization track points schematic diagram of the present invention；
Fig. 2：In a certain iteration cycle of the present invention, first time state transition path schematic diagram；
Fig. 3：In a certain iteration cycle of the present invention, second of state transition path schematic diagram；
Fig. 4：In the simulating, verifying of the present invention, unmanned plane starting point schematic diagram is initialized；
Fig. 5：The conflict Resolution path profile of existing ant group algorithm；
Fig. 6：The result of calculation of existing ant group algorithm；
Fig. 7：The conflict Resolution path profile of existing ACS algorithm；
Fig. 8：The result of calculation of existing ACS algorithm；
Fig. 9：The conflict Resolution path profile of the paths planning method of the present invention；
Figure 10：The result of calculation of the paths planning method of the present invention.
Specific implementation mode
In order to have further understanding to technical scheme of the present invention and advantageous effect, it is described in detail below in conjunction with the accompanying drawings
Technical scheme of the present invention and its advantageous effect of generation.
The substantially flow of ant group algorithm is：
1, after departure place A and destination B that flight is determined, multiple boats are initialized between departure place A and destination B
Mark point, as shown in Figure 1, the part that dotted line surrounds is multiple track points of initialization.
2, ant number m is initialized, every ant has gone to mesh from departure place A by the selection of multiple track points
Ground B, complete first time iteration.
3, after have passed through first time iteration, all ants are again from departure place, by the selection of multiple track points,
Destination B is gone to again, completes second of iteration.
4, it repeats the above process, until completing scheduled iterations.
During successive ignition, the course line path of ant levels off to optimal route gradually, selected optimal route
Gradually actual optimal route is leveled off to.
Ant is in the selection course of track points, and there are multiple paths (i, j), wherein i represents the flight path being presently in
Point, j indicates the track points that ant subsequent time may move towards, for example, first, shown in Figure 2, it is assumed that at the beginning of the present invention
Beginning has changed 3 ants, and 3 ants are directed to departure place A from departure place A, next track points may be point C, D or
E, therefore, for this 3 ants, i represents departure place A, and j represents point C, D or E；Then, shown in Figure 3, warp
It crosses, the selection of first track points, 3 ants have gone to C points, D points and E points respectively, next for this 3 ants
Track points may be point F, G or H：For the ant of C points, i represents point C, j and represents point F, G or H；Correspondingly, for D
For the ant of point, i represents point D, and j represents point F, G or H；For the ant of E points, i represents point E, j and represents point F, G
Or H, and so on.
For various deficiencies existing for existing ant group algorithm, shape of the present invention from ant between track points and track points
Three aspects of determination of state transition rule, pheromone updating rule and pheromones increment between different iteration cycles are changed
Into, it is proposed that a kind of new ant group algorithm.
One, to the improvement of node transition rule
The precocious phenomenon generated because accelerating algorithmic statement is not can be well solved for existing ant group algorithm, the present invention
On the basis of existing ant group algorithm, it is proposed that new Discontinuous Factors q0, q0=1/et/b；T is current iterations, and b is
Constant；
The node transition rule of improved ant group algorithm is：
Wherein, pp represents the mode in ant selection path, and q is in the equally distributed random number in [0,1] section, and ant is every
A i points, can randomly generate a q value；Also, different ants have different q values, q values to obey at different track points i
It is uniformly distributed, in each iteration, selects all update before next track points；
τijIt indicates in the current iteration period, the pheromone concentration on path (i, j), ηijIt indicates in the current iteration period
In, ant goes to the expected degree of track points j, and η from track points iij=1/dij；
dijIndicate the distance of ij point-to-point transmissions；
allowedkIndicate that ant k allows the set for accessing track points in next step；α and β is respectively the important journey of cumulative information
Spend the factor and the heuristic function significance level factor.
That is, according to the present invention when carrying out state transfer, in current iteration cycle, if certain ant is at some
Constant q on track points i meets q≤q0, then ant is from all corresponding track points j, the τ corresponding to selection oneij α﹒ ηij β
It is worth maximum track points j, as the next track points of this ant, if constant q of the ant on some track points i is unsatisfactory for q
≤q0, then ant randomly choose a paths from possible path (i, j) group.
By Discontinuous Factors q0Calculation formula it is found that Discontinuous Factors increase with iterations, value is gradually reduced；Cause
This, at algorithm initial stage, Discontinuous Factors are relatively large, so having continued τ in path candidateij α﹒ ηij βMaximum path is selected in probability
The advantage high much larger than other paths, search range Relatively centralized, initial stage search efficiency, as iterations increase, disturbance because
Son is gradually reduced, that is, is randomly choosed probability and increased, expand the range of choice of understanding, and select probability not only selects currently preferably to solve,
Also have an opportunity to select other solutions, in this way by probability reasonable distribution in each stage, actually increases the overall situation of innovatory algorithm
Search capability makes algorithm have and jumps out precocious ability.
Two, to the improvement of pheromone updating rule
Existing ACS algorithm uses two kinds of pheromone updating rules of global and local, however, inventor is by surveying
Examination is found：If two kinds of update rules are simultaneously using that can not receive better effect, optimization quality has dropped instead.Because such as
Every ant of fruit pass through a certain path when all impression information element, can make the pheromone concentration on this path rise rapidly and other
The pheromone amount difference in path increases, if not jumping out precocious measure effectively, is easy to make on local optimum path
Pheromones increase is too fast, is absorbed in local optimum, that is, is absorbed in precocity, causes pheromones superfluous, and efficiency of algorithm is low,
If each ant all impression information elements, are almost all gathering on each paths, are causing letter in this way
Preferentially rule has been desalinated in the waste that breath element is launched, and since pheromones bulk deposition wastes so that and efficiency of algorithm reduces,
Within the defined acceptable calculating time, it cannot get ideal optimal result, i.e., it is also not converged just to have stopped.
Therefore, in the pheromone updating rule of ant group algorithm used in the present invention, local updating rule has been abandoned, has only been adopted
With overall situation update rule, that is, it is to work as that the shortest path in all paths for meeting constraints that all ants pass by is taken when starting
Preceding globally optimal solution, and fresh information element, carry out then as the best values of these current globally optimal solutions are taken after each iteration
Pheromone update.
The update rule of its pheromone concentration is：
τij(t=1)=(1- ρ) τij(t)+ρ ﹒ n ﹒ Δs τij(t)
Wherein, τij(t+1) it is the pheromone concentration on path (i, j) in the following iteration period；ρ is the volatilization of pheromones
Parameter, value is between [0,1]；N is the ant sum in all paths (i, j) of passing by a upper iteration cycle, n≤m；Δτij(t)
It is every ant to the pheromones contribution margin of respective path.
In the present invention, ant evaporation and release pheromone on belonging to the side of optimal path so far, when ant passes by certain
When side, if this edge is that optimal path ant can remove a certain amount of pheromones in the side so far, and it is updated information
Element had both retained the possibility that follow-up ant explores remaining path, also retained the possibility that global optimum is selected as in this path, in conjunction with disturbing
Reason makes algorithm have the stronger ability for jumping out precocity.
Three, to the improvement of pheromones increment
Due to lacking for algorithm initial stage pheromones accumulation, pheromone concentration difference unobvious are so lead to algorithm on each paths
Initial stage convergence is slow, and therefore, in the present invention, the pheromones incremental mode of improved ant group algorithm is combined with elitism strategy, in difference
Iteration cycle in, in the corresponding all paths (i, j) of track points i, using following formula determine the pheromones on each path increase
Amount：
If path (i, j) is current globally optimal solution, Δ τij(t)=1/Cgb；
If path (i, j) is current global most inferior solution, Δ τij(t)=- 1/Cg b；
Path if (i, j) between current globally optimal solution and current global most inferior solution, Δ τij(t)=0；Wherein,
CgbFor the path length in current global optimum path.
Therefore, the present invention after each iteration terminates based on the enhancing additional compared with pheromones on shortest path, more bad road
Pheromone concentration on diameter additionally weakens to increase the difference of pheromone concentration between optimal solution and solution inferior, to make optimal solution
To the more excellent attraction of ant colony, accelerate algorithm initial stage convergence rate.
In the present invention, so-called current global optimum path, corresponding is some i determined in this iteration cycle
On point, the optimal path in multiple paths (i, j) determined by the j points for the determination walked out with all ants is opposite, current complete
The definition of office's most minor path is similar.For example, it please refers to shown in Fig. 3, in some iteration cycle, for C points, if
Ant on C points has moved towards F points, G points and H points respectively, then current global optimum path and current global most minor path are from route
It is selected in CF, CG and CH, if the ant on C points has only moved towards F points and G points, current global optimum path and current complete
Office's most minor path is selected from route CF and CG, that is, when selecting current global optimum and most minor path, be from ant
It chooses in the fixed path covered, for the path that ant has been covered, the pheromone concentration on these paths is carried out
Update, using the foundation for selecting path as ant in the next iteration period, carrying out state transfer.
Four, convergence proves
Start below to the convergence of improved ant group algorithm into line justification, it was demonstrated that thinking is as follows：Two are provided first
Proposition illustrates that the pheromones in each edge have maximum value, and after finding optimal path, and the pheromones on optimal path are
Bounded.Secondly, two variable is provided, it was demonstrated that Ant ColonySystem can find optimal path arbitrarily to level off to 1 probability, and
After finding optimal path, after fully big iterations, the pheromones on all optimal paths are all higher than non-optimal path
On pheromones.
If pheromones are only volatilized, it is intended to 0.
Proposition 1：Pheromones in each edge have maximum value
(1) maximum information element increment=m/lmin
By the pheromone updating rule τ of the present inventionij(t=1)=(1- ρ) τij(t)+ρ ﹒ n ﹒ Δs τij(t) known to：
For most minor path, pheromone concentration thereon is bound to reduce in the next iteration period；
For optimal path, because there is release (reducing a part) in the pheromone concentration in current iteration period, but it is same
When will produce incrementss, therefore the increase and decrease of pheromones is unknown；
For the path between optimal path and most minor path, pheromone concentration thereon is in the next iteration period
In be also bound to reduce.
Since the increase and decrease amount of pheromones is determined by the length in path, for initializing the mulitpath of track points
(i, j) certainly exists the shortest path (i, j) of a determining length, it is assumed that the length of lmin, when this paths is as most
When shortest path, Δ τij(t)=1/Cgb=1/lmin；When this paths is as most minor path, Δ τij(t)=- 1/Cgw=-1/
lmin。
That is,Maximum value=m/lmin, meaning indicates that all ants are all passed by this paths, and institute
Some ants are maximum value 1/l to the pheromones contribution margin of this pathsmin。
(2) likewise, it can be appreciated that for the pheromones on the mulitpath (i, j) between the track points that initialized
Concentration τ ij (0) certainly exist a maximum initial information element concentration τ ij (max).
(3) we assume that certain paths is in all iterative process, have and be used as optimal path in t iteration, never make
To cross most minor path, intermediate path was not also done, also, when being used as optimal path every time, pheromones increment is maximum value
m/lmin, enable b=m/lmin, then after all iterative process, the pheromone concentration on the path changes following Formula Series
It is shown：
τij(1)=(1- ρ) τij(0)+ρb；
τij(2)=(1- ρ) τij(1)+ρ b=(1- ρ) [(1- ρ) τij(0)+ρb]+ρb
=(1- ρ)2τij(0)+ρ(1-ρ)b+ρb；
……
When t infinities, τij(t)=b.
(4) therefore, the number with the paths as optimal path increases, and the pheromone concentration value on the path is by first
Beginning pheromone concentration value τij(0) close to maximum information element increment b, that is, the pheromone concentration value on the paths is small always
In max { τij(0), b }, due to τij(0)≤τij(max), then, the pheromone concentration during the path any iteration always≤
max{τij(max),b}。
Certainly, in actual conditions, in different iteration cycles, pheromones increment, which differs, establishes a capital as b, but is not difficult in the path
Understand, identical as the iterations of optimal path in the path, which must be in pheromones increment
For maximum when, corresponding final pheromone concentration it is maximum (because in the case that pheromone concentration is certain in the current iteration period,
Pheromones increment is bigger, and pheromone concentration value is bigger in next iteration cycle), that is, above-mentioned formula reasoning is an ideal
Situation, in a practical situation, the final pheromone concentration of Actual path also certain≤max { τij(max),b}。
Also, in actual conditions, any paths, it is also possible to when presence as most minor path or intermediate path,
However, since most minor path and the corresponding pheromone updating rule of intermediate path are reduced for pheromone amount, it can be appreciated that such feelings
Under condition, the final pheromone concentration in the path also certain≤max { τij(max),b}。
Therefore, for ant group algorithm used in the present invention, the pheromone concentration on any paths, no matter it is repeatedly
Generation during how to change, the upper limit≤max { τij(max),b}。
(5) likewise, can be released according to the formula in (3)：When the pheromones on certain paths are in each iterative process
In reduce, and when each pheromones decrement is maximum decrement b, by unlimited iteration, the letter on this paths
The plain concentration of breath is gradually by τij(0)-b is leveled off to.
That is, for ant group algorithm used in the present invention, the pheromone concentration on any paths, lower limit is certain
≥-b。
Therefore, proposition 1 must be demonstrate,proved, i.e. τmin=-b, τmax=max { τij(max),b}。
Theorem 1：The ant group algorithm that the present invention uses can with arbitrarily level off to 1 convergence in probability in optimal path, i.e., pair
In arbitrarily small ε>A 0 and fully big iterations t, the general of optimal path is had found in preceding t iteration at least once
Rate meets：
Here ε indicates arbitrarily small positive number, refers to " how small just having how small positive number ", how small what you can imagine has
It can think also small that this just can guarantee that the item (or value of function) of ordered series of numbers wants how close at a distance from certain number (i.e. limiting value) than you
Just there is unlimited taxis that is how close, that is, ensureing the limit.It proves in detail：
According to pseudorandom scaling rule, it is assumed that the no relevant maximum information element path path (i, j), selection path (i,
J) probability is the probability for randomly choosing path, i.e. P (q>q0)·pij, so in arbitrary an iteration n, make any specific
The probability selected for：
Wherein, | V | indicate the feasible subsequent maximum number of stationary nodes.
The solution s ' of any generation, including optimal solution s* ∈ S*, the probability of generation be：
The probability of each grey iterative generation solution
Wherein l<+ ∞ is the maximum length of sequence.So
The probability of n times grey iterative generation solution
Therefore,In addition, for an arbitrarily small ε>For 0, when n is sufficiently large, have：
P*(n)≥1-ε
It proves：In the ant group algorithm that the present invention uses, the pheromones τ in any limitij(t)∈[τmin,τmax], if meeting
The minimum probability of transition probability formula is p 'min>0,It indicates to define probability in the case of worst optimizing.
In Basic Ant Group of Algorithm, pminIndicate minimum transition probability,It indicates to define probability under the conditions of worst optimizing,
Then have
So in ant group algorithm used in the present invention, have
Then general solution s ' generations probabilityWherein n is the maximum length of sequence.It, can since t is fully big
An optimal solution is found in guarantee, so finding the probability of optimal solution at least onceIt is possible thereby to
Go outTheorem must be demonstrate,proved.
Theorem 2：After finding first optimal solution, since global information element updates rule, in each generation later, belong to optimal
The information content solved on element is all more than the information content in other elements.And the pheromone amount being not belonging on optimal solution element is continuous
It reduces, until minimizing value τminUntil.
It is described as with mathematical linguistics：It is rightThere is τij(t)>τkl(t) and
It proves：From the t for finding optimal solution for the first time*In generation, starts, and the pheromones only belonged on optimal solution element increase,
Pheromones on remaining solution element are reduced, it is known that reduce to τminUntil.We do the worst it is assumed that setting (i, j) ∈ s again*, andPheromones τkl(t*)=τmax.Then arrive t*+ t ' for when, the pheromones on (k, l) become：
τkl(t*+ 1)=max { τmin,(1-ρ)·τmax}
τkl(t*+ 2)=max { τmin,(1-ρ)2·τmax}
……
τkl(t*+ t ')=max { τmin,(1-ρ)t′·τmax}
So
Five, the modeling of conflict Resolution problem and analogue simulation
1, conflict Resolution problem models
Planning hedging path is the purpose of multiple no-manned plane hedging problem, and to make hedging path and the Reciprocal course of unmanned plane
Minimum compared to delay sum of the distance, to realize that flight path is most short, burnup is minimum.Defining optimization object function is：
Wherein SiIt is delay distances of the unmanned plane i because of the Reciprocal course generation relatively that avoids conflicting,It changes in kth time for unmanned plane i
The physical location in generation,For i Reciprocal course kth time iteration theoretical position；N indicates the sum of unmanned plane.
And the distance between arbitrary two airplanes i and j meet at the kth iteration：
Wherein, reqThe minimum interval between unmanned plane, since various unmanned plane performance differences are larger, so according to every frame nobody
Machine performance characteristics, it is proposed that be suitble to the minimum safety interval of unmanned plane, specific formula as follows：
Wherein, VfMaximum forward speed, VbFor maximum astern speed, VaFor the maximum perpendicular rate of climb, VdDecline for maximum
Speed, V1For maximum horizontal lateral velocity, τ is monitoring system refresh rate.
2, simulating, verifying
MATLAB emulation is carried out to the hedging problem of four frame unmanned planes, in same height above sea level plane.One is built first
A 200*200m2Region, and be arranged four frame unmanned planes starting point, they fly from respective starting point in opposite directions respectively.If respectively
Remain a constant speed, rectilinear flight, then four frame unmanned planes will mutually conflict in intermediate circled, as shown in Figure 4.
By aircraft hedging problem and existing ant group algorithm, ACS algorithm and and method knot provided by the invention
It closes, is emulated, three kinds of methods are compared.In emulation, ant sum is chosen for m=80, ρ=0.35, Q=1000, repeatedly
For times NCmax=20.
The unmanned plane conflict Resolution track of Basic Ant Group of Algorithm is as shown in figure 5, Fig. 6 is as iterations increase solution derailing
The result of calculation of mark, as seen from the figure, Basic Ant Group of Algorithm convergence rate are slower, are not cooked up in regulation iterations
Path completely is freed, does not find optimal solution, the accident that unmanned plane can be caused also to bump against in a practical situation.
The conflict Resolution track of ACS algorithm and path optimization result are as shown in Figure 7, Figure 8, as seen from the figure ant colony system
The problem of algorithm of uniting is accelerated compared to Basic Ant Group of Algorithm convergence rate, but algorithm initial stage easily converges on non-optimal solution is not solved
Certainly, non-optimal solution is selected when algorithm proceeded to for 5 generation comes, and does not obtain optimum results, ant colony does not find optimal
Path is freed, this will result in the loss of unnecessary energy, reduces unmanned plane during flying and executes task efficiency.
The method of the present invention is applied in multiple no-manned plane conflict Resolution problem, the unmanned plane it can be seen from Fig. 9, Figure 10
It has been cooked up in less iterations and has freed path, ensure that the flight safety of unmanned plane first, and in the 7th iteration
When algorithm start to rapidly converge near a value, but due to the effect of Discontinuous Factors in innovatory algorithm, converge to
Value is abandoned, and optimum value continues to be searched, and finds optimal solution when 12 generation.
To sum up, the flying object conflict Resolution paths planning method provided by the invention based on ant group algorithm, for existing
Ant group algorithm and ACS algorithm are advised in various deficiencies present on multiple no-manned plane conflict Resolution problem by being shifted in state
Discontinuous Factors are added in then, so that algorithm is had and jumps out precocious ability；Rule is updated by using global information element, is avoided
Pheromones waste, and so that algorithm is compared ACO and ACS efficiency and significantly improve, and it is big that cooperation Discontinuous Factors make algorithm jump out precocious ability
It is big to be promoted；By using elitism strategy to pheromones increment, increases pheromone concentration gap on algorithm initial stage difference path, accelerate
The convergence rate of ant group algorithm；Also, algorithm used in the present invention has convergence.Simulation result shows compared to more existing
Some ant group algorithms and ACS algorithm, the unmanned plane that the present invention can successfully make four framves that will collide is out of danger, and
And algorithm more existing ant group algorithm and ACS algorithm in terms of jumping out precocious ability and convergence rate are all significantly increased.
Although the present invention is illustrated using above-mentioned preferred embodiment, the protection model that however, it is not to limit the invention
It encloses, any those skilled in the art are not departing within the spirit and scope of the present invention, and opposite above-described embodiment carries out various changes
It is dynamic still to belong to the range that the present invention is protected with modification, therefore protection scope of the present invention is subject to what claims were defined.
Claims (8)
1. a kind of flying object conflict Resolution paths planning method based on ant group algorithm, which is characterized in that include the following steps：
Step S1：Initialize iterations, ant number m, cumulative information significance level factor-alpha, the heuristic function significance level factor
β, multiple track points between departure place and destination and the initial information element concentration between each track points；
Step S2：Every ant repeatedly from origin to destination between through different track points cover whole process, complete repeatedly repeatedly
Generation, and then select optimal route；
Wherein, ant is when selecting track points, it then follows following rules：
Wherein, pp represents the mode in ant selection path, and q is in the equally distributed random number in [0,1] section, and ant is in each i
Point can randomly generate a q value；Also, different ants have different q values at different track points i；
I indicates that the track points that ant is presently in, j indicate the track points that ant subsequent time may move towards；
τijIt indicates in the current iteration period, the pheromone concentration on path (i, j), ηijIt indicates in the current iteration period, ant
Ant goes to the expected degree of track points j, and η from track points iij=1/dij；
dijIndicate the distance of ij point-to-point transmissions；
allowedkIndicate that ant k allows the set for accessing track points in next step；
q0=1/et/b；T is current iterations, and b is constant；
pij kIt indicates to be more than q as q0When, ant randomly chooses a paths from possible path (i, j) group.
2. the flying object conflict Resolution paths planning method based on ant group algorithm as described in claim 1, it is characterised in that：
In different iteration cycles, the initial information element concentration update rule between each track points is only with overall situation update rule.
3. the flying object conflict Resolution paths planning method based on ant group algorithm as claimed in claim 2, it is characterised in that：
In different iteration cycles, the global update rule of the pheromone concentration on path (i, j) is：
τij(t=1)=(1- ρ) τij(t)+ρ ﹒ n ﹒ Δs τij(t)
Wherein, τij(t+1) it is the pheromone concentration on path (i, j) in the following iteration period；ρ is the volatilization parameter of pheromones,
Its value is between [0,1]；N is the ant sum in all paths (i, j) of passing by a upper iteration cycle, n≤m；Δτij(t) it is every
The pheromones contribution margin of ant to respective path.
4. the flying object conflict Resolution paths planning method based on ant group algorithm as claimed in claim 3, it is characterised in that：
In different iteration cycles, pheromones increment is determined using following formula：
If path (i, j) is current globally optimal solution, Δ τij(t)=1/Cgb；
If path (i, j) is current global most inferior solution, Δ τij(t)=- 1/Cgb；
Path if (i, j) between current globally optimal solution and current global most inferior solution, Δ τij(t)=0；
Wherein, CgbFor the path length in current global optimum path.
5. the flying object conflict Resolution paths planning method based on ant group algorithm as described in any one of claim 1-4,
It is characterized in that：In the successive ignition period, the pheromone concentration on path (i, j) is between one between maximum value and minimum value.
6. the flying object conflict Resolution paths planning method based on ant group algorithm as described in any one of claim 1-4,
It is characterized in that：In the successive ignition period, the pheromone concentration bounded on optimal path component part is 2 points adjacent.
7. the flying object conflict Resolution paths planning method based on ant group algorithm as described in any one of claim 1-4,
It is characterized in that：In the successive ignition period, the Ant ColonySystem can with arbitrarily level off to 1 probability close to optimal path.
8. the flying object conflict Resolution paths planning method based on ant group algorithm as described in any one of claim 1-4,
It is characterized in that：In the successive ignition period, after finding optimal path, by fully big iterations, all optimal paths
On pheromone concentration be above the pheromone concentration on non-optimal path.
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