CN104268721B - A kind of aircraft landing runway system of selection of the monkey colony optimization algorithm based on integer coding - Google Patents
A kind of aircraft landing runway system of selection of the monkey colony optimization algorithm based on integer coding Download PDFInfo
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Abstract
The invention provides a kind of more scientific and effective, local optimum will not be absorbed in so that the aircraft landing runway system of selection of the minimum monkey colony optimization algorithm based on integer coding of total time delays.It comprises the following steps：1st, the related information on airport is read；2nd, monkey group's algorithm (IMA) parameter and population scale size, iterations of setting integer coding；3rd, iteration starts, and sets t=1；4th, to choosing two points in every monkey current location neighborhood, movement is preferably put in selection position, and this process of repetition climbs number of times until setting；5th, judge whether to reach that prestige hops number, 6 are gone to step if reaching；Otherwise, every monkey, using this new position as the starting point for getting over journey, goes to step 4 by finding a more excellent position within sweep of the eye；6th, judge whether to reach iterations, if reaching, go to step 7；Otherwise, to every monkey, another monkey is randomly selected as it and turns over fulcrum, 4 are gone to step；7th, algorithm is terminated.
Description
Technical Field
The invention relates to an aircraft landing runway selection method based on an integer coding monkey swarm optimization algorithm.
Background
The problem of airplane scheduling is a classical NP-hard problem, which aims at determining a set of optimal landing sequences and corresponding landing times for a given set of runways and a set of airplanes to be landed, so that the sum of the deviations of the actual landing times of these airplanes from the planned landing times is minimized, while at the same time requiring that the minimum time interval between any two flights should be met. The number of air transports of passengers and cargo has increased dramatically due to the rapid development of economy, accounting for the total number of passengers arriving and delivered at international airports in 2007 and 2008 as 48.69 and 48.75 billion times, respectively, and this data is growing in the next 20 years at a four percent rate. Since the increase of the number of flights inevitably results in that the aircraft cannot land in the planned time, the aircraft inevitably consumes more fuel, increases the operation cost of the airline company and causes more air pollution, and therefore, the search for a landing sequence of the aircraft with the minimum cost plays a very important role in reducing the consumption of fuel, the cost of the airline company and the pollution to the atmosphere. Aircraft landing problems fall into two categories: runway independent aircraft landing problems and runway dependent aircraft landing problems. The runway independent aircraft landing scheduling problem is the runway allocated for landing aircraft independently according to the earliest landing time, however in reality this situation is rarely the case because aircraft approach the airport with different earliest landing times on different runways. The runway-dependent aircraft landing problem is more consistent with the situation in real life, so that the method brings great attention and research to scholars, and common methods such as genetic algorithm, scattering algorithm, bionic algorithm and other intelligent optimization algorithms. The present invention is primarily concerned with the problem of landing aircraft with runway dependence.
At present, the algorithm systems mainly used for solving the problem of selecting the aircraft landing runway with the minimum total time delay under the condition of meeting the time interval between two flights include four GA algorithm systems, an SS algorithm system, a BA algorithm system and a GLS algorithm system. However, the three systems, namely the GA algorithm system, the SS algorithm system and the BA algorithm system, among the four algorithms described above have the disadvantages that the performance is obviously reduced along with the increase of the airport scale, and the systems are not suitable for large airports, while the GLS algorithm system is well adapted to large airports, but the GLS algorithm system is unique and not beneficial to the healthy development of the market, so that an algorithm system with performance comparable to or better than that of the GLS algorithm for solving the problem of aircraft landing with runway dependence is currently required.
In addition, the applicant of the patent of the invention finds that the Monkey swarm Algorithm has good effect on solving continuous and large-scale multimodal problems, and the Monkey swarm Algorithm (MA) is a novel swarm intelligence optimization Algorithm proposed by Zhao and Tang of Tianjin university in 2008 for solving large-scale and multimodal optimization problems, the method has good effect in solving continuous and large-scale multimodal problems, but the basic monkey group algorithm is not suitable for solving discrete combinatorial optimization problems, and the applicant of the patent finds a technical scheme based on the monkey group algorithm when the monkey group algorithm is actually applied to solve the problem of selecting the landing runway of the airplane, after the monkey group in the algorithm is iterated for multiple times, the group loses diversity, so that the algorithm can fall into local optimization, the sum of the deviation between the actual landing time and the planned landing time of the airplane cannot be optimally realized, and the minimum take-off and landing time interval between any two flights can be met. If this problem can be solved, the performance of the monkey swarm algorithm system can be at least as good as the GLS algorithm system.
In summary, there is a need in the art for a method for selecting an aircraft landing runway that is more scientific and efficient, does not fall into local optima, and minimizes the total time delay while satisfying the time interval between two flights.
Disclosure of Invention
The invention aims to solve the technical problem of providing an airplane landing runway selection method based on Integer coding Monkey swarm optimization Algorithm (IMA) which is more scientific and effective, cannot be trapped in local optimization and enables total time delay to be minimum under the condition of meeting the time interval between two flights.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: an aircraft landing runway selection method based on an integer coding monkey swarm optimization algorithm comprises the following steps:
step 1: reading flight information, runway information, earliest landing time of each flight on each runway and time interval information of every two flights of an airport;
step 2: setting IMA algorithm system parameters, population size and iteration times;
and step 3: the algorithm system starts iteration, and t is set to be 1;
and 4, step 4: climbing process: selecting two points in the neighborhood of the current position of each monkey, selecting a point with a better position to move, and repeating the process until the set climbing times;
and 5: judging whether the hope-jump times are reached, and if so, turning to the step 6; otherwise, each monkey searches a better position in the visual field range, and the new position is used as the starting point of the climbing process, and the step 4 is executed;
step 6: judging whether the iteration times are reached, and if so, turning to the step 7; otherwise, randomly selecting another monkey as a turning fulcrum of each monkey, turning over in a turning interval, taking the new position of the monkey group as a starting point of the climbing process, and turning to the step 4, wherein t is t + 1;
and 7: the algorithm terminates.
Preferably, IMA refers to a monkey swarm algorithm based on integer coding, first, M represents the number of monkey swarm, N represents the number of landing airplanes, for each monkey, the position corresponds to a decision vector of one dimension, each flight corresponds to one dimension of the monkey, i.e. the value of each dimension should be randomly rounded over the interval [1, N ], so that the actual position of each monkey represents a solution to the airplane landing problem.
Preferably, the crawling process in step 4 is performed on monkey i at a position Xi＝(xi1,xi2,…,xin) The climbing process is specifically designed as follows:
1) randomly generating two vectors Δ Xi＝(Δxi1,Δxi2,…,ΔxiN) And satisfy
When solving the aircraft landing problem, the number of runways is generally an integer greater than or equal to 1, so the climbing step length a is set to be an integer;
2) calculating f (X)i-ΔXi) And f (X)i+ΔXi)；
3) If f (X)i-ΔXi)＞f(Xi) And f (X)i-ΔXi)＞f(Xi+ΔXi) Then let Xi＝Xi-ΔXi；
If f (X)i+ΔXi)＞f(Xi) And f (X)i+ΔXi)＞f(Xi-ΔXi) Then let Xi＝Xi+ΔXi；
4) And repeating the steps 1) to 3) until the objective function value is not changed or the set climbing times are reached.
Preferably, the hope-jump process is specifically designed as follows:
1) in the interval (x)ij-b,xij+ b), j-1, 2, …, n randomly generating an integer yjAnd Y ═ Y (Y)1,y2,…,yN)；
2) If f (Y) > f (X)i) Then let Xi＝Y；
3) And taking Y as a new initial position, and repeating the climbing process.
Preferably, the crossing over in the crossing over interval in step 6 is specifically designed as follows: for monkey i, its position can be represented as Xi＝(xi1,xi2,…,xin) I-1, 2, …, M, edge turning process as follows:
1) randomly generating a real number theta in the turning interval [ c, d ];
2) randomly selecting an integer k on the [1, M ], and taking the position of the monkey k as a turning point of the monkey i;
3) to pairLet Y be (Y)1,y2,…,yN) (ii) a Wherein,
yj＝xij+round(θ|xkj-xij|)；
4) let XiThe flipping process is repeated as Y.
After adopting the structure, the invention has the following beneficial effects: the invention provides a monkey swarm optimization algorithm based on integer coding, which aims to avoid the problem that the monkey swarm loses diversity after multiple iterations, so that the algorithm can fall into local optimization. Experiments show that the diversity of the population can be increased by adopting the strategy of the edge turning process, so that the algorithm is not easy to fall into the local optimum, therefore, the position of one monkey is randomly selected in the turning process to be used as the turning point of another monkey, the turning points of each monkey are different, the diversity of the population is increased, and the algorithm can be effectively prevented from falling into the local optimum. The test on the aircraft landing problem example shows that the integer coding-based monkey swarm optimization algorithm has good performance in solving the runway-dependent aircraft landing problem.
In conclusion, the invention provides the aircraft landing runway selection method based on the integer-coding monkey swarm optimization algorithm, which is more scientific and effective, does not get into local optimization, and enables the total time delay to be minimum under the condition of meeting the time interval between two flights.
Detailed Description
The present invention is described in further detail below.
The invention provides an aircraft landing runway selection method based on an integer coding monkey swarm optimization algorithm, which comprises the following steps:
step 1: reading flight information, runway information, earliest landing time of each flight on each runway and time interval information of every two flights of an airport;
step 2: setting IMA algorithm system parameters, population size and iteration times;
and step 3: the algorithm system starts iteration, and t is set to be 1;
and 4, step 4: climbing process: selecting two points in the neighborhood of the current position of each monkey, selecting a point with a better position to move, and repeating the process until the set climbing times;
and 5: judging whether the hope-jump times are reached, and if so, turning to the step 6; otherwise, each monkey searches a better position in the visual field range, and the new position is used as the starting point of the climbing process, and the step 4 is executed;
step 6: judging whether the iteration times are reached, and if so, turning to the step 7; otherwise, randomly selecting another monkey as a turning fulcrum of each monkey, turning over in a turning interval, taking the new position of the monkey group as a starting point of the climbing process, and turning to the step 4, wherein t is t + 1;
and 7: the algorithm terminates.
Preferably, IMA refers to a monkey swarm algorithm based on integer coding, first, M represents the number of monkey swarm, N represents the number of landing airplanes, for each monkey, the position corresponds to a decision vector of one dimension, each flight corresponds to one dimension of the monkey, i.e. the value of each dimension should be randomly rounded over the interval [1, N ], so that the actual position of each monkey represents a solution to the airplane landing problem.
Preferably, the crawling process in step 4 is performed on monkey i at a position Xi＝(xi1,xi2,…,xin) The climbing process is specifically designed as follows:
1) randomly generating two vectors Δ Xi＝(Δxi1,Δxi2,…,ΔxiN) And satisfy
When solving the aircraft landing problem, the number of runways is generally an integer greater than or equal to 1, so the climbing step length a is set to be an integer;
2) calculating f (X)i-ΔXi) And f (X)i+ΔXi)；
3) If f (X)i-ΔXi)＞f(Xi) And f (X)i-ΔXi)＞f(Xi+ΔXi) Then let Xi＝Xi-ΔXi；
If f (X)i+ΔXi)＞f(Xi) And f (X)i+ΔXi)＞f(Xi-ΔXi) Then let Xi＝Xi+ΔXi；
4) And repeating the steps 1) to 3) until the objective function value is not changed or the set climbing times are reached.
Preferably, the hope-jump process is specifically designed as follows:
1) in the interval (x)ij-b,xij+ b), j-1, 2, …, n randomly generating an integer yjAnd Y ═ Y (Y)1,y2,…,yN)；
2) If f (Y) > f (X)i) Then let Xi＝Y；
3) And taking Y as a new initial position, and repeating the climbing process.
Preferably, the crossing over in the crossing over interval in step 6 is specifically designed as follows: for monkey i, its position can be represented as Xi＝(xi1,xi2,…,xin) I-1, 2, …, M, edge turning process as follows:
1) randomly generating a real number theta in the turning interval [ c, d ];
2) randomly selecting an integer k on the [1, M ], and taking the position of the monkey k as a turning point of the monkey i;
3) to pairLet Y be (Y)1,y2,…,yN) (ii) a Wherein,
yj＝xij+round(θ|xkj-xij|)；
4) let XiThe flipping process is repeated as Y.
In implementing the method of the present invention, the user needs to know the basic monkey swarm algorithm. The basic monkey group algorithm is set forth below: the thought of the monkey group algorithm is derived from three processes designed by simulating climbing, watching, jumping, turning and other actions expressed in the mountain climbing process of a monkey group in the nature: the crawling process mainly searches the local optimal solution of the current position through multiple crawls. The process of looking for and jumping from is to find a point better than the current solution through looking after the local optimal solution is reached, and jump away from the current point, so as to speed up the speed of searching the optimal solution by the algorithm. The main purpose of the turning process is to transfer from the current search area to other areas so as to avoid the search process from being trapped in local optimization. The MA has the advantages that when the high-dimensional optimization problem is solved, the consumed time is mainly the calculation of the pseudo gradient of the objective function during each iteration in the climbing process, namely, only objective function values of two adjacent positions of the current position need to be calculated and are irrelevant to the dimension of the decision vector, so that the 'dimensional disaster' cannot be caused, and meanwhile, the MA has strong mining capacity and generally cannot cause local optimization. Therefore, MA has been successfully applied to solve various optimization problems, such as power line extension planning problems[7]The system comprises a structural health monitoring sensor optimization problem, an intrusion detection problem, cluster analysis, a hybrid optimization algorithm and the like. However, the monkey group algorithm itself has drawbacks, i.e., low calculation accuracy, large calculation time, and easy escape from the search area during the process.
The basic monkey group algorithm is designed by simulating various actions in the process of climbing a mountain by a monkey group in nature, and mainly comprises five processes: representation of solutions, initialization, crawling process, hope-jump process and turning process.
Representation of the solution: first, the space dimension of the problem to be solved is represented by a positive integer n, the population size is represented by M, and then the position of the ith monkey is represented by the following formula: xi＝(xi1,xi2,…,xin) 1,2, …, M, each component x in the formulaijRepresenting the actual position of each monkey in each dimension. The actual position of each monkey actually represents a decision vector of the optimization problem.
Initialization: the initialization of the population has an important influence on the overall convergence and optimization effect of the algorithm, the population initialization is in the optimal solution neighborhood, the convergence speed of the algorithm is high, the solving precision is high, if the population initialization is in a large range and is far away from the optimal solution, the convergence speed of the algorithm is low, and the obtained overall optimal solution precision is not high. If the population initialization is within a small range, the algorithm is prone to fall into a locally optimal solution. Therefore, the basic monkey swarm algorithm is initialized randomly in a solution space, and the process is as follows:
xi,j＝xmin,j+(xmax,j-xmin,j)·rand
wherein xmin,jAnd xmax,jThe sub-tables represent the upper and lower bounds in the jth dimension of the optimization problem, and rand yields a range of [0, 1]]The real number of (2).
Climbing process: the climbing process of the monkey swarm algorithm is a process for gradually improving the objective function value of the optimization problem through iteration[6]Unlike the Newton method using the gradient method, the monkey swarm algorithm uses a pseudo-gradient[12][13]The idea of (1) is to calculate the objective function value of two adjacent points at the current position only, and compare the processes of gradual movement. The climbing process comprises the following steps:
1) randomly generating a vector DeltaXi＝(Δxi1,Δxi2,…,Δxin) Component Δ xijIt should satisfy:
the parameter a (a is more than 0) is a crawling process step length (climbing step length), the size of the parameter a is mainly determined according to the space dimension of the optimization problem, the larger the space dimension is, the larger the climbing step length is, the smaller the space dimension is, and the smaller the climbing step length is.
2) Computingj is 1,2, …, n. Vector fi'(xi)＝(fi1′(xi),fi2′(xi),…fin′(xi) Is called an objective function at point xiThe pseudo gradient of (a).
3) Let yj＝xij+a·sign(fij'(xi) J ═ 1,2, …, n, and Y ═ Y (Y)1,y2,…,yn)。
4) If Y is in the feasible solution area, then put XiY; otherwise, X is maintainediThe value is unchanged.
And (4) repeating the steps 1) to 4) until the set maximum climbing times are reached or the objective function value is unchanged in the two iteration processes.
The inspection-jumping process: after the monkey group is climbed for a set number of times, each monkey reaches the highest peak of the current position, namely reaches the local optimal value[6]. At this time, the monkey looks for a point better than the current position within the visual field by looking for the action, and then jumps away from the current position. The process is mainly used for accelerating the speed of finding the optimal solution of the problem by the monkey swarm algorithm. The method comprises the following steps:
1) in the interval (x)ij-b,xij+ b), j ═ 1,2, …, n, a real number y is randomly generatedjAnd Y ═ Y (Y)1,y2,…,yn)。
2) If Y satisfies the constraint and f (Y) > f (X)i) Then put XiY. If not, then,repeating step 1) until a point Y satisfying the condition is generated. Here, only the value of the objective function is greater than or equal to XiPoint replacement of (2) Xi。
3) The climbing process is repeated with Y as the initial position.
Where b is the visual field of the monkey, whose size is determined mainly by the solution space of the objective function. The larger the feasible domain of the general optimization problem, the larger the value of b.
Turning over: the main purpose of the flipping process is to force the monkey cluster to move from the current search area to a new area, thereby avoiding trapping in local optimality. The centers of the positions of all the monkeys are taken as fulcrums, and each monkey turns to a new area along the direction pointing to the fulcrums or the opposite direction. For the ith monkey, the process was as follows:
1) a real number α is randomly generated in the interval c, d. Wherein [ c, d ] is called a turn interval, the selection of the size is determined according to the size of the solution space of the optimization problem, and the larger the feasible domain of the general optimization problem is, the larger the absolute values of the turn intervals c and d are.
2) Let yj＝xij+α(pj-xij) And is andj-1, 2, …, n, the midpoint of the positions of all monkeys. Point P ═ P (P)1,p2,…,pn) Called the turning point.
3) If Y is ═ Y1,y2,…,yn) If the constraint condition is satisfied, setting XiY. Otherwise, repeating the steps 1) and 2) until a feasible point Y is generated.
In step 2), if the parameter α is greater than 0, the monkey will be turned over along the direction pointing to the fulcrum, otherwise, the monkey will be turned over along the opposite direction, and the monkey group can also be used when selecting the turning fulcrumAs the pivot of the turning section, using the formula yj＝p'j+α(p'j-xij) Or yj＝xij+α|p'j-xijAnd | j ═ 1,2, …, n, to update the post-rollover position of the monkey group during rollover.
Further, the problem with runway dependent aircraft landing scheduling is to find the best scheduling sequence, runway and corresponding landing time for a given set of landing aircraft, minimizing the total time delay if the time interval between two flights is met. The model is defined by Beasley, and its mathematical model is described as follows:
min
s.t.
wherein A represents a set of waiting to land aircraft; r represents a set of runways; eikIndicating the earliest landing time for the ith flight to land on the kth runway; tau isiThe minimum value of the earliest landing time on all landing runways of the ith flight is represented; sijRepresents the minimum time interval between flight i and flight j on the same runway; x is the number ofiRepresents the scheduled landing time for flight i; lambda [ alpha ]ikAnd gammaijIs a decision index variable, lambda if flight i falls on k runwayik1, otherwise equal to λik0; if flight i and flight j land on the same runway then γij0, otherwise, γij1. Equation (1) represents an objective function equal to the scheduled landing time x for each flightiWith minimum earliest landing time τiThe sum of the squares of the differences. Equations (2) - (6) are constraints of the model, and equation (2) ensures that each landing time must be set after the earliest landing time for aircraft i to land on runway k; equation (3) ensures that the time interval between two aircraft should be met; formula (4) ensures that each aircraft lands on only one runway; equations (5) and (6) represent the feasible values of the variables; n and m represent the number of airplanes and the number of runways, respectively.
The invention adopts a Monkey group Algorithm which is improved by self innovation in specific implementation, namely, an Integer Monkey Algorithm (IMA) based on Integer coding, and the specific process is as follows:
1. and (3) an encoding mode: firstly, the number of monkey groups is represented by M, the number of aircraft landing is represented by N, for each monkey, the position of the monkey corresponds to an N-dimensional decision vector, each flight corresponds to a dimension of the monkey, namely the value of each dimension is randomly rounded on an interval [1, N ], and thus the actual position of each monkey represents a solution of the aircraft landing problem. As described in table 1, table 1 shows the coding method for the 12 monkeys scheduled for 3 runways. The first dimension represents the 1 st airplane on the 1 st runway, the second dimension represents the 2 nd airplane landing on the 3 rd runway, and so on.
| 1 | 3 | 2 | 3 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 2 |
Coding method for monkeys for listing 112 flights with 3 runways
As can be seen from table 1, the aircraft landing on runway 6.1 are numbered 1, 8, 11; the number of the airplane which runs to 2 and lands is 3, 5, 7, 10, 12; the aircraft landing on the runway 3 are numbered 2, 4, 6, 9.
2. Improved climbing process: because of the integer coding mode, the position of the monkey i is Xi＝(xi1,xi2,…,xin) The improved climbing process is designed as follows:
1) randomly generating two vectors Δ Xi＝(Δxi1,Δxi2,…,ΔxiN) And satisfy
When solving the aircraft landing problem, the climbing step length a is generally set to an integer because the number of runways is generally an integer greater than or equal to 1.
2) Calculating f (X)i-ΔXi) And f (X)i+ΔXi)。
3) If f (X)i-ΔXi)＞f(Xi) And f (X)i-ΔXi)＞f(Xi+ΔXi) Then let Xi＝Xi-ΔXi；
If f (X)i+ΔXi)＞f(Xi) And f (X)i+ΔXi)＞f(Xi-ΔXi) Then let Xi＝Xi+ΔXi。
4) And repeating the steps 1) to 3) until the objective function value is not changed or the set climbing times are reached.
3. Improved watch-jump process: aiming at an integer coding mode, the improved hope-jump process is designed as follows:
1) in the interval (x)ij-b,xij+ b), j-1, 2, …, n randomly generating an integer yjAnd Y ═ Y (Y)1,y2,…,yN)。
2) If f (Y) > f (X)i) Then let Xi＝Y。
3) And taking Y as a new initial position, and repeating the climbing process.
4. The improved turning process comprises the following steps: in the basic MA, the objective of the flipping process is to force the monkey group to flip over to a new field, which can effectively avoid the monkey group from falling into local optimum, and meanwhile, the monkey group reaches a new position in the flipping process, which is beneficial to maintaining the diversity of the group, and the center position of the monkey group is used as the flipping point of the monkey group in the original flipping process. However, when solving the runway-dependent aircraft landing problem, after a plurality of iterations, the roll-over process may fail and may fall into local optimality, resulting in a loss of diversity of the population. Therefore, the turning process is improved, and the position of another monkey is randomly selected by each monkey to serve as the turning point of the monkey, so that the diversity of the population can be kept, and the algorithm is effectively prevented from falling into local optimum. For monkey i, its position can be expressed as:
Xi＝(xi1,xi2,…,xin) I-1, 2, …, M, edge turning process as follows:
1) randomly generating a real number theta in the flip interval [ c, d ].
2) Randomly selecting an integer k on the [1, M ], and taking the position of the monkey k as a turning point of the monkey i;
3) to pairLet Y be (Y)1,y2,…,yN). Wherein,
yj＝xij+round(θ|xkj-xij|)
4) let XiThe flipping process is repeated as Y.
5. The implementation steps of solving the aircraft landing problem by the integer coding monkey group algorithm are as follows:
step 1: reading flight information, runway information, the earliest landing time of each flight on each runway and interval information between every two flights;
step 2: setting IMA parameters, population size and iteration times;
and step 3: starting iteration, and setting t to be 1;
and 4, step 4: climbing process: selecting two points in the neighborhood of the current position of each monkey, selecting a point with a better position to move, and repeating the process until the set climbing times;
and 5: judging whether the hope-jump times are reached, and if so, turning to the step 6; otherwise, each monkey searches a better position in the visual field range, and the new position is used as the starting point of the climbing process, and the step 4 is executed;
step 6: judging whether the iteration times are reached, and if so, turning to the step 7; otherwise, randomly selecting another monkey as a turning fulcrum of each monkey, turning over in a turning interval, taking the new position of the monkey group as a starting point of the climbing process, and turning to the step 4, wherein t is t + 1;
and 7: the algorithm terminates.
The simulation experiments relating to the method of the present invention are as follows:
1. an experimental operating platform: the experimental program operating environment is as follows: a processor: AMD Athlon (tm) II X4640, dominant frequency: 3.01GHz, memory: 3.00GB, operating System: windows XP, integrated development environment: matlab 2012 a.
2. Algorithm comparison analysis: to show the validity and correctness of the proposed IMA algorithm. 4 examples in the literature were tested. And compared with algorithms GA, SS, BA, GLS, respectively, and experimental data for these four algorithms are from literature published in the prior art. IMA parameter setting: the climbing step length a is equal to 1, the climbing times are set to 5, the monkey view field b is equal to 1, the hope-jump times are set to 2, the turning interval [ c, d ] [ -1,1], the monkey group number M is equal to 10, and the iteration times are set to 50. Examples H-12-3, H-15-3, H-20-5 are from the literature and C-12-3 is from the literature. The experimental data are from the literature.
| Test examples | Best value | GA | SS | BA | GLS | IMA |
| H-12-3 | 3.5 | 3.50 | 3.75 | 3.75 | 3.50 | 3.50 |
| H-15-3 | 12.25 | 12.50 | 12.25 | 12.25 | 12.25 | 12.25 |
| H-20-5 | 7.75 | 12.00 | 8.75 | 9.75 | 7.75 | 7.75 |
| C-12-3 | 11.25 | 11.25 | 11.25 | 11.25 | 11.25 | 11.25 |
Table 24 test results of the examples
Table 2 records the optimal values obtained by the algorithms GA, SS, BA, GLS and IMA, which were run 20 times independently. As can be seen from the table, for the example H-12-3, the algorithms GA, GLS and IMA can obtain the optimal values thereof, and SS and BA can only obtain the local optimal value of 3.75; for example H-15-3, which has 15 flights and is distributed to 3 independent runways, the optimal solution of the algorithms SS, BA, GLS and IMA can be found by 12.25, while the global optimal value cannot be obtained by GA, and the result is 12.50; for example H-20-5, the global optimum 7.75 can be found by algorithms GLS and IMA, but the optimum cannot be obtained by other algorithms, the optimum value of GA is 12.00, and the results of SS and BA are 8.75 and 9.75 respectively, thus showing that the performances of GA, SS and BA are obviously reduced along with the increase of problem scale; for example C-12-3, each algorithm can obtain a globally optimal solution 11.25 to the problem. Tables 3 through 6 record the optimal landing sequences for examples H-12-3, H-15-3, and H-20-5. For example C-12-3, since flights UA532, UA599, NW357 and AA129 are the same at the earliest landing time on each runway and 4 flights are of the same type, the locations of the 4 flights in their scheduling sequences can be interchanged so that the optimal solution vector for this example is multiple, i.e., there are multiple optimal landing sequences, one of which is recorded in table 6.
TABLE 3 example H-12-3 optimal scheduling
TABLE 4 optimal scheduling for example H-15-3
| Runway 1 | NW410 | DL200 | DL510 | UA1133 | AA335 | AA205 |
| Scheduling time | 6 | 7.5 | 9 | 10 | 15 | 16.5 |
| Delay of | 0 | 0.5 | 0 | 0 | 0 | 1.5 |
| Runway 2 | SW200 | DL3319 | ||||
| Scheduling time | 7 | 8 | ||||
| Delay of | 1 | 1 | ||||
| Runway 3 | UA410 | SW185 | AA1225 | UA123 | SW442 | |
| Scheduling time | 4 | 6 | 7 | 8 | 10 | |
| Delay of | 0 | 0 | 0 | 1 | 0 | |
| Runway 4 | AA127 | DL1920 | UA555 | SW250 | ||
| Scheduling time | 6 | 7 | 8 | 9.5 | ||
| Delay of | 0 | 1 | 1 | 0.5 | ||
| Runway 5 | NW2123 | AA1410 | DL130 | |||
| Scheduling time | 5 | 7 | 9 | |||
| Delay of | 0 | 0 | 0 |
TABLE 5 optimal scheduling for example H-20-5
TABLE 6 optimal scheduling for example C-12-3
Therefore, when solving the runway-dependent aircraft landing problem, the algorithms GLS and IMA have a good effect, when the scale of the problem is increased, the performance of the algorithms GA, SS and BA is obviously reduced, particularly the GA is better than that of the SS and BA when 12 flights are taken, when the number of flights is increased to 15, the performance is poorer, when the number of flights is increased to 20, the performance is far worse than that of other algorithms, the performance of the algorithms GLS and IMA is obviously stronger than that of other algorithms, and when the number of flights is increased to 20, the optimal solution of the problem can still be obtained.
3. Algorithm population diversity: in the basic MA, because the process of turning over after multiple iterations is invalid, the population diversity is reduced, the algorithm is easy to fall into local optimization, in order to increase the population diversity, one monkey randomly selects the position of the other monkey as the fulcrum of the turning over process, so that the turning over fulcrum of each monkey in the turning over process is possibly different, and the situation that the monkey cluster is concentrated in a smaller area and the population loses the diversity when the turning over is carried out can be effectively avoided. The MA and IMA population diversity were tested using examples H-15-3 and H-20-5, respectively, with the same initial population, and tables 7-8 recording the positions of the IMA and MA population generations 1, 15 and 30.
TABLE 7 iterative variation of MA and IMA populations in example H-15-3
TABLE 8 iterative variation of MA and IMA populations in example H-20-3
As can be seen from tables 7-8, for example H-15-3, in the case of the same population, MA converges at the 15 th generation, the positions of all monkey groups are (1,3,3,3,1,1,3,1,1,1,1,2,3,2,3), and the positions of all the subsequent generation monkey groups are unchanged until the algorithm is finished, the monkey groups fall into local optima and cannot jump out, and finally, the global optima cannot be obtained; IMA also maintained population diversity in generations 15 and 30; for example H-20-5, MA positions all monkey groups in generation 30 (5,1,1,1,1,5,1,4,3,1,3,3,4,2,3,3,4,5,2,2) until the end of the algorithm the position of the monkey group remained unchanged, finding the optimal result of 13.50, whereas IMA positions were not the same for the monkey groups in generation 30. Therefore, the position of one monkey is randomly selected to be used as the turning point of the other monkey, the diversity of the population can be increased, and the algorithm is effectively prevented from falling into local optimum.
The invention and its embodiments have been described above without limitation to the description, and the actual structure is not limited to them. In summary, those skilled in the art should appreciate that they can readily use the disclosed conception and specific embodiments as a basis for designing or modifying other structures for carrying out the same purposes of the present invention without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (3)
1. An aircraft landing runway selection method based on an integer coding monkey swarm optimization algorithm is characterized in that: it comprises the following steps:
step 1: reading flight information, runway information, earliest landing time of each flight on each runway and time interval information of every two flights of an airport;
step 2: setting IMA algorithm system parameters, population size and iteration times;
and step 3: the algorithm system starts iteration, and t is set to be 1;
and 4, step 4: climbing process: selecting two points in the neighborhood of the current position of each monkey, selecting a point with a better position to move, and repeating the process until the set climbing times;
and 5: judging whether the hope-jump times are reached, and if so, turning to the step 6; otherwise, each monkey searches a better position in the visual field range, and the new position is used as the starting point of the climbing process, and the step 4 is executed;
step 6: judging whether the iteration times are reached, and if so, turning to the step 7; otherwise, randomly selecting another monkey as a turning fulcrum of each monkey, turning over in a turning interval, taking the new position of the monkey group as a starting point of the climbing process, and turning to the step 4, wherein t is t + 1;
and 7: the algorithm is terminated;
the IMA is a monkey swarm algorithm based on integer coding, firstly, M represents the number of monkey swarm, N represents the number of landing airplanes, for each monkey, the position of the monkey corresponds to an N-dimensional decision vector, each flight corresponds to one dimension of the monkey, namely, the value of each dimension is randomly rounded on the interval [1, N ], and N represents the number of airplanes; thus the actual position of each monkey represents a solution to the aircraft landing problem;
the climbing process in the step 4 refers to that for the monkey i, the position is Xi＝(xi1,xi2,…,xin) The climbing process is specifically designed as follows:
1) randomly generating two vectors Δ Xi＝(Δxi1,Δxi2,…,ΔxiN) And satisfy
When solving the aircraft landing problem, the number of runways is generally an integer greater than or equal to 1, so the climbing step length a is set to be an integer;
2) calculating f (X)i-ΔXi) And f (X)i+ΔXi)；
3) If f (X)i-ΔXi)＞f(Xi) And f (X)i-ΔXi)＞f(Xi+ΔXi)Then let Xi＝Xi-ΔXi；
If f (X)i+ΔXi)＞f(Xi) And f (X)i+ΔXi)＞f(Xi-ΔXi) Then let Xi＝Xi+ΔXi；
4) And repeating the steps 1) to 3) until the objective function value is not changed or the set climbing times are reached.
2. The method of claim 1, wherein the method comprises: the hope-jump process of step 5 is specifically designed as follows:
1) in the interval (x)ij-b,xij+ b), b represents the monkey field of view, the size of which is determined from the solution space of the objective function; j is 1,2, …, n is randomly generated an integer yjAnd Y ═ Y (Y)1,y2,…,yN)；
2) If f (Y) > f (X)i) Then let Xi＝Y；
3) And taking Y as a new initial position, and repeating the climbing process.
3. The method of claim 1, wherein the method comprises: the crossing in the turning interval in the step 6 is specifically designed as follows: for monkey i, its position can be expressed as
Xi＝(xi1,xi2,…,xin) I-1, 2, …, M, edge turning process as follows:
1) randomly generating a real number theta in the turning interval [ c, d ]; c and d represent the turn-over interval, and the selection of the size is determined according to the size of the solution space of the optimization problem;
2) randomly selecting an integer k on the [1, M ], and taking the position of the monkey k as a turning point of the monkey i;
3) to pairLet Y be (Y)1,y2,…,yN) (ii) a Wherein,
yj＝xij+round(θ|xkj-xij|)；
4) let XiThe flipping process is repeated as Y.
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