[0032] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments.
[0033] refer to Figure 1-5 , a differential evolution algorithm and application based on wavelet basis function and optimal mutation strategy, including the following steps:
[0034] Step 1: In (x max ,x min ) randomly generate an initial population X i =(x 1 ,x 2 …x i ), and initialize parameters, population size NP=100, dimension D=30, maximum number of iterations G max =2000; initial iteration number G=1;
[0035] Step 2: If it is the first generation, execute step 3, otherwise, skip step 3 and execute step 4;
[0036] Step 3: Use five mutation operations to generate five mutation vectors respectively, calculate the fitness values of the five mutation vectors, compare the fitness values, and select the mutation vector with the smaller fitness value as the mutation vector in step 3, and Save the evolution strategy of the mutation vector with the minimum fitness value as the optimal evolution strategy;
[0037] Step 4: Perform mutation operation with the optimal strategy selected by the first generation;
[0038] Step 5: Carry out the crossover operation, generate a random number in (0, 1) and compare it with the crossover rate CR, if it is less than CR, select the mutation vector generated in step 2 as the test vector, otherwise, select the contemporary target vector as the test vector;
[0039]Step 6: Carry out the selection operation, calculate the fitness value of the target vector and the test vector, compare, and select the smaller fitness value to enter the next generation population;
[0040] Step 7: If the maximum number of iterations G is reached max = 2000, output the optimal value, otherwise skip to step 2.
[0041] Further, the wavelet basis function needs to be used to control the F value of the parameter during the operation, and the expression is as follows:
[0042]
[0043] where x is a random number between (0,1).
[0044] Further, when solving complex optimization problems, the first generation of evolution uses DE algorithms with five different evolution strategies to solve the fitness function value, and selects the mutation vector with the best fitness value as the mutation vector in the selection operation. The strategy corresponding to the mutation vector of the degree value is called the optimal evolution strategy, and then in the remaining number of iterations, the determined optimal evolution strategy is used to complete the solution of the complex optimization problem until the error requirement or the number of iterations are met to improve the algorithm. The local search ability ensures the global search characteristics of the algorithm. For different complex optimization problems, an optimal mutation strategy DE algorithm can be determined after the first iteration to complete the optimization of complex optimization problems.
[0045] Further, the uniform distribution is used to improve the crossover probability CR during the operation, and its expression is as follows:
[0046] CR=Norm(0,1);
[0047] By setting the cross probability CR to a random number, the diversity of parameter values of the DE algorithm is increased, so that the algorithm can still automatically generate parameter values suitable for the current search needs when faced with problems without any prior knowledge. improve the performance of the algorithm.
[0048] In this embodiment, in solving practical optimization problems (such as the life maximization problem in wireless sensor network coverage optimization, the cost minimization problem in logistics vehicle path planning, etc.), a certain evaluation method is often used to construct the objective function, so as to The actual problem is abstracted into the objective function optimization problem, and the objective function is optimized by the evolutionary algorithm, and different evolutionary algorithms show different optimization performance when optimizing the objective problem. In order to evaluate the performance of each algorithm, the standard test function is usually used as The objective function is tested.
[0049] In order to verify the validity of the algorithm, the algorithm is tested by 11 test functions, in which Table 1 gives the expressions, value ranges, and minimum values of these 11 functions, where D is the dimension, and it is the same as that of the standard DE. Five strategies are compared, and in Table 2, the parameter settings of the algorithm are given, including the population of the algorithm and the number of iterations.
[0050] Table 1: Test functions
[0051]
[0052]
[0053] Among the 11 functions, the test function f 1 ~f 4 , f 6 , f 7 is a unimodal function, which is mainly used to evaluate the accuracy and convergence speed of various versions of the DE algorithm. f 8 ~f 11 For multimodal functions, multimodal test functions are easy to make the population fall into local optimum, so they are mainly used to evaluate the global search performance and stability of the DE algorithm. The present invention adopts 11 standard test functions to test the performance of the algorithm.
[0054] Table 2: Algorithm parameter settings
[0055]
[0056] In Table 3, the test results of 11 test functions are compared with the five basic differential evolution strategies. Among them, best represents the optimal value of the algorithm, mean represents the average value obtained by the algorithm, and std represents the standard of the algorithm Difference.
[0057] Table 3: Comparison of the results of WMSDE and the five strategies of differential evolution respectively
[0058]
[0059]
[0060]
[0061] Among them, the test function f 1 ~f 3 , f 7 is a unimodal function, which is mainly used to evaluate the accuracy and convergence speed of various versions of the DE algorithm. f 8 , f 10 As multimodal functions, multimodal test functions are easy to make the population fall into local optimum, so they are mainly used to evaluate the global search performance and stability of DE algorithm.
[0062] In Table 3, in the test function f 1 ~f 3 , the algorithm has relatively good optimal value, mean and standard deviation no matter in 30-dimensional or 50-dimensional, and in the function f 1 ~f 2 Can take the minimum value of the function 0, in the function f 6 , f 4 , the five strategies and their WMSDE can take the minimum value of the function 0, in the function f 5 , the performance is not good, the possible reason is that the function is a unimodal function when the independent variable is 2-3 dimensions, it is difficult to find the global minimum value, and the performance of each strategy on the function is not excellent. 7 Compared with the other five strategies, although strategy 4 is a better result, WMSDE shows better results compared with strategy 4 in terms of optimal value and average value. In the function f 8 Compared with other algorithms, it has a good performance in the mean and optimal value, and the optimal value of the function is obtained, indicating that the stability of the algorithm is excellent, in the function f 9 and f 11 Among them, strategy 1 and strategy 5 cannot obtain the optimal value, and the remaining strategies and WMSDE can obtain the optimal value. In the function f 10 Although each strategy has obtained a relatively small value, it has not reached the optimal value of the function 0, but the WMSDE algorithm has obtained a relatively optimal value with a standard deviation of 0, which shows the optimization ability and stability of the algorithm. Again The optimization ability and stability of the algorithm are better.
[0063] In the test function f 1 , it can be seen that the WNSDE algorithm shows good performance in the early stage of iteration, the iterative curve declines quickly, and the optimization accuracy is high. Compared with other DE strategies, the overall optimization ability is strong and the convergence is high. In the test function f 2 Among them, the WMSDE algorithm shows relatively good advantages. In the whole iteration, the optimal value found is lower than other strategies. Compared with the other five mutation strategies, the optimization ability is strong. In the test function f 3 , the WMSDE algorithm is better than other strategies in terms of optimization ability and convergence, showing global search ability and optimization speed, in the function f 4 , f 11 and f 6 , it is obvious that the WMSDE effect is excellent, both in terms of value and convergence, in the function f 5 , the performance is not good, the possible reason is that the function is a unimodal function when the independent variable is 2-3 dimensions, and it is difficult to find the global minimum. In the test function f 7 Although it does not show good convergence and solution accuracy, it has the same effect compared with other strategies, in the test function f 8 , the WMSDE algorithm is significantly better than the other five strategies in both the optimization ability and the global search ability. In the function f 9 In the test function f10, the optimal value can be found before 200 generations, and the optimal value found is better than the optimal value of other strategies , after 200 generations, WMSDE has been in the optimal state, indicating that WMSDE has strong convergence ability and optimization ability.
[0064] According to the test results of the function, for the unimodal function of the WMSDE algorithm, the algorithm convergence curve shows a monotonically decreasing trend, and quickly reaches the optimal value, or continues to move toward the optimal value. For multimodal functions, the algorithm curve has multiple inflection points. , constantly jumping out of the local optimal value of the function and approaching the global optimal solution, which shows that the WMSDE algorithm has good adaptability to test functions of different complexity, and can effectively enhance the global search ability.
[0065] To sum up, under the standard DE algorithm, the DE performance of different strategies is quite different. Improper strategy selection may not obtain satisfactory results, while the WMSDE algorithm avoids the defects of each strategy. In view of the above-mentioned various DE evolution strategies With their respective advantages and disadvantages, it is impossible to generalize which evolutionary model is better and which evolutionary model is relatively weak. However, various evolutionary models have common characteristics, that is, the recombination method adopted is between the reference individual and its different individuals. Linear combination, the WMSDE algorithm makes five evolutionary strategies cooperate with each other. It is no longer just a complete random search, but a purposeful search in the better direction of the difference vector, which not only strengthens the local search ability of the algorithm, but also guarantees The global search feature of the algorithm.
[0066] Table 4 lists the comparison between WMSDE algorithm and DE2/F algorithm, MEDE algorithm, pADE algorithm and RMDE algorithm, where best represents the optimal value of the algorithm, mean represents the average value obtained by the algorithm, and std represents the standard deviation of the algorithm.
[0067] Table 4: 30-dimensional and 50-dimensional function test results
[0068]
[0069]
[0070] It can be seen from Table 4 that the algorithm obtains the optimal solution of most functions, and the optimal value, average value and error are better than other algorithms. test function f 1 , f 2 , f 3 , f 5 is a unimodal function, which is mainly used to evaluate the accuracy and convergence speed of various versions of the DE algorithm. f 9 ~f 11 As multimodal functions, multimodal test functions are easy to make the population fall into local optimum, so they are mainly used to evaluate the global search performance and stability of DE algorithm.
[0071] in the function f 1 On the 30-dimensional or 50-dimensional, the algorithm has relatively good optimal value, mean and standard deviation, and can take the minimum value of the function 0, in the function f 2 Among them, the DE2/F algorithm, MEDE algorithm, pADE algorithm and RMDE algorithm obtained relatively small values, but did not reach the optimal value 0 of the function, but the WMSDE algorithm not only obtained the optimal value of the function's minimum value, but also the average value. When the minimum value is reached, the standard deviation is 0, which shows the optimization ability and stability of the algorithm. In the function f 3 Although the WMSDE algorithm does not get the optimal value of the function, 0, compared with the other four algorithms, the optimal value is about 100 orders of magnitude different, and the mean value also shows better results, with a standard deviation of 0. , indicating the stability of the algorithm during optimization, when testing the function f 5 , the performance is not good, the possible reason is that the function f 5 When the independent variable has 2-3 dimensions, it is a unimodal function. When the dimension of the independent variable increases, f 5The number of minimum values of the function increases accordingly, and its global minimum is located in a parabolic valley, which is easy to find, but due to the small change of the function value within the valley, it is difficult to find the global minimum, in the function f 9 Compared with other algorithms, it has a good performance in the mean and optimal value. Although the pADE algorithm obtains the minimum value of the function in both the optimal value and the mean value, the WMSDE algorithm is not inferior, and the function is the most The figure of merit is 0, and the mean is also 0, indicating that the algorithm has excellent stability. For the function f 10 , among the four algorithms, the pADE algorithm achieved the optimal value of 8.88E-16, and the standard deviation was 0. Compared with it, WMSDE also obtained the same value, and the effect was no worse than other algorithms. 11 Among them, the DE2/F algorithm and the MEDE algorithm find the optimal value of the function 0 during optimization, but the mean and standard deviation effect is not very good, but the WMSDE algorithm can achieve the optimal value no matter in 30 or 50 dimensions. 0, and the standard deviation value is also 0, which again shows that the algorithm has good optimization ability and stability.
[0072] In summary, from the test results of the unimodal function, it shows that the algorithm performs well on the unimodal function, and the improved algorithm has better accuracy and convergence speed. The better effect of the above, so that the algorithm is not easy to make the population fall into the local optimum, and better find the optimal solution. The improved algorithm is not only in the global optimization ability, algorithm convergence speed, algorithm accuracy and stability. are better than the other four algorithms. And WMSDE is not easy to fall into local optimum, and is higher than other DEs in terms of overall performance.
[0073] Airport parking space allocation verification based on WMSDE algorithm:
[0074] First build a multi-objective optimization model for parking space allocation in hub airports
[0075] Optimization objective function of parking space allocation
[0076] (1) The objective function with the most balanced idle time at the parking stand
[0077] The allocation of parking spaces ensures a balanced distribution of idle time. If there is a small-scale short-term delay, it can play a buffering role. Only a little adjustment can make the flight run normally, and it also ensures the utilization rate of each parking space. balance. Therefore, the most balanced idle time of the parking stand is selected as the optimization objective, and its objective function is established as:
[0078]
[0079] n represents the total number of flights, m represents the number of parking spaces; S ik is the idle time of this stand when flight i arrives at stand k; SS k Indicates the idle time of the parking bay.
[0080] (2) The objective function of the shortest walking distance of passengers
[0081] Passengers' satisfaction with airport services is directly related to the operation of civil aviation. The less distance a traveler travels at the airport, the better the traveler's rating. Therefore, the shortest walking distance of passengers is selected as the optimization goal. Establish its objective function as:
[0082]
[0083] q ij refers to the number of passengers transferred in flight i assigned to gate j; f j Refers to the distance that passengers need to travel to reach the gate j; y ij is a 0-1 variable; i represents the flight, and j represents the parking lot.
[0084] (3) The objective function of the most fully utilized large parking spaces
[0085] Large parking spaces can accommodate all aircraft, while small parking spaces can only accommodate small aircraft. In actual operation, if too many large parking spaces are occupied by small and medium-sized aircraft too early, then the large aircraft arriving later will have fewer allocation options, and even be forced to go to the apron; at the same time, large flights often carry a large number of passengers More, once going to the tarmac will inconvenience more passengers, and the impact angle on satisfaction is greater. Therefore, large parking spaces should be allocated to large aircraft as much as possible to ensure passenger satisfaction while giving full play to the functions of parking spaces and related equipment. Therefore, selecting the most fully utilized large parking spaces is the optimization goal, and its objective function is established as follows:
[0086]
[0087] G ij Refers to small and medium-sized aircraft parked on large parking spaces and small aircraft parked on medium-sized parking spaces.
[0088] (4) The highest occupancy efficiency is based on the seat
[0089] From the perspective of airport management, under the condition of satisfying flight operation safety, parking the same type of flight at the corresponding parking space can greatly improve the efficiency of the use of the parking space and save the operation and use cost of the parking space. Not only that, but it can also help the airport to park more flights and expand the number of aircraft that can be parked at the airport.
[0090] Therefore, the objective function based on the model with the highest occupancy rate is:
[0091]
[0092] (5) Minimum flight - seat matching difference
[0093] In the process of parking bay allocation, large parking bays can park large, medium and small models: medium-sized bays can park small and medium models, and small parking bays can only park small models. But in principle, the largest aircraft type allowed should be allocated to the corresponding parking space as much as possible. Therefore, the minimum flight-stand matching difference is used as an optimization objective for the allocation of stands:
[0094]
[0095] where ρ ik Indicates the ratio of the difference between the size of the largest aircraft type that can be parked at the seat k minus the size of the aircraft corresponding to the flight and the largest aircraft seat in the terminal it belongs to.
[0096] Unquantized Processing of Objective Function
[0097] This article involves a multi-objective model, so a set of objective functions F is added 1 (x),F 2 (x),...F n (x) to represent the objective function, where n is the number of single objective functions.
[0098] Considering all the single objective functions comprehensively, the establishment of the parking space allocation problem model of the hub airport is as follows:
[0099] min[F 1 (x),F 2 (x),...F n (x)]
[0100] When solving a multi-objective model, the complex multi-objective model can be transformed into a single-objective model. The commonly used transformation methods mainly include linear weighting method, square sum weighting method and constraint method. This paper chooses the linear weighting method which is convenient to operate and has better effect. Using the weighting method to set the weight factor Wi≥0 (i=1,2,...n), the objective function can be expressed as:
[0101]
[0102] because [F 1 (x),F 2 (x),…F n (x)] are different objective functions with their own dimensions, so the objective function needs to be processed without quantification.
[0103] Let F i 0 =max[|Fi|], and F i 0 ≠0, then the objective function after non-quantization processing is:
[0104]
[0105] Therefore, the objective function of airport parking space allocation after unquantified processing is:
[0106]
[0107] Restrictions:
[0108]
[0109] G r ≥F i (y ir =1)
[0110] L ik -E ik ≥5Z ijk =1
[0111] F nearF farg i
[0112] Airport parking space allocation results based on WMSDE algorithm
[0113] Experimental data and environment
[0114] Experimental environment selection: Intel(R)core(TM)i5-7400 CPU 3.00GHz, 8G RAM, Windows 10, MATLAB R2018a
[0115] The data selected in the experiment is the flight parking space allocation data of Guangzhou Baiyun Airport, and the parking space pre-allocation is carried out for 30 parking spaces on July 26, 2015 and 250 flights in the airport within one day on the 26th. Read the information of the parking bays, record the start time when 30 parking bays are occupied for the first time, and the end time when all 250 flights depart. The parking spaces are divided into three types: large, medium and small according to the size of the aircraft that can be stored, and flights are also divided into three types: large, medium and small. The large parking space can store all models, the medium parking space can store medium and small models, and the small parking space can only park small machines. All flights that are not assigned to a stand are parked on the tarmac.
[0116] Table 5: Data of parking spaces at Baiyun Airport
[0117]
[0118] Table 6: Data of some flights at Baiyun Airport
[0119]
[0120]
[0121] The selected experimental parameters are that the individual dimension is 5, the population size is 250, and 20 experiments are performed for 200 iterations.
[0122] The WMSDE algorithm is used to solve the multi-objective optimization model of airport parking space allocation. The algorithm is independently executed 20 times, and the best parking space allocation result in the 20 experiments is selected for analysis. The obtained parking space allocation results are shown in Table 7.
[0123] Table 7: The results of the allocation of airport parking spaces
[0124]
[0125]
[0126]It can be seen from the parking space allocation results that 241 of the 250 flights were allocated to 30 parking spaces, and 9 flights were allocated to the apron, and the parking space allocation rate was 96.4%. From the point of view of the number of flights allocated to each parking space, the number of flights allocated to each parking space is relatively balanced, and the idle time of each parking space is relatively balanced, which enables the staff to have sufficient time for scheduling, which not only avoids the waste of idle parking spaces, but also There is no excessive use, so that airline resources have been allocated and utilized more reasonably. Therefore, using the WMSDE algorithm to solve the multi-objective optimization model of airport parking space allocation, only a few flights parked on the apron, and a better parking space allocation result was obtained.
[0127] Aiming at the shortcomings of the DE algorithm in solving problems, such as solving accuracy, poor convergence and diversity of solutions, the invention uses the wavelet basis function to improve the control parameter F, and generates different F values through the wavelet basis function during the iteration to achieve Changing the search step size and giving the algorithm different search step sizes in different search stages will help the algorithm to quickly converge to a good subspace and accurately find a better solution. At the same time, the normal distribution is used to improve the CR value and improve the performance of the algorithm , put forward the optimal strategy, make the five strategies complement each other, and find the optimal strategy. From the simulation experiment, the WMSDE algorithm for unimodal functions, the algorithm convergence curve shows a trend of monotonous decline, and quickly reaches the optimal value, or continues to the optimal value. value is advancing. For multimodal functions, there are multiple inflection points in the algorithm curve, constantly jumping out of the local optimal value of the function and approaching the global optimal solution. The WMSDE algorithm achieves better results on unimodal and multimodal functions, indicating that the algorithm has high precision and fast convergence speed. Therefore, it is not easy for the algorithm to make the population fall into the local optimum, and it is better to find the optimal solution. It shows that the WMSDE algorithm has good adaptability to test functions of different complexity, and can effectively enhance the global search ability. Provides a good choice for single-objective optimization problems.
[0128] From the experiment of solving the actual problem of parking space allocation, the WMSDE algorithm has strong global optimization ability and optimization efficiency, can effectively obtain ideal parking space allocation results, and improve the utilization rate of airport parking spaces and passenger satisfaction. The waste of key resources of the airport is avoided, and the work and rest time of the airport staff are reasonably arranged.
[0129] The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited to this. The equivalent replacement or change of the inventive concept thereof shall be included within the protection scope of the present invention.
