Novel dynamic self-adaptive whale differential intelligent optimization algorithm

Abstract

The invention relates to the technical field of swarm intelligent optimization algorithms, and discloses a novel dynamic adaptive whale differential intelligent optimization algorithm, which comprises the following steps: designing a random search global exploration and bubble net attack local development stage of a dynamic probability balance whale optimization algorithm; an updating rule of a contraction bounding and bubble net attack stage containing adaptive weight is designed, the influence of the optimal position of the population is dynamically balanced, and the convergence speed of the algorithm for finding the optimal solution is accelerated; designing a Levy flight function to enhance the local optimization capability in a random search stage, and overcoming the problems of small population difference and easy falling into local optimum; the whale population is updated and iterated by using variation, crossover and selection of a differential evolution algorithm, so that the population diversity is increased, and the limitation problems of large population difference and slow convergence speed are overcome.

Description

[0001] The present invention belongs to the technical field of swarm intelligence optimization algorithms, and in particular relates to a novel dynamic adaptive whale differential intelligent optimization algorithm. Background Art

[0002] The design of tension / compression springs, welded beams and cantilever beams is a complex, nonlinear, multi-dimensional optimization problem with a large number of complex constraints. The core goal is to identify the best solution among many possible solutions to maximize the satisfaction of all constraints. This makes the solution of tension / compression springs, welded beams and cantilever beam design problems a very challenging task.

[0003] Traditional optimization methods such as gradient descent and Newton's method rely on traversing the entire solution space to find the optimal solution, which is not only time-consuming, but also unable to complete the optimization as the complexity of the problem increases. The whale optimization algorithm was proposed, which has become a powerful tool for solving optimization problems due to its unique ability to simulate the predation behavior of humpback whales. Compared with other swarm intelligence algorithms, the whale optimization algorithm shows higher computational accuracy, faster convergence speed, and stronger robustness in different environments.

[0004] Although the Whale Optimization Algorithm has made significant progress in the field of optimization for complex practical engineering applications, like other swarm intelligence algorithms, it may still face technical bottlenecks such as slow convergence and falling into local optimality when dealing with higher-dimensional and more complex optimization problems. Therefore, how to improve the Whale Optimization Algorithm, improve its calculation accuracy and convergence performance and avoid falling into local optimality is a problem that needs to be solved when the Whale Algorithm solves optimization problems and is applied to complex practical engineering problems. Summary of the invention

[0005] The present invention overcomes the deficiencies in the above-mentioned prior art and provides a new type of dynamic adaptive whale differential intelligent optimization algorithm. It aims at multi-dimensional constrained complex engineering optimization problems, overcomes the limitations of large data search space and surge in data population, and breaks through the bottleneck problem of large sample data differences, slow algorithm convergence speed, small sample data differences, and easy to fall into local optimality. It is used to solve engineering optimization problems in complex manufacturing processes such as springs and welding, and achieve high-performance goals of high optimization accuracy, fast convergence speed, and short calculation cycle for multi-dimensional constrained complex engineering optimization problems.

[0006] The technical solution of the present invention is achieved in this way:

[0007] A novel dynamic adaptive whale differential intelligent optimization algorithm, the method comprising:

[0008] S1: Introduce two core mechanisms in the dynamic probability balance whale difference algorithm: random search global exploration and bubble net predation local development. If the random probability is less than the dynamic probability, the position of the whale population is updated through the shrinking encirclement or random search mechanism. If the random probability is greater than or equal to the dynamic probability, the position of the whale is updated through the bubble net attack mechanism.

[0009] S2: Introduce Lévy flight into the random search mechanism of the whale difference algorithm. In the global search phase of the algorithm, the whale position is updated by introducing the random search mechanism of Lévy flight.

[0010] S3: Design new adaptive weights to dynamically adjust the influence of the current optimal position of the population. The local search phase of the algorithm updates the position of the whale by introducing the shrinking encirclement and bubble net attack mechanism of adaptive weights.

[0011] S4: If the number of observations meets the set update conditions, individuals with fitness values ​​worse than the optimal position in the current population are randomly selected to perform mutation, crossover and selection operations of the differential evolution algorithm. Better individuals are selected through greedy selection operations to enter the next population of the whale differential algorithm for iterative update.

[0012] Furthermore, a dynamically changing probability is designed in S1 to balance the global exploration and local development capabilities of the algorithm. The dynamic probability formula is as follows:

[0013]

[0014] Among them, w1, w2 are any constant values ​​in [0, 1], t is the current number of iterations, and T is the maximum number of iterations.

[0015] Furthermore, the random prey search method of Lévy flight introduced in S2 is as follows:

[0016] The Lévy flight is incorporated into the exploration phase of the whale algorithm. The step size of the Lévy flight is used to update the position of the humpback whale and can be described by changing the following expression:

[0017]

[0018] θ=θ0|X rand -X(t)|

[0019]

[0020] Where X rand is the selected random position vector, Γ(x) is the Gamma function, constant θ0=0.01, constant β=1.5, sign[rand-1 / 2] has three values: -1, 0 or 1, represents dot product, μ,v follows normal distribution, Lévy flight follows Lévy distribution, and s is the random flight step size.

[0021] Furthermore, the implementation method of introducing the shrinking surround and bubble net attack mechanism with adaptive weight in S3 is as follows:

[0022] An adaptive weight is introduced into the optimal individual position of the whale, and the adaptive weight is defined as ω. The formula of the adaptive weight is as follows:

[0023]

[0024] Where t is the current iteration number and T is the maximum iteration number. The whale update position formula is as follows:

[0025]

[0026] Among them, ω is the defined adaptive weight, P is the defined dynamic probability, A and C are coefficient vectors, X best (t) is the position vector of the best fitness obtained so far, X(t) is the position vector of the ith whale at iteration t, p is a random number in [0,1], |X best (t)-X(t)| is the distance vector between the i-th whale and its prey. The position of the i-th whale is the best solution obtained so far. b is a constant used to define the shape of the logarithmic spiral. l is a random number in [-1,1].

[0027] Furthermore, the method of embedding the whale optimization algorithm into the differential evolution algorithm in S4 is as follows:

[0028] When the number of observations is greater than or equal to 2, the individuals in the random whale population whose fitness values ​​are worse than the optimal position in the current population undergo mutation, crossover and selection operations of the differential evolution algorithm. The better individuals are selected through greedy selection operations to enter the next population of the whale algorithm for iterative update. When the differential evolution algorithm ends, the number of observations is reset to zero. Every three times the whale algorithm is run, the differential evolution algorithm is used to iteratively update the position of the selected whale individuals. The implementation method is as follows:

[0029] Mutation operation:

[0030] v i,G+1 =x R1,G +F·(x R2,G -x R3,G ),

[0031] Where G is the current evolution, R1, R2, R3 are randomly selected integers between 1 and N (population size) that are different from i, F is a scaling factor whose value is between [0, 2], and x R1,G ,xR2,G ,x R3,G is the position vector of a randomly selected individual whale in the current iteration.

[0032] Crossover operation:

[0033]

[0034] Among them, r j [0,1] is the random number between [0,1] calculated for the jth time, CR is the crossover rate, and the value of CR is between [0,1], r(i) is a random integer between [1,D], D is the dimension of the mutation vector, and v i,j,G+1 is the position vector corresponding to the i-th individual in the population after mutation, x i,j,G+1 is the position vector corresponding to the i-th individual in the current population.

[0035] Select an action:

[0036]

[0037] Among them, F(U i,G ) is the fitness value corresponding to the experimental vector, F(X i,G ) is the fitness value corresponding to the target vector, U i,G is the position vector corresponding to the i-th individual in the population after crossover, X i,G is the position vector corresponding to the i-th individual in the current iteration population.

[0038] The invention firstly initializes the individuals of the population randomly, then balances the random search global exploration and bubble net attack local development mechanism of the whale optimization algorithm through dynamic probability, and designs the Lévy flight function to enhance the local optimization ability of the random search stage, so as to overcome the problem that the population difference is small and it is easy to fall into the local optimum; secondly, the whale population is updated by using the shrinking encirclement and bubble net attack update mechanism containing adaptive weights, dynamically balances the influence of the optimal position of the population, and accelerates the convergence speed of the algorithm to find the optimal solution; finally, when the number of observations reaches the upper limit, it is judged whether it is the optimal position, if so, it is retained, otherwise, the mutation, crossover and selection mechanism of differential evolution are used to perform mixed operations to avoid the algorithm from falling into the local optimum.

[0039] The design starting point, concept and beneficial effects of the present invention using the above technical solution are:

[0040] (1) The present invention introduces dynamic probability, balances the global exploration and local development capabilities of the whale algorithm, and improves the problem of poor convergence performance of the whale optimization algorithm when solving optimization problems;

[0041] (2) The present invention introduces adaptive weights to dynamically adjust the influence of the optimal position, thereby solving the problem of slow convergence speed of the whale optimization algorithm when solving optimization problems, so that the algorithm can find the optimal solution faster and more effectively;

[0042] (3) The present invention designs an operating mechanism to embed the whale optimization algorithm into the differential evolution algorithm, and increases the diversity of the population through the mutation, crossover and selection operations of differential evolution, so that the whale optimization algorithm effectively avoids falling into the local optimum too early, and greatly improves the convergence effect of the algorithm;

[0043] (4) The novel dynamic adaptive whale differential intelligent optimization algorithm proposed in the present invention has high computational accuracy and fast convergence speed, and avoids the problem that traditional algorithms are prone to fall into local optimality. It can effectively solve global optimization problems and is widely used in the fields of optimization solution of practical engineering problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A step diagram of a novel dynamic adaptive whale differential intelligent optimization algorithm provided by the present invention;

[0045] Figure 2 It is a flow chart of a novel dynamic adaptive whale differential intelligent optimization algorithm of the present invention;

[0046] Figure 3 The algorithm of the present invention in Example 1 is compared with other intelligent optimization algorithms (whale optimization algorithm, differential evolution algorithm, gray wolf optimization algorithm) in f1, f2, f6, f7, f 10 and f 12 Convergence result comparison chart on functions;

[0047] Figure 4 This is a structural diagram of a welded beam in Embodiment 2 of the present invention;

[0048] Figure 5 This is a cantilever beam structure diagram in the second embodiment of the present invention;

[0049] Figure 6 This is a structural diagram of a tension / compression spring in Embodiment 2 of the present invention;

[0050] Figure 7 It is a convergence result diagram of the welded beam structure optimization of the algorithm of the present invention in the second embodiment;

[0051] Figure 8 This is a graph showing the convergence results of the cantilever beam structure optimization in the second embodiment of the algorithm of the present invention;

[0052] Fig. 9 This is a graph showing the convergence results of the tension / compression spring structure optimization using the algorithm of the present invention in Example 2. DETAILED DESCRIPTION

[0053] In order to enable relevant technical personnel in the field to more clearly understand the above-mentioned purposes, features and advantages of the present invention, a new type of dynamic adaptive whale differential intelligent optimization algorithm of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0054] like Figure 1 , 2 As shown in the figure, a new dynamic adaptive whale differential intelligent optimization algorithm is proposed. The specific steps are as follows:

[0055] S1: Population initialization

[0056] In the optimization process of the algorithm, the randomness and ergodicity of the initialization population in the solution space are very important, which greatly affects the accuracy of solving the optimization problem. The present invention adopts the random initialization method of the original algorithm, and the initialization is as follows:

[0057] X i =lb+rand·(ub-lb)

[0058] Among them, X i is the position vector of the ith whale, lb, ub are the search lower and upper bounds of the search space, and rand is a random number in [0,1].

[0059] S2: Iterative Update

[0060] Iterative update is the most core step of the entire algorithm in the optimization process. The iterative update of the whale optimization algorithm is mainly achieved by imitating the hunting method of humpback whales. It is mainly divided into three update mechanisms: shrinking and surrounding prey mechanism, bubble net attack mechanism and random search for prey mechanism. In iterative updates, the update rule is the key to affecting the algorithm's optimization ability. The standard whale optimization algorithm assumes that there is a 50% probability of selecting the shrinking and surrounding mechanism and the bubble net attack mechanism. Although this enhances the local search ability of the algorithm to a certain extent, the convergence effect is relatively general. In order to improve the convergence effect of the whale optimization algorithm, the present invention introduces adaptive weights, dynamic probabilities and Lévy flight strategies, and the implementation method is as follows:

[0061] S2-1: Introducing the adaptive weight shrinking and surrounding prey mechanism:

[0062] X(t+1)=ω·X best (t)-A·|C·X best (t)-X(t)|

[0063] Among them, ω is the adaptive weight, A and C are coefficient vectors, and X best(t) is the position vector of the best fitness obtained so far, X(t) is the position vector of the ith whale after iteration t, p is a random number in [0,1]. If a better solution appears after each iteration, the position vector X corresponding to the best solution should be updated in time. best (t). The adaptive weight update formula is as follows:

[0064]

[0065] Among them, t is the current iteration number and T is the maximum iteration number.

[0066] S2-2: Introducing the bubble network attack mechanism with adaptive weights:

[0067] X(t+1)=|X best (t)-X(t)|·e bl ·cos(2πl)+ω·X best (t)

[0068] Among them, |X best (t)-X(t)| is the distance vector from the i-th whale to its prey (the best solution obtained so far), X best (t) is the position vector of the best fitness obtained so far, b is a constant used to define the shape of the logarithmic spiral, and l is a random number in [-1,1].

[0069] The probability P that changes dynamically with the number of iterations is introduced to make full use of the two mechanisms of whales updating their positions, enhance the algorithm's search ability, and thus improve the algorithm's solution accuracy. The update formula for dynamic probability is as follows:

[0070]

[0071] Among them, w1, w2 are any constant values ​​in [0, 1], t is the current number of iterations, and T is the maximum number of iterations.

[0072] The position update formula of the whale optimization algorithm after introducing the dynamic probability P is:

[0073]

[0074] Among them, ω is the defined adaptive weight, P is the defined dynamic probability, A and C are coefficient vectors, X best (t) is the position vector of the best fitness obtained so far, X(t) is the position vector of the ith whale at iteration t, p is a random number in [0,1], |X best (t)-X(t)| is the distance vector from the ith whale to its prey (the best solution obtained so far), b is a constant used to define the shape of the logarithmic spiral, and l is a random number in [-1,1].

[0075] S2-3: The random search for prey using Lévy flight is implemented as follows:

[0076] A whale position is randomly selected, and other whale groups search for prey around the random whale. Lévy flight is incorporated into the exploration phase of WOA, which expands the search space through small steps and occasional large steps or long-distance jumps, improves global search capabilities, and even speeds up convergence. The step size of Lévy flight is used to update the position of the humpback whale, which can be described by changing the following expression:

[0077]

[0078] θ=θ0|X rand -X(t)|

[0079]

[0080] Among them, X rand is the position vector of the selected random whale, X(t) is the position vector of the whale after the current iteration t times, Γ(x) is the Gamma function, constant θ0=0.01, constant β=1.5, sign[rand-1 / 2] has three values: -1, 0 or 1, represents dot product, μ,v follows normal distribution, Lévy flight follows Lévy distribution, and s is the random flight step size.

[0081] S3: Jump out of local optimum

[0082] In the prior art, many algorithms have the disadvantage of being easily trapped in local optimality, which will directly lead to poor convergence effect of the algorithm. The whale optimization algorithm has such a problem. In order to solve the above problems of the whale optimization algorithm, the present invention embeds the whale optimization algorithm into the differential evolution algorithm. When the number of observations of a whale individual position exceeds the upper limit, the whale individual updates the whale position through the mutation, crossover and selection operations of differential evolution. The implementation method is as follows:

[0083] Mutation operation:

[0084]

[0085] Where G is the current evolution, R1, R2, and R3 are randomly selected integers between 1 and N (population size) that are different from i. are the position vectors of three individuals randomly selected from the population, F is the scaling factor, and the value of F is between [0,2].

[0086] Crossover operation:

[0087] After the mutation process, the parameters of the mutation vector are mixed with the parameters of another predetermined target vector according to certain rules to generate individuals. The test individuals generated by the crossover operation are: U i,G+1 =[u i,1,G+1 ,u i,2,G+1 ,…,u i,j,G+1 ,…,u i,D,G+1 ].

[0088]

[0089] Among them, r j [0,1] is the random number between [0,1] calculated for the jth time, CR is the crossover rate, and the value of CR is between [0,1]. i,j,G+1 is the position vector of the jth calculated value of the ith individual after mutation, x i,j,G+1 is the j-th calculated position vector of the i-th individual in the whale population, r(i) is a random integer between [1,D], and D is the dimension of the mutation vector.

[0090] Select an action:

[0091] After mutation and crossover operations, an experimental vector is generated. Evaluate the fitness value of the experimental vector and a target vector, and select a better one to enter the next population of WOA through greedy selection operation. The update formula is as follows:

[0092]

[0093] Among them, F(U i,G ) is the fitness value corresponding to the experimental vector, F(X i,G ) is the fitness value corresponding to the target vector, U i,G is the position vector corresponding to the i-th individual in the population after crossover, X i,G is the position vector corresponding to the i-th individual in the current population. By adjusting F and CR, the whale optimization algorithm can be helped to jump to local search to capture prey, while improving the stability of the whale optimization algorithm.

[0094] The principle of the invention is as follows: firstly, the individuals of the population are randomly initialized, and then the random search global exploration and bubble net attack local development mechanisms of the dynamic probability balance whale optimization algorithm are used, and at the same time, the Lévy flight function is designed to enhance the local optimization ability of the random search stage, so as to overcome the problem that the population difference is small and it is easy to fall into the local optimum; secondly, the whale population is updated by using the shrinking encirclement and bubble net attack update mechanism containing adaptive weights, the influence of the optimal position of the population is dynamically balanced, and the convergence speed of the algorithm to find the optimal solution is accelerated; finally, when the number of observations reaches the upper limit, it is judged whether it is the optimal position, if it is, it is retained, otherwise, a mixed operation is performed through the mutation, crossover and selection mechanism of differential evolution to avoid the algorithm from falling into the local optimum.

[0095] Embodiment 1:

[0096] The proposed algorithm is tested on 15 classic benchmark test functions in the CEC 2005 test set, including 7 unimodal test functions, 5 multimodal test functions and 2 fixed multimodal test functions. The unimodal test function is used to test the convergence performance of the algorithm, while the multimodal test function can test the ability of the algorithm to escape from the local optimum in addition to the convergence performance of the algorithm.

[0097] In order to verify the effectiveness of the novel dynamic adaptive whale differential intelligent optimization algorithm IHWOADE proposed in the present invention, the optimization results of IHWOADE are compared with the other three algorithms, namely: whale optimization algorithm (WOA), differential evolution algorithm (DE) and gray wolf optimization algorithm (GWO). By comparing with WOA, DE and GWO, the algorithm performance of IHWOADE is verified. In order to enable technicians in this field to see the experimental results more intuitively, the present invention gives the performance of these five algorithms in the test functions f1, f2, f6, f7, f in 30 dimensions. 10 and f 12 The experimental results simulation diagram on Figure 3 shown.

[0098] Parameter setting and result analysis:

[0099] In order to obtain more reliable and more accurate experimental results, the parameter settings of these four algorithms are very important. In order to make the comparative experiment more fair and objective, the initial population and the number of iterations are set to the same value and each test function is independently run 30 times in 30 dimensions. In order to make the experimental results more intuitive, the present invention uses the Wilcoxon pairwise comparisons method to analyze the experimental results. The symbols "+", "-" and "≈" respectively indicate that the performance of IHWOADE is better than, worse than, and has no significant difference from other algorithms. The specific experimental results are shown in Table 1.

[0100] Table 1:

[0101]

[0102] Comparison with standard algorithms (DE, GWO):

[0103] From Table 1, we can see that in the 30-dimensional space, except for the f5 test function, the effect of IHWOADE is not as good as that of GWO algorithm. 14 The results on the test function are not as good as those of the DE algorithm, but the best results are achieved on other test functions. Figure 3 It can be seen that the convergence performance of IHWOADE is very good and has a significant lead. According to these experimental data, it can be intuitively seen that IHWOADE outperforms the standard whale optimization algorithm in all aspects, which verifies the effectiveness of the whale optimization algorithm introducing dynamic probability, adaptive weights and Lévy flight function.

[0104] Comparison with algorithm WOA:

[0105] As can be seen from Table 1, in 30 dimensions, IHWOADE performs better than WOA in most test functions. Figure 3 It can be seen that IHWOADE can quickly reach the optimal value 0 in the optimization process of the test function, but WOA mostly falls into the local optimum during the iteration process. This verifies the effectiveness of embedding the whale optimization algorithm into the differential evolution algorithm.

[0106] In summary, compared with other algorithms, the IHWOADE proposed in the present invention has obvious improvements in solution accuracy and convergence speed and is not prone to falling into local optimality.

[0107] Embodiment 2:

[0108] The present invention applies the algorithm to practical engineering problems, taking the welding beam structure optimization problem, the cantilever beam structure optimization problem, and the tension / compression spring structure optimization problem as examples.

[0109] Engineering problems are problems that arise in the process of designing, building and maintaining various structures or systems, such as welded beam design, robot gripper problem, cantilever beam design and tension / compression spring design. These problems may occur in any engineering field, including mechanical, electrical, construction, etc., and their complexity ranges from simple design defects to more complex system failures. Solving these engineering problems requires a fundamental understanding of the basic principles and processes of the system. When optimizing these problems, many traditional optimization algorithms usually have poor results or even fail to find the best solution. Therefore, it is very important to improve the optimization performance of practical engineering problems by improving the algorithm. The present invention applies the proposed algorithm to practical engineering problems and achieves good optimization results. This embodiment will introduce the optimization of the proposed algorithm on the welded beam design problem, the cantilever beam structure optimization problem and the tension / compression spring structure optimization problem.

[0110] The design optimization problem of welded beam structure is a typical structural engineering optimization problem. Its core goal is to minimize the design and manufacturing cost of welded beams while meeting certain strength, stability and functional requirements. This problem is very common in industrial manufacturing, building structures and mechanical engineering, and is of great significance for improving engineering efficiency and economic benefits. Figure 4 As shown, the problem contains 5 constraints, including 4 design variables: h represents the height of the weld, L represents the length of the clamped bar, t represents the height of the bar, and b represents the thickness of the bar. The mathematical model formula of this problem is as follows:

[0111] Objective function:

[0112]

[0113] Constraints:

[0114]

[0115] Constraint scope:

[0116] P=6000lb,L=14in,δ max =0.25in

[0117] E = 30 × 1 6 psi,G=12×10 6 psi

[0118] τ max =13600psi,σ max =30000psi

[0119] 0.1≤x1≤2,0.1≤x2≤10,0.1≤x3≤10,0.1≤x4≤2

[0120]

[0121] The cantilever beam consists of five hollow units with square cross-sections. Figure 5 As shown, each unit is defined by a variable, and the thickness is constant, so there are 5 structural parameters, namely the side lengths of the square x1, x2, x3, x4, x5. The goal of the cantilever arm optimization design is to minimize the weight of the beam, and the constraint condition is to satisfy a vertical displacement constraint. The mathematical model formula is expressed as follows:

[0122] Objective function:

[0123]

[0124] Constraints:

[0125]

[0126] Constraint scope:

[0127] 0.01≤x i ≤100,i=1,2,3,4,5

[0128] The goal of the tension / compression spring design problem is to minimize the weight of the spring. The optimal design must satisfy the constraints of minimum deflection, vibration frequency, and shear stress. The three design variables are the spring coil diameter (d), spring coil diameter (D), and the number of coils (N). The structure of the tension / compression spring is as follows: Figure 6 The mathematical model formula is as follows:

[0129] Objective function:

[0130]

[0131] Constraints:

[0132]

[0133] Constraint scope:

[0134] 0.05≤x1≤2.00,0.25≤x2≤1.30,2.00≤x3≤15.0

[0135] Parameter setting and result analysis:

[0136] In order to obtain more accurate experimental results, the parameter setting of IHWOADE is particularly important. The specific parameters are shown in Table 2.

[0137] Table 2:

[0138]

[0139] The experimental results are as follows Figure 7 , 8 As shown in Figure 9, it can be seen from the experimental results that the application of IHWOADE in the design problems of welded beam structures, cantilever beam structures and tension / compression spring structures is very successful and has achieved good results.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A new dynamic adaptive whale differential intelligent optimization algorithm, characterized in that: The method comprises: S1: Introduce two core mechanisms in the dynamic probability balance whale difference algorithm: random search global exploration and bubble net predation local development. If the random probability is less than the dynamic probability, the position of the whale population is updated through the shrinking encirclement or random search mechanism. If the random probability is greater than or equal to the dynamic probability, the position of the whale is updated through the bubble net attack mechanism. S2: Introduce Lévy flight into the random search mechanism of the whale difference algorithm. In the global search phase of the algorithm, the whale position is updated by introducing the random search mechanism of Lévy flight. S3: Design new adaptive weights to dynamically adjust the influence of the current optimal position of the population. The local search phase of the algorithm updates the position of the whale by introducing the shrinking encirclement and bubble net attack mechanism of adaptive weights. S4: If the number of observations meets the set update conditions, individuals with fitness values ​​worse than the optimal position in the current population are randomly selected to perform mutation, crossover and selection operations of the differential evolution algorithm. Better individuals are selected through greedy selection operations to enter the next population of the whale differential algorithm for iterative update.

2. According to claim 1, a novel dynamic adaptive whale differential intelligent optimization algorithm is characterized in that: In S1, a dynamically changing probability is designed to balance the global exploration and local development capabilities of the algorithm. The dynamic probability formula is as follows: Among them, w1, w2 are arbitrary constant values ​​in [0, 1], t is the current number of iterations, and T is the maximum number of iterations.

3. According to claim 1, a novel dynamic adaptive whale differential intelligent optimization algorithm is characterized in that: The random search method for prey introduced in S2 using Lévy flight is as follows: The Lévy flight is incorporated into the exploration phase of the whale algorithm. The step size of the Lévy flight is used to update the position of the humpback whale, which can be described by changing the following expression: θ=θ0|X rand -X(t) Where X rand is the selected random position vector, Γ(x) is the Gamma function, constant θ0=0.01, constant β=1.5, sign[rand-1 / 2] has three values: -1, 0 or 1, represents dot product, μ,v follows normal distribution, Lévy flight follows Lévy distribution, and s is the random flight step size.

4. According to claim 1, a novel dynamic adaptive whale differential intelligent optimization algorithm is characterized in that: The implementation method of the shrinking encirclement and bubble net attack mechanism with adaptive weights introduced in S3 is as follows: An adaptive weight is introduced into the optimal individual position of the whale, and the adaptive weight is defined as ω. The formula of the adaptive weight is as follows: Among them, t is the current iteration number, T is the maximum iteration number; the whale update position formula is as follows: Among them, ω is the defined adaptive weight, P is the defined dynamic probability, A and C are coefficient vectors, X best (t) is the position vector of the best fitness obtained so far, X(t) is the position vector of the ith whale at iteration t, p is a random number in [0,1], |X best (t)-X(t)| is the distance vector between the i-th whale and its prey. The position of the i-th whale is the best solution obtained so far. b is a constant used to define the shape of the logarithmic spiral. l is a random number in [-1,1].

5. According to claim 1, a novel dynamic adaptive whale differential intelligent optimization algorithm is characterized in that: The way to embed the whale optimization algorithm into the differential evolution algorithm in S4 is as follows: When the number of observations is greater than or equal to 2, the individuals in the random whale population whose fitness values ​​are worse than the optimal position in the current population undergo mutation, crossover and selection operations of the differential evolution algorithm. The better individuals are selected through the greedy selection operation to enter the next population of the whale algorithm for iterative update. When the differential evolution algorithm ends, the number of observations is reset to zero. Every three times the whale algorithm is run, the differential evolution algorithm is used to iteratively update the position of the selected whale individuals. The implementation is as follows: Mutation operation: Where G is the current evolution, R1, R2, R3 are randomly selected integers between 1 and N (population size) that are different from i, and F is a scaling factor whose value is between [0, 2]. is the position vector of the individual whale randomly selected in the current iteration; Crossover operation: Among them, r j [0,1] is the random number between [0,1] calculated for the jth time, CR is the crossover rate, and the value of CR is between [0,1], r(i) is a random integer between [1,D], D is the dimension of the mutation vector, and v i,j,G+1 is the position vector corresponding to the i-th individual in the population after mutation, x i,j,G+1 is the position vector corresponding to the i-th individual in the current population; Select an action: Among them, F(U i,G ) is the fitness value corresponding to the experimental vector, F(X i,G ) is the fitness value corresponding to the target vector, U i,G is the position vector corresponding to the i-th individual in the population after crossover, X i,G is the position vector corresponding to the i-th individual in the current iteration population.

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