A lithium ion battery capacity prediction method

Abstract

The application relates to the technical field of battery life prediction, and discloses a lithium ion battery capacity prediction method, which comprises the following steps: obtaining lithium ion battery data, performing normalization processing and variational mode decomposition preprocessing on a battery capacity sequence to obtain a data set serving as model input; performing multi-scale decomposition on the battery capacity sequence obtained by S01 by using a self-adaptive mode selection mechanism based on an MAPE criterion, to obtain intrinsic mode functions (IMFs) of the best decomposition mode number; the lithium battery data is preprocessed by using variational mode decomposition (VMD), the battery capacity sequence is multi-scale decomposed by using a self-adaptive mode selection mechanism based on an MAPE criterion, and intrinsic mode functions (IMFs) of the best decomposition mode number are obtained; a self-adaptive step Gaussian random walk strategy, an auxiliary correction strategy and a differential evolution strategy are introduced to improve a white whale optimization algorithm (WOA), so that the robustness of the algorithm and the precision of the final solution are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of battery life prediction, in particular to a lithium ion battery capacity prediction method. BACKGROUND

[0002] With the rapid development of new energy vehicles and energy storage systems, lithium ion batteries have become the core energy unit due to their high energy density, long cycle life and low self-discharge rate. To ensure system operation safety, prolong battery life and improve maintenance efficiency, it is of great significance to accurately predict the remaining useful life (RUL) of lithium ion batteries, which not only enables full life cycle management, but also provides a scientific basis for fault warning and resource scheduling.

[0003] In actual service process, the capacity degradation process of lithium ion battery has significant nonlinearity and uncertainty, accompanied by complex phenomena such as capacity regeneration and fluctuation, which seriously affects the predictability and stability of the model, and brings challenges to the RUL prediction method based on data-driven. At present, long short-term memory network (LSTM) is widely used in battery life prediction due to its advantages in time series modeling, but the regeneration phenomenon and noise fluctuation in the capacity curve can easily cause trend aliasing, reducing the prediction accuracy and generalization ability.

[0004] To improve the modelability of capacity sequence, various signal decomposition methods such as wavelet decomposition, empirical mode decomposition (EMD) and complementary ensemble empirical mode decomposition (CEEMD) are introduced in many practical applications, but these methods have problems such as insufficient high-frequency disturbance extraction ability, mode aliasing or mode redundancy, and high computational complexity. Variational mode decomposition (VMD) has advantages in suppressing mode aliasing and signal redundancy due to its controllable mode number and penalty term adjustment mechanism, and has achieved certain results in battery life prediction. However, the mode number and penalty factor of existing VMD depend on artificial setting, lack of adaptive mechanism, and are easy to cause over-decomposition or under-decomposition, affecting the decomposition quality and prediction performance.

[0005] On the other hand, the performance of the LSTM network depends largely on the reasonable configuration of hyperparameters. The traditional grid search or experience setting method is inefficient and easy to fall into local optimum when facing high-dimensional nonlinear optimization problems. The Whale Optimization Algorithm (WOA) is applied to hyperparameter optimization because of its strong global search ability, but it still has problems such as premature convergence and insufficient local search ability, which limits the further improvement of model performance. SUMMARY

[0006] In view of the above shortcomings and deficiencies in the prior art, the present application provides a lithium ion battery capacity prediction method, comprising the following steps:

[0007] Step S01, obtaining lithium ion battery data to obtain a battery capacity sequence;

[0008] Step S02, normalizing and VMD preprocessing the battery capacity sequence obtained in S01 as the model input data set, and dividing the model input data set into a test data set and a training data set;

[0009] The VMD preprocessing based on the adaptive mode selection mechanism of the MAPE criterion performs multi-scale decomposition on the battery capacity sequence obtained in S01 to obtain the intrinsic mode function IMF of the optimal decomposition mode number k;

[0010] Specifically, it comprises:

[0011] S201, setting the initial parameter mode number k of VMD and the maximum number of iterations, and decomposing the battery capacity sequence into a plurality of intrinsic mode functions IMF through the VMD algorithm;

[0012] S202, calculating the MAPE value of the mode number k and k+1 times, and the mathematical model is:

[0013] ;

[0014] Wherein, N is the number of battery capacity sequence, f is the battery capacity sequence; and represents the superposition of the intrinsic mode function IMF obtained by VMD decomposition;

[0015] S203, calculating the difference D between the MAPE obtained by the kth and k+1th decomposition;

[0016] ;

[0017] Wherein, D is the difference index, is the MAPE value under the kth decomposition, is the MAPE value under the k+1th decomposition;

[0018] S204, judging the value of D, if D<=0.0002, output the current optimal modal number k; otherwise, increase k by 1, iterate to the maximum iteration number, and output the k value at this time as the current optimal modal number;

[0019] Step S03, the white whale optimization algorithm WOA is improved, the adaptive step size Gaussian walking strategy is introduced to update the position of the whale individual, the auxiliary correction strategy is introduced to update the position of the leader whale, the differential evolution strategy is introduced to make the whale population perform mutation, crossover and selection operations in turn, the optimal position of the whale individual is updated, and the improved white whale optimization algorithm IWOA is obtained;

[0020] Step S04, the improved white whale optimization algorithm IWOA is used to optimize the key parameters of the long short-term memory network LSTM, and an IWOA-LSTM capacity prediction model is constructed;

[0021] Step S05, the training data set in step S02 is used to train the IWOA-LSTM capacity prediction model in step S04, and the optimal parameters are output, and a VMD-IWOA-LSTM capacity prediction model is constructed;

[0022] Step S06, the test data set in step S02 is used as the input of the VMD-IWOA-LSTM capacity prediction model trained in step S05, and the life of the lithium battery is predicted.

[0023] The normalization processing in the step S02 is to normalize the data to the interval [0, 1] by using the MinMaxScaler function in Python. The input of the model in S06 step is processed by inverse normalization.

[0024] The position update formula of the whale individual position updated by introducing the adaptive step size Gaussian walking strategy in the step S03 is represented as:

[0025] ;

[0026] ;

[0027] Wherein, represents the current step size; t is the current iteration round; is the maximum allowed iteration number; is the step size adjustment coefficient; represents a random variable conforming to the normal distribution; A represents the dimension of the problem; x is the position vector of the i-th individual in the population; i is the individual number;

[0028] The position update formula of the leader whale position updated by introducing the auxiliary correction strategy is represented as:

[0029] ;

[0030] wherein, is the 2nd optimal whale position, is the current leader whale, if the generated new position is more optimal, it will be taken as the new leader whale individual;

[0031] The differential evolution strategy is introduced to make the whale population perform mutation, crossover and selection operations in turn, and update the optimal position of the whale individual, wherein the mutation operation formula is represented as:

[0032] ;

[0033] is a mutation vector; indicate three non-repeated individual indexes randomly selected in the population; a scaling factor F ∈ (0, 1) is a constant parameter for controlling the amplitude of the differential vector, and is used for adjusting the influence degree of the difference between individuals;

[0034] After the mutation operation is completed, in order to generate a new candidate solution, the current individual and the corresponding mutation vector are required to perform a binary crossover operation, so as to obtain an experimental vector ; the crossover process can be represented as follows:

[0035] ;

[0036] is an integer randomly selected in the index set , and is used for ensuring that the mutation vector has at least one dimension introduced into the experimental vector; a crossover probability is a constant defined in the interval , and is used for controlling the information fusion degree between the mutation and the original individual;

[0037] In the selection stage, a tournament strategy is adopted to perform winner screening between the experimental vector and the original individual , and the individual with better fitness is selected as the next generation individual by comparing the objective function values corresponding to the two individuals, and the selection operation can be represented as follows: ;

[0038] indicates the objective function corresponding to the optimization problem to be solved, and is used for evaluating the fitness or target value of the individual.

[0039] Compared with the prior art, the present application has the following beneficial technical effects and advantages:

[0040] The application carries out pretreatment on lithium battery data through VMD, carries out multi-scale decomposition on the battery capacity sequence based on the adaptive mode selection mechanism of MAPE criterion, obtains the intrinsic mode function (IMF) of the optimal decomposition mode number, introduces the adaptive step Gauss walk strategy to update the position of the whale individual, introduces the auxiliary correction strategy to update the position of the leader whale, introduces the differential evolution strategy to make the whale population carry out mutation, crossover and selection operations in turn to improve the white whale optimization algorithm (WOA), enhance the global search ability, the accuracy and efficiency in local development, avoid the singleness of the population, have higher applicability to different algorithm parameters, and improve the robustness of the algorithm and the accuracy of the final solution. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 The flowchart of step S02 of the application is shown in the figure;

[0042] Figure 2 The battery life prediction flowchart based on the VMD-IWOA-LSTM model of the application is shown in the figure;

[0043] Figure 3 The MAPE change trend graph under different mode numbers of the application is shown in the figure;

[0044] Figure 4 The battery life prediction curve graph of the 70% training set of the B05 battery under different models of the application is shown in the figure;

[0045] Figure 5 The evaluation index error comparison graph of the 70% training set of the B05 battery under different models of the application is shown in the figure;

[0046] Figure 6 The battery life prediction curve graph of the 60% training set of the B05 battery under different models of the application is shown in the figure;

[0047] Figure 7 The evaluation index error comparison graph of the 60% training set of the B05 battery under different models of the application is shown in the figure. DETAILED DESCRIPTION

[0048] The application will be described in detail below, but the protection scope of the application is not limited by the drawings.

[0049] The application provides a lithium ion battery capacity prediction method, as shown in Figure 1 and 2 , comprising the following steps:

[0050] Step S01, collect a certain lithium-ion battery life data set, which is collected under constant ambient temperature (about 24 ℃) and is obtained by performing a charge-discharge cycle test on a cylindrical 18650 type lithium-ion battery with a nominal capacity of 2.0 Ah. The charging stage adopts the constant current-constant voltage (CC-CV) mode: first, charge at a constant current of 1.5 A to 4.2 V, then switch to constant voltage mode to maintain a voltage of 4.2 V until the charging current decays to 20 mA; the discharge stage adopts a constant current discharge strategy, the current is 2.0 A, and is terminated when the battery terminal voltage drops to 2.7 V (B0005), 2.5 V (B0006) and 2.2 V (B0007) respectively, obtaining a battery capacity sequence.

[0051] Step S02, normalize the battery capacity sequence obtained in S01 and perform VMD preprocessing, and the model input data set is divided into test data set and training data set;

[0052] When input to the network model for training, the input and output features have different dimensions and scales, so the data needs to be normalized. The MinMaxScaler function in Python is used to normalize the data to the [0, 1] interval, and the input of the model in step S06 is normalized.

[0053] The VMD algorithm includes five key parameters: input signal (i.e. battery capacity sequence), modal number k, penalty factor α, noise tolerance τ, and convergence threshold ε. Parameters α, τ, ε are often taken as empirical values (such as α=100, τ=0, ε= ), compared with the modal number k, which is the key to optimizing the decomposition result, as shown in the MAPE trend chart under different modal numbers. Figure 3

[0054] When k is too small, different frequency components in the signal may be mixed into the same mode, resulting in impure decomposition results and limited expression ability; on the contrary, if k is too large, the signal will be over-decomposed, and the information originally belonging to a single mode will be split into multiple redundant or repeated sub-modes, thereby introducing redundant features and causing the "information pollution" phenomenon. In order to overcome this problem, this paper first proposes an improved VMD method, taking the mean absolute percentage error (MAPE) as the evaluation index, and through iterative search, the modal number k is adaptively converged to the optimal value, so as to realize high-quality modal decomposition.

[0055] The VMD preprocessing based on the adaptive modal selection mechanism of the MAPE criterion performs multi-scale decomposition on the battery capacity sequence obtained in S01 to obtain the intrinsic modal function IMF of the optimal decomposition modal number k.

[0056] ​In particular, comprising:

[0057] S201, set the initial parameter modal number k of VMD and the maximum iteration number, decompose the battery capacity sequence into a plurality of intrinsic mode functions IMF through the VMD algorithm.

[0058] S202, calculate the MAPE values of the modal numbers k and k+1, and the mathematical model is:

[0059] ;

[0060] Wherein, N is the number of battery capacity sequence, f is the battery capacity sequence; and Indicates the superposition of the intrinsic mode function IMF obtained by VMD decomposition.

[0061] S203, find the difference D between the MAPE obtained by the kth and k+1th decomposition;

[0062] ;

[0063] Wherein, D is the difference index, is the MAPE value under the kth decomposition, is the MAPE value under the k+1th decomposition.

[0064] S204, judge the value of D, if D<=0.0002, output the current optimal modal number k; otherwise, increase k by 1, iterate to the maximum iteration number, and output the k value at this time as the current optimal modal number.

[0065] In this embodiment, the three batteries B05, B06 and B07 are subjected to variational mode decomposition VMD, the initial modal number k is set to 2, and the maximum iteration number is set to 5.

[0066] Table 1 difference in MAPE under different iteration numbers:

[0067] .

[0068] As shown in Table 1, it can be seen that the B05 and B07 batteries satisfy the algorithm termination condition at the 4th iteration, and the B06 battery reaches convergence at the 5th iteration. Therefore, the finally determined VMD optimal modal component number is: B05 battery is 4 modes, B06 battery is 5 modes, and B00 battery is 4 modes.

[0069] Step S03, the white whale optimization algorithm WOA is improved, the adaptive step size Gaussian walk strategy is introduced to update the position of the whale individual, the auxiliary correction strategy is introduced to update the position of the leader whale, the differential evolution strategy is introduced to make the whale population perform mutation, crossover and selection operations in turn, the optimal position of the whale individual is updated, and the improved white whale optimization algorithm IWOA is obtained.

[0070] Specifically, the adaptive step size Gaussian walk strategy is an algorithm method suitable for continuous optimization problems. The strategy generates a random step size through Gaussian distribution, and dynamically adjusts the size of the step size according to the current optimization state, so as to effectively balance the exploration and utilization capabilities.

[0071] The adaptive step size Gaussian walk strategy is introduced to update the position of the whale individual, and the update formula is represented as:

[0072] ;

[0073] ;

[0074] Wherein, step represents the current step size; t is the current iteration round; is the maximum allowed number of iterations; is the step size adjustment coefficient; rand represents a random variable conforming to the normal distribution; A represents the dimension of the problem; x is the position vector of the i-th individual in the population; i is the individual number.

[0075] The Gaussian walk step size is dynamically adjusted according to the current iteration number and the optimal solution fitness: a larger step size is used in the early stage of the algorithm, so that the individual can search the solution space in a larger range and improve the global exploration ability; a smaller step size is used in the later stage of the algorithm, so as to carry out fine search near the high-quality solution and improve the local development ability. The disturbance vector generated by the Gaussian distribution makes the whale individual produce a certain random offset near the current position, which can effectively prevent the population from falling into local optimum and accelerate the convergence speed.

[0076] In the whale optimization algorithm, the leader whale represents the optimal individual in the current population. In order to assist the position update and improve the optimization effect, the second whale is designed to optimize and adjust the position of the leader whale in each dimension. The fitness of the second whale in the population is lower than that of the leader whale, and the strategy aims to accelerate the convergence speed of the whole population. The update formula of the position of the leader whale updated by the auxiliary correction strategy is represented as:

[0077] ;

[0078] Wherein, is the position of the second whale, is the current leader whale, if the new position generated is better, it will be used as the new leader whale individual.

[0079] The strategy selects several elite individuals with the best fitness in each iteration, and uses their position vectors to correct the positions of common individuals, guiding the population to converge to the high-quality solution region. In the correction process, the guiding degree is controlled by combining a random weight factor, which maintains the exploration of the global space and accelerates the convergence to the optimal solution. This method can fully utilize the information of high-quality individuals, shorten the convergence time, and improve the solution quality.

[0080] The difference is introduced into the population by relying on the bionic strategy, prompting the individual to jump out of the current region, thereby effectively avoiding the risk of falling into local optimum. To improve the ability of WOA to jump out of local optimum and expand the search space, the differential evolution mechanism is integrated into the WOA framework.

[0081] The introduction of the differential evolution strategy enables the whale population to perform mutation, crossover and selection operations in turn, updating the optimal position of the whale individual, wherein the mutation operation formula is represented as:

[0082] ;

[0083] is the mutation vector; , wherein i represents the index of the current individual in the population; the scaling factor F∈(0, 1) is a constant parameter for controlling the amplitude of the differential vector, which is used to adjust the influence degree of the difference between individuals.

[0084] After completing the mutation operation, a new candidate solution needs to be generated by performing binary crossover operation on the current individual and its corresponding mutation vector , thereby obtaining the experimental vector ; the crossover process can be represented as follows: ;

[0085] is a random integer selected from the index set , which is used to ensure that at least one dimension of the mutation vector is introduced into the experimental vector; the crossover probability is a constant defined in the interval , which is used to control the information fusion degree between the mutation and the original individual;

[0086] In the selection stage, the tournament strategy is used to select the winner between the experimental vector and the original individual , and the individual with better fitness is selected as the next generation individual by comparing the objective function values corresponding to the two individuals, and the selection operation can be represented as follows: ;

[0087] Indicates the objective function corresponding to the optimization problem to be solved, used to evaluate the fitness or target value of the individual.

[0088] The strategy increases the diversity of the population and the variability of the search direction by selecting several different individuals, calculating their difference vectors and adding them to the base vector to generate a new solution. The crossover and mutation mechanism of differential evolution enables the newly generated solution to have strong ability to jump out of local optimum. In the iteration process of WOA, the differential evolution strategy can continuously provide potential high-quality solutions in the global range, improving the robustness of the algorithm and the accuracy of the final solution.

[0089] Step S04, the improved white whale optimization algorithm IWOA is used to optimize the key parameters of the long short-term memory network LSTM, and an IWOA-LSTM capacity prediction model is constructed;

[0090] Step S05, the training data set in step S02 is used to train the IWOA-LSTM capacity prediction model in step S04, and the optimal parameters are output, and a VMD-IWOA-LSTM capacity prediction model is constructed;

[0091] Step S06, the test data set in step S02 is used as the input of the VMD-IWOA-LSTM capacity prediction model trained in step S05, and the life of the lithium battery is predicted.

[0092] To verify the effectiveness of VMD-IWOA-LSTM, the present application compares and analyzes it with LSTM, VMD-LSTM, WOA-LSTM and CNN-LSTM models.

[0093] As Figure 4 and 5 The B05 battery 70% training set battery life prediction result curve and error comparison diagram is shown in FIGS. 1 and 2, and the prediction accuracy of the classical LSTM model is the lowest: the root mean square error (RMSE) of the B05 battery is 3.00%, the mean absolute percentage error (MAPE) is 1.43%, and the mean absolute error (MAE) is 2.03%. Although the RUL prediction performance of VMD-LSTM is better than that of LSTM, the error fluctuation is large. In contrast, the VMD-IWOA-LSTM model proposed in this paper shows significant advantages: the root mean square error (RMSE) of the B05 battery is only 1.09%, the mean absolute percentage error (MAPE) is as low as 0.54%, and the mean absolute error (MAE) is reduced to 0.85%. In summary, the prediction error of VMD-IWOA-LSTM is the smallest, and the predicted value is most consistent with the true value.

[0094] As Figure 6 and 7The B05 battery 60% training set battery life prediction result curve and error comparison chart are shown, the prediction accuracy of the classic LSTM model is the lowest: the root mean square error (RMSE) of the B05 battery is 3.00%, the mean absolute error (MAE) is 2.03%, and the mean absolute percentage error (MAPE) is 2.01%. The VMD-IWOA-LSTM model proposed in the application shows obvious advantages: the root mean square error (RMSE) of the B05 battery is only 2.24%, the mean absolute percentage error (MAPE) is as low as 1.57%, and the mean absolute error (MAE) is reduced to 1.03%. In summary, the prediction effect of the VMD-IWOA-LSTM is the best, which reflects that the application has good robustness.

[0095] The application pre-processes the lithium battery data by the variational modal decomposition VMD, performs multi-scale decomposition on the battery capacity sequence based on the self-adaptive modal selection mechanism of the MAPE criterion, obtains the intrinsic modal function IMF of the optimal number of decomposition modes, introduces the adaptive step Gaussian walk strategy to update the position of the whale individual, introduces the auxiliary correction strategy to update the position of the leader whale, introduces the differential evolution strategy to make the whale population perform mutation, crossover and selection operations in turn to improve the whale optimization algorithm WOA, enhance the global search ability, and the accuracy and efficiency in local development, avoid the singleness of the population, have higher applicability to different algorithm parameters, and improve the robustness of the algorithm and the accuracy of the final solution.

[0096] Although the embodiments of the application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the application, and any modification, modification, replacement and modification of the above embodiments by those skilled in the art are within the scope of the application.

[0097] The above is only the preferred embodiment of the application, and does not limit the application, any modification, equivalent replacement, improvement, etc. within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. A method of predicting the capacity of a lithium-ion battery, characterized by, The method comprises the following steps: Step S01, obtaining lithium ion battery data to obtain a battery capacity sequence; Step S02, performing normalization processing and VMD preprocessing on the battery capacity sequence obtained in S01, taking the data set as the model input, and dividing the model input data set into a test data set and a training data set; The VMD preprocessing is based on an adaptive mode selection mechanism of the MAPE criterion to perform multi-scale decomposition on the battery capacity sequence obtained in S01 to obtain an intrinsic mode function IMF of the optimal decomposition mode number k; Specifically, the method comprises the following steps: S201, setting the initial parameter mode number k of VMD and the maximum number of iterations, and decomposing the battery capacity sequence into a plurality of intrinsic mode functions IMF through the VMD algorithm; S202, calculating the MAPE values of the mode numbers k and k+1, and the mathematical model is: ； Wherein, N is the number of battery capacity sequences, f is the battery capacity sequence; and represents the superposition of the intrinsic mode functions (IMFs) obtained by VMD decomposition. S203, calculating the difference D between the MAPE values obtained by the kth and k+1th decompositions; ； wherein D is a difference indicator, MAPEk is the MAPE value at the kth decomposition, MAPEk+1 is the MAPE value at the k+1th decomposition; S204, judging the value of D, if D<=0.0002, output the current optimal mode number k; otherwise, increase k by 1, iterate to the maximum number of iterations, and output the k value at this time as the current optimal mode number; Step S03, improving the WOA algorithm, introducing an adaptive step Gaussian walk strategy to update the position of the whale individual, introducing an auxiliary correction strategy to update the position of the leader whale, and introducing a differential evolution strategy to make the whale population perform mutation, crossover and selection operations in turn, update the optimal position of the whale individual, and obtain the improved IWOA algorithm; Step S04, optimizing the key parameters of the LSTM network by using the improved IWOA algorithm, and constructing an IWOA-LSTM capacity prediction model; Step S05, training the IWOA-LSTM capacity prediction model in step S04 by using the training data set in step S02, outputting the optimal parameters, and constructing a VMD-IWOA-LSTM capacity prediction model; Step S06, taking the test data set in step S02 as the input of the VMD-IWOA-LSTM capacity prediction model trained in step S05 to predict the life of the lithium battery.

2. The method of claim 1, wherein: The normalization processing in the step S02 is to normalize the data to The input of the model in the step S06 is subjected to the inverse normalization processing.

3. The method of claim 1, wherein: The update formula of the position of the whale individual updated by introducing the adaptive step Gaussian walk strategy in step S03 is represented as: ； ； wherein, denotes the current step size; t is the current iteration round; is the maximum allowed number of iterations; is the step size adjustment coefficient; denotes a random variable following a normal distribution; A represents the dimension of the problem; x is the position vector of the i-th individual in the population; i is the individual number; The update formula of the position of the leader whale updated by introducing the auxiliary correction strategy is represented as: ； wherein, is the 2nd best whale position, is the current lead whale, if the generated new position is better, make it the new lead whale individual; The differential evolution strategy is introduced to make the whale population perform mutation, crossover and selection operations in turn, and update the optimal position of the whale individual, wherein the mutation operation formula is represented as: ； is a mutation vector; denotes the indices of three non-repeated individuals randomly selected in the population; the scaling factor F ∈ (0, 1) is a constant parameter controlling the amplitude of the difference vector, used to adjust the influence degree of the difference between individuals; After the mutation operation is completed, to generate a new candidate solution, the current individual a mutation vector corresponding thereto a binary crossover operation is performed, thereby obtaining an experimental vector The crossover process can be represented as follows: ； is a random integer selected from the index set to ensure that the mutation vector has at least one dimension introduced into the trial vector; crossover probability is a constant defined in the interval to control the degree of information fusion between the mutation and the original individual; In the selection stage, a tournament strategy is adopted to perform winner screening between the experimental vector and the original individual , and the individual with better fitness is selected as the next generation individual by comparing the objective function values of the two individuals. The selection operation can be expressed as follows: ; represents an objective function corresponding to the optimization problem sought, used to evaluate the fitness or objective value of an individual.

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