Radar array sparse optimization method based on improved fireworks algorithm

Abstract

The invention discloses a radar array sparse optimization method based on an improved fireworks algorithm, and relates to the field of radar communication. The method comprises the following steps: firstly, setting parameters such as an array radius and an array element number, initializing a firework population and calculating an initial fitness value; and then, judging whether a termination condition is met or not, and if not, entering iteration. In the iteration process, a spark individual exploration solution space is generated through explosion operation, and mutation operation is carried out on sparks to expand the diversity of solutions. And meanwhile, a simulated annealing mechanism is combined, the probability of inferior solution receiving is controlled according to the temperature, local optimum is avoided, and the global search capability is enhanced. And finally, the next generation of firework population is optimized through selection operation, iterative optimization is continuously carried out, and the optimal solution is output until the termination condition is met. According to the method, initialization and explosion strategies of the firework algorithm are improved, a simulated annealing mechanism is combined, the global optimization capability is improved, the sidelobe level and the number of array elements are reduced, the system performance is optimized, and the hardware cost and the calculation complexity are remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of radar communication, and specifically to a method for sparse optimization of a radar array based on an improved fireworks algorithm. Background Art

[0002] Compared with traditional phased array radar technology, multiple-input multiple-output (MIMO) radar can effectively form a larger observation aperture and a higher sampling density by virtue of its excellent spatial diversity, frequency diversity, and waveform diversity characteristics. These advantages are of great significance in reducing the influence of clutter and noise, expanding the virtual array element aperture, optimizing target detection and tracking performance, and improving direction-finding resolution and direction-finding accuracy. However, the existing array configurations usually adopt common topological structures such as uniform linear arrays, parallel linear arrays, or uniform circular arrays. The multiple transmit and receive system often increases the system complexity, which restricts the engineering and practical application processes of radar systems. In contrast, sparse arrays significantly increase the virtual degrees of freedom by increasing the element spacing, while suppressing the mutual coupling effect, reducing the noise coherence, and effectively reducing resource waste by relying on their low redundancy characteristics, thereby significantly improving the calculation efficiency.

[0003] Common non-uniform arrays include minimum redundancy arrays, nested arrays, co-prime arrays, etc. These array forms have received extensive attention in array design due to their unique structural characteristics. The minimum redundancy array aims to reduce redundant array elements and achieve a higher degree of freedom with as few array elements as possible, but it lacks a general closed-form expression and has a high design complexity; the nested array achieves a high degree of freedom through the nested structure of sub-arrays, but the existence of dense sub-arrays is likely to lead to performance limitations; the co-prime array improves the virtual aperture and resolution ability through specific element spacing relationships, but array holes may appear, affecting the performance consistency. Therefore, in practical applications, sparse arrays need to be further optimized to achieve the optimal layout design of non-uniform arrays, so as to better meet the actual needs.

[0004] Jiao Yongchang et al. applied the particle swarm optimization algorithm to the antenna pattern synthesis problem and gave application examples. Zhang Wei et al. applied the simulated annealing method to the sparse array optimization problem of MIMO radar. With the sidelobe level of the virtual transceiver combined beam as the optimization target, by optimizing the positions of the transmit and receive array elements, good sidelobe levels were achieved without broadening the main lobe. According to the existing technical literature, traditional intelligent optimization algorithms such as simulated annealing algorithms, genetic algorithms, and particle swarm optimization algorithms have been widely applied to array optimization problems and achieved a series of good results, but there are still problems such as being prone to falling into local optima and having a slow convergence speed.

[0005] Therefore, an array optimization method that can quickly perform the layout of sparse antenna array elements and effectively suppress the maximum sidelobe is needed. Summary of the Invention

[0006] Aiming at the disadvantages of slow convergence speed and easy convergence to local optimum of existing stochastic optimization methods, the fireworks algorithm combines the advantages of particle swarm optimization and genetic algorithm based on an explosion-based search mechanism, and introduces the idea of immune concentration, enabling the fireworks population to be more evenly distributed in different regions, avoiding aggregation phenomena, and reducing the probability of falling into local optimum solutions. However, there are still problems such as uneven distribution of the initial population and insufficient pertinence of the spark generation strategy in the traditional fireworks algorithm for discrete optimization problems. A radar array sparse optimization method based on an improved fireworks algorithm disclosed in the present invention significantly enhances the global search ability and convergence performance of the algorithm by combining a simulated annealing mechanism. Specific improvement measures include: using the Sobol sequence to generate the initial population to improve the uniform distribution of the population; adjusting the spark generation strategy according to the discrete characteristics of the array optimization problem to make it more suitable for the layout optimization of sparse arrays. While ensuring the convergence speed of sparse array optimization, the improved algorithm can effectively suppress the maximum sidelobe of the array, reduce the working cost and computational amount of the antenna system, and improve the overall performance.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A radar array sparse optimization method based on an improved fireworks algorithm, the method steps are as follows:

[0009] Step 1: Set parameters such as the array radius and the number of array elements, and initialize the fireworks population;

[0010] Step 2: Set the optimization objective function and calculate the initial fitness value accordingly;

[0011] Step 3: Determine whether the termination condition is satisfied. If it is satisfied, the algorithm terminates and outputs the optimized sparse array design scheme; otherwise, go to Step 4;

[0012] Step 4: Enter the iterative loop, perform the explosion operation, and generate sparks through the explosion;

[0013] Step 5: Perform the mutation operation, and the fireworks generate sparks through mutation;

[0014] Step 6: Use the simulated annealing mechanism to control the probability of accepting inferior solutions according to the temperature to avoid local optimum;

[0015] Step 7: Select the next generation of fireworks population, update the global fitness value, and go to Step 3;

[0016] As a further solution of the present invention: in the first step, the number of transmitting array elements Nt, the number of receiving array elements Nr, the number of initial populations N, and the number of function evaluations M are set; the dimension of each fireworks individual is set to D; the fireworks population is initialized: the positions of the array elements are binary coded, if there is an array element at this position, it is in the "activated" state and set to 1; if there is no array element at this position, it is in the "dormant" state and set to 0; N D-dimensional "0 / 1" vectors x are randomly initialized. (i) , each x (i) represents a firework, which is formed by concatenating the transmitting sequence and the receiving sequence; to ensure that the array aperture remains unchanged, the first and last positions of the transmitting sequence and the receiving sequence should always be 1. The initialization samples uniformly distributed are generated using the Sobol sequence. For the generated Sobol sequence matrix, the threshold method is used to map real numbers to binary values 0 / 1. To ensure that the transmitting sequence contains Nt - 2 1s at random positions and the receiving sequence contains Nt - 2 1s at random positions, after initialization, check whether the total number of 1s in the transmitting sequence is Nt. If it is insufficient, randomly select the current position that is 0 and set it to 1 until Nt - 2 1s are reached; if it is excessive, randomly select the current position that is 1 and set it to 0 to ensure that the total number is Nt - 2. The same inspection operation is performed on the receiving sequence.

[0017] As a further solution of the present invention: the purpose of optimizing the sparse array of the MIMO radar in the second step is to obtain a better main lobe to sidelobe ratio. Therefore, the optimization objective function is set as:

[0018]

[0019] In the formula, p s,max is the highest value level in the sidelobe region of the radiation pattern; p m,max is the highest value level in the main lobe region; μ start can distinguish the main lobe from the sidelobe and keep the main lobe within a certain range; μ end takes the value of 1.

[0020] As a further solution of the present invention: in the third step, the termination condition is set as the number of function evaluations.

[0021] As a further solution of the present invention: In the explosion operation of step four, in order to adapt to the array optimization problem, the explosion method of the original fireworks algorithm is modified, and the explosion method is defined as: according to the size of the explosion radius of the fireworks, the perturbation interval is dynamically selected in the transmitting and receiving arrays, and the reverse order operation is performed, that is, the order of the array elements in this interval is reversed, that is, the first element and the last element in the interval are exchanged, and so on until all the elements in the interval are reversed; the i-th element to the i + k-th element in the array are perturbed, which is defined as exchanging the i-th element and the i + k-th element, and the i + 1-th element and the i + (k - 1)-th element are exchanged, and so on to complete the perturbation. At the same time, it should be noted that the head and tail positions of the corresponding sequence of the array must always be 1 and do not participate in the position perturbation.

[0022] As a further solution of the present invention: In the mutation operation of step five, in order to adapt to the array optimization problem, the mutation method of the original fireworks algorithm is modified, and the mutation method is defined as: excluding the head and tail, randomly select an integer number of 1s from the remaining positions and modify them to 0; in each mutation, in order to ensure that the number of array elements remains unchanged, an equal number of randomly selected positions of 0 need to be modified to 1 at the same time.

[0023] As a further solution of the present invention: The simulated annealing mechanism introduced in step six enables a poor solution to have a certain probability of being accepted, improving the ability of the fireworks algorithm to jump out of the local optimum. Each time a firework undergoes explosion and mutation, a new candidate solution is generated, and the quality of each candidate solution can be measured by the fitness function. The quality difference of the candidate solution is defined as:

[0024] ΔF = fitness ( old ) -fitness ( new )

[0025] When generating a new candidate solution each time, we calculate the probability of accepting a poor solution according to the quality difference and the current temperature T:

[0026]

[0027] If ΔF ≤ 0 (that is, the new solution is better), directly accept the new solution; if ΔF > 0 (that is, the new solution is worse), then accept this solution with probability P ( ΔF; The probability of accepting a poor solution is controlled by the temperature decay in simulated annealing. As the algorithm iterates, the temperature gradually decreases, and the decay strategy is as follows:

[0028] T k+1 = αT k

[0029] Among them, T kis the current temperature, and α is the attenuation factor (usually taking values from 0.9 to 0.99).

[0030] As a further solution of the present invention: in step seven, according to the criterion that the farther the sum of the distances of a spark compared to other sparks, the greater the chance of being selected, the roulette wheel strategy is used for selection, and then go to step 3.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] 1. The present invention improves the fireworks algorithm. By improving the initialization and explosion strategies of the fireworks algorithm, the solution space is effectively expanded. Combining with the simulated annealing mechanism, the premature convergence problem in the later iteration of the fireworks algorithm is effectively overcome, enabling the algorithm to more comprehensively explore potential high-quality solutions and avoid falling into local optima.

[0033] 2. The optimized sparse array layout significantly reduces the sidelobe level, improves the pattern performance of the array, thereby enhancing the signal resolution ability, and has better iteration speed and optimization effect than the original algorithm;

[0034] 3. On the basis of maintaining the main performance indicators, the optimized algorithm can significantly reduce the number of array elements required, thus simplifying the hardware design. By optimizing the array layout, the hardware resources required for the array are significantly reduced, and the cost of system construction and maintenance is reduced. Brief Description of the Drawings

[0035] Figure 1 is the flow chart of the MIMO radar sparse array optimization method based on the improved fireworks algorithm.

[0036] Figure 2 is the perturbation strategy of the explosion operation of the improved fireworks algorithm.

[0037] Figure 3 is the diagram of the positions of the transmitting array elements and receiving array elements obtained after optimization using the improved fireworks algorithm.

[0038] Figure 4 is the comparison diagram of the virtual transceiver directions obtained after optimization using different algorithms.

[0039] Figure 5 is the comparison diagram of the fitness value changes of different algorithms based on Monte Carlo experiments.

[0040] Figure 6 is the comparison diagram of the global fitness value changes of different algorithms during the optimization process. Detailed Embodiments

[0041] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with 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, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0042] Please refer to Figures 1 to 6 , in an embodiment of the present invention, a method for sparse optimization of a radar array based on an improved fireworks algorithm has the following method steps:

[0043] Step 1: Set the number of transmitting array elements Nt, the number of receiving array elements Nr, the number of initial populations N, and the number of function evaluations M; set the dimension of each fireworks individual to D; initialize the fireworks population: perform binary encoding on the array element positions. If there is an array element at this position, it is in the "activated" state and set to 1; if there is no array element at this position, it is in the "dormant" state and set to 0; randomly initialize N D-dimensional "0 / 1" vectors x( i ), each x( i ) represents a firework, which is formed by concatenating the transmitting sequence and the receiving sequence; to ensure that the array aperture remains unchanged, the first and last positions of the transmitting sequence and the receiving sequence should always be 1. Use the Sobol sequence to generate uniformly distributed initialization samples. For the generated Sobol sequence matrix, use the threshold method to map real numbers to binary values 0 / 1. To ensure that the transmitting sequence contains Nt - 2 1s at random positions and the receiving sequence contains Nr - 2 1s at random positions, after initialization, check whether the total number of 1s in the transmitting sequence is Nt. If it is insufficient, randomly select the current position that is 0 and set it to 1 until Nt - 2 1s are reached; if there are too many, randomly select the current position that is 1 and set it to 0 to ensure that the total number is Nt - 2. The receiving sequence also performs the above check operation.

[0044] Step 2: The purpose of optimizing the sparse array of the MIMO radar is to obtain a better main lobe to sidelobe ratio. Therefore, the optimization objective function is set as:

[0045]

[0046] In the formula, p s,max is the highest value level in the sidelobe region of the radiation pattern; p m,max is the highest value level in the main lobe region; the value of μ start can distinguish the main lobe from the sidelobe and keep the main lobe within a certain range. During simulation, set μ start = 0.04; the value of μ end is 1.

[0047] Step 3: Determine whether the termination condition is met. If it is, terminate the algorithm and output the optimized sparse array design scheme; otherwise, go to Step 4 and set the termination condition as the number of function evaluations.

[0048] Step 4: Figure 2 It is a schematic diagram of the element perturbation for the explosion operation. When performing the explosion operation, first calculate the number of sparks and the explosion radius according to the fitness value. The number of sparks S i and the explosion radius A i The expressions are:

[0049]

[0050] where M and A respectively limit the maximum number of sparks and the maximum explosion radius; f ( x i) represents the fitness value of the firework; Y max and Y min respectively represent the worst and the best fitness values of the fireworks; ε is a very small constant to avoid the invalidation of the formula, with an order of magnitude of about 1e - 15; N is the total number of fireworks.

[0051] To ensure that the number of sparks in excellent fireworks is not too large to cause waste of resources due to duplicate solutions, and the number of sparks in ordinary fireworks is not too small to affect the diversity of the algorithm, it is necessary to reasonably limit the number of sparks. The corrected expression is:

[0052]

[0053] where is the corrected number of sparks; a and b are given constants; round represents the rounding function.

[0054] When performing the explosion operation, to adapt to the array optimization problem, the explosion method of the original fireworks algorithm is modified. The explosion method is defined as: according to the size of the explosion radius of the firework, dynamically select the perturbation interval in the transmitting and receiving arrays, and perform the reverse order operation, that is, reverse the order of the elements in this interval, that is, exchange the positions of the first and the last elements in the interval, and so on until all the elements in the interval are reversed; the perturbation of the i - th element to the (i + k)-th element in the array is defined as exchanging the positions of the i - th element and the (i + k)-th element, and the (i + 1)-th element and the (i+(k - 1))-th element, and so on to complete the perturbation. At the same time, it should be noted that the first and the last positions of the corresponding sequence of the array must always be 1 and do not participate in the position perturbation.

[0055] Step 5: When performing the mutation operation, to adapt to the array optimization problem, the mutation method of the original fireworks algorithm is modified. The mutation method is defined as follows: After excluding the first and last elements, randomly select an integer number of 1s from the remaining positions and modify them to 0; in each mutation, to ensure that the number of array elements remains unchanged, an integer number of randomly selected positions of 0 need to be modified to 1 at the same time.

[0056] When generating sparks through the explosion and mutation operations in Step 4 and Step 5, it is necessary to check whether the new solution is within the specified range. If it exceeds the specified range, according to the mapping rule, map the solution outside the feasible region back into the feasible region; after completing the explosion and mutation operations, it is necessary to check the number of activated array elements in the sparks (the first and last array elements should always be in the activated state). If the number is less than or more than the set number of array elements, close or open them to meet the requirements of the number of array elements.

[0057] Step 6: The simulated annealing mechanism enables a relatively poor solution to have a certain probability of being accepted, improving the ability of the fireworks algorithm to jump out of the local optimum. Each time a firework undergoes explosion and mutation, a new candidate solution is generated. The quality of each candidate solution can be measured by the fitness function. The quality difference of the candidate solutions is defined as:

[0058] ΔF = fitness(old) - fitness(new )

[0059] When generating a new candidate solution each time, we calculate the probability of accepting a relatively poor solution based on the quality difference and the current temperature T:

[0060]

[0061] If ΔF ≤ 0 (i.e., the new solution is better), directly accept the new solution; if ΔF > 0 (i.e., the new solution is worse), then accept this solution with probability P ( ΔF; control the probability of accepting a relatively poor solution through the temperature decay in simulated annealing. As the algorithm iterates, the temperature gradually decreases, and the decay strategy is as follows:

[0062] T k+1 = αT k

[0063] where, T k is the current temperature, and α is the decay factor (usually taking values from 0.9 to 0.99).

[0064] Step 7: After retaining the optimal individual, according to the criterion that the farther the sum of the distances of a spark is from other sparks, the greater the chance of being selected, use the roulette wheel strategy for selection to form the next generation of fireworks population, and at the same time update the global fitness value, then go to Step 3.

[0065] The effects of the present invention can be further illustrated by the following simulation experiments.

[0066] Set up a typical MIMO array: the number of transmitting array elements \(N_t = 16\), arranged on the grid at integer multiples of half-wavelength within the range of \(0\sim32\lambda\); the number of receiving array elements \(N_r = 8\), arranged on the grid at integer multiples of half-wavelength within the range of \(0\sim16\lambda\); the initial population number \(N = 20\), the number of function evaluations \(10000\), the correlation coefficient of explosion intensity is \(50\), the maximum number of explosion sparks is \(20\), the minimum number of explosion sparks is \(2\), the number of mutation sparks is \(10\), the explosion radius coefficient of the transmitting array is \(14\), and the explosion radius coefficient of the receiving array is \(6\); conduct 100 Monte Carlo experiments.

[0067] As shown in the appendix Figures 3 to 6 shown, where;

[0068] Figure 3 represents the map of the positions of the transmitting array elements and the receiving array elements obtained after optimization using the improved fireworks algorithm.

[0069] The finally optimized array element positions: \(0\ 5\ 9\ 15\ 19\ 21\ 22\ 24\ 25\ 30\ 34\ 39\ 53\ 57\ 62\ 64\ 0\ 7\ 12\ 13\ 14\ 18\ 25\ 32\)

[0070] Figure 4 represents the comparison diagram of the virtual transceiver directions obtained after optimization using the fireworks algorithm, the simulated annealing algorithm, and the improved fireworks algorithm. It can be seen from the figure that the fireworks algorithm, the simulated annealing algorithm, and the improved fireworks algorithm all have a relatively narrow main lobe width, but the peak sidelobe level corresponding to the improved fireworks algorithm is lower than that of the fireworks algorithm and the simulated annealing algorithm. The improved fireworks algorithm can optimize the peak sidelobe level to \(-23.81151\ dB\), while the fireworks algorithm and the simulated annealing algorithm are \(-21.50994\ dB\) and \(-22.12885\ dB\) respectively. Compared with the fireworks algorithm and the simulated annealing algorithm, the maximum sidelobe is reduced by \(2.30157\ dB\) and \(1.68266\ dB\).

[0071] Figures 5 to 6 shows the change curves of the fitness values of different algorithms during the entire iteration process, as well as the average fitness change curve obtained from 100 Monte Carlo experiments. It can be observed that compared with the fireworks algorithm and the simulated annealing algorithm, the improved fireworks algorithm achieves the lowest maximum sidelobe and a faster convergence speed than the fireworks algorithm and the simulated annealing algorithm. This shows that the improved fireworks algorithm is more efficient, has a stronger ability to jump out of local optima, and has better performance. Moreover, in the initial iteration of the improved fireworks algorithm, the fitness curve drops faster, indicating that it has a higher optimization speed.

Claims

1. A radar array sparse optimization method based on an improved fireworks algorithm, characterized in that: The improved fireworks algorithm combined with simulated annealing mechanism is adopted, the initial population is generated using the sobol sequence, and some appropriate changes are made to the way the explosion strategy generates sparks in view of the discrete characteristics of the array optimization problem; the steps of this method include the following: Step 1: Set the array radius, number of elements and other parameters to initialize the fireworks population; Step 2: Set the optimization objective function and calculate the initial fitness value based on it; Step 3: Determine whether the termination condition is met. If so, the algorithm terminates and outputs the optimized sparse array design solution. Otherwise, proceed to step 4. Step 4: Enter the iterative loop, perform the explosion operation, and generate sparks through the explosion; Step 5: Perform mutation operation, fireworks generate sparks through mutation; Step 6: Use simulated annealing mechanism to control the probability of accepting inferior solutions according to temperature to avoid local optimality; Step 7: Select the next generation of fireworks population, update the global fitness value, and go to step 3.

2. The radar array sparse optimization method based on the improved fireworks algorithm according to claim 1, characterized in that: In the step 1, the number of transmitting array elements Nt, the number of receiving array elements Nr, the number of initial populations N, and the number of function evaluations M are set; the dimension of each firework individual is set to D; the firework population is initialized: the array element position is binary-coded, and if there is an array element at this position, it is in the "activated" state and is set to 1; if there is no array element at this position, it is in the "dormant" state and is set to 0; N D-dimensional "0 / 1" vectors x( i ), each x( i ) represents a firework, which is composed of a transmitting sequence and a receiving sequence connected in series; to ensure that the array aperture remains unchanged, the first and last positions of the transmitting sequence and the receiving sequence must always be 1, and the Sobol sequence is used to generate uniformly distributed initialization samples. For the generated Sobol sequence matrix, the threshold method is used to map real numbers to binary values ​​0 / 1. To ensure that the transmitting sequence contains Nt-2 1s at random positions and the receiving sequence contains Nt-2 1s at random positions, after completing the initialization, check whether the total number of 1s in the transmitting sequence is Nt. If it is less than Nt, randomly select the position that is currently 0 and set it to 1 until it reaches Nt-2 1s; If there are too many, randomly select the position that is currently 1 and set it to 0 to ensure that the total number is Nt-2. The receiving sequence is also checked as above.

3. The radar array sparse optimization method based on the improved fireworks algorithm according to claim 1, characterized in that: The purpose of the MIMO radar sparse array optimization in step 2 is to obtain a better main-sidelobe ratio, so the optimization objective function is set to: In the formula, p s,max is the maximum level in the sidelobe area of ​​the pattern; p m,max is the highest level in the main lobe area; μ start The value of can distinguish the main lobe from the side lobe and keep the main lobe within a certain range; end The value is 1.

4. The radar array sparse optimization method based on the improved fireworks algorithm according to claim 1, characterized in that: In step three, the termination condition is set to the number of function evaluations.

5. The radar array sparse optimization method based on the improved fireworks algorithm according to claim 1, characterized in that: In the step 4, when performing the explosion operation, in order to adapt to the array optimization problem, the explosion mode of the original fireworks algorithm is modified, and the explosion mode is defined as: according to the size of the fireworks explosion radius, the perturbation interval is dynamically selected in the transmitting and receiving arrays, and the reverse operation is performed to reverse the order of the array elements in the interval, that is, the first array element and the last array element in the interval are exchanged, and so on, until the array elements in the entire interval are reversed; the i-th array element to the i+k-th array element in the array are perturbed, which is defined as exchanging the i-th array element with the i+k-th array element, the i+1-th array element with the i+(k-1)-th array element, and so on to complete the perturbation. At the same time, it should be noted that the first and last positions of the sequence corresponding to the array must always be 1 and do not participate in the position perturbation.

6. The radar array sparse optimization method based on the improved fireworks algorithm according to claim 1, characterized in that: When performing the mutation operation in step 5, in order to adapt to the array optimization problem, the mutation method of the original fireworks algorithm is modified, and the mutation method is defined as: after excluding the head and the tail, an integer number of 1s are randomly selected from the remaining positions and modified to 0; in each mutation, in order to ensure that the number of array elements remains unchanged, the 0s in the corresponding integer random positions must be modified to 1 at the same time.

7. The radar array sparse optimization method based on the improved fireworks algorithm according to claim 1, characterized in that: The simulated annealing mechanism introduced in step 6 allows a certain probability that a poor solution can be accepted, thereby improving the ability of the fireworks algorithm to jump out of the local optimum. The quality of the new candidate solutions generated by the explosion and mutation of the fireworks can be measured by the fitness function. The quality difference of the candidate solutions is defined as: ΔF = fitness (old) - fitness (new). Each time a new candidate solution is generated, the probability of accepting a poor solution is calculated based on the quality difference and the current temperature T: If ΔF≤0 (i.e. the new solution is better), the new solution is directly accepted; if ΔF>0 (i.e. the new solution is worse), the solution is accepted with probability P(ΔF).

8. The radar array sparse optimization method based on the improved fireworks algorithm according to claim 1, characterized in that: In step 7, according to the principle that the farther the spark is from the sum of the distances of other sparks, the greater the chance of being selected, the roulette strategy is used for selection, and then the process goes to step 3.

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