CN104155852B

CN104155852B - A kind of optimization method of litho machine light source

Info

Publication number: CN104155852B
Application number: CN201410422502.3A
Authority: CN
Inventors: 王磊; 王向朝; 李思坤; 闫观勇; 杨朝兴
Original assignee: Shanghai Institute of Optics and Fine Mechanics of CAS
Current assignee: Beijing Guowang Optical Technology Co Ltd
Priority date: 2014-08-26
Filing date: 2014-08-26
Publication date: 2016-04-13
Anticipated expiration: 2034-08-26
Also published as: CN104155852A

Abstract

A light source optimization method for a lithography machine, using pixelated light sources as particles, using the sum of the squares of each point of the difference between the ideal figure and the photoresist image corresponding to the mask under the current light source illumination mode as the objective function, using linearly decreasing weights and The particle swarm optimization algorithm of the compression factor can iteratively optimize the light source graphics by updating the speed and position information of the particles. The invention effectively improves the imaging quality of photolithography, and has the advantages of simple principle, easy realization and fast convergence speed.

Description

A method for optimizing light source of lithography machine

技术领域technical field

本发明涉及光刻机，尤其涉及一种用于光刻机的光源优化方法。The invention relates to a photolithography machine, in particular to a light source optimization method for a photolithography machine.

背景技术Background technique

光刻技术是极大规模集成电路制造中最为关键的技术之一，光刻分辨率决定集成电路图形的特征尺寸。在曝光波长与数值孔径一定的情况下，需要通过改善光刻胶工艺和采用分辨率增强技术来减小工艺因子，从而提高光刻分辨率。光源优化(SourceOptimization，SO)作为一种重要的分辨率增强技术，通过改变光源强度分布来调整入射光的强度和方向。SO既可以单独使用，也可以作为光源掩模优化(SourceMaskOptimization，SMO)的一部分使用以提高光刻成像性能。Photolithography is one of the most critical technologies in the manufacture of very large-scale integrated circuits, and the resolution of lithography determines the feature size of integrated circuit graphics. In the case of certain exposure wavelength and numerical aperture, it is necessary to reduce the process factor by improving the photoresist process and adopting resolution enhancement technology, so as to improve the photolithography resolution. As an important resolution enhancement technology, Source Optimization (SO) adjusts the intensity and direction of incident light by changing the intensity distribution of the light source. SO can be used alone or as a part of Source Mask Optimization (SMO) to improve lithographic imaging performance.

SO具有成本低、容易实现的优点，因而得到了广泛的研究。近来，FlexRay等自由照明技术为SO提供了更高的自由度。Granik对光源的不同表达方式和优化目标函数进行了分类(参见在先技术1，Granik,Y,“Sourceoptimizationforimagefidelityandthroughput”,JournalofMicrolithographyMicrofabricationandMicrosystems,2004.3(4):p.509-522)。Kehan等从理论和仿真上对基于像素表示的SO的优点进行了证明(参见在先技术2，Kehan,T.,etal,“Benefitsandtrade-offsofglobalsourceoptimizationinopticallithography”,ProceedingsoftheSPIE-TheInternationalSocietyforOpticalEngineering,2009.7274:p.72740C(12pp.)-72740C(12pp.))。另一方面，SO是SMO的重要组成部分。自Rosenbluth等首先提出光源与掩模联合优化的思想以来，已有许多算法应用于SMO。其中，Erdmann等提出的基于遗传算法的SMO(参见在先技术3，Erdmann,A.,etal,“Towardautomaticmaskandsourceoptimizationforopticallithography”,Microlithography2004.InternationalSocietyforOpticsandPhotonics)，不需要掌握光刻的先验知识，可以选择任意的成像模型和优化目标，具有潜在并行性，避免了解析方法难以应用于复杂优化的问题。然而，遗传算法编码比较复杂，其交叉和变异都具有典型的组合特征，优化过程只对染色体的片段操作，收敛速度较慢。另外，在先技术3中的光源图形由描述常规照明、环形照明、二极照明或四极照明的简单参数表示，其优化的自由度受到很大的限制。SO has the advantages of low cost and easy implementation, so it has been extensively studied. Recently, free lighting techniques such as FlexRay provide SO with a higher degree of freedom. Granik classifies different expressions of light sources and optimization objective functions (see prior art 1, Granik, Y, "Source optimization for image fidelity and throughput", Journal of Microlithography Microfabrication and Microsystems, 2004.3(4): p.509-522). Kehan etc. proved the advantages of SO based on pixel representation from theory and simulation (see prior art 2, Kehan, T., et al, "Benefits and trade-offs of global source optimization in optical althography", Proceeding of the SPIE-The International Society for Optical Engineering, 2009.7274: p.72740C (12pp. )-72740C(12pp.)). On the other hand, SO is an important part of SMO. Since Rosenbluth first proposed the idea of joint optimization of light source and mask, many algorithms have been applied to SMO. Among them, the SMO based on genetic algorithm proposed by Erdmann et al. (see prior art 3, Erdmann, A., et al, "Towardautomaticmaskandsourceoptimizationforopticallithography", Microlithography2004.InternationalSocietyforOpticsandPhotonics), does not need to master the prior knowledge of lithography, and can choose any imaging model and optimization objectives, with potential parallelism, avoiding the problem that analytical methods are difficult to apply to complex optimization. However, the coding of genetic algorithm is relatively complicated, and its crossover and mutation both have typical combination characteristics. The optimization process only operates on the fragments of chromosomes, and the convergence speed is slow. In addition, the light source pattern in prior art 3 is represented by simple parameters describing conventional lighting, ring lighting, dipole lighting or quadrupole lighting, and the degree of freedom for optimization is greatly limited.

发明内容Contents of the invention

本发明提供一种基于粒子群优化算法的光刻机光源优化方法。本方法将像素化的光源编码为粒子，利用含有线性递减惯性权重和压缩因子的粒子群算法，通过更新粒子的速度与位置信息不断迭代优化光源图形。该方法原理简单，易于实现，增加了优化自由度，有效提高了光源优化效率。本方法适用于需要光源优化的光刻系统。The invention provides a photolithography machine light source optimization method based on particle swarm optimization algorithm. This method encodes the pixelated light source into particles, uses the particle swarm algorithm with linearly decreasing inertia weight and compression factor, and continuously iteratively optimizes the light source graphics by updating the speed and position information of the particles. The method is simple in principle, easy to implement, increases the optimization degree of freedom, and effectively improves the efficiency of light source optimization. This method is suitable for photolithography systems that require light source optimization.

本发明的技术解决方案如下：Technical solution of the present invention is as follows:

一种基于粒子群优化算法的光源优化方法，具体步骤为：A light source optimization method based on particle swarm optimization algorithm, the specific steps are:

①初始化光源图形J的大小为N_s×N_s,设置光源图形J上发光区域的亮度值为1，不发光区域的亮度值为0，光源图形J的坐标为(f,g)；①Initialize the size of the light source graphic J as N _s ×N _s , set the luminance value of the luminous area on the light source graphic J to 1, the luminance value of the non-luminous area to 0, and the coordinates of the light source graphic J to be (f, g);

初始化掩模图形M的大小为N_m×N_m，设置掩模图形M上透光部分的透射率为1，阻光部分的透射率为0，掩模图形M的坐标为(x,y)；Initialize the size of the mask pattern M to be N _m ×N _m , set the transmittance of the light-transmitting part on the mask pattern M to 1, and the transmittance of the light-blocking part to 0, and the coordinates of the mask pattern M are (x, y) ;

初始化目标图形I_t＝M；初始化光刻胶阈值t_r和灵敏度α；初始化粒子群规模N、学习因子c₁和c₂、惯性权重最大值ω_max和最小值ω_min；初始化各粒子的位置和速度其中i(1≤i≤N)为粒子编号，j(j≥1)为粒子维度，k(k＝1)为迭代次数；初始化评价函数阈值Fs、最大迭代次数k_m；Initialize the target graph I _t = M; initialize the photoresist threshold t _r and sensitivity α; initialize the particle swarm size N, learning factors c ₁ and c ₂ , inertia weight maximum value ω _max and minimum value ω _min ; initialize the position of each particle and speed Wherein i (1≤i≤N) is the particle number, j (j≥1) is the particle dimension, k (k=1) is the number of iterations; initialize the evaluation function threshold Fs, the maximum number of iterations k _m ;

②初始化光源图形J对应的控制变量θ，θ(f,g)表示坐标为(f,g)的控制变量θ，对应于某粒子的位置信息x_i,j；② Initialize the control variable θ corresponding to the light source pattern J, θ(f, g) represents the control variable θ with coordinates (f, g), corresponding to the position information x _{i, j} of a certain particle;

③采用粒子群算法优化控制变量θ，并计算第k次迭代时的光源图形J^(k)，公式如下：③Using the particle swarm optimization algorithm to optimize the control variable θ, and calculate the light source pattern J ^(k) at the kth iteration, the formula is as follows:

${J J}^{((k k))} = = \frac{11 + + {θ θ}^{((k k))}}{22},,$

式中，θ^(k)表示第k(1≤k≤k_m，且k为正整数)次迭代时的控制变量θ值；In the formula, θ ^(k) represents the control variable θ value at the kth (1≤k≤k _m , and k is a positive integer) iteration;

④采用光刻仿真软件，由光源图形J^(k)和掩模图形M得到第k次迭代时的空间像I_a ^(k)，并计算第k次迭代时的光刻胶像I_r ^(k)，公式如下：④ Using lithography simulation software, the spatial image I _a ^(k) at the kth iteration is obtained from the light source pattern J ^(k) and the mask pattern M, and the photoresist image I _r ⁽ k) at the kth iteration is calculated ⁾ , the formula is as follows:

${I I}_{r r}^{((k k))} ((x x,, y the y)) = = sig sig {{{I I}_{a a}^{((k k))} ((x x,, y the y))}} = = \frac{11}{{11 + + e e}^{- - α α (({I I}_{a a} ((x x,, y the y)) - - {t t}_{r r}))}};;$

⑤计算第k次迭代时的评价函数值F^(k)，公式如下：⑤ Calculate the evaluation function value F ^(k) at the kth iteration, the formula is as follows:

${F f}^{((k k))} = = {| | | | {I I}_{r r}^{((k k))} - - {I I}_{t t} | | | |}_{22}^{22} = = \underset{y the y}{Σ Σ} \underset{x x}{Σ Σ} {(({I I}_{r r}^{((k k))} ((x x,, y the y)) - - {I I}_{t t} ((x x,, y the y))))}^{22};;$

⑥定义第k次迭代时粒子本身所找到的使得评价函数值最小的位置为第k次迭代时的个体极值 ⑥ Define the position where the particle itself finds the minimum value of the evaluation function at the kth iteration as the individual extremum at the kth iteration

第k次迭代时，将F^(k)与对应的评价函数值比较，如果F^(k)小于对应的评价函数值，则更新为θ^(k)(f,g)，其中θ^(k)(f,g)为第k次迭代时的θ(f,g)；At the kth iteration, combine F ^(k) with Corresponding evaluation function value comparison, if F ^(k) is less than Corresponding evaluation function value, update is θ ^(k) (f,g), where θ ^(k) (f,g) is θ(f,g) at the kth iteration;

⑦定义第k次迭代时整个种群中粒子找到的使得评价函数值最小的位置为第k次迭代时的全局极值 ⑦ Define the position where the particles in the entire population find the minimum value of the evaluation function at the kth iteration is the global extremum at the kth iteration

第k次迭代时，将F^(k)与对应的评价函数值比较，如果F^(k)小于对应的评价函数值，则更新为θ^(k)(f,g)；At the kth iteration, combine F ^(k) with Corresponding evaluation function value comparison, if F ^(k) is less than Corresponding evaluation function value, update is θ ^(k) (f,g);

⑧计算粒子第(k+1)次的速度和位置 ⑧Calculate the velocity of the particle (k+1) times and location

${x x}_{i i,, j j}^{((k k + + 11))} = = {x x}_{i i,, j j}^{((k k))} + + {v v}_{i i,, j j}^{((k k + + 11))},, j j = = 1,2 1,2 . . . . . . d d,,$

式中，压缩因子C＝c₁+c₂，In the formula, the compression factor C=c ₁ +c ₂ ,

惯性权重 $ω = ω_{\max} - \frac{k (ω_{\max} - ω_{\min})}{k_{m}},$ inertia weight $ω = ω_{\max} - \frac{k (ω_{\max} - ω_{\min})}{k_{m}},$

为第k次迭代时第i个粒子第j维上的 is the i-th particle on the j-th dimension at the k-th iteration

为第k次迭代时第g个粒子第j维上的 is the value of the g-th particle on the j-th dimension at the k-th iteration

⑨如果F^(k)小于Fs，或者k大于k_m，进入步骤⑩，否则返回步骤③；⑨If F ^(k) is less than Fs, or k is greater than k _m , go to step 10, otherwise return to step ③;

⑩终止优化，为全局极值p_g，将p_g所表示的信息作为优化后光源输出。⑩ Terminate optimization, is the global extremum p _g , and the information represented by p _g is output as the optimized light source.

与在先技术3相比，本发明具有以下优点：Compared with prior art 3, the present invention has the following advantages:

1.本发明涉及的光源由像素表示，具有更高的优化自由度。1. The light source involved in the present invention is represented by pixels, which has a higher degree of freedom in optimization.

2.本发明使用粒子群优化算法进行光源优化，相较于遗传算法，该优化方法具有原理简单、参数较少、收敛速度快的优点，从而降低了优化复杂度，有效提高了优化效率。2. The present invention uses the particle swarm optimization algorithm to optimize the light source. Compared with the genetic algorithm, the optimization method has the advantages of simple principle, fewer parameters, and fast convergence speed, thereby reducing optimization complexity and effectively improving optimization efficiency.

附图说明Description of drawings

图1是光刻机系统原理示意图；Figure 1 is a schematic diagram of the principle of the lithography machine system;

图2是本发明所采用的初始光源示意图；Fig. 2 is the initial light source schematic diagram that the present invention adopts;

图3是本发明所采用的掩模图形示意图；Fig. 3 is a schematic diagram of a mask pattern used in the present invention;

图4是本发明采用图3所示掩模图形由初始光源照明成像获得的掩模空间像示意图；Fig. 4 is a schematic diagram of the mask aerial image obtained by the initial light source illumination imaging using the mask pattern shown in Fig. 3 in the present invention;

图5是本发明采用图3所示掩模图形由初始光源照明成像获得的掩模光刻胶像示意图；Fig. 5 is a schematic diagram of the mask photoresist image obtained by the initial light source illumination and imaging by using the mask pattern shown in Fig. 3 in the present invention;

图6是采用本发明优化后得到的光源示意图；Fig. 6 is a schematic diagram of a light source obtained after optimization by the present invention;

图7是本发明采用图3所示掩模图形由优化后光源照明成像获得的掩模空间像示意图；Fig. 7 is a schematic diagram of the mask aerial image obtained by the optimized light source illumination imaging using the mask pattern shown in Fig. 3 according to the present invention;

图8是本发明采用图3所示掩模图形由优化后光源照明成像获得的掩模光刻胶像示意图；Fig. 8 is a schematic diagram of the mask photoresist image obtained by using the mask pattern shown in Fig. 3 from the optimized light source illumination imaging according to the present invention;

图9是采用本发明进行光源优化的流程图。Fig. 9 is a flow chart of light source optimization using the present invention.

具体实施方式detailed description

下面结合实施例和附图对本发明作进一步说明，但不应以此实施例限制本发明的保护范围。The present invention will be further described below in conjunction with the examples and drawings, but the examples should not limit the protection scope of the present invention.

图1是本发明采用的光刻机系统原理图，由图可见本方法涉及包含光刻机照明系统光源1，掩模2，投影物镜3，硅片4。图2是本发明所采用的初始光源照明模式示意图，初始光源照明模式为四极照明，大小为11×11个像素点，白色区域亮度值为1，黑色区域亮度值为0，光源照明模式部分相干因子σ＝0.2。图3是本发明所采用的掩模图形示意图，掩模图形大小为81×81个像素点，210nm×210nm，特征尺寸CD为45nm，掩模类型为二值掩模，白色区域透过率取值为1，黑色区域透过率取值为0。光刻机工作波长λ为193nm，光刻机的数值孔径NA＝1.35，折射率n＝1.44，缩放倍率R＝4。Fig. 1 is a schematic diagram of the lithography machine system used in the present invention, as can be seen from the figure, the method involves a light source 1 comprising a lithography machine lighting system, a mask 2, a projection objective lens 3, and a silicon wafer 4. Fig. 2 is a schematic diagram of the initial lighting mode of the light source used in the present invention, the initial lighting mode of the light source is quadrupole lighting, the size is 11×11 pixels, the brightness value of the white area is 1, and the brightness value of the black area is 0, the part of the lighting mode of the light source The coherence factor σ=0.2. Fig. 3 is a schematic diagram of the mask pattern used in the present invention, the size of the mask pattern is 81×81 pixels, 210nm×210nm, the characteristic size CD is 45nm, the mask type is a binary mask, and the transmittance of the white area is taken as The value is 1, and the transmittance of the black area is 0. The working wavelength λ of the lithography machine is 193nm, the numerical aperture NA of the lithography machine is 1.35, the refractive index n=1.44, and the scaling factor R=4.

本发明基于粒子群优化算法的光刻机光源优化方法，步骤如下：The method for optimizing the light source of a lithography machine based on the particle swarm optimization algorithm in the present invention has the following steps:

①初始化光源图形J的大小为11×11,设置光源图形J上发光区域的亮度值为1，不发光区域的亮度值为0，光源图形坐标为(f,g)；①Initialize the size of the light source graphic J to 11×11, set the brightness value of the luminous area on the light source graphic J to 1, the brightness value of the non-luminous area to 0, and the coordinates of the light source graphic to (f, g);

初始化掩模图形M的大小为81×81，设置掩模图形M上透光部分的透射率为1，阻光部分的透射率为0，掩模图形坐标为(x,y)；Initialize the size of the mask pattern M to be 81×81, set the transmittance of the light-transmitting part on the mask pattern M to 1, and the transmittance of the light-blocking part to 0, and the coordinates of the mask pattern are (x, y);

初始化目标图形I_t＝M；初始化光刻胶阈值t_r＝0.25和灵敏度α＝25；初始化粒子群规模N＝30、学习因子c₁＝c₂＝2.05、惯性权重最大值ω_max＝0.9和最小值ω_min＝0.4；各粒子的初始位置x_i,j随机产生，各粒子的速度v_i,j为0到π之间的随机数，其中i(1≤i≤N)为粒子编号，j(j≥1)为粒子维度；初始化评价函数阈值Fs＝180、最大迭代次数k_m＝60。Initialize target graph I _t =M; initialize photoresist threshold t _r =0.25 and sensitivity α=25; initialize particle swarm size N=30, learning factor c ₁ =c ₂ =2.05, maximum value of inertia weight ω _max =0.9 and The minimum value ω _min =0.4; the initial position x _i,j of each particle is randomly generated, and the velocity v _i,j of each particle is a random number between 0 and π, where i (1≤i≤N) is the particle number, j (j≥1) is the particle dimension; initialize the evaluation function threshold Fs=180, and the maximum number of iterations k _m =60.

②初始化光源图形J对应的控制变量θ，θ(f,g)表示坐标为(f,g)的θ，对应于某粒子的位置信息x_i,j。② Initialize the control variable θ corresponding to the light source pattern J, θ(f,g) represents θ with coordinates (f,g), corresponding to the position information x _i,j of a certain particle.

${J J}^{((k k))} = = \frac{11 + + {θ θ}^{((k k))}}{22},,$

式中，θ^(k)表示第k(1≤k≤k_m，且k为正整数)次迭代时的控制变量θ值。In the formula, θ ^(k) represents the control variable θ value at the kth (1≤k≤k _m , and k is a positive integer) iteration.

${I I}_{r r}^{((k k))} ((x x,, y the y)) = = sig sig {{{I I}_{a a}^{((k k))} ((x x,, y the y))}} = = \frac{11}{{11 + + e e}^{- - α α (({I I}_{a a} ((x x,, y the y)) - - {t t}_{r r}))}} . .$

${F f}^{((k k))} = = {| | | | {I I}_{r r}^{((k k))} - - {I I}_{t t} | | | |}_{22}^{22} = = \underset{y the y}{Σ Σ} \underset{x x}{Σ Σ} {(({I I}_{r r}^{((k k))} ((x x,, y the y)) - - {I I}_{t t} ((x x,, y the y))))}^{22} . .$

第k次迭代时，将F^(k)与对应的评价函数值比较，如果F^(k)小于对应的评价函数值，则更新为θ^(k)(f,g)，其中θ^(k)(f,g)为第k次迭代时的θ(f,g)。At the kth iteration, combine F ^(k) with Corresponding evaluation function value comparison, if F ^(k) is less than Corresponding evaluation function value, update is θ ^(k) (f,g), where θ ^(k) (f,g) is θ(f,g) at the kth iteration.

第k次迭代时，将F^(k)与对应的评价函数值比较，如果F^(k)小于对应的评价函数值，则更新为θ^(k)(f,g)。At the kth iteration, combine F ^(k) with Corresponding evaluation function value comparison, if F ^(k) is less than Corresponding evaluation function value, update is θ ^(k) (f,g).

⑨如果F^(k)小于Fs，或者k大于k_m，进入步骤⑩，否则返回步骤③。⑨If F ^(k) is less than Fs, or k is greater than k _m , go to step 10, otherwise return to step ③.

采用本实施例中的条件，优化后的光源照明模式如图6所示，掩模空间像如图7所示，掩模光刻胶像如图8所示。采用该光源优化方法，评价函数即图形误差降低了66.1％，有效提高了光刻系统的分辨率。Using the conditions in this embodiment, the optimized illumination mode of the light source is shown in FIG. 6 , the spatial image of the mask is shown in FIG. 7 , and the photoresist image of the mask is shown in FIG. 8 . By adopting the light source optimization method, the evaluation function, that is, the graphics error, is reduced by 66.1%, and the resolution of the photolithography system is effectively improved.

Claims

1. A photolithography machine light source optimization method is characterized in that the method comprises the following steps:

①Initialize the size of the light source graphic J as N _s ×N _s , set the luminance value of the luminous area on the light source graphic J to 1, the luminance value of the non-luminous area to 0, and the coordinates of the light source graphic J to be (f, g);

Initialize the size of the mask pattern M to be N _m ×N _m , set the transmittance of the light-transmitting part on the mask pattern M to 1, and the transmittance of the light-blocking part to 0, and the coordinates of the mask pattern M are (x, y) ;

Initialize the target graph I _t = M; initialize the photoresist threshold t _r and sensitivity α; initialize the particle swarm size N, learning factors c ₁ and c ₂ , inertia weight maximum value ω _max and minimum value ω _min ; initialize the position of each particle and speed Where i is the particle number, 1≤i≤N, j is the particle dimension, j≥1, k is the number of iterations, k=1; initialize the evaluation function threshold Fs, the maximum number of iterations k _m ;

② Initialize the control variable θ corresponding to the light source pattern J, θ(f, g) represents the control variable θ with coordinates (f, g), corresponding to the position information x _{i, j} of a certain particle;

③Using the particle swarm optimization algorithm to optimize the control variable θ, and calculate the light source pattern J ^(k) at the kth iteration, the formula is as follows:

{J J}^{((k k))} = = \frac{11 + + {θ θ}^{((k k))}}{22},,

In the formula, θ ^(k) represents the control variable θ value at the kth iteration, where k is a positive integer whose value range is 1≤k≤k _m ;

④ Using lithography simulation software, the spatial image I _a ^(k) at the kth iteration is obtained from the light source pattern J ^(k) and the mask pattern M, and the photoresist image I _r ⁽ k) at the kth iteration is calculated ⁾ , the formula is as follows:

{I I}_{r r}^{((k k))} ((x x,, y the y)) = = s the s i i g g {{{I I}_{a a}^{((k k))} ((x x,, y the y))}} = = \frac{11}{11 + + {e e}^{- - α α (({I I}_{a a} ((x x,, y the y)) - - {t t}_{r r}))}};;

⑤ Calculate the evaluation function value F ^(k) at the kth iteration, the formula is as follows:

{F f}^{((k k))} = = | | | | {I I}_{r r}^{((k k))} - - {I I}_{t t} | | {| |}_{22}^{22} = = \underset{y the y}{Σ Σ} \underset{x x}{Σ Σ} {(({I I}_{r r}^{((k k))} ((x x,, y the y)) - - {I I}_{t t} ((x x,, y the y))))}^{22};;

⑥ Define the position where the particle itself finds the minimum value of the evaluation function at the kth iteration as the individual extremum at the kth iteration

At the kth iteration, combine F ^(k) with Corresponding evaluation function value comparison, if F ^(k) is less than Corresponding evaluation function value, update is θ ^(k) (f,g), where θ ^(k) (f,g) is θ(f,g) at the kth iteration;

⑦ Define the position where the particles in the entire population find the minimum value of the evaluation function at the kth iteration is the global extremum at the kth iteration

At the kth iteration, combine F ^(k) with Corresponding evaluation function value comparison, if F ^(k) is less than Corresponding evaluation function value, update is θ ^(k) (f,g);

⑧Calculate the velocity of the particle (k+1) times and location

{x x}_{i i,, j j}^{((k k + + 11))} = = {x x}_{i i,, j j}^{((k k))} + + {v v}_{i i,, j j}^{((k k + + 11))},, j j = = 11,, 22 ... ... d d,,

In the formula, the compression factor

inertia weight

ω = ω_{m a x} - \frac{k (ω_{m a x} - ω_{\min})}{k_{m}},

is the individual extremum of the i-th particle on the j-th dimension at the k-th iteration

is the global extremum on the jth dimension of the entire population at the kth iteration

⑨If F ^(k) is less than Fs, or k is greater than k _m , go to step 10, otherwise return to step ③;

⑩ Terminate optimization, is the global extremum p _g , and the information represented by p _g is output as the optimized light source.