CN117151212A - Parameter calibration method and device of parallel genetic algorithm based on self-adaptive strategy - Google Patents
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Abstract
The invention discloses a parameter calibration method and device of a parallel genetic algorithm based on a self-adaptive strategy. The method optimizes crossover, mutation and migration operators based on a self-adaptive strategy of the population discrete degree, and improves the population evolution efficiency by using a coarse-granularity parallel computing model. The invention can optimize and improve Genetic Algorithm (GA), and dynamically and automatically cross, mutate and migrate according to the evolution state of the population, thereby avoiding the algorithm from sinking into a local optimal solution, ensuring the expansion and propagation of excellent individuals among sub-populations, and improving the global optimizing capability, solving precision and convergence speed of the algorithm.
Description
Technical Field
The invention relates to the technical field of hydrology and water conservancy, in particular to a parameter calibration method and device of a parallel genetic algorithm based on a self-adaptive strategy.
Background
When the hydrologic model is adopted for runoff simulation and prediction, the simulation precision of the model is determined to a certain extent by the parameter calibration result. The traditional parameter calibration mainly depends on manual experience to search the parameter space, and as different drainage basins have different characteristic parameters, the parameter space is as high as more than ten dimensions, the calculation amount of the space search is huge, and the manual search mode can not meet the application requirement of a model.
With the development of artificial intelligence algorithms, a large number of algorithms are applied to parameter calibration of hydrologic models, such as Genetic Algorithm (GA), particle swarm algorithm (PSO), bayesian algorithm (BOA), complex cross evolution algorithm (SCE-UA), and the like. For a Genetic Algorithm (GA), the GA is used as a global automatic optimization algorithm, and has the advantages of simplicity, flexibility, strong robustness, good expansibility and the like for the problem of multi-dimensional parameter optimization, but in practical application, the GA has the defects of unstable convergence result, easy local convergence, high optimizing time consumption and the like.
Disclosure of Invention
In order to solve the technical problems, the invention provides a parameter calibration method and device of a parallel genetic algorithm based on an adaptive strategy. In the method and the device, genetic Algorithm (GA) can be optimized and improved, and the crossover, variation and migration of the Genetic Algorithm (GA) can be dynamically and automatically carried out according to the population evolution state, so that the algorithm is prevented from sinking into a local optimal solution, the expansion and propagation of excellent individuals among sub-populations are ensured, and the global optimizing capability, solving precision and convergence speed of the algorithm are improved.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
the parameter calibration method of the parallel genetic algorithm based on the self-adaptive strategy comprises the following steps:
Step 1, determining a parameter range of each parameter in a hydrological model, and carrying out real number coding and random generation on an initial population;
step 2, dividing the initial population into a plurality of sub-populations, and enabling each sub-population to independently and concurrently execute genetic operation on different processors;
step 3, taking the qualification rate of the total flood, the peak flood and the peak current time as optimization targets, establishing a multi-target optimized objective function, taking the forward index of the objective function as an fitness function, calculating the fitness of each individual in the sub-population, and determining the next generation of individuals based on elite retention strategies and competitive bidding selection methods;
step 4, performing adaptive simulation binary crossover and adaptive polynomial mutation operation on the next generation of individuals;
step 5, judging whether the current evolution algebra reaches the maximum iteration times, if so, merging the sub-populations to output an optimal solution set; if not, entering the next step;
step 6, judging whether the cross variation cycle times reach a preset value, if so, carrying out self-adaptive migration, mutually exchanging a plurality of individuals among the sub-populations, and turning to step 3; if not, go to step 3.
Preferably, determining the parameter range of each parameter in the hydrologic model specifically comprises the following steps:
Determining a waiting calibration parameter, wherein the waiting calibration parameter comprises a evaporation conversion coefficient K, an upper layer tension water storage capacity WUM, a lower layer tension water storage capacity WLM, a deep layer emission coefficient C, a total tension water storage capacity WM, a tension water storage capacity curve index B, a drainage basin water impermeable area IM, a free water storage capacity SM, a free water storage capacity curve index EX, an in-soil outflow coefficient KI, an in-soil outflow coefficient CI, a subsurface runoff extinction coefficient CG, a river network water extinction coefficient CS and a flood time L, and adopting a fixed structural constraint: total tension water storage capacity wm=upper tension water storage capacity WUM +lower tension water storage capacity wlm+deep tension water storage capacity WDM, groundwater outflow coefficient kg+in-soil outflow coefficient ki=0.7;
and determining the parameter range of the waiting-to-be-rated parameter.
Preferably, the next generation of individuals is determined based on elite retention strategies and competitive race selection methods, and specifically comprises the following steps:
the population individuals with optimal fitness are reserved, and excellent individuals are selected from the rest parent individuals through a competitive bidding competition selection method;
the individual with the optimal fitness and the excellent individual are taken as the next generation individuals.
Preferably, the expression of the objective function is:
F＝max(u 1 *QR v +u 2 *QR p +u 3 *QR t )
QR in v Is the qualification rate of the total floodQR p Is the qualification rate of flood peak flow> QR t Time-of-peak qualification rate->m is the number of field floods participating in the calculation; n is n v 、n p 、n t Respectively the number of qualified floods relative to the total amount of floods, the peak flow rate and the peak time; u (u) 1 、u 2 、u 3 Respectively the weight of the total flood qualification rate, the peak flood qualification rate and the peak time qualification rate.
Preferably, the adaptive analog binary crossover and adaptive polynomial mutation operation on the next generation individual specifically comprises the following steps:
the expression of the crossover probability is:
the expression of the mutation probability is:
k in 1 、k 2 、k 3 、k 4 For the self-adaptive control parameter, f is the fitness of the population, f' is the larger fitness value in the two individuals to be crossed, f max For maximum fitness of population, f min Gamma, the minimum fitness of the population 0 Discrete coefficients, gamma, of fitness function for the primary population t The fitness function discrete coefficient of the population of the t generation;
the expression of the crossover operator is:
c 1 ＝0.5[(1+β)p 1 +(1-β)p 2 ]
c 2 ＝0.5[(1-β)p 1 +(1+β)p 2 ]
wherein the method comprises the steps of
In p 1 And p 2 C is the parent before crossing 1 And c 2 For cross-generated offspring, beta is the distribution factor, u c Is [0,1]Random number, eta c In the form of a cross-distribution index,is eta c Upper limit value of>Is eta c Lower limit value of (2);
the expression of the mutation operator is:
v′ k ＝v k +δ(h k -l k )
Wherein the method comprises the steps of
δ 1 ＝(v k -l k )/(h k -l k )
δ 2 ＝(h k -v k )/(h k -l k )
V in k Is the father before mutation, v' k Progeny of the mutation, h k Upper limit of variation of variables, l k Is the lower limit of variation, delta is the variation coefficient, u m Is [0,1]Random number, eta m In order to obtain the mutation distribution index,is eta m Upper limit value of>Is eta m Lower limit value of (2).
Preferably, there are p individuals in the population, each individual having w variables, the population being represented by a matrix of p x w, x ij As matrix elements, the expression of the discrete coefficient γ is:
in which x is ij As matrix elements, k j Is the variable mean value.
Preferably, the adaptive migration specifically includes the following steps:
calculating the discrete degree and average fitness value of each sub-population, wherein the discrete degree is represented by a population discrete coefficient gamma;
selecting a population with the smallest average fitness value as an immigrating population, and selecting a population with the smallest gamma value as an immigrating population; and using the population with the second smallest population average fitness value as an immigrating population, and selecting the population with the second smallest gamma value as an immigrating population until a unidirectional ring topological structure is formed among all sub-populations.
Preferably, when the population average fitness value and the gamma value are selected to be the same population, the current migration operation is abandoned and the next pair of population migration is performed.
Preferably, the expression of the population average fitness is:
f in i The fitness value of the population individuals is p, and the number of the population individuals is p.
Based on the above, the invention also discloses a parameter calibration device of the parallel genetic algorithm based on the self-adaptive strategy, which comprises: a data encoding module and a calculating module, wherein,
the data coding module is used for determining the parameter range of each parameter in the hydrologic model, and real number codes and randomly generates an initial population;
the computing module is used for dividing the initial population into a plurality of sub-populations, so that each sub-population is independently and concurrently executed on different processors; establishing a multi-objective optimized objective function by taking the qualification rate of the total flood, the peak flood and the peak current time as optimization targets, calculating the fitness of each individual in the sub-population by taking the forward index of the objective function as a fitness function, and determining the next generation of individuals based on elite retention strategies and bidding competition selection methods; performing adaptive simulation binary crossover and adaptive polynomial mutation operation on the next generation of individuals; judging whether the current evolution algebra reaches the maximum iteration times, if so, merging the sub-populations to output an optimal solution set; if not, judging whether the cross variation cycle times reach a preset value, if so, performing self-adaptive migration, mutually exchanging a plurality of individuals among the sub-populations, and continuing genetic operation; if not, continuing the genetic operation.
Based on the technical scheme, the invention has the beneficial effects that: the Genetic Algorithm (GA) is optimized and improved, and 3 indexes for flood forecast precision assessment are firstly oriented: the qualification rate of the total flood quantity, the peak flood quantity and the peak time is established, a multi-objective optimization system is established, the multi-objective optimization problem is solved into a single-objective optimization problem through a weight method, and the complexity of an algorithm is reduced; the population discrete coefficients capable of reflecting the population evolution degree are designed, the adaptive crossover, mutation and migration operators are optimized, the optimizing efficiency of the algorithm is improved, and the Adaptive Genetic Algorithm (AGA) is constructed; optimizing an overall computing architecture by adopting a coarse-granularity parallel computing model, and after each sub population is distributed to independent threads, performing iterative optimization respectively to improve the evolution efficiency; through the improvement, a parallel genetic algorithm (PAGA) based on a self-adaptive strategy is finally constructed, and the algorithm can be dynamically and automatically crossed, mutated and migrated according to the population evolution state, so that the algorithm is prevented from falling into a local optimal solution, the expansion and propagation of excellent individuals among sub-populations are ensured, and the global optimizing capacity, solving precision and convergence speed of the algorithm are improved. The PAGA algorithm is applied to the parameter calibration of the Xinanjiang model in the Tunxi river basin, the GA algorithm and the AGA algorithm are selected for comparison analysis, and the comprehensive performance of the PAGA algorithm is verified by simulating typical field floods in terms of calibration efficiency, calibration convergence, calibration stability and calibration effect.
Drawings
FIG. 1 is a flow diagram of a method for parameter calibration of parallel genetic algorithms based on adaptive strategies in one embodiment;
FIG. 2 is a schematic representation of the distribution of the streams of streams and hydrographic station nets in one embodiment;
FIG. 3 is a parallel acceleration ratio line graph in one embodiment;
FIG. 4 is a graph of parallel efficiency lines in one embodiment;
FIG. 5 is a schematic diagram of the convergence process of the GA, AGA and PAGA algorithms in one embodiment;
FIG. 6 is a schematic diagram of the evolution process of the PAGA algorithm for different colony sizes in one embodiment;
fig. 7 is a schematic diagram of a measured flow and an analog flow process line of a field flood in one embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
As shown in fig. 1, the present embodiment combines the characteristics of the new anjiang model parameters to provide a parameter calibration method of a parallel genetic algorithm based on an adaptive strategy, and the method optimizes crossover, mutation and migration operators based on the adaptive strategy of the population discrete degree, and improves the population evolution efficiency by using a coarse-granularity parallel calculation model, and specifically includes the following steps:
step 1, determining a parameter range of each parameter in a hydrological model, and carrying out real number coding and random generation on an initial population;
Step 2, dividing the initial population into a plurality of sub-populations, and enabling each sub-population to independently and concurrently execute genetic operation on different processors;
step 3, taking the qualification rate of the total flood, the peak flood and the peak current time as optimization targets, establishing a multi-target optimized objective function, taking the forward index of the objective function as an fitness function, calculating the fitness of each individual in the sub-population, and determining the next generation of individuals based on elite retention strategies and competitive bidding selection methods;
step 4, performing adaptive simulation binary crossover and adaptive polynomial mutation operation on the next generation of individuals;
step 5, judging whether the current evolution algebra reaches the maximum iteration times, if so, merging the sub-populations to output an optimal solution set; if not, entering the next step;
step 6, judging whether migration conditions are met, if yes, carrying out self-adaptive migration, mutually exchanging a plurality of individuals among sub-populations, and turning to step 3; if not, go to step 3.
The Xinanjiang model can be divided into four modules: vapor emission calculations, flow production calculations, water source partitioning and pooling calculations. The three-water source Xinanjiang model with the largest application currently comprises 18 parameters, and the model parameters can be divided into four main categories according to the structural characteristics of the model: (1) parameters of the evapotranspiration method. The evaporation coefficient K, the upper tension water storage capacity WUM, the lower tension water storage capacity WLM, the deep tension water storage capacity WDM and the deep evaporation coefficient C; (2) a flow-producing parameter. Total tension water storage capacity WM, tension water storage capacity curve index B, watershed water-impermeable area IM; (3) Water source partition parameters. Free water storage capacity SM, free water storage capacity curve index EX, in-soil outflow coefficient KI and groundwater outflow coefficient KG; (4) a confluence parameter. The soil flux regression coefficient CI, the subsurface runoff regression coefficient CG, the river network water regression coefficient CS, the flood delay time L, and two parameters KE and XE in Ma Sijing methods. Since KE and XE have well-established calculation methods, optimization methods are generally not employed for inference. By fixing the structural constraints wm= WUM +wlm+wdm, kg+ki=0.7, the parameters to be calibrated relate to a total of 14 parameters, the parameter ranges of which are shown in table 1.
TABLE 1 parameter ranges for each Module of Xinanjiang model
In the embodiment, a calculation framework of a Genetic Algorithm (GA) is improved based on a coarse-grained parallel calculation model, and meanwhile, aiming at the defects of the GA algorithm, an adaptive strategy is adopted to optimally design main steps of crossing, mutation and migration of population evolution, so that a parallel genetic algorithm (PAGA) based on the adaptive strategy is constructed, and the overall operation strategy is shown in a table 2:
table 2 operating strategy of the PAGA algorithm
In the parameter calibration method of the parallel genetic algorithm based on the adaptive strategy of one embodiment, a selection process of an objective function is further provided:
the selection of the objective function is directly related to the optimization result of the hydrologic model parameters, and multiple elements of hydrologic simulation are difficult to comprehensively consider by a single objective function, so that multiple elements are necessary to be adoptedThe individual objective functions optimize the model parameters. In order to better control the total flood quantity, the peak flood quantity and the peak current time, the embodiment combines the hydrologic information forecast specification to ensure that the total flood quantity qualification rate (QR v ) Peak flood flow Qualification Rate (QR) p ) And peak time yield (QR) t ) As an objective function, the formula is as follows:
wherein m is the number of field floods participating in the calculation; n is n v 、n p 、n t Respectively, the number of floods qualified with respect to total amount of floods, peak flow, peak time. The adoption of a plurality of objective functions can ensure that the simulation result is closer to the actual situation, but the calculation complexity is increased suddenly, the optimization speed is reduced, the plurality of objective functions are given different weights by a weight method, the multi-objective optimization is converted into single-objective optimization, and the objective function formula is as follows:
F＝max(u 1 *QR v +u 2 *QR p +u 3 *QR t ) (4)
Wherein F is an objective function and a forward index can be directly used as a fitness function (F), u 1 、u 2 、u 3 Respectively the weight of the total flood qualification rate, the peak flood qualification rate and the peak time qualification rate.
The parameter calibration method of the parallel genetic algorithm based on the adaptive strategy in one embodiment further comprises the selection process of the adaptive cross variation:
the crossover and mutation are important steps for influencing the convergence speed and the searching capability of the GA algorithm, and in order to avoid the premature phenomenon of the GA algorithm, the local searching capability and the convergence of the algorithm are enhanced, and the value of the crossover and mutation process can be more reasonable and effective by adopting a self-adaptive strategy. The self-adaptive design of the GA algorithm needs to fully consider two factors of the evolution degree of the population and the fitness of individuals, based on the two factors, a population discrete coefficient reflecting the population discrete degree is constructed, and the self-adaptive crossover and mutation operator is designed by combining the judgment of the individual fitness value, so that the problems of poor local searching capability, easiness in premature and the like of the GA algorithm are solved.
1) Adaptive operator
Under the general condition, an initial population is generated by adopting a random algorithm to ensure the global searching capability of the GA algorithm, so that population individuals are diversified and are in a high discrete state at the initial stage of evolution, when the population evolves to a certain stage, partial individuals in the population gradually approach to the optimal solution, a large number of identical individuals appear, the population discreteness is reduced, and the degree of evolution of the population can be reflected by the population discreteness. The degree of dispersion of the population can be represented by the sum of Euclidean distances between all individuals and the center point of the current population, but because the parameters of the Xinenjiang model have different dimensions, when the Euclidean distance is used, the condition that a certain variable is over-weighted easily occurs, and therefore the average value of the variable needs to be divided. In the design herein, there are p individuals in a population, each individual has w variables, the population is represented by a matrix of p x w, x ij The population discrete coefficient gamma is constructed on the basis of matrix elements, and the formula is as follows:
k in j Is the variable mean value. Gamma is a dimensionless number and the discrete coefficient gamma of the population at the initial stage of evolution 0 Maximally, as the population evolves, individuals gradually approach the optimal solution, repeated individuals gradually increase, the discreteness is smaller and smaller, and in theory, gamma approaches 0, so that gamma can be reduced t And gamma is equal to 0 The ratio of (2) is used as a self-adaptive control parameter to flexibly adjust the crossover and mutation processes.
2) Adaptive cross variation probability
The improved adaptive genetic algorithm crossover probability and variation probability formula is as follows by combining population discrete coefficients:
k in 1 、k 2 、k 3 、k 4 For the self-adaptive control parameter, f is the fitness of the population, f' is the larger fitness value in the two individuals to be crossed, f max For maximum fitness of population, f min Gamma, the minimum fitness of the population 0 Discrete coefficients, gamma, of fitness function for the primary population t The fitness function discrete coefficient of the population of the t generation; and is a decreasing function, gradually approaching 0 along with the evolution of the population; for the whole population, larger P is adopted at the early stage of evolution c And P m The space search of variables is enhanced, the evolution efficiency is improved, the population gradually approaches to the global optimal solution in the later period of evolution, and smaller P is adopted c And P m Making it stably converged to the optimal solution; for individuals with high fitness value, smaller P is adopted c And P m The good gene is reserved, and individuals with small fitness value adopt relatively larger P c And P m And the evolution efficiency is improved.
3) Adaptive analog binary interleaving
Because the parameters of the Xinanjiang model are optimized with more variables, a simulated binary crossover method (SBX) is used as a crossover operator, and the calculation method is as follows:
c 1 ＝0.5[(1+β)p 1 +(1-β)p 2 ] (8)
c 2 ＝0.5[(1-β)p 1 +(1+β)p 2 ] (9)
wherein β is determined by the random dynamics of formula 10:
in p 1 And p 2 C is the parent before crossing 1 And c 2 For cross-generated offspring, beta is the distribution factor, u c Is [0,1]Random number, eta c Is a cross distribution index. Cross distribution index η c The size of (a) determines the gap between the offspring and the parent, eta in the traditional SBX method c Is a fixed value. However, in the initial stage of evolution, the population dispersion degree is large, and a larger search space is needed to improve the convergence rate; in the later period of evolution, individuals are mainly distributed near the global optimal solution, the population dispersion degree is small, and a smaller search space is needed to enable the precision of local search to be higher, so that the global optimal solution is easier to obtain. In order to obtain better evolutionary effect in practical application, the self-adaptive cross distribution index based on population discrete coefficients is provided, and the formula is as follows:
In the middle ofIs eta c Upper limit value of>Is eta c The formula can adopt proper eta according to the evolution degree of the population c The value ensures that the whole evolution process can carry out space search in a proper range, and improves the convergence speed and convergence precision of the algorithm.
4) Adaptive polynomial variation
The method adopts a polynomial mutation method (PM) as a mutation operator, is mainly used for improving the local searching capability of a genetic algorithm and preventing premature convergence, and comprises the following steps of:
v' k ＝v k +δ(h k -l k ) (12)
wherein δ is determined by the random dynamics of formula (13):
wherein delta 1 And delta 2 ：
δ 1 ＝(v k -l k )/(h k -l k ) (14)
δ 2 ＝(h k -v k )/(h k -l k ) (15)
V in k Is the father before mutation, v' k Progeny of the mutation, h k Upper limit of variation of variables, l k Is the lower limit of variation, delta is the variation coefficient, u m Is [0,1]Random number, eta m The adaptive improvement principle is similar to that of the cross distribution index, and the formula is as follows:
in the middle ofIs eta m Upper limit value of>Is eta m The formula can carry out a large-range space search at the initial stage of evolution according to the evolution degree of the population, and strengthen individual variation; in the later stage of evolution, proceedAnd the smaller-range space search promotes individual convergence to the optimal solution.
The parameter calibration method of the parallel genetic algorithm based on the adaptive strategy in one embodiment further comprises the process of adaptively migrating the topology, and specifically comprises the following steps:
The coarse-granularity parallel computing model divides an original population into a plurality of sub-populations, each sub-population independently performs evolution iteration, and performs individual exchange among the sub-populations according to a certain topological structure to complete migration operation. Because migration among sub-populations helps to attract good individuals and enrich the diversity of the populations and avoid premature phenomenon, topology and scale of migration are important issues of concern.
This embodiment employs a one-way ring migration topology that, although converging at a relatively slow rate, ensures the diffusion of good genes between sub-populations. The traditional unidirectional ring migration topology structure is random migration, or migration among sub-populations is performed according to the numbering sequence after each sub-population is numbered. In the embodiment, the discrete degree and average fitness of the sub population are used as the basis, the migration topology direction is determined in a self-adaptive mode, and blindness and fixation during migration of the traditional parallel genetic algorithm are avoided. The degree of population dispersion is represented by a population dispersion coefficient gamma of formula (5), and the average population fitness is as follows:
f in i The fitness value of the population individuals is p, and the number of the population individuals is p. Population average fitness f avg The reaction is the optimizing level of the population, and the population discrete coefficient gamma reaction is the convergence level of the population.
After the number of cross variation cycles reaches a preset value, the sub-populations are respectively according to f avg And gamma values are arranged from small to large, f is selected first avg Selecting the population with the smallest value as the immigrating population, selecting the population with the smallest gamma value as the immigrating population, and the like to drive f avg The population with the second smallest value is taken as the migratory populationSelecting the population with the second smallest gamma value as an immigrating population until a unidirectional ring topological structure is formed among all sub-populations, if the population is based on f avg And if the value and the gamma value are selected to be the same population, discarding the current migration operation and carrying out migration of the next population. F according to sub-population avg And gamma value self-adaptively controls the migration direction of each sub-population, can fully consider the evolution state of each sub-population, select individuals from sub-populations with poor optimizing level to migrate into sub-populations with small discreteness, improve the diversity of the populations and avoid premature populations; and selecting excellent individuals from the sub-population with higher optimizing level to migrate into the sub-population with higher discreteness, guiding the population to evolve towards the optimal solution, and accelerating the population convergence. The number of the sub-population output individuals responsible for the migration is two, one is the individual with the optimal fitness value, and the other is the individual with the largest variation of the sub-population discrete coefficient gamma responsible for the migration. On one hand, the strategy can enable excellent individuals to be timely and effectively spread, and plays a role in guiding the evolution direction to a certain extent; on the other hand, the diversity of the migrated sub-population can be increased, and the sub-population is prevented from falling into local optimum.
Experiment and analysis
The Tunxi river basin is positioned in the southern Anhui mountain area in Anhui province, and the river basin area is 2696.76km 2 The river is 157km in mountain area of the Ganjing border of Zhejiang, the river is 157km; the river is located on the south side of Huangshan and the south side of Huangshan, the flow is short, and the river length is about 70km. The average air temperature of the Tunxi river is about 17 ℃ for many years, the rainfall is full, the average rainfall is about 1800mm for many years, and the rainfall is distributed unevenly among the years. The patterns of the Tunxi river basin are high and low in the west, and vegetation in the river basin is good, and the patterns mainly comprise evergreen conifer forest, evergreen broadleaf forest, shrubs, pastures and crop lands, and the soil types mainly comprise loam, clay loam, sandy loam and sandy clay loam. The river runoff has relatively large annual and international changes, and belongs to a typical moist area. The distribution of rainfall stations in the streams and the water system are shown in fig. 2.
According to the rainfall site conditions of the Tunxi river basin, a Thiessen polygon method is used for carrying out river basin blocking, the river basin is divided into 11 unit river basins in total, 59 flood is selected from 2006 to 2016 in the river basin, the front 49 fields are subjected to Xinanjiang model parameter calibration, the back 10 fields are subjected to parameter verification, and four aspects of calibrating efficiency, calibrating convergence, calibrating stability and calibrating effect are respectively used for analyzing and discussing Genetic Algorithm (GA), adaptive Genetic Algorithm (AGA) and parallel genetic algorithm (PAGA) based on an adaptive strategy, wherein the AGA algorithm is not subjected to parallel calculation improvement, so that the related steps of population division, adaptive migration and the like are not carried out, and other evolution steps are consistent with the PAGA algorithm. The computing environment of the example is an HPE ProLiant DL560 Gen10 server, 2 Yingte to Qiangjin 6148 processors, 20 cores and 128G memory, and the computing program is realized by Java language programming. The test parameter settings are shown in table 1:
TABLE 3GA, AGA and PAGA algorithm parameter settings
1. Efficiency rating
In order to analyze the calibration efficiency of the PAGA algorithm under different population sizes and parallel nuclear numbers, the calibration efficiency of the PAGA algorithm is evaluated by adopting two indexes of an acceleration ratio S and an efficiency E for measuring the performance of the parallel algorithm, and the calculation method is shown in a formula (18) and a formula (19).
T is in s Representing the algorithm serial calculation time, t p Representing algorithm parallel computing time, and C representing the number of cores involved in parallel computing. As can be seen from table 4, fig. 3 and fig. 4, the GA and AGA algorithms under serial calculation conditions are very time-consuming in the model parameter-rated optimizing process, and the calculation time increases rapidly as the population scale increases. The AGA algorithm is improved on the basis of the GA algorithm by adopting the self-adaptive strategy, so that the complexity of the fitness calculation and cross mutation process is higher than that of the GA algorithm, and the result is thatThe calculation time consumption is increased by more than 70%, when the population size is 800, the time consumption reaches 2188s, and if the hydrologic data volume and the population size are further improved, the time consumption can not meet the requirement of calibrating the real-time property. After the AGA algorithm is improved by adopting the coarse-granularity parallel computing model, the main conclusion of analysis is as follows:
TABLE 4 calculation results of GA, AGA and PAGA in different calculation environments
1) Parallel acceleration ratio. The calculation acceleration effect of the PAGA is remarkable, the PAGA needs 321s and 265s under the environment of 8 cores and 10 cores, and the calculation time is reduced by 85.3 percent and 87.9 percent respectively. Under the condition that the population is 800, the acceleration ratio in a 10-kernel environment is 4.4 times that in a 2-kernel environment.
2) Parallel efficiency. Under the same population scale, the parallel efficiency gradually decreases along with the increase of the number of the parallel computing kernels; as population size increases, the reduction in parallel efficiency gradually decreases. For example, when the population scale is 100, and the number of cores in parallel computation is increased from 2 to 10, the parallel efficiency is reduced from 0.89 to 0.69, and the reduction is 22.4%; at a population size of 800, when the number of cores of parallel computation is increased from 2 to 10, the parallel efficiency is reduced from 0.95 to 0.83, and the reduction is 12.6%. The main reason is that the increase of the number of cores increases the resource consumption of the system memory, the thread scheduling management, the communication among sub-populations and the like, increases the kernel overhead, and reduces the parallel efficiency, so that the actual parallel acceleration ratio is smaller than the number of cores for parallel calculation; in addition, as the coarse-granularity parallel computing model is adopted, communication among sub-populations is only carried out when migration conditions are met, the total time consumption of communication expenditure is far less than complex computing time such as individual fitness and cross variation, and the total time consumption of communication expenditure is remarkably reduced along with the increase of population scale, so that the overall amplitude of parallel efficiency is reduced.
Research results show that after the coarse-granularity parallel computing model is combined with the self-adaptive improvement strategy, the model parameter calibration efficiency of the genetic algorithm can be effectively improved.
2. Rate convergence
And (3) optimizing and calibrating parameters of the Xinanjiang model by adopting GA, AGA and PAGA algorithms in the research of calibrating convergence, and outputting an optimal value of a population objective function after each iteration operation so as to analyze the convergence of three optimization algorithms. Meanwhile, in order to ensure the parallel efficiency, the parallel kernel number of the PAGA algorithm in the research of the part is 4. Fig. 5 reflects the convergence process of three optimization algorithms at a population size of 400, and the main conclusion of the analysis is as follows:
1) The GA algorithm converges earliest, the local optimal solution can be obtained without improvement in 78 th iteration, the AGA and PAGA algorithms can intermittently jump out of the local optimal solution, and the optimal solution is obtained in 107 iterations and 122 iterations respectively, mainly because the GA algorithm adopts fixed cross variation parameters for the whole population evolution period and all individuals, on one hand, individuals with high fitness value are easily damaged to influence the optimizing effect, on the other hand, individuals with low fitness are not facilitated to strengthen the space search, the diversity of the population is influenced, and the phenomenon of 'precocity' of the local optimal solution in the whole population is caused. The self-adaptive improvement strategy of AGA and PAGA algorithm comprehensively considers two factors of the evolution degree of population and the individual fitness, and for the whole population, larger P should be adopted at the early stage of evolution c 、P m 、η c And eta m Global search is carried out in the range of the value range space, the population diversity is improved, the population gradually approaches to the global optimal solution in the later period of evolution, and smaller P should be adopted c 、P m 、η c And eta m The search is enhanced in the local area, so that the local area is stably converged to the optimal solution; for individuals with high fitness value, relatively small P is adopted c And P m The good gene is reserved, and individuals with small fitness value adopt relatively larger P c And P m And the evolution efficiency is improved. After self-adaptive improvement, the AGA and PAGA algorithms are comprehensively guaranteed to have high-efficiency global searching capability in the early stage, continuously jump out of the local optimal value, and stably converge in the later stageAnd (5) an optimal solution.
2) The convergence of the PAGA algorithm is weaker than that of the AGA algorithm, the required iteration times for obtaining the optimal value is higher than that of the AGA algorithm, mainly because the single population adopted by the AGA algorithm is evolved, the fitness calculation is carried out before each evolution, the optimal individuals are reserved by adopting an elite strategy, the guiding function of the excellent individuals on the whole population can be fully exerted, and the evolution efficiency of the population is improved; however, because the population of the AGA algorithm is single, even if the cross mutation process is optimized by adopting a self-adaptive strategy, the population diversity is inevitably reduced in the later period of evolution, and most individuals are concentrated near the optimal individuals, so that the optimization is stagnated. When the PAGA algorithm executes migration operation, each sub-population migrates according to a unidirectional ring structure, and migration among the sub-populations only involves two individuals, so that excellent individuals can be transferred slowly among the sub-populations, and the excellent individuals can be unfavorable to exert the guiding function in the early stage of evolution; from another angle, the independent evolution of each sub-population well maintains the population diversity, and when the dispersion of a certain sub-population is small, individuals promoting the population diversity are introduced to avoid being trapped into local optimum, and when the dispersion of a certain sub-population is high, excellent individuals are introduced to guide the population evolution by combining the self-adaptive migration topology method; therefore, the PAGA algorithm can continuously jump out of the local optimum and gradually approach to the global optimum, and an optimum solution superior to the AGA algorithm is obtained.
The analysis described above demonstrates that the PAGA algorithm can only obtain good simulation results with a sufficiently large number of iterations. In the process of attempting to increase the number of populations in order to increase the convergence rate of the PAGA algorithm, fig. 6 reflects the convergence process of the PAGA algorithm with a parallel kernel number of 4 and different population sizes, it can be seen that as the population size increases, the optimizing speed of the algorithm is continuously increased, the iteration number required for convergence is reduced, the curve is gradually smoothed, the convergence result is also continuously approximated to the optimal solution, the final convergence optimal value tends to be stable when the population size is 400, and further attempting to increase the population size does not significantly improve the convergence result. The increase of the population overall scale means that the individual diversity of the sub population is improved in the initial stage of evolution, the number of excellent individuals is higher than that of the small-scale population, and the rapid evolution of the initial population to the optimal solution direction is facilitated based on elite retention strategy; meanwhile, the diversity of the population is also beneficial to preventing the population from falling into local optimum, so that the whole iterative process is smoother; however, the large population clearly increases the amount of calculation, resulting in a longer convergence time.
3. Stability rating
And repeatedly calculating the GA, AGA and PAGA algorithms for 50 times under the conditions that the parallel kernel is 4, the iteration times are different and the cluster sizes are different, and stabilizing the objective function value variance analysis algorithm from the average objective function value, the maximum objective function value, the minimum objective function value and the objective function value variance analysis algorithm.
1) The maximum objective function value and the average objective function value of the GA, AGA and PAGA algorithms are not obviously improved along with the increase of the iteration times of the population when the population scale is 400, the minimum objective function value is continuously increased, the standard deviation of the objective function values is gradually reduced, the objective function values of the AGA and PAGA algorithms are superior to the GA algorithm under various conditions, and the AGA algorithm is minimum in the aspect of the standard deviation of the objective function, which shows that the AGA and the PAGA algorithm have higher stability, because the AGA and the PAGA algorithm adopting the self-adaptive strategy can perform search with a larger space range at the initial stage of evolution, are beneficial to optimizing, strengthen local area search at the later stage of evolution, and are beneficial to converging, so the AGA algorithm has better optimizing capability and stability relative to the GA algorithm; for the AGA algorithm before parallel improvement, individuals for improving population diversity cannot be obtained through a migration mode, each sub population of the PAGA algorithm is independently evolved, excellent individuals can be exchanged through migration at intervals, and individuals for increasing the sub population discreteness can be migrated to enrich population diversity, so that the PAGA algorithm can obtain an optimal value better than the AGA algorithm, and the PAGA algorithm can still continuously exchange individuals to maintain population diversity in a convergence stage, so that the stability of the PAGA algorithm is weaker than that of the AGA algorithm.
Table 5 comparison of objective function values for GA, AGA and PAGA algorithms at different iteration times
2) According to the method, when the iteration number is 200, as the population size is increased, the maximum objective function values of the GA, AGA and PAGA algorithms are improved to a certain stage, no obvious improvement exists, the average objective function value and the minimum objective function value are continuously increased, the standard deviation of the objective function values is gradually reduced, and the fact that the number of individuals in the population is increased is favorable for improving the optimizing capability and stability of the algorithms under the condition of a small-scale population is indicated, but under the condition of a large-scale population, the change of the maximum objective function value shows the randomness of the searching direction of the genetic algorithm, and the further improvement of the population size has no obvious influence on the optimizing capability.
Table 6 comparison of objective function values for GA, AGA and PAGA algorithms at different cluster scales
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In conclusion, under the conditions of small-scale initial population and fewer iteration times, the PAGA algorithm is adopted to better approach to the global optimal solution, so that the problem that the genetic algorithm is easy to fall into local optimal is avoided.
4. Rating effect
The calibration effect of the PAGA algorithm on the Xinanjiang model is evaluated by adopting the simulation error of the field flood, the model parameter results obtained by optimizing the GA, AGA and PAGA algorithms are shown in a table 7, the flood simulation error statistics of partial field times (10 fields respectively) of the periodic rate and the inspection period are shown in a table 8, the relative error and the deterministic coefficient of the flood, the peak flow and the peak time are mainly adopted as flood evaluation indexes, the prediction precision of each algorithm is analyzed according to the 'hydrological information prediction standard', the qualified ratio of the total flood quantity in 49 field floods with the periodic PAGA algorithm rate is 40/49, and the qualification rate is 81.6%; the qualified ratio of flood peak flow is 42/49, and the qualification rate is 85.7%; the qualified peak time is 44/49, and the qualification rate is 89.8%; the overall average value is 0.89, and the deterministic coefficient is more than 0.8, the duty ratio is more than 40/49,0.9, and the duty ratio is more than 15/49. In 10 floods in the verification period, 1 field exists in the total flood amount and the peak time disqualification of the PAGA algorithm, 2 fields exist in the disqualification of the peak flow, 1 field exists in the certainty coefficient lower than 0.8, the total flood qualification rate is greater than 0.86, and the certainty coefficient average value is 0.84; 2 fields exist for unqualified flood total quantity of the AGA algorithm, 1 field exists for unqualified flood peak flow and peak current time, 2 fields exist for a deterministic coefficient lower than 0.8, the total flood qualification rate is greater than 0.86, and the deterministic coefficient average value is 0.83; each of the total flood and the peak flood of the GA algorithm is provided with 2 fields, the peak current time is provided with 1 field, the certainty coefficient is lower than 0.8 and is provided with 3 fields, the total flood qualification rate is higher than 0.83, and the certainty coefficient average value is 0.81.
By the analysis and comparison of the table 8 and the fig. 7, the simulation effect after the calibration of the PAGA algorithm is more similar to the actual flood runoff process, the deviation of the GA algorithm is the largest, and the AGA algorithm is the second time. The simulation result of the field flood shows that the parameter calibration of the coarse-grained parallel calculation model and the adaptive strategy improved genetic algorithm and applied to the Xinanjiang model is feasible, and the model parameters with high quality can be obtained.
TABLE 7 model parameters results of PAGA rating
Table 8 table for simulating error of flood in stream basin
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Summary of experimental analysis: genetic algorithm is an effective method for calibrating hydrologic model parameters, however, the space-time data scale is increased due to hydrologic refinement simulation, the calculation complexity is increased due to various improved GA algorithms, and the efficiency of traditional serial calculation is difficult to meet the requirement of hydrologic model parameter calibration work. The method utilizes a coarse-granularity multi-process parallel computing model, combines an adaptive strategy to improve a GA algorithm, provides an adaptive parallel genetic algorithm (PAGA), and applies the PAGA to field flood simulation of a Tunxi river basin, and the research result is as follows:
1) The PAGA algorithm of the self-adaptive strategy is adopted, the crossover and mutation operators can be automatically adjusted according to the evolution degree of the population and the individual fitness, the convergence speed is improved by adopting higher crossover mutation probability and larger search space at the early stage of evolution, the convergence precision is improved by adopting lower crossover mutation probability and smaller search space at the later stage of evolution, and the whole process can be guaranteed to evolve in a better strategy;
2) By using the coarse-grain parallel computing model, the parameter rating time consumption can be greatly reduced, and the more the number of cores participating in parallel computing is, the less the computing time consumption is. By combining the self-adaptive migration topology method, the migration direction can be self-adaptively controlled, blindness and fixity during migration of the traditional parallel genetic algorithm are avoided, the diversity of sub-populations is ensured, excellent individuals are promoted to diffuse among the sub-populations, the whole population is guided to evolve towards an optimal solution, and population convergence is accelerated;
3) The method is characterized in that a plurality of targets for evaluating the flood forecasting precision are comprehensively considered through a weight method, and mainly comprise the total flood qualification rate, the peak flow qualification rate and the peak time qualification rate, the total qualification rate of the verification period field flood simulation reaches more than 86%, and the requirements of actual hydrologic forecasting are met.
The research result shows that the PAGA algorithm can effectively improve the defects of the traditional GA algorithm, has better global searching capability and calibration efficiency, and provides a new path for hydrologic model parameter calibration. In this embodiment, in consideration of the parallel efficiency, only the performance of the PAGA algorithm in the operating environment with the number of parallel kernels being less than or equal to 10 is considered, but multiple factors such as the number of parallel kernels, the sub-population size, the migration period, the migration size and the like may be further adjusted according to actual requirements, so as to optimize the PAGA algorithm.
In one embodiment, a parameter calibration device of a parallel genetic algorithm based on an adaptive strategy is provided, which comprises: a data encoding module and a calculating module, wherein,
the data coding module is used for determining the parameter range of each parameter in the hydrologic model, and real numbers code and randomly generate an initial population;
the computing module is used for dividing the initial population into a plurality of sub-populations, so that each sub-population is independently and concurrently executed on different processors respectively; establishing a multi-objective optimized objective function by taking the qualification rate of the total flood, the peak flood and the peak current time as optimization targets, calculating the fitness of each individual in the sub-population by taking the forward index of the objective function as a fitness function, and determining the next generation of individuals based on elite retention strategies and bidding competition selection methods; performing adaptive simulation binary crossover and adaptive polynomial mutation operation on the next generation of individuals; judging whether the current evolution algebra reaches the maximum iteration times, if so, merging the sub-populations to output an optimal solution set; if not, judging whether the migration condition is met; if yes, carrying out self-adaptive migration, mutually exchanging a plurality of individuals among the sub-populations, and continuing genetic operation; if not, continuing the genetic operation.
The foregoing description is merely a preferred embodiment of the parameter calibration method and apparatus for parallel genetic algorithm based on adaptive strategy disclosed in the present invention, and is not intended to limit the scope of the embodiments of the present specification. Any modification, equivalent replacement, improvement, or the like made within the spirit and principle of the embodiments of the present specification should be included in the protection scope of the embodiments of the present specification.
Claims (10)
1. The parameter calibration method of the parallel genetic algorithm based on the self-adaptive strategy is characterized by comprising the following steps of:
step 1, determining a parameter range of each parameter in a hydrological model, and carrying out real number coding and random generation on an initial population;
step 2, dividing the initial population into a plurality of sub-populations, and enabling each sub-population to independently and concurrently execute genetic operation on different processors;
step 3, taking the qualification rate of the total flood, the peak flood and the peak current time as optimization targets, establishing a multi-target optimized objective function, taking the forward index of the objective function as an fitness function, calculating the fitness of each individual in the sub-population, and determining the next generation of individuals based on elite retention strategies and competitive bidding selection methods;
step 4, performing adaptive simulation binary crossover and adaptive polynomial mutation operation on the next generation of individuals;
Step 5, judging whether the current evolution algebra reaches the maximum iteration times, if so, merging the sub-populations to output an optimal solution set; if not, entering the next step;
step 6, judging whether the cross variation cycle times reach a preset value, if so, carrying out self-adaptive migration, mutually exchanging a plurality of individuals among the sub-populations, and turning to step 3; if not, go to step 3.
2. The parameter calibration method of parallel genetic algorithm based on adaptive strategy according to claim 1, wherein the parameter range of each parameter in the hydrological model is determined, and the method specifically comprises the following steps:
determining a waiting calibration parameter, wherein the waiting calibration parameter comprises a evaporation conversion coefficient K, an upper layer tension water storage capacity WUM, a lower layer tension water storage capacity WLM, a deep layer emission coefficient C, a total tension water storage capacity WM, a tension water storage capacity curve index B, a drainage basin water impermeable area IM, a free water storage capacity SM, a free water storage capacity curve index EX, an in-soil outflow coefficient KI, an in-soil outflow coefficient CI, a subsurface runoff extinction coefficient CG, a river network water extinction coefficient CS and a flood time L, and adopting a fixed structural constraint: total tension water storage capacity wm=upper tension water storage capacity WUM +lower tension water storage capacity wlm+deep tension water storage capacity WDM, groundwater outflow coefficient kg+in-soil outflow coefficient ki=0.7;
And determining the parameter range of the waiting-to-be-rated parameter.
3. The parameter calibration method of the parallel genetic algorithm based on the adaptive strategy according to claim 1, wherein the next generation individual is determined based on the elite retention strategy and the competitive race selection method, and the method specifically comprises the following steps:
the population individuals with optimal fitness are reserved, and excellent individuals are selected from the rest parent individuals through a competitive bidding competition selection method;
the individual with the optimal fitness and the excellent individual are taken as the next generation individuals.
4. The parameter calibration method of parallel genetic algorithm based on adaptive strategy according to claim 1, wherein the expression of the objective function is:
F＝max(u 1 *QR v +u 2 *QR p +u 3 *QR t )
QR in v Is the qualification rate of the total floodQR p Is the qualification rate of flood peak flow> QR t Time-of-peak qualification rate->m is the number of field floods participating in the calculation; n is n v 、n p 、n t Respectively the number of qualified floods relative to the total amount of floods, the peak flow rate and the peak time; u (u) 1 、u 2 、u 3 Respectively the weight of the total flood qualification rate, the peak flood qualification rate and the peak time qualification rate.
5. The parameter calibration method of parallel genetic algorithm based on adaptive strategy according to claim 1, wherein the performing the adaptive simulated binary crossover and adaptive polynomial mutation operation on the next generation individual specifically comprises the following steps:
The expression of the crossover probability is:
the expression of the mutation probability is:
k in 1 、k 2 、k 3 、k 4 For the self-adaptive control parameter, f is the fitness of the population, f' is the larger fitness value in the two individuals to be crossed, f max For maximum fitness of population, f min Gamma, the minimum fitness of the population 0 Discrete coefficients, gamma, of fitness function for the primary population t The fitness function discrete coefficient of the population of the t generation;
the expression of the crossover operator is:
c 1 ＝0.5[(1+β)p 1 +(1-β)p 2 ]
c 2 ＝0.5[(1-β)p 1 +(1+β)p 2 ]
wherein the method comprises the steps of
In p 1 And p 2 C is the parent before crossing 1 And c 2 For cross-generated offspring, beta is the distribution factor, u c Is [0,1]Random number, eta c In the form of a cross-distribution index,is eta c Upper limit value of>Is eta c Lower limit value of (2);
the expression of the mutation operator is:
v′ k ＝v k +δ(h k -l k )
wherein the method comprises the steps of
δ 1 ＝(v k -l k )/(h k -l k )
δ 2 ＝(h k -v k )/(h k -l k )
V in k Is the father before mutation, v' k Progeny of the mutation, h k Upper limit of variation of variables, l k Is the lower limit of variation, delta is the variation coefficient, u m Is [0,1]Random number, eta m In order to obtain the mutation distribution index,is eta m Upper limit value of>Is eta m Lower limit value of (2).
6. The method for calibrating parameters of parallel genetic algorithm based on adaptive strategy according to claim 5, wherein the population is provided with p individuals, each individual has w variables, the population is represented by p x w matrix, and x ij As matrix elements, the expression of the discrete coefficient gamma is as follows:
in which x is ij As matrix elements, k j Is the variable mean value.
7. The parameter calibration method of parallel genetic algorithm based on adaptive strategy according to claim 1, wherein the adaptive migration specifically comprises the following steps:
calculating the discrete degree and average fitness value of each sub-population, wherein the discrete degree is represented by a population discrete coefficient gamma;
selecting a population with the smallest average fitness value as an immigrating population, and selecting a population with the smallest gamma value as an immigrating population; and using the population with the second smallest population average fitness value as an immigrating population, and selecting the population with the second smallest gamma value as an immigrating population until a unidirectional ring topological structure is formed among all sub-populations.
8. The method for calibrating parameters of parallel genetic algorithm based on adaptive strategy according to claim 7, wherein when the population average fitness value and the gamma value are selected to be the same population, the current migration operation is abandoned and the next population pair is migrated.
9. The parameter calibration method of parallel genetic algorithm based on adaptive strategy according to claim 7, wherein the expression of population average fitness is:
F in i The fitness value of the population individuals is p, and the number of the population individuals is p.
10. The parameter calibration device of the parallel genetic algorithm based on the self-adaptive strategy is characterized by comprising the following components: a data encoding module and a calculating module, wherein,
the data coding module is used for determining the parameter range of each parameter in the hydrologic model, and real number codes and randomly generates an initial population;
the computing module is used for dividing the initial population into a plurality of sub-populations, so that each sub-population is independently and concurrently executed on different processors; establishing a multi-objective optimized objective function by taking the qualification rate of the total flood, the peak flood and the peak current time as optimization targets, calculating the fitness of each individual in the sub-population by taking the forward index of the objective function as a fitness function, and determining the next generation of individuals based on elite retention strategies and bidding competition selection methods; performing adaptive simulation binary crossover and adaptive polynomial mutation operation on the next generation of individuals; judging whether the current evolution algebra reaches the maximum iteration times, if so, merging the sub-populations to output an optimal solution set; if not, judging whether the cross variation cycle times reach a preset value, if so, performing self-adaptive migration, mutually exchanging a plurality of individuals among the sub-populations, and continuing genetic operation; if not, continuing the genetic operation.
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