Precision agriculture administration primarily based on a surrogate mannequin assisted multiobjective algorithmic framework

Precision agriculture administration primarily based on a surrogate mannequin assisted multiobjective algorithmic framework

Research space

The examine space is positioned in Lintong District, Xi’an Metropolis, Shaanxi Province, China (34° 21′ 59.94″, 109° 12′ 51.012″) (Meteorologists, 2020b). The examine space is positioned in northwestern China (Fig. 1), which is a Heat temperate semi-humid continental local weather with distinct chilly, heat, dry and moist seasons. Winter is chilly, windy, foggy, and with little rain or snow. Spring is heat, dry, windy, and variable. The summer time is scorching and wet, with outstanding droughts and thunderstorms, and excessive wind. Autumn is cool, the temperature drops quickly and autumn showers are apparent. The annual common temperature is 13.0–13.7 °C, the coldest January common temperature is −1.2–0 °C, the most well liked July common temperature is 26.3–26.6 °C, the annual excessive minimal temperature is −21.2 °C, Lantian December 28, 1991, the annual excessive most temperature is 43.4 °C, Chang’an June 19, 1966. Annual precipitation is 522.4–719.5 mm, growing from north to south. July and September are the 2 apparent peak precipitation months. The annual sunshine hours vary from 1646.1 to 2114.9 h. The dominant wind route varies from place to position, with the northeast wind in Xi’an, west wind in Zhouzhi and Huxian, east-northeast wind in Gaoling and Lintong, southeast wind in Chang’an, and northwest wind in Lantian. Meteorological disasters embrace drought, steady rain, heavy rain, flooding, city flooding, hail, gale, dry scorching wind, excessive temperature, lightning, sand and dirt, fog, haze, chilly wave, and low-temperature freeze.

Determine 1
figure 1

Location of the sphere of examine (The satellite tv for pc imagery supporting this examine was obtained utilizing Baidu Maps (Android model— The URL is (,5210675.606268121,8.67z.).

Wheat (XiNong 805) was planted on September 24, 2019 and matured for harvest on Could 28, 2020 (We warrant that we’ve the suitable to gather and handle wheat (XiNong 805). As well as, the examine is in compliance with related institutional, nationwide, and worldwide tips.). Among the many six methods within the experiment (Desk 1), we centered on methods 1 and 4, fastened irrigation dates optimization and stuck fertilizer software dates optimization. Based mostly on the customized of the examine space, three days of diffuse irrigation have been chosen for Technique 1. Three days of fertilization of the urea and three days of irrigation have been chosen for Technique 4. One of the best follow for Technique 1 was complete irrigation of 201 mm for the full season and a complete of 7388 kg/ha of wheat was obtained for this simulation, whereas one of the best follow for Technique 4 was complete irrigation of 197 mm for the full season and a complete fertilizer software of 282 kg/ha for the full season. A complete of 7894 kg/ha of wheat was obtained for this simulation.

Desk 1 Particulars of the 6 methods of the experimental setup.

DSSAT mannequin

DSSAT, probably the most broadly used crop development fashions, is an built-in laptop system developed by the College of Hawaii underneath the authority of the U.S. Company for Worldwide Improvement (USAID). It goals to combination varied crop fashions and standardize the format of mannequin enter and output variables to facilitate the diffusion and software of fashions7, thereby accelerating the diffusion of agricultural know-how and offering choice making and countermeasures for the rational and environment friendly use of pure sources in creating nations.

The DSSAT 4.5 mannequin integrates all crop fashions into the simulation pathway-based CSM (Cropping System Mannequin) farming system mannequin, which makes use of a set of simulated soil moisture, nitrogen, and carbon dynamics codes, whereas crop development and growth are stimulated by means of the CERES37,38, CROPGRO39, CROPSIM, and SUBSOR modules. DSSAT is relevant to single websites or identical sort zones and might be extrapolated to the regional degree by means of Geographic Data System (GIS).

DSSAT–CSM simulates the expansion strategy of crops grown on a uniform land space underneath prescribed or simulated administration40, and the modifications in soil water, carbon and nitrogen with underneath tillage techniques. The DSSAT mannequin is a call help system supported by crop simulation fashions, which, along with information help, offers strategies for calculating and fixing issues, and offers decision-maker with the outcomes of their choices. It additionally offers scientific choices for farmers to supply completely different cultivation administration measures (e.g., correct fertilization and irrigation for crops) in numerous climatic years.

Inputs and outputs of the mannequin

The DSSAT mannequin has 4 major user-editable enter recordsdata and varied output recordsdata. The enter recordsdata embrace crop administration7,41, soil, climate, and cultivar parameter recordsdata; the output recordsdata embrace three varieties: (1) output recordsdata, (2) seasonal output recordsdata, and (3) diagnostic and administration recordsdata.

Crop administration information: Crop administration information offers primary details about crop development. Detailed and correct parameter provision is the premise for bettering the accuracy of mannequin simulation. Crop administration parameters embrace crop selection, soil sort, meteorological identify, earlier season crop, sowing interval, sowing density, sowing depth, irrigation quantity and time, fertilizer software quantity and time, the preliminary situation of the soil, pest administration, tillage frequency and technique, and so on. A few of these parameters are usually not simply out there in discipline experiments and might be obtained from different take a look at websites or from current documentation. Then again, if there are lacking values within the mannequin, it’ll improve the simulation error of the mannequin (this example is tough to keep away from). Due to this fact, on this examine, the parameters have been chosen primarily based on the precept of being each detailed and simply out there.

Soil information Soil information incorporates varied parameters of the soil part aircraft, together with soil shade, soil slope, soil capability, natural carbon, soil nitrogen content material, drainage properties, the proportion of clay, particles, and stones within the soil. Just like the governing paperwork, the extra full the parameters the smaller the error worth of the simulation. The assorted bodily and chemical properties of the soil for this examine have been obtained from the China Soil Database on the time of the examine. The assorted bodily and chemical properties of the soil for this examine have been obtained from the China Soil Database.

Climate information The DSSAT mannequin makes use of every day climate information as climate enter information for the mannequin. The mannequin requires a minimal of 4 every day climate information so as to precisely simulate the water cycle in soil crops (Fig. 2). These are:(1) every day photo voltaic radiation vitality (MJM); (2) every day most temperature (°C); (3) every day minimal temperature (°C); and (4) every day precipitation (mm). Climate information have been obtained from the China Meteorological Administration. Climate information have been obtained from the China Meteorological Administration.

Determine 2
figure 2

Precipitation and most and minimal temperatures throughout 2019–2020.

Mannequin calibration Adjusting the cultivar parameter is essential to precisely simulate the native rising setting. On this experiment, we collected discipline information for 2019 and 2020, and adjusted the parameters within the cultivar parameter recordsdata by trial-and-error technique to make the simulation course of extra intently match the precise native crop development course of.

Multi-objective optimization algorithm

Multi-objective optimization methods have been efficiently utilized in lots of real-world issues. Typically42,43,44, MOPs produce a set of optimum options that collectively signify a trade-off between conflicting targets, and such options are referred to as Pareto optimum options (PS). These PS can not make any answer higher with out compromising the opposite options. Due to this fact, when fixing multi-objective issues, extra PS are wanted to seek out. Some MOPs purpose to seek out all PS or a minimum of a consultant subset of them.

A multi-objective optimization downside might be acknowledged as follows:

$$mathrm{min }Fleft(xright)={({f}_{1}left(xright),dots ,{f}_{ok}(x))}^{T}$$


$$mathrm{topic;to};xin Omega$$


the place (Omega) is the choice house,(F:Omega to {R}^{ok}) consists of (ok) real-value goal capabilities and ({R}^{ok}) is named the target house. The attainable goal set is outlined because the set ({F(x)in Omega }).

NSGA-II optimizer

We use non-dominated sorting genetic algorithm (NSGA-II) for Multiobjective optimization in R language. The NSGA-II algorithm is a classical multi-objective evolutionary algorithm with exceptional ends in fixing 2-objective and 3-objective issues45. It maintains the convergence velocity and variety of options by quick non-dominated sorting and crowding distance, selects the subsequent inhabitants by elite choice technique.

Goal operate

The multi-objective optimization downside varies a number of variables to maximise or reduce two or extra goal issues. Within the case of crop manufacturing, the place decision-makers change irrigation and fertilizer software to maximise advantages, this examine focuses on when to use irrigation or fertilizer on the sphere and the way a lot irrigation or nitrogen fertilizer to use.

There are numerous crop fashions out there that can be utilized as optimization goal capabilities, and DSSAT is unquestionably the only option as a result of it’s simple to make use of and well-proven36. The consumer runs the mannequin by getting into outlined soil, climate, selection, and crop administration recordsdata, that are fed into the core of the mannequin, the Crop Simulation Mannequin (CSM). The mannequin simulates the expansion, growth, and yield of crops grown on a uniform land space underneath administration, in addition to modifications in soil water, carbon, and nitrogen over time underneath cropping techniques. The CSM itself is a extremely modular mannequin system consisting of various sub-modules. Researchers have validated the output of those sub-modules as an entire underneath varied crops, local weather, and soil situations.

Utilizing DSSAT, it’s simple to design a set of goal capabilities and optimize them, as in our case.

$$mathrm{Max}:Y=mathrm{DSSAT}left.left( {i}_{a0},dots ,{i}_{mathrm{aj}},{f}_{mathrm{a}0},dots ,{f}_{mathrm{advert}},{D}_{i}proper.proper)$$






the place (Y) is yield,(I) is the full quantity of irrigation, (F) is the full quantity of nitrogen software, ({i}_{an}) is the quantity of irrigation at one time, ({f}_{am}) is the quantity of nitrogen utilized at one time, (j) is various purposes of irrigation, and (d) is various nitrogen purposes. ({D}_{i}) is a random date mixture of irrigation time and fertilizer software time.

All different variables (e.g., local weather, soil, location, crop selection) are saved fixed through the optimization course of. The irrigation unit is mm and the nitrogen software unit is kg/ha, the irrigation and nitrogen software quantities are constructive integers by default (integer arithmetic reduces this system operating time).

Knowledge-driven evolutionary algorithms

Typically, the important thing to DDEAs is to scale back the required FEs and help evolution by means of information. The info is usually utilized by means of surrogate mannequin. Using appropriate surrogate mannequin can be utilized rather than actual FEs46. Thus, DDEAs have extra benefits over EAs in fixing costly issues.

When it comes to algorithmic framework, DDEAs comprise two components: surrogate mannequin administration (SMM) and evolutionary optimization half (EOP)47,48. The SMM half is used so as to acquire higher approximations, whereas EOPs will use surrogate fashions in EAs to help evolution. DDEAs might be divided into two varieties: on-line DDEAs and offline DDEAs23. On-line DDEAs might be evaluated by actual FEs with extra new information. This new info can present SMM with extra info and assemble a extra correct surrogate mannequin49. Since DSSAT can acquire new information by means of FEs through the EOP course of, the strategy used on this paper is on-line DDEAs. In distinction, offline DDEAs can solely drive evolution by means of historic information.

Radial Foundation Perform (RBF) community is a single hidden layer feedforward neural community that makes use of a radial foundation operate because the activation operate for the hidden layer neurons, whereas the output layer is a linear mixture of the outputs of the hidden layer neurons. RBF was used to approximate every goal operate. In line with the investigation of multi-objective optimization issues with excessive computational price, radial foundation capabilities are sometimes used because the surrogate mannequin, primarily as a result of RBF networks can approximate arbitrary nonlinear capabilities with arbitrary accuracy and have international approximation functionality, which essentially solves the native optimum downside of BP networks, and the topology is compact, the structural parameters might be discovered individually, and the convergence velocity is quick.

On this paper, a brand new data-driven method is proposed and place it within the lower-level optimization of the framework. RBF is utilized because the surrogate mannequin and NSGA-II because the optimizer. Particulars are described in Algorithm 1.

Knowledge-driven technique particulars

figure a

In step 1, the preliminary guardian inhabitants is generated by randomly choosing factors and the dimensions is (N). In step 2, we run DSSAT (N) instances to find out the target operate values of the (N) preliminary inhabitants options. Subsequent, the algorithm then loops by means of the generations. Firstly of every loop, surrogate fashions, which one goal prepare one surrogate and denoted by ({s}_{t}^{left({f}_{1}proper)}) , have been educated by the already obtained goal operate values (step 3.1). The trial offspring ({P}_{i}^{^{prime}}left(tright)={ {x}_{1}^{^{prime}}left(tright),dots ,{x}_{u}^{^{prime}}left(tright)}) are generated by SBX and PM (step 3.2), then the educated surrogate mannequin is used to foretell the target operate values of trial offspring (step 3.3). The expected goal operate values are sorting by Pareto non-dominated and crowding distance (step 3.4), then (r) offspring (Q_{i} left( t proper) = left{ {x^{primeprime}_{1} left( t proper), ldots ,x^{primeprime}_{r} left( t proper)} proper}) are chosen from the trial offspring (step 3.5).The offspring are evaluated by the DSSAT (step 3.6), and after combining the guardian inhabitants and offspring inhabitants (step 3.7), the brand new guardian inhabitants are chosen by Pareto non-dominated and crowding distance sorting (step 3.8).

Most extension distance

MED guides a small variety of people to approximate your entire PF. MED is outlined as observe:

$$mathrm{MED}left({P}_{t}^{left(qright)}proper)=mathrm{ND}left({P}_{t}^{left(qright)}proper)instances mathrm{TD}left({P}_{t}^{left(qright)}proper)$$


the place

$$mathrm{ND}left({P}_{t}^{left(qright)}proper)=underset{z,qne z}{mathrm{min}}sum_{m=1}^{M}left|{f}_{m}^{left(qright)}-{f}_{m}^{left(zright)}proper|$$


({P}_{t}^{left(qright)}) is the qth particular person in inhabitants Pt on the tth technology. (mathrm{ND}left({P}_{t}^{left(qright)}proper)) calculates the minimal distance between ({P}_{t}^{left(qright)}) and ({P}_{t}^{left(zright)}). The bigger (mathrm{ND}left({P}_{t}^{left(qright)}proper)) worth means a greater particular person variety. (mathrm{TD}left({P}_{t}^{left(qright)}proper)) calculates the summation of distance between ({P}_{t}^{left(qright)}) and ({P}_{t}^{left(zright)}). The bigger (mathrm{TD}left({P}_{t}^{left(qright)}proper)) worth implies that the answer ({P}_{t}^{left(qright)}) has moved away from different people. A bigger MED worth implies that a person extends the general boundary and a person acquires higher variety.

Modeling course of

To maximise crop yield and optimize the use effectivity of water and fertilizer in a given setting, BSBOP framework is proposed. Crop development is simulated by DSSAT, the data-driven method reduces the runtime of the general framework whereas discovering optimum administration methods. The general framework contains 4 major components: upper-level screening, upper-level optimization, lower-level optimization and lower-level screening (Fig. 3).

Determine 3
figure 3

Proposed built-in bi-level screening, bi-level optimization and DSSAT framework.

Higher-level screening The climate file in DSSAT was loaded by R language. The info are pre-processed with precipitation and photo voltaic radiation info to slender down the date vary for irrigation and fertilizer software. In different phrases, the date ranges for choosing irrigation and fertilization are restricted by the ULS.

Higher-level optimization Producing random mixtures of dates by the Latin hypercube sampling technique (LHS). The upper-level screening begins with referencing the 2 variables (variety of irrigation and nutrient software occasions). LHS makes use of these variables to generate a collection of uniformly distributed random day mixtures. For instance, date mixtures generated by the LHS may very well be Could 15, July 18 and August 1 for irrigation and Could 30, June 30 and July 18 for nutrient software. From the collection of uniformly distributed random day mixtures, one shall be chosen and integrated into the lower-level optimization.

Decrease-level optimization The agricultural administration technique is optimized by the net data-driven method proposed in Algorithm 1. Assuming three irrigation and three nitrogen software occasions are given, these occasions shall be integrated into the LOP, which consists of the RBF and NSGA-II. The inhabitants dimension of this paper is 105. The variety of iterations varies in keeping with the completely different methods, and the target operate values are calculated by DSSAT. The principle thought of making use of Evolutionary multi-objective algorithms(EMO) and RBF to DSSAT is to generate numerous trial offspring by conventional Simulated Binary Crossover (SBX) and Polynomial Mutation (PM), after which consider them utilizing the educated surrogate mannequin50. The target values of the analysis have been then ranked by Pareto non-dominated and crowding distance, and the highest 105 people have been chosen from numerous trial offspring, after which a small variety of people out of 105 have been chosen by Most Extension Distance (MED) for actual operate analysis, after which mix the dad and mom and offspring to pick the subsequent technology of oldsters by Pareto non-dominated and crowding distance sorting. Moreover, within the numerical experiments, to make sure the prevalence of the algorithm and scale back the experimental complexity, we use a comparatively easy radial foundation operate (RBF) surrogate. The NSGA-II algorithm can be utilized for each bi-objective and tri-objective issues, so it will probably optimize the system by beginning with probably the most vital goal after which including extra targets. For every answer within the inhabitants, the target capabilities (1: maximize yield, 2: reduce irrigation software, 3: reduce nitrogen fertilizer software) shall be evaluated by invoking the DSSAT mannequin for these dates and the quantity of fertilizer irrigation utilized. Populations shall be examined towards the termination standards (most variety of iterations allowed). If the termination standards are usually not glad, the inhabitants evolves and is re-evaluated once more. The method is repeated till the termination criterion is glad after which the native Pareto entrance of the chosen day mixture is saved. After every iteration of the UOP, the brand new native Pareto is mixed with the worldwide Pareto frontier. Within the subsequent step, if there are any remaining day mixtures, the above course of is repeated for every new day mixture till all generated random day mixtures have been processed.

Decrease-level screening Firstly, the Ok-means technique is used to display screen the worldwide Pareto options with larger yield. Then, secondary screening takes financial effectivity as the target and optimizes it by Differential Evolution (DE) algorithm. Lastly, the regionally applicable answer is intelligently chosen.

Optimization methods and configuration

As a result of complexity of the issue, a BSBOP framework was proposed on this examine. Resulting from numerous variables behind irrigation and fertilization, traversal date for optimization seems to be significantly troublesome and time-consuming, assuming that solely irrigation is optimized for 120 days of the expansion cycle and the decision-maker has 0-150 mm of water per day, then there are ({151}^{120}) completely different options. If each irrigation and fertilization are thought-about, then there are ({151}^{120}cdot {151}^{120}) completely different options. Due to this fact, this examine tries to scale back the variety of variables whereas minimizing the operating time of the algorithm.

Right here we hypothesize that extra precision and efficient agricultural administration might be carried out by means of the proposed framework. Not solely can crop yields be elevated, but additionally irrigation software and fertilizer software might be decreased, whereas the options obtained have essential steerage for decision-makers: such because the number of irrigation and fertilizer software dates through the rising season of the crop, the number of irrigation and fertilizer software quantities, and the connection between financial advantages and software prices. To check this speculation, completely different optimization methods have been developed and evaluated (Desk 1). Every optimization technique was geared toward maximizing yield whereas minimizing useful resource wastage.

The assorted methods are listed under (Desk 1). Technique 1—Mounted irrigation dates: Holding the variety of irrigation days and all parameters fixed, solely the quantity of irrigation on every date is modified, making an attempt to scale back the quantity of irrigation as a lot as attainable, make it simple to match the outcomes with greatest practices. Technique 2—Optimum irrigation dates: Traverse by means of the irrigation dates to optimize irrigation, and attempt to discover a higher mixture of irrigation dates (optimum dates) and higher quantity of irrigation over the wheat development cycle. Technique 3—Optimum irrigation dates primarily based on surrogate mannequin: RBF is added to Technique 2, which makes it attainable to scale back a number of time. Technique 4—Mounted fertilizer software date: Utilizing the optimum irrigation date present in Technique 2 whereas holding the variety of days of fertilization and all different parameters fixed, irrigation and fertilization are optimized in an try to reduce the quantity of irrigation and fertilizer utilized. Technique 5—Optimum fertilizer software date: whereas making certain the optimum irrigation date, traverse the fertilizer software date for optimization, looking for out the potential yield of the crop. Technique 6—Optimum fertilizer software date primarily based on surrogate mannequin: RBF is launched primarily based on Technique 5. The time consumption was decreased.

The stopping criterion on this examine is when the optimization outcomes converge visually. The algorithm inhabitants dimension was set to 105, and the technology of offspring used conventional polynomial Mutation. The variety of hidden layers of the surrogate mannequin is the same as the dimension of the choice variables, the training charge is 0.01, the Gaussian kernel operate is chosen because the activation operate of the hidden layer within the RBF community. The neurons facilities are generated by the Ok-means clustering technique. The width parameter of the operate is generated by calculating the variance of every cluster. The optimization weight parameters are chosen by the recursive least sq. technique. It’s because using the least sq. technique is prone to encounter conditions the place matrix inversion is troublesome. Due to this fact, recursive least squares (RLS) is usually used to present a recursive type of the matrix wherein the inverse must be discovered, making it computationally simpler.