## Abstract

In this paper, an optimization model is formulated and optimal cropping pattern is suggested. Conjunctive use of water is not feasible for the study area as groundwater is the only source to fulfil irrigation demand. Water resources for the study area are limited. Best utilization of available water resources for increased net benefits is always advisable. Sinnar Taluka of Nasik district of Maharashtra state in India is considered as a study area. An existing cropping pattern is studied extensively and a new cropping pattern is suggested. Teaching–learning-based algorithm (TLBO) and particle swarm optimization (PSO) algorithm are applied to solve the optimization model. TLBO algorithm provides higher net returns as compared to PSO algorithm. TLBO and PSO saves up to 16.52% of water and benefits are increased by 35.81%. The study area is overexploited, this is fact. The new cropping pattern is suggested by considering minimum rainfall, i.e., 400 mm, so that in years when rainfall is above minimum rainfall the groundwater levels will be raised. In the proposed cropping pattern a few crop areas are majorly increased and a few crop areas are majorly reduced. The remaining crop areas are minorly increased or reduced and net benefits are increased and water demand decreased.

## Introduction

Groundwater resource becomes very important where surface water resource is not available. In such cases, all human needs regarding water are fulfilled by groundwater only. Rainfall is the only source for groundwater recharge. Other sources are manmade runoff conservation structures. In such cases, in many places mining of groundwater resource takes place. In this study, the authors first carried out recharge estimation of Sinnar Taluka (MS, India). The study indicated that Sinnar Taluka has limited water resources because average rainfall is 500 mm and also there is no major river or canal. The major business of Sinnar Taluka is agriculture. In the study area, every year, farmers plan the cropping pattern on the basis of rainfall forecasting information and previous years' experience. The farmers in the study area have complained about losses due to the current cropping pattern, lack of water supply and dryness of wells. This has happened because the study area is totally dependent on groundwater source. Recharge is a very slow process. In recent years, due to climate change, uncertainty is involved in rainfall. On the other hand, in such a situation, farmers have been constantly extracting groundwater which causes mining and imbalance in the groundwater reservoir.

All of these problems come under the groundwater management problem. Water and land are the important resources which lead to agricultural development. Optimal use of these resources results in increased net benefits and better utilization of these resources. The farmers are unable to make optimal use of available resources because of uncertainty involved in the water supply and a lack of knowledge. In actual practice, when water is sufficiently available, farmers may use more water than is required for maximum production. In the study area, farmers do not use advanced methods of water application such as drip irrigation. Due to this it is necessary to plan the best cropping pattern and the best methods of water application for optimal scientific use of resources.

Optimization is one of the scientific tools that help researchers to get the best results under the given conditions. It is the process of finding the conditions that give the maximum or minimum value of a function. LINGO, an optimization software package, is available to solve optimization problems (Mainuddin *et al*., 1997; Dahiphale *et al*., 2014). Optimization may be a single objective or multi-objective optimization (Yang *et al*., 2001; Lalehzari *et al*., 2016). There are many optimization methods such as linear programming and nonlinear programming (Benli & Kodal, 2003; Gharaman & Sepaskhan, 2004; Azimi *et al*., 2013; Singh & Panda, 2013), dynamic programming (Karamouz *et al*., 2010), integer programming, stochastic programming, etc. Recently, some methods have become available which are based on certain biological, molecular and neurological phenomena, e.g., genetic algorithm (Oluwole *et al*., 2014) is an evolutionary algorithm and particle swarm optimization (PSO) is a swarm intelligence algorithm (Noory *et al*., 2012; Shaikh *et al*., 2015). Neural network methods and fuzzy optimization methods are also well known methods of optimization. Li *et al*. (2016) developed a multi-objective fuzzy programming model (IMOFP). In recent years, water resources researchers have also been using new algorithms to find the best solution to problems. Evolutionary algorithms and swarm intelligence-based algorithms are gaining in popularity. They give good results as compared to traditional optimization methods. However, these algorithms require their own algorithm-specific control parameters apart from common controlling parameters. The algorithm-specific parameters require proper tuning. Tuning is an important factor which affects the performance of the above-mentioned algorithms. The improper tuning of algorithm-specific parameters either increases the computational effort as well as leading to local optimal solution.

Considering these facts, the teaching–learning-based optimization (TLBO) algorithm (Rao *et al*., 2011) does not require any algorithm-specific parameters. It requires only common control parameters like population size and number of generations for its working. The TLBO algorithm possesses excellent exploration and exploitation capabilities; it is less complex and has also proved its effectiveness in solving single-objective and multi-objective optimization problems. The TLBO algorithm has been widely applied by optimization researchers in various fields of engineering in order to solve continuous and discrete optimization problems in mechanical engineering, electrical engineering, civil engineering, computer science, etc. (Rao, 2015).

In this work, the TLBO and PSO algorithms are used to determine the optimum cropping pattern to maximize net annual returns. The methodology section describes the mathematical formulation of the optimization problem in detail. For increased net annual returns, proper utilization of available land and water resources is necessary. Here, mathematical models are developed based on the data collected from the database of government agencies, interviewing the farmers in the region and a practical survey of the region. Constraints are the total cultivable area and limit on cultivable land available for growing each crop.

### Hypothesis

- 1.
Increased net benefits from proposed cropping pattern.

- 2.
Less utilization of water for proposed cropping pattern than existing pattern.

The next section describes the geographical aspects of the study area.

## Study area

The Nasik district of Maharashtra lies between 19°35′ and 20°50′ northern latitude and 73°16′ and 74°56′ eastern longitude with an area of 15,530 km^{2} (Figure 1). Godavari and Girna are the main rivers flowing through this district. Nasik district is divided into 15 taluka. Sinner is one of the taluka. It lies between 19°85′ northern latitude and 74°00′ eastern longitude. In Sinnar Taluka, reddish brown and medium light brownish black soil is found. The area is covered by Deccan Trap basalt. Weathered, fractured basalt is found. The groundwater in Deccan Trap basalt occurs mostly in the upper weathered and fractured parts down to 20–25 m depth. In places, potential zones are encountered at deeper levels in the form of fractures and inter-flow zones. The upper weathered and fractured parts form phreatic aquifers and the groundwater occurs under water table (unconfined) conditions. At deeper levels, the groundwater occurs under semi-confined to confined conditions. The study area has reached 99% groundwater development, thus the government of Maharashtra has decided not to undertake further groundwater development. There is no major river in Sinnar Taluka. The climate of Sinner is dry except in the southwest monsoon season. The year may be divided into three seasons, i.e., pre-monsoon, monsoon and post-monsoon. Average annual temperature is 25 °C. Average annual rainfall is 500 mm. The total geographical area of Sinner taluka is 1,360 km^{2}. Out of this total area the cultivable area is 871.2 km^{2}. An area of 116.55 km^{2} benefits from minor irrigation schemes. Paddy, kh. jawar, barley, maize, pulses, groundnut, soyabean, cotton, onion, wheat, sugarcane and vegetables are the major crops grown in the study area.

## Methodology

### Existing cropping pattern

As per the existing cropping pattern, the total groundwater extraction is 15,400 ha·m and net annual returns are 1,101.15 million rupees. A total of 34 crops are grown in one year and the total area under these crops in all zones is 87,100 ha. In the present case, mining is observed. Total groundwater extracted is more than the total groundwater recharge. Table 1 shows the existing cropping pattern of the study area.

Sr. no. | Crops | Area of zone 1 in ha | Area of zone 2 in ha | Area of zone 3 in ha | Total area in ha | Irrigation requirement in m | Total irrigation requirement in ha·m |
---|---|---|---|---|---|---|---|

1 | Green gram | 250 | 570 | 0 | 820 | 0.4097 | 335.95 |

2 | Potato | 200 | 100 | 55 | 355 | 0.3309 | 117.46 |

3 | Tomato | 550 | 270 | 181 | 1,001 | 0.4432 | 443.64 |

4 | Chilli | 35 | 3 | 19 | 57 | 0.492 | 28.04 |

5 | Field beans | 150 | 138 | 72 | 360 | 0.424 | 152.64 |

6 | Cabbage | 250 | 62 | 0 | 312 | 0.492 | 153.50 |

7 | Cauliflower | 320 | 50 | 7 | 377 | 0.492 | 185.48 |

8 | Carrot | 54 | 230 | 125 | 409 | 0.492 | 201.22 |

9 | Bringle | 40 | 80 | 30 | 150 | 0.5562 | 83.43 |

10 | Lady finger | 42 | 104 | 3 | 149 | 0.5632 | 83.91 |

11 | Bottle gourd | 55 | 73 | 136 | 264 | 0.5632 | 148.68 |

12 | Bitter gourd | 15 | 63 | 3 | 81 | 0.5632 | 45.61 |

13 | Sponge gourd | 25 | 15 | 1 | 41 | 0.5632 | 23.09 |

14 | Radish | 20 | 15 | 0 | 35 | 0.534 | 18.69 |

15 | Spinach | 50 | 105 | 0 | 155 | 0.492 | 76.26 |

16 | Fenugreek | 75 | 110 | 85 | 270 | 0.492 | 132.84 |

17 | Coriander | 310 | 215 | 60 | 585 | 0.492 | 287.82 |

18 | Rice | 671 | 370 | 0 | 1041 | 0.4043 | 420.87 |

19 | Jawar-k | 29 | 0 | 0 | 29 | 0.0684 | 1.98 |

20 | Bajra | 3,521 | 4,219 | 9,983 | 17,723 | 0.0678 | 1,201.61 |

21 | Maize | 3,005 | 929 | 9,493 | 13,427 | 0.0792 | 1,063.41 |

22 | Arhar | 244 | 114 | 148 | 506 | 0.2989 | 151.24 |

23 | Mung bean | 51 | 69 | 28 | 148 | 0.0829 | 12.26 |

24 | Black gram | 7 | 20 | 11 | 38 | 0.0939 | 3.56 |

25 | Groundnut | 1,140 | 532 | 671 | 2,343 | 0.0832 | 194.93 |

26 | Soyabean | 13,367 | 1,063 | 7,140 | 21,570 | 0.038 | 819.66 |

27 | Cotton | 0 | 0 | 1,650 | 1,650 | 0.1101 | 181.66 |

28 | Onion | 2,357 | 1,024 | 1,137 | 4,518 | 0.1337 | 604.05 |

29 | Jawar-R | 695 | 720 | 3,691 | 5,106 | 0.2869 | 1,464.91 |

30 | Wheat | 1,862 | 650 | 762 | 3,274 | 0.5319 | 1741.44 |

31 | Maize-R | 329 | 375 | 207 | 911 | 0.3185 | 290.15 |

32 | Horse gram | 944 | 1,060 | 1,428 | 3,432 | 0.7455 | 2,558.55 |

33 | Onion-R | 3,383 | 921 | 1,353 | 5,657 | 0.3279 | 1,854.93 |

34 | Sugarcane | 110 | 5 | 211 | 326 | 0.9828 | 320.39 |

87,100 | 15,400 |

Sr. no. | Crops | Area of zone 1 in ha | Area of zone 2 in ha | Area of zone 3 in ha | Total area in ha | Irrigation requirement in m | Total irrigation requirement in ha·m |
---|---|---|---|---|---|---|---|

1 | Green gram | 250 | 570 | 0 | 820 | 0.4097 | 335.95 |

2 | Potato | 200 | 100 | 55 | 355 | 0.3309 | 117.46 |

3 | Tomato | 550 | 270 | 181 | 1,001 | 0.4432 | 443.64 |

4 | Chilli | 35 | 3 | 19 | 57 | 0.492 | 28.04 |

5 | Field beans | 150 | 138 | 72 | 360 | 0.424 | 152.64 |

6 | Cabbage | 250 | 62 | 0 | 312 | 0.492 | 153.50 |

7 | Cauliflower | 320 | 50 | 7 | 377 | 0.492 | 185.48 |

8 | Carrot | 54 | 230 | 125 | 409 | 0.492 | 201.22 |

9 | Bringle | 40 | 80 | 30 | 150 | 0.5562 | 83.43 |

10 | Lady finger | 42 | 104 | 3 | 149 | 0.5632 | 83.91 |

11 | Bottle gourd | 55 | 73 | 136 | 264 | 0.5632 | 148.68 |

12 | Bitter gourd | 15 | 63 | 3 | 81 | 0.5632 | 45.61 |

13 | Sponge gourd | 25 | 15 | 1 | 41 | 0.5632 | 23.09 |

14 | Radish | 20 | 15 | 0 | 35 | 0.534 | 18.69 |

15 | Spinach | 50 | 105 | 0 | 155 | 0.492 | 76.26 |

16 | Fenugreek | 75 | 110 | 85 | 270 | 0.492 | 132.84 |

17 | Coriander | 310 | 215 | 60 | 585 | 0.492 | 287.82 |

18 | Rice | 671 | 370 | 0 | 1041 | 0.4043 | 420.87 |

19 | Jawar-k | 29 | 0 | 0 | 29 | 0.0684 | 1.98 |

20 | Bajra | 3,521 | 4,219 | 9,983 | 17,723 | 0.0678 | 1,201.61 |

21 | Maize | 3,005 | 929 | 9,493 | 13,427 | 0.0792 | 1,063.41 |

22 | Arhar | 244 | 114 | 148 | 506 | 0.2989 | 151.24 |

23 | Mung bean | 51 | 69 | 28 | 148 | 0.0829 | 12.26 |

24 | Black gram | 7 | 20 | 11 | 38 | 0.0939 | 3.56 |

25 | Groundnut | 1,140 | 532 | 671 | 2,343 | 0.0832 | 194.93 |

26 | Soyabean | 13,367 | 1,063 | 7,140 | 21,570 | 0.038 | 819.66 |

27 | Cotton | 0 | 0 | 1,650 | 1,650 | 0.1101 | 181.66 |

28 | Onion | 2,357 | 1,024 | 1,137 | 4,518 | 0.1337 | 604.05 |

29 | Jawar-R | 695 | 720 | 3,691 | 5,106 | 0.2869 | 1,464.91 |

30 | Wheat | 1,862 | 650 | 762 | 3,274 | 0.5319 | 1741.44 |

31 | Maize-R | 329 | 375 | 207 | 911 | 0.3185 | 290.15 |

32 | Horse gram | 944 | 1,060 | 1,428 | 3,432 | 0.7455 | 2,558.55 |

33 | Onion-R | 3,383 | 921 | 1,353 | 5,657 | 0.3279 | 1,854.93 |

34 | Sugarcane | 110 | 5 | 211 | 326 | 0.9828 | 320.39 |

87,100 | 15,400 |

### Cost and benefit analysis

A detailed survey of the study area is carried out and the cost of production and the yield of various crops calculated. Similarly, groundwater cost is also estimated with the help of Maharashtra State Electricity Board. It is 0.16 Rs/m^{3}. The cost of artificial recharge is also obtained from Minor Irrigation Department, Nasik. It is 0.9 Rs/m^{3}. The net annual benefits are 1,101.15 million rupees from the existing cropping pattern.

*NR*in Rs) from the mixed cropping pattern of the study area. The objective function is expressed by Equation (1):

The area under consideration consists of three zones and each zone consists of 33 crops. *NR* is net annual returns, *nz* is number of zones (1, 2, 3), *nc* is number of crops (1, 2, 3….33), *Azc* is area of each crop in each zone in m^{2}, *NR _{c}* is net returns for each crop in Rs/m

^{2},

*CGW*is cost of pumping groundwater from natural recharge in Rs/m

_{n}^{3},

*GW*is groundwater from natural recharge in m

_{n}^{3},

*CGW*is cost of artificial recharge,

_{A}*GW*is artificial recharge in m

_{A}^{3}. The net annual returns per square metre for the existing cropping patterns are shown in Figure 2.

### Constraints

#### Area constraint

#### Constraint on maximum and minimum allowable area

*c*’ in a particular zone ‘

*z*’ must not violate the constraints expressed by Equation (3): where

*A*

_{zc}^{min}is minimum crop area in each zone in m

^{2},

*A*

_{zc}^{max}is maximum crop area in each zone in m

^{2}.

The constraint is introduced to fulfil socio-economic needs. Different socio-economic considerations are introduced in the model by this constraint.

#### Water requirement constraint

*CWR*is irrigation requirement in m.

_{c}It is necessary to assess the water requirement for various crops for crop management in any area. Hence, crop water requirement for various crops is found using software Cropwat 8 (Allen *et al*., 1998). The crop water requirement for each crop is presented in Figure 3.

*GW*is the natural recharge in m

_{n}^{3}. The availability of natural groundwater varies from year to year. It is mainly dependent on rainfall. Total annual groundwater recharge changes from year to year. Hence, groundwater recharge (

*GW*in m

_{n}^{3}) is expressed in terms of rainfall (

*P*mm) by Equation (5):

Equation (5) is developed by formulating a groundwater budget model (Varade & Patel, 2018). There are 17 observation wells in the study area. The groundwater levels are recorded by the Groundwater Surveys and Development Agency (GSDA) in four different months, namely, January, March, May and October. For the present study, groundwater data are obtained from GSDA. Using these data, an equation for estimation of groundwater recharge (Equation (5)) was developed by the authors.

The next section provides details for the TLBO algorithm which is used to obtain the solution of the optimization problem.

### Details of algorithm which is used for current optimization problem

#### Teaching–learning-based optimization

*s*in each candidate solution

*xi*is modified according to Equations (6) and (7): where for

*i*∈ [1,

*N*] and independent variable

*s*∈ [1,

*n*], where

*N*is the population size,

*n*is the total number of independent variables,

*xt*is the best individual in the population (i.e., the teacher),

*r*is the random number taken from a uniform distribution on [0, 1], and

*Tf*is the teaching factor and is randomly set equal to either 1 or 2 with equal probability. The new solution is obtained after the teacher phase

*xi*′ replaces the previous solution

*xi*if it is better than

*xi*. As soon as the teacher phase ends the learner phase commences. The learner phase mimics the act of knowledge sharing between two randomly selected learners. The learner phase entails updating each learner based on another randomly selected learner as follows: if is better than otherwise

For *i* ∈ [1, *N*] and independent variable *s* ∈ [1, *n*], where *k* is the random integer in [1, *N*] such that *k* ≠ *i*, and *r* is a random number taken from a uniform distribution on [0, 1]. Again, the new candidate solution obtained after the learner phase *xi*″ replaces the previous solution *xi*′ if it is better than the previous solution *xi*′ (Rao & Rai, 2016).

In this research the variable is cropping area. Thus, the TLBO algorithm is applied for the developed optimization problem and the algorithm provides best values of variable by using the above explained philosophy of the algorithm. By using the TLBO algorithm, the net benefits are found. For a detailed explanation about the workings of the TLBO algorithm, readers may refer to https://sites.google.com/site/tlborao. The computer program for the TLBO algorithm was developed in Matlab R2013a.

#### Particle swarm optimization

*p*-best) of the particle. The best position taken by all particles so far is called the global best (

*g*-best) position of the search. The new position and velocity of each particle is obtained based on its previous position, the

*p*-best and the

*g*-best of the search (Kennedy & Eberhart, 1995). The PSO starts by generating random solutions. Each particle as the individual solution (X

_{i}= [x

_{i,1},x

_{i,2},…,x

_{i,d}]) is moved around in the search-space according to its velocity, which has d dimensional vectors (V

_{i}= [v

_{i},

_{1},vi,

_{2},…,v

_{i},

_{d}]), the same as the number of decision variables. The corresponding fitness value of each particle is calculated and the velocity of the ith particle is presented, as follows: where

*d*is the number of dimensions,

*i*= 1,2,3,….

*S*,

*j*= 1,2,3,….

*d*,

*r*

_{1}and

*r*

_{2}are to be chosen randomly between [0,1],

*x*is the position vector,

_{ij}*v*is the velocity vector.

_{ij}*c*

_{1}and

*c*

_{2}are the acceleration coefficients and

*w*is the inertia coefficient. For details about the workings of the PSO algorithm, readers may refer to http://www.swarmintelligence.org.

### Tuning of population size

In order to set the population size for the TLBO algorithm and PSO algorithm a number of trial runs are conducted with different population sizes varying from 10 to 50. The algorithms are executed 30 times independently with a randomly generated initial population for each run, for all the above-mentioned population sizes. Based on these trial runs a population size of 20 is selected for the PSO algorithm and of 25 for the TLBO algorithm.

### Convergence criteria

In this work, the standard deviation is considered as the convergence criteria. At the end of every generation the standard deviation for a set of best solutions provided by the algorithm in the previous ten generations is calculated. The algorithm is said to have converged when the standard deviation becomes zero, which indicates that there is no improvement in the result provided by the algorithm in the last ten generations.

The optimization problem is now solved using the PSO algorithm. PSO is a well-known optimization algorithm and has successfully achieved the global optimal solution for solving a number of complex engineering optimization problems. Therefore, the PSO algorithm is now applied in order to search the optimal solution for the optimization problem formulated in this work. The working of the PSO algorithm is largely dependent on common control parameters such as population size and number of generations and the algorithm-specific parameters like inertia coefficient (*w*) and acceleration coefficient (*c*_{1} and *c*_{2}). In order to fix the values of the control parameters, a number of trial runs are conducted by considering various combinations of population size, *w*, *c*_{1} and *c*_{2}. The PSO algorithm provided the best result for a population size of 20, *w* = 0.9, *c*_{1} = 2, *c*_{2} = 2. Now, for this combination of control parameters, the PSO algorithm is executed 30 times independently, each time with a randomly generated initial population. The convergence graphs for the best runs of the PSO and TLBO algorithms are shown in Figures 4 and 5.

As per the philosophy of the PSO algorithm, each particle as the individual solution is moved around in the search-space according to its velocity. Here, the problem variable is cropping area. The PSO algorithm is applied to the developed optimization model and run for 30 independent runs. As per the philosophy of PSO explained above, it gave the best value of variable, i.e., cropping area. It provided the solution of optimization problem, i.e., net benefits.

## Results and discussion

Net annual returns provided by the existing cropping pattern are 1,101.15 million Rs, by PSO are 1,466.3 million Rs and by TLBO are 1,495.5 million Rs. Comparison of the existing cropping pattern with the cropping patterns of PSO and TLBO is shown in Table 2. In the proposed cropping pattern the water allocation is reduced and net benefits are increased. The proposed cropping pattern obtained from TLBO is given in Table 3.

Cropping pattern | Existing | PSO | TLBO |
---|---|---|---|

Allocated area ha | 87,100 | 70,800 | 75,358.04 |

Allocated water ha·m | 15,400 | 12,356 | 12,855.83 |

Net benefits million Rs | 1,101.15 | 1,466.3 | 1,495.5 |

Cropping pattern | Existing | PSO | TLBO |
---|---|---|---|

Allocated area ha | 87,100 | 70,800 | 75,358.04 |

Allocated water ha·m | 15,400 | 12,356 | 12,855.83 |

Net benefits million Rs | 1,101.15 | 1,466.3 | 1,495.5 |

Sr. no. | Crops | Area of zone 1 in ha | Area of zone 2 in ha | Area of zone 3 in ha | Total area in ha |
---|---|---|---|---|---|

1 | Green gram | 106.2195 | 300 | 0 | 406.2195 |

2 | Potato | 350 | 251.6391 | 110.1711 | 711.8102 |

3 | Tomato | 550 | 270 | 181 | 1,001 |

4 | Chilli | 51.55823 | 4.455402 | 28.14858 | 84.16221 |

5 | Field beans | 114.2774 | 62.94891 | 19.41276 | 196.6391 |

6 | Cabbage | 337.5601 | 84.94167 | 0 | 422.5018 |

7 | Cauliflower | 360.895 | 57 | 8 | 425.895 |

8 | Carrot | 57.73678 | 237.6776 | 135.0688 | 430.4832 |

9 | Bringle | 45.42662 | 90.23876 | 34.43341 | 170.0988 |

10 | Lady finger | 48.16811 | 116.8726 | 3.487212 | 168.528 |

11 | Bottle gourd | 50 | 71.55246 | 133.3097 | 254.8621 |

12 | Bitter gourd | 14 | 62 | 2.9885 | 78.9885 |

13 | Sponge gourd | 30.185 | 18.43355 | 1.294063 | 49.91261 |

14 | Radish | 15 | 14.85947 | 0 | 29.85947 |

15 | Spinach | 49.30366 | 88.75372 | 0 | 138.0574 |

16 | Fenugreek | 75 | 104.492 | 39.78095 | 219.2729 |

17 | Coriander | 310 | 206.7883 | 51.88618 | 568.6745 |

18 | Rice | 1,101.181 | 1,011.222 | 0 | 2,112.403 |

19 | Jawar-k | 29.57283 | 0 | 0 | 29.57283 |

20 | Bajra | 3,500 | 3,156.727 | 4,781.109 | 11,437.84 |

21 | Maize | 5,000 | 1,408.225 | 12,500 | 18,908.22 |

22 | Arhar | 209.7311 | 114 | 139.78 | 463.5111 |

23 | Mung bean | 50 | 24.28567 | 30 | 104.2857 |

24 | Black gram | 7 | 18 | 10.00543 | 35.00543 |

25 | Groundnut | 4,082.798 | 1,989.242 | 2,400 | 8,472.04 |

26 | Soyabean | 5,532.328 | 447.2547 | 2,491.966 | 8,471.549 |

27 | Cotton | 0 | 0 | 2,000 | 2,000 |

28 | Onion | 2,500 | 1,283.129 | 1,141.224 | 4,924.354 |

29 | Jawar-R | 695 | 720 | 300 | 1715 |

30 | Wheat | 1,132.341 | 150 | 1,083.603 | 2,365.945 |

31 | Maize-R | 969.1114 | 1,300 | 600 | 2,869.111 |

32 | Horse gram | 139.9751 | 248.3431 | 360 | 748.3182 |

33 | Onion-R | 3,021.998 | 1,000 | 986.5149 | 5,008.513 |

34 | Sugarcane | 91.89952 | 7.426564 | 236.0857 | 335.4118 |

Sr. no. | Crops | Area of zone 1 in ha | Area of zone 2 in ha | Area of zone 3 in ha | Total area in ha |
---|---|---|---|---|---|

1 | Green gram | 106.2195 | 300 | 0 | 406.2195 |

2 | Potato | 350 | 251.6391 | 110.1711 | 711.8102 |

3 | Tomato | 550 | 270 | 181 | 1,001 |

4 | Chilli | 51.55823 | 4.455402 | 28.14858 | 84.16221 |

5 | Field beans | 114.2774 | 62.94891 | 19.41276 | 196.6391 |

6 | Cabbage | 337.5601 | 84.94167 | 0 | 422.5018 |

7 | Cauliflower | 360.895 | 57 | 8 | 425.895 |

8 | Carrot | 57.73678 | 237.6776 | 135.0688 | 430.4832 |

9 | Bringle | 45.42662 | 90.23876 | 34.43341 | 170.0988 |

10 | Lady finger | 48.16811 | 116.8726 | 3.487212 | 168.528 |

11 | Bottle gourd | 50 | 71.55246 | 133.3097 | 254.8621 |

12 | Bitter gourd | 14 | 62 | 2.9885 | 78.9885 |

13 | Sponge gourd | 30.185 | 18.43355 | 1.294063 | 49.91261 |

14 | Radish | 15 | 14.85947 | 0 | 29.85947 |

15 | Spinach | 49.30366 | 88.75372 | 0 | 138.0574 |

16 | Fenugreek | 75 | 104.492 | 39.78095 | 219.2729 |

17 | Coriander | 310 | 206.7883 | 51.88618 | 568.6745 |

18 | Rice | 1,101.181 | 1,011.222 | 0 | 2,112.403 |

19 | Jawar-k | 29.57283 | 0 | 0 | 29.57283 |

20 | Bajra | 3,500 | 3,156.727 | 4,781.109 | 11,437.84 |

21 | Maize | 5,000 | 1,408.225 | 12,500 | 18,908.22 |

22 | Arhar | 209.7311 | 114 | 139.78 | 463.5111 |

23 | Mung bean | 50 | 24.28567 | 30 | 104.2857 |

24 | Black gram | 7 | 18 | 10.00543 | 35.00543 |

25 | Groundnut | 4,082.798 | 1,989.242 | 2,400 | 8,472.04 |

26 | Soyabean | 5,532.328 | 447.2547 | 2,491.966 | 8,471.549 |

27 | Cotton | 0 | 0 | 2,000 | 2,000 |

28 | Onion | 2,500 | 1,283.129 | 1,141.224 | 4,924.354 |

29 | Jawar-R | 695 | 720 | 300 | 1715 |

30 | Wheat | 1,132.341 | 150 | 1,083.603 | 2,365.945 |

31 | Maize-R | 969.1114 | 1,300 | 600 | 2,869.111 |

32 | Horse gram | 139.9751 | 248.3431 | 360 | 748.3182 |

33 | Onion-R | 3,021.998 | 1,000 | 986.5149 | 5,008.513 |

34 | Sugarcane | 91.89952 | 7.426564 | 236.0857 | 335.4118 |

From Tables 1 and 3 it can be noted that there are major changes in areas of few crops and minor changes in areas of most of the crops. Here, the reasons for major changes in areas of crops are discussed as those crops brought major changes in net benefits. The areas of crop no. 2 (potato), 18 (rice), 21 (maize), 25 (groundnut) and 31 (maize R.) are increased majorly. The areas of these crops are increased by 100.51%, 102.92%, 40.82%, 261.58% and 214.94%, respectively. From Figures 2 and 3, it is found that crop water requirement of these crops is less and benefits are greater. Hence, the areas of these crops are majorly increased. The areas of crop no. 1 (green gram), 5 (field beans), 20 (bajra), 26 (soyabean), 29 (rabi jawar), 32 (horse gram) are reduced majorly. The areas of these crops are reduced by 50.46%, 45.37%, 35.46%, 60.72%, 66.41% and 78.19%, respectively. From Figures 2 and 3, it can be noted that the crop water requirement is less to moderate, but net annual returns are much less. These are not profitable crops. Hence the area of these crops is majorly reduced. For the rest of the crops the change in area is minor as the benefit or loss from these crops is less and crop water requirement is moderate to high.

The above discussion shows that the proposed cropping pattern and net annual returns are justifiable. The results obtained from TLBO are validated by PSO. It is seen that net annual returns obtained from PSO are near to TLBO.

## Conclusions

Optimization of the cropping pattern for the study area, i.e., Sinnar Taluka, Nasik, Maharashtra, India was carried out in this work. The objective of this work was to search for the optimal cropping pattern which would maximize the net annual returns for the study area and, at the same time, utilize the available groundwater resource conservatively. For this purpose, mathematical models for net annual returns were formulated. These models were solved using PSO and TLBO algorithms in order to search for the optimal cropping pattern (Table 3). The existing cropping pattern yields net benefits of 1,101.15 million rupees. The proposed cropping pattern by TLBO yields net returns of 1,495.5 million rupees, 35.81% higher than the net annual returns provided by the existing cropping pattern. The water is also allocated optimally (see Table 1).

The results show that the TLBO algorithm has allocated optimum water to the proposed number of crops without the need of mining. In the existing cropping pattern, 154 Mm^{3} water is used by farmers. The study area is overexploited, which is a fact. However, the new cropping pattern is suggested by considering minimum rainfall, i.e., 400 mm, so that the years when rainfall is above minimum the groundwater levels will be raised. Another point is that sugarcane is a high water consuming crop; however, the net benefits from sugarcane are also high so the area is minorly increased. In the Results and discussion section it is described that in the proposed cropping pattern a few crop areas are majorly increased and a few crop areas are majorly reduced. The rest of crop areas are minorly increased or reduced. Sugarcane comes in that category. Net benefits are increased and water demand is decreased due to major increase and minor reduction in areas of a few crops.

The existing cropping pattern has been the same for many years and may not utilize natural resources with maximum economic efficiency. The implementation of the cropping pattern proposed in this work will utilize the natural resources with maximum economic efficiency. It will also help to maintain groundwater reservoir in a balanced condition which may prevent problems like scarcity of water for irrigation in the study area. The following policy instruments are required to effect the changes in cropping pattern recommended by the study:

- 1.
The proposed cropping pattern is designed considering assured groundwater supply. Hence, farmers' should not grow water-intensive crops beyond the prescribed allocated land to a particular crop, e.g., sugarcane. If the farmer takes such a crop beyond the prescribed land limit they should be penalized for heavily electricity charges.

- 2.
To use the available groundwater effectively, all farmers in the study area should compulsorily use drip irrigation methods for greater success of the proposed cropping pattern.

- 3.
Quotas should be established for wells for the extraction of water for individual farmers. If a farmer pumps more than their quota they should be assessed for a tax; if a farmer pumps less than their quota, the tax should be rebated.

- 4.
As per policy number 3, the landowner should not get permission to dig wells beyond a certain limit as their water quotas are established, and therefore all farmers will be assured groundwater for beneficial use.

- 5.
The farmers who adopt water conservation schemes on their own farms to increase artificial recharge quantity should be rewarded by local government.

In the Introduction, a hypothesis is included. The results support the hypothesis. The net benefits from the proposed cropping pattern are higher than the benefits from the existing cropping pattern. Also, the water utilized by the proposed cropping pattern is less than the water utilized by the existing cropping pattern. On the basis of results, the policy instruments are also suggested as above.

## Acknowledgements

The authors would like to thank S.V. National Institute of Technology, Surat, India for providing support during the research work. Help extended by the Senior Geologist, Groundwater Surveys and Development Agency, Nasik, India, Executive Engineer, Nasik Irrigation Department, Nasik, India, Taluka Agricultural Officer, Sinnar, India and other various government agencies of MS, India by providing required data and in different ways during research work is acknowledged.