n developing countries, the agricultural sector's performance determines overall economic growth, trade expansion, and increased income-earning opportunities. Implementing policies that encourage greater agricultural productivity, Profitability and sound environmental management is very much needed. In today's globalized world every sector of the economy needs to reorient itself to meet the changing demand. This is very much required as the need patterns of the individuals are getting transformed by the intensity of the local and global forces. The rural sectors of the developing countries are not exceptions in this regard. The sudden boom in food retail sectors has also changed the orientation and status of farming from purely individualistic to group oriented activities in India. At this instance it is inevitable for a country like India to improve its agriculture production not only to meet the demand of food grains for the growing population but also to improve the economic conditions of the majority population who live in rural areas. As a result of losing land due to growing population and industrialization, the production of crop per unit area must be increased by proper utilization of resources. One way of increasing production of crops is by increasing the area under cultivation. Planning of crops is the most crucial factor of Agriculture Planning which depends on several resources like availability of land, water, labour, machinery and capital. About ?, ? -Selection Grade Lecturer, Department of Technical Education, Government of Andhra Pradesh, India -530 007 About ? -Professor, Department of Mechanical Engineering, Andhra University, Visakhapatnam, Andhra Pradesh, India -530 003 Ahmad et al. (1990) used LP model for developing optimal farm plans for small farmers in Leiah Tehsil and Faisalabad. Srinivasa Raju and Nagesh Kumar (2000) developed a LP irrigation planning model for the evaluation of irrigation development strategy and applied to a case study of Sri Rama Sagar project, Andhra Pradesh, India with the objective of maximization of net benefits. As evolutionary algorithms offer relatively more flexible way to analyze and solve realistic engineering problems is increased. The best known algorithms in this class are Genetic Algorithms (GAs).The Genetic Algorithm (GA) imitates the natural Darwinian evolution process, was originally conceived by John Holland (1975) of the University of Michigan, Ann Arbor.

Two important flavors of GA are Binary GA and Real parameter GA. The binary GA is not suitable to achieve any arbitrary precision in the solution. The more the required precision, then the larger is the string length. If the string length is large, the population size is large (Goldberg et al., 1992), thereby increasing the computational complexity of the algorithm. To overcome this difficulty and to increase the precision it is more logical to represent the variables which are continuous by real parameter values (floating point numbers). Real coded or floating point representation has a very good usage because of the empirical findings that real codlings have worked well in a number of practical applications. The real parameter GA has also the advantage of less required storage space than the binary GA because a single real parameter value represents the variable instead of m (bits) integers. Also real parameter GAs deal with real parameter values and bring the GA technique a step closer to the classical optimization algorithms (Deb, 2001).

In this paper, single objective optimization models are developed by considering the strategy of the decision maker/ policy makers. Further the models are solved through real parameter Genetic Algorithm approach.

Enhancing productivity growth in a sustainable way that makes economic, social and environmental sense and delivers food security is key issue in determining the strategies for growth in agriculture sector. The highest leverage point could be a shift from individual crop-focused research to an eco-region specific strategy. Agricultural research and development strategies must take into account natural resource endowments and also the prevailing socioeconomic conditions (as reflected in current crop patterns, yields, market access and so on) under which farmers work.

In this context, three objectives namely, maximization of production, maximization of profit and minimization of fertilizer consumption are modeled by considering the strategies with social, economic and environmental sense for optimal land allocation. The following steps explain the formulation and complete solution procedure for optimal allocation of land for major crops under three strategies. a) Notations L = Total area of land (hectares) available under cultivation EMD = Estimated number of man days (days) available throughout the year. EMH = Estimated number of machine hours (hrs.) available throughout the year.

[WA ] s = Total amount of water (cm) available during the seasons s.

[PR ] cvs = Production (quintal ) per unit area of land cultivated for the variety v of crop c during the seasons s.

[Md ] cvs = Man days (days) required per unit area of land cultivated for the crop c, variety v during the season s.

[mh ] cvs = Machine hours (hrs.) required for tillage per unit area of land cultivated for the variety v of crop c during the season s.

[ WC ] cvs = Amount of water consumed (cm) per hectare of land cultivated during a season s for the crop c of variety v.

Three strategies namely, societal, economic and environmental are considered in this study. Societal Strategy: Increase in agricultural productivity must be accelerated to bring down current levels of food insecurity and meet the food and income needs of new populations. Hence, due consideration shall be given for Maximization of production. To meet the demand of food-stuff the annual production of all the major crops must be maximized. The mathematical formulation of the objective is shown below.

Subject to constraints given in section 2.3 Economical strategy: The agricultural sector's performance determines overall economic growth, trade expansion, and increased income-earning opportunities of farmers. Implementing policies that encourage, Profitability is very much needed. To increase the economical and social status of the farmers the net profit must be maximized. The mathematical formulation of the objective is shown below. To reduce the environmental pollution and cost of fertilizer the fertilizer consumption must be minimized. The mathematical formulation of the objective is shown below.

Subject to constraints given in section 2.3

In agriculture planning, optimal land allocation depends on various constraints. The mathematical formulations of the constraints considered in this work are as follows. Land (C 1 ) : It is necessary to utilize the land in all seasons because of its limited availability.

coi where H for all c i and s S = =

After harvesting a crop in a season, the available land can be reutilized for cultivating the crops in the next season. The formulated models may be solved through various optimization techniques. In this study a real parameter GA approach is used to solve models

The mechanism of real parameter GA consists of the following components.

? Genetic representation for potential solutions to the problem ? An initial population of potential solutions ? Evolution function ( fitness function ) that plays the role of the environment, rating solutions in terms of their fitness ? Genetic operators that alter the composition of children ( reproduction, crossover and mutation) ? Values for various parameters that the GA uses ( population size, number of generations, probabilities of applying genetic operators )

III.

The model formulated in the previous section is explained with a case study of Visakhapatnam district in Andhra Pradesh, India. According to the climatic conditions, two cropping seasons Kharif and Rabi are considered. The main crops cultivated during Kharif (June to September) and Rabi (October to February) seasons are Paddy, Black Gram, Green Gram, Ragi, Maize, Groundnut, Chillies, Sugarcane. Sugarcane is perennial crop and occupies the land in both the seasons. After harvesting the crops of short period in the Kharif season, the same land is utilized for cultivating late variety of Maize. Similarly in the Rabi season after harvesting the early variety of crops Black Gram and Green gram, the same land is utilized for cultivating late variety of same crops. In the model formulation, the crops are numbered as c = 1 for Paddy, c = 2 for Black ram, c = 3 for Green Gram, c = 4 for Ragi, c = 5 for Maize, c = 6 for Groundnut, c = 7 for Chillies and C = 8 for Sugar Cane, Seasons are denoted as S = 1 for Kharif and S = 2 for Rabi, Varieties are denoted as V = 1 for first variety or early variety and V = 2 for second variety or late variety. The data for the available resources, defined coefficients of objectives and constraints are presented in Table 1 and 2 The multi objective problem converted to a single objective problem and is solved through real parameter genetic algorithm. The real coded GA used to find the optimum solution implements a tournament selected scheme, where two solutions are compared and the best in terms of objective function value is selected. Crossing over is done by the simulated binary crossover SBX operator which works with two parent solutions and creates two offspring (Deb and Agarwal, 1995). To create a mutated value, the polynomial mutation operator (Deb, 2001) is used. The exponents used for SBX and mutation are 2 and 100 respectively. Constraints are handled using Deb's parameter-less approach (Deb, 2000).

In most of the constrained optimization problems, the fitness function is obtained by adding a penalty proportional to the constraint violations to the objective function value. The constraint handling methods can be classified into five categories (Michalewicz et al. 2000). They are the methods based on preserving feasibility of solutions, penalty function, feasible over infeasible solutions, decoders and hybrid methods. Among these methods the method feasible over infeasible solutions is found to have more efficient and more robust than the penalty based methods (Deb, 2000). This method sometimes called as Deb's penalty parameter less approach and the same is used in the present work.

As GAs do not have a mathematical convergence, a parametric study is carried out by varying crossover probability (Pc), mutation probability (Pm), population size (Ps), and number of generations (Gn). By this study the best value of the each objective function was found with the best set of GA parameters obtained. The best GA parameters obtained are Pc=0.81, Pm=0.01, Ps=30,Gn=150.

IV.

Table 3 shows the results obtained for optimal land allocation for Societal, Economical and Environmental strategies for eight major crops through GA by considering the best combination of GA parameters. The results exhibits that the total land utilization for eight major crops in kharif season with societal, economical and environmental strategies are 87.96%, 88.05 and 87.17% respectively. Similarly, land utilization in rabi season are 67.72%, 67.32% and 66.28%. It also shows that there is a maximum land allocation (228403.284 hectares) by economical strategy as compared with other strategies. Comparison of land allocation for eight major crops among three strategies is shown in the figure 1. From the figure 1 it is observed that there is marked difference in land allocation in environmental strategy for the crops -paddy (H111), Maize (H111) and sugarcane (H811) when compared with the other strategies. From figure 2, it is observed that there is variation in level of achievement of the objectives with environmental strategy when compared to the other strategies.

V.

This paper presents three strategies for optimal allocation of land for eight major crops in two seasons and for two crop varieties of Visakhapatnam district in Andhra Pradesh, India. The models proposed in this paper are solved through real parameter GA for optimal solution by parametric study.

The land planning based on the results achieved with the help of genetic algorithm will lead towards a development strategy in the rural sector through agriculture. In a country like India whose rural economy is mostly agriculture based, a sustainable development in the context of globalization is only possible by way of improved land, societal, economical and environmental strategies by reorganizing land allocation system for various agricultural activities keeping in view of the local and market requirements. This model is based on single objective optimization depending on the strategy of the agriculture planners subject to the resource and conditional constraints. By using this model the cultivated land can be reorganized to get maximum satisfaction of the stakeholders of the rural area and hence lead to sustainable development in agriculture. The model developed does not taken care of uncertainty in the objectives and constraints. Future researchers may also include vagueness and stochastic uncertainty in decision variables, coefficients, objectives and constraints.