This paper presents how the genetic algorithms (GAs) can be used to the fuzzy goal programming (FGP) formulation of land allocation problems for optimal production of seasonal crops in agricultural system. In the proposed approach, utilization of total available land for cultivation, aspiration levels of the production of crops, expected profit from the farm as well as certain ratios in fractional form for crops production and profit achievement are fuzzily described in the decision making context. In the model formulation, achievement of highest membership value (unity) of the defined fuzzy goals to the extent possible by minimizing the under-deviational variables of the defined membership goals on the basis of priorities and thereby measuring the degree of optimality of the aspired goal levels are considered. In the solution process, the proposed GA method is used in an iterative manner for satisfying the goal levels on the basis of needs and desires of the decision maker (DM). To illustrate the potential use of the approach, the case example of the Nadia district, West Bengal, India is considered. The obtained solution is compared with the existing cropping plan of the district as well as the solution of the FGP approach studied previously.
Keywords: Cropping plan, Fuzzy goal, Fuzzy goal programming, Genetic algorithm,
[...] Moitra, “Fuzzy goal programming approach to long-term land allocation planning in agricultural system: A case study” in Proceedings of the 5th International conference in advances in pattern recognition (ICAPR2003), Allied Publishers Pvt., Ltd., pp.441- A. Biswas and B. B. Pal, “Application of fuzzy goal programming technique to land us planning in agricultural system”, Omega, Vol pp B.B. Pal and B. N. Moitra, “Using fuzzy goal programming for Long range production planning in Agricultural systems”, Indian Journal of Agricultural Economics, Vol No pp.75– R. [...]
[...] The arithmetic crossover operator (single-point crossover) of a genetic system is applied here in the sense that the resulting offspring always satisfy the linear constraints set S Here a chromosome is selected as a parent, if for a defined random number r r < Pc is satisfied. Here single-point crossover for two parents E1, E2 S is defined as X1 = α1E1 + α2E2, X2 = α2E1 + α1E2, for producing two offspring X1 and X2, where α2 0 with α1 = 1 always belong to and where S is a convex set. [...]
[...] In this article, a GA method is introduced to the FGP formulation of land allocation problem on a long-term basis for optimal cropping plan in agriculture systems. In the context of using GA method, the roulette –wheel selection scheme, arithmetic crossover and random mutation are used as genetic operators. In the solution process, the proposed GA is used in an iterative manner to the preemptive priority based FGP model of the problem. In the decision process, the goal satisficing philosophy in FGP is used for achievement of linear as well as ratio goals to their aspired levels (unity) to the extent possible in the decision making context. [...]
[...] Table VI: Production achievement with crisp resource and ratio constraints Crop Land allocation Jute 112.85 Sugarcane 1.766 Rice 277.34 Wheat 63.85 Mustard 60.10 Potato 5.50 Pulses 51.20 Production The total profit obtained here is Rs Lac Conclusion The main advantage of the GA based FGP approach presented here is that the proper decision for allocation of cultivable land regarding optimal production of crops on the basis of the needs and desires of the society can be made in the decision making situation. [...]
[...] The production structure for the existing cropping plan (2005–2006) of the District is presented in the Table–V. Table Land allocation and production of crops recorded in the year 2005 2006 Crop Land allocation Production Jute Sugarcane Rice Wheat Mustard Potato Pulses The total profit obtained under the existing cropping plan is Rs Lac. A comparison of the model solution with the results in the Table IV and Table V shows that the solution under the proposed approach is better for the view-point of achieving the aspired goal levels defined in the decision making context. [...]
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