A Comparative Study of State-of-the-Art Evolutionary Multi-objective Algorithms for Optimal Crop-mix

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www.seipub.org/ijast

International Journal of Agricultural Science and Technology (IJAST) Volume 2 Issue 1, February 2014 doi: 10.14355/ijast.2014.0301.02

A Comparative Study of State-of-the-Art Evolutionary Multi-objective Algorithms for Optimal Crop-mix planning Oluwole. A. Adekanmbi*1, Oludayo. O. Olugbara2, Josiah Adeyemo3 E-Skills Institute Co-Lab, Durban University of Technology, P.O. Box 1334, Durban, 4000, South Africa

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Department of Civil Engineering and Surveying, Durban University of Technology, P.O. Box 1334, Durban, 4000, South Africa

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adekanmbioluwole@gmail.com; 2oludayoo@dut.ac.za; 3josiaha@dut.ac.za

*1

Abstract This study compared the performances of three state-of-theart evolutionary multi-objective optimization algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGA-II), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II ( ε -NSGA-II) and the Epsilon-Dominance Multi-Objective Evolutionary Algorithm ( ε MOEA), on a constrained biobjective crop-mix planning problem (BCP). The BCP test case objectives were to: (i) maximize crop production and (ii) minimize planting area. The BCP problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the evolutionary multi-objective optimization algorithms. The performances of the three algorithms were assessed and compared using three performance metrics (additive epsilon indicator, inverted generational distance and spacing). For the comparative study, a graphical comparison with respect to true Pareto front of optimal crop planning problem was provided. Results of the analyses indicated that the ε MOEA greatly outperforms the NSGAII and the ε -NSGA-II. Keywords Algorithm; Crop; Planning; Constrained; Objective; Optimal; Optimization

Introduction The increasing growth of human population worldwide calls for sustainable growth of agricultural products to meet the primary need of the population (Lewandowski, Härdtlein, and Kaltschmitt, 1999). The amount of crop produced by agricultural farm will influence profit earned on farm and market prices. If a farm produces a crop in plenty, the market price of crop lowers which favours consumers. Conversely, if they produce in a small amount, the market price may move up and consumers are stuck as they need buy at more expensive price. The constant increase in human population and their activities have intensified pressure on land use for farming. Consequently, the

effective planning of crop production in a particular season is an extremely important task from economic perspective. The crop planning problem is similar to the financial portfolio, that is, a farmer uses his limited land effectively by growing various crops as an investor distributes his funds to some financial stock for “low risk, high returns”. Of course, the farm needs the profit information of the crop. This profit information depends upon yield rate, market prices and many other factors. Allocation of the right area of land for the appropriate crop is a task and we may define the planting area as discrete random variable in crop planning. This approach is an alternative, but it is not realistic in any agricultural planning situation to define the allocation of planting area as continuous random variable, because it is difficult. In an agricultural planning situation, optimal production of crops highly depends on the proper allocation of land in different season for cultivating the crops and adequate supply of productive resources to the planning unit. Many practical problems such as travelling salesman, time tabling and portfolio selection are frequently solved using optimization techniques. Most of these problems involve instantaneous optimization of several incommensurable and often conflicting decision objectives. Although these problems are eminent in engineering and financial sectors, there have related optimization problems in agricultural systems such as crop planning (Adeyemo, Bux, and Otieno, 2010; Chetty and Adewumi, 2013; Sarker and Ray, 2009), irrigation planning (Adeyemo and Otieno, 2010; Bai and Liang, 2012; Sethi, Kumar, Panda, and Mal, 2002) and crop selection (Brunelli and von Lücken, 2009). Each of the multi-objective evolutionary algorithm selected has been demonstrated to be


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