Keywords: multi-objective evolutionary algorithms, parallel island model, threads, greenhouse crops, resource optimization.

The southeast region of Spain is one of the most important vegetable production areas of the country. One of the keys to the economic growth of the area has been the use of underground water in a place where rain is scarce. But the context of economical crisis as well as the increasing demand of water, are becoming the subject of concern to the development of the region. There are three distinct problems that need to be solved to allow the development of the region without taxing its future: to reduce economical risks, to reduce the water consumption and to maximize the economic profits (gross margin).

One traditional way to solve this problem is by creating a simple aggregate function that includes all the objectives to optimize as a weighted sum [1,2], which allows the relative importance of each objective to be fixed with ease, but it has a drawback: the relative importance of each objective is fixed, so an optimization procedure would produce one single solution.

On the other hand multi-objective evolutionary algorithms (MOEAs) are commonly used to solve complex problems by using the concept of Pareto-optimization, which, instead of giving a scalar value to each solution, establishes relationships between solutions according to Pareto-dominance relations to find a set of solutions as a representative sample of the true Pareto-optimal front [3].

It is also possible to improve the quality of the solutions that a MOEA can produce by means of employing techniques such as the parallel island model [4]. The purpose of this paper is to use this model with the intention of expanding the number of objectives to optimize by using several isolated populations exploring different two dimensional search spaces and migrating the best subjects to nearby populations. The goal is to fuel the generation of solutions that are optimal in both search spaces to generate a three objective Pareto front that is the solution of a larger problem.

The three-objective Pareto fronts obtained from the experiments run using the parallel island model are consistent with the results obtained in previous works [5] when considering the objectives they share (risk and gross margin), so the results obtained from the simulations can be applied to choose the right surface for the different crop alternatives to increase the economic benefits while keeping risks low and reducing water consumption.

1

J.M. Sumpsi, F. Amador, C. Romero, "On farmers' objectives: A multi-criteria approach", European Journal of Operation Research, 96, 64-71, 1997. doi:10.1016/0377-2217(95)00338-X

2

F. Amador, J.M. Sumpsi, C. Romero, "A non-interactive methodology to asses farmers' utility functions: An application to large farms in Andalusia, Spain", European Review of Agricultural Economics, 25(1), 92-109, 1998. doi:10.1093/erae/25.1.92

3

D. Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning", Addison Wesley, New York, 1989.

4

D. Whitley, S. Rana, R.B. Heckendorn, "The island model genetic algorithm: On separability, population size and convergence", Journal of Computing and Information Technology, 7, 33-47, 1998.

5

A. Márquez, A. Manzano-Agugliaro, R Gil, C. Cañero-León, F. Montoya, R. Baños, "Multiobjective evolutionary optimization of greenhouse vegetable crop distributions", in "Proceedings of the IJCCI 2009 International Joint Conference on Computational Intelligence", INSTICC, 2009.

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