Abstract
The selection of sugarcane varieties is an important problem faced by companies in Brazil that exploit sugarcane harvest for energy production. In the light of current concerns regarding the reduction of environmental damage and the efficiency of the production system, research into this problem is called for. In this context the authors begin by outlining the sugarcane variety selection problem in accordance with technical constraints with the purpose of minimizing collection and transport costs and maximizing energy balance obtained from residues of the sugarcane harvest. They then present a previously developed model for the problem within bi-objective binary linear programming and study its computational complexity. Fundamentally, this paper is devoted to the application of a bi-objective genetic heuristic to the question addressed. A computational experiment, performed by resorting to a test set including real and semi-randomly generated instances, is then reported. The results prove the high quality of the heuristic in terms of solution quality, besides computing time. For these reasons, this will be an appropriate tool to help sugarcane company managers to plan their producing activities.
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Acknowledgements
We thank FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo, Grant No. 2009/14901-4 and No. 2010/07585-6, Brazil), FUNDUNESP (Fundação para o Desenvolvimento da UNESP, Brazil) and PROPG UNESP for their financial support. The research of the second author was also partially funded by FCT (Fundação para a Ciência e Tecnologia, Portugal) under the project POCTI/ISFL/152.
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Appendix
Appendix
Tables A1, A2 and A3 include the real data used through the computational experiments.
All the semi-randomly generated cases were generated on the basis of small fields of 405 ha, each consisting of 20 plots, aggregated in four tracts, and built through a sequential process described by the pseudocode in Figure A1.
When building a semi-random instance of 405 ha (cases I1–I20), the algorithm SimulSmall starts up by selecting a pattern for the plantation area, step 1. The pattern is randomly chosen from the four patterns shown in Figure A2, with a uniform discrete distribution. The mill's location—step 2 of the algorithm—is then randomly chosen (again uniform discrete distribution) among four possibilities, as illustrated in Figure A3. In this figure, the rectangle represents the entire small field to be planted. The distances of the possible locations of the mill to the nearest border of the field are calculated.
In step 3, each tract of the pattern is split into a certain number of equal area plots as indicated in Figure A2, thus defining the 20 plots for the SSVP instance. The linking distances to the mill, for all the plots to be found in a tract, are approximated by measuring the distance from the central point of the tract to the edge of the field, point X—thus assuming that each truck goes straight through the field to that border point—and then from X to the engine, and back again. We are dealing with Euclidian distances. Figure A4 illustrates how the simulated distances are calculated. Consider that pattern 2 and location 1 have already been selected. Let us determine the distances for the three plots of tract 3. First, the distance from the central point of tract 3 to border point X is calculated. It is then added to 20 (see Figure A3) and finally doubled. The resulting value is the simulated distance for all the three plots of tract 3.
The three other groups of instances correspond to medium-sized dimension fields—I21–I40 and I41–I60—and high dimension fields—I61–I80. All were built by grouping a specific number of small fields, each consisting of 405 ha. Similar sizes and shapes are commonly found in the companies in the region addressed. Figure A5 illustrates a medium dimension case of 1 215 ha. All instances of this same area are built by aggregating three small fields that are randomly chosen from the four possible patterns in Figure A2. Each of the fields of 3 645 ha corresponds to nine small fields and each of the 6 075 ha fields is made up of 15 small fields.
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de Oliveira Florentino, H., Pato, M. A bi-objective genetic approach for the selection of sugarcane varieties to comply with environmental and economic requirements. J Oper Res Soc 65, 842–854 (2014). https://doi.org/10.1057/jors.2013.21
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DOI: https://doi.org/10.1057/jors.2013.21