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Top1. Introduction
Contemporary fruit growers are confronted with a real challenge. They must not only address the impact of climate change on their farms, but they also must meet the social demand for healthy and high-quality products and reduced use of pesticides. Many studies have noted that fruit quality build-up and fruit sensitivity (i.e. resistance) to diseases result from interactive physiological processes. These processes also depend on the fruit genotype, on its environment, and, of course, on the cultural practices carried out by the fruit growers. Therefore, researchers believe that optimizing the genotype-by-environment-by-practices interactions could aid the fruit growers in facing the above-mentioned challenge. This optimization involves identifying a set of good combinations of genetic resources and cultural practices adapted to specific environments.
Given the complexity of fruit production systems, an integrative modeling approach is useful for studying the strong genotype-by-environment-by-practices interactions (Chenu et al., 2009; G.L. Hammer, Chapman, van Oosterom, & Podlich, 2005; G. L. Hammer, Kropff, Sinclair, & Porter, 2002; Reymond, Muller, Leonardi, Charcosset, & Tardieu, 2003). The idea is to use physiological models to analyze the plant traits and their development under the control of the environment and the genome (White & Hoogenboom, 2003; Yin, Kropff, & Stam, 1999; Yin, Struik, Tang, Qi, & Liu, 2005). The genetic information is included in the physiological models via the genetic parameters. Next, the combination of genetic parameters is optimized to design virtual ideotypes that are adapted to the target environments and cultural practices (Letort, Mahe, Cournede, De Reffye, & Courtois, 2008; Tardieu, 2003). This model-based design approach could contribute to reducing the number of time- and cost-consuming field experiments and could also lead to rapid identification of the best ideotypes and the evaluation of the long-term effects of climate change (Mayer, 2002; Ould-Sidi & Lescourret, 2011).
In a previous work, we proposed a model-based design approach to reduce the sensitivity of peach fruit to a storage disease (brown rot) while guaranteeing the fruit quality, therefore enhancing the ecological, economical and health benefits (Quilot-Turion et al., 2012). We used the ‘Virtual Fruit’ (Genard, Bertin, Gautier, Lescourret, & Quilot, 2010) model and formulated the studied case as a constrained Multi-objective Optimization Problem (MOP). The decision variables in our problem are six genetic parameters of the virtual fruit model identified via sensitivity analysis and based on expert choice. Three antagonist criteria related to fruit quality (fruit fresh mass and sugar contents) and its sensitivity to brown rot (crack density) must be optimized, and six bounding constraints must also be satisfied (Quilot-Turion, et al., 2012). This formulation represents a relatively small but highly difficult multi-objective optimization problem. In addition to its nonlinear and non-convex nature, another difficulty in addressing this problem is the “black box” nature of the physiological models in general and of the “virtual fruit” in particular. Indeed, both the criteria and constraints of the formulated problem are black-box functions, i.e., we have no knowledge of the algebraic expressions of these functions in terms of the decision variables. Conventional optimization techniques, e.g., the gradient-based method, and linear, non-linear, and quadratic programming, are generally not adapted to this type of problem (Ramesh, Kannan, & Baskar, 2012), and more effective methods, e.g., the Multi-objective Evolutionary Algorithms (MOEAs)(Letort, et al., 2008; Quilot-Turion, et al., 2012) and Multi-Objective Particle Swarm Optimization (MOPSO) (Kadrani, Ould Sidi, Quilot-Turion, Genard, & Lescourret, 2012; Qi, Ma, Hu, de Reffye, & Cournede, 2010), have recently been proposed for this purpose. Therefore, we use one algorithm of each one of these two methods to address the model-based design of the virtual fruit ideotypes.