Comparison of Evolutionary and Swarm Intelligence-based Approaches in the Improvement of Peach Fruit Quality

Abstract

(ProQuest: ... denotes formulae omitted.)1. IntroductionModeling and simulation are increasingly used to tackle the complexity of agricultural production systems (Hammer, et al., 2001; Mayer, 2002). Innovative perspectives of evolution towards systems respectful of the environment, producing safe food, and ensuring the economic viability of farms are now requested. One promising perspective aims to identify the best combinations of genetic resources and cultural practices adapted to specific agro-environmental conditions optimizing the trade-off between economic, ecological, and environmental antagonistic criteria. In this work, we deal with the case of brown rot which is one of the main diseases causing large economic losses for peach growers. The challenge is to build-up a tool to conceive innovative management strategies that optimize genotype-environment-practices interactions to limit fruit contamination by brown rot while keeping or improving fruit quality (sweetness and fruit fresh mass). Hence the design of peach ideotypes for a given set of cultural practices and for a specific environment is governed by a set of objective functions and constraints.Several methods have been proposed to deal with multi-objective optimization problems. Two types of approaches can be distinguished: the aggregative approaches and the Pareto dominance based approaches. In this paper, we investigated two major families of the Pareto dominance algorithms: the Multi-Objective Evolutionary Algorithms (MOEAs) and the Multi-Objective Particle Swarm Optimization (MOPSO). These two families are nature inspired and are population-based approaches as they use a set of solutions which evolve within the search space.In recent decades, a wide range of MOEAs has been developed (Horn, Nafploitis & Goldberg, 1994; Knowles & Corne, 1999; Zitzler, Deb & Thiele, 2000; Zitzler, Laumanns & Thiele, 2001). One of the most cited MOEAs is the Non-dominated Sorting Genetic Algorithm II (NSGA-II) (Deb et al, 2002). This success story of NSGA-II could be attributed, as announced by Deb et al. (2002), to its low level of computational requirements, its elitist approach, and its simple constraint handling method. For these reasons, NSGA-II has become the reference for researchers in the field of MOEAs.MOPSO are more recent algorithms which are based on biological metaphor. These algorithms are inspired by the movement of birds, fishes, or others organisms in their search for food. Large number of MOPSO algorithms was proposed in the literature (Coello- Coello, Pulido & Lechuga, 2004; Fieldsend & Singh, 2002; Li, 2003; Reyes-Sierra & Coello-Coello, 2006). The diversity maintenance mechanism of MOPSO, while seeking global Pareto-optimal solutions, is rather poor compared with other MOEAs such as NSGA-II. This motivated some researchers to introduce into MOPSO algorithms some procedures from the MOEAs such as elitism, diversity operators, mutation operators, constraint handling and crowding distance (Coello- Coello, Pulido & Lechuga, 2004)Raquel and Naval have proposed an algorithm that called MOPSO-CD (Raquel & Naval, 2005) which incorporates the crowding distance computation and the constraints handling of NSGA-II.In this study, we choose to compare the performance of the NSGA-II with those of MOPSO-CD with respect to the improvement of peach fruit quality. Both algorithms NSGA-II and MOPSO-CD were interfaced with the 'Virtual Fruit' process-based model which describes quality traits of peach fruit during the growth stage (Genard, et al., 2007; Genard et al., 2010; Lescourret & Genard, 2005). The performance of each algorithm is analyzed qualitatively by comparing the non-dominated Pareto front and the performance measures.The rest of this paper is organized as follows. The modeling of the peach fruit quality with the problem formulation is discussed in Section 2. Section 3 presents a brief description of NSGA-II and MOPSO-CD. …