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Compromising NSGA-II performances and stopping criteria: case of virtual peach design

Abstract : Multiobjective evolutionary optimization algorithms allow exploring highly dimensional search (decision) spaces in a reasonable computation time. These methods provide the decision-maker with a set of diversified solutions. The decision-maker will thus have the final choice of the best suited trade-off between criteria. However, a difficulty when using these algorithms is the convenient time to stop computation. Generally, one uses a predefined maximum number of generations as stopping criterion. Unfortunately, this can lead to many unnecessary generations and thus decrease the ratio of solution quality by computation time. Authors of [4] discussed this aspect, and illustrated it with the well-known NSGA-II (Non-dominated Sorting Genetic Algorithm II)[2]. They introduced a new stopping criterion which may partly remedy to this drawback. This criterion consists of stopping the process when the algorithm has performed a given number of iterations without improvement. It is based on the standard deviation of the crowding distance, a diversity control measure of NSGA-II, during a given number of iterations. Authors have tested their criterion only in the case of unconstrained and bi-objective problems and they claimed that it is difficult to use this criterion with NSGA-II for more than 2 criteria and for constrained optimization problems. Consequently, the question we address here is the possibility to use this stopping criterion to improve NSGA-II computation time in case of a constrained three-objective optimization problem. Thus, we compared the results obtained with the original version of NSGA-II to those obtained when modifying this original version by including this stopping criterion. In both studies we used the ‘Virtual Fruit’, a process-based model [3]. Six genetic parameters of the model constitute the decision variables of our problem and will be combined to create the genotypes by optimization. Three traits of fruit quality and sensitivity to brown rot simulated by the model were taken into account to evaluate the solutions (genotypes). Six constraints were also considered. The population size, 400, and the number of generations, 1500, were chosen after performing many preliminary simulations with the original version of the NSGA-II algorithm (data not shown). In order to choose the best values of the two parameters involved in the stopping criterion (L the length of the time window and the threshold value δ lim) adapted to the population size considered, we tested different combinations of values (20, 40, 60, and 80 generations for L combined with values of 0.001, 0.005, 0.0075, and 0.0001 for δ lim). Values of 0.001 and 20 were selected respectively for the threshold and length of time window. We repeat simulations of both versions 13 times. We compared the performances of the two versions using standard performance metrics and statistical analysis. Coverage set, spacing, and dominated volumes ration metrics[1] were used together with the computational time to compare the performances of the original (or) and the modified (sd: standard deviation) versions of NSGA-II. Results are given in table 1. We concluded that the NSGA-II with the stopping criterion based on the standard deviation find very similar results compared to the original NSGA-II but in less computational time.
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Submitted on : Saturday, June 6, 2020 - 4:22:52 AM
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  • HAL Id : hal-02807655, version 1
  • PRODINRA : 199135



Mohamed Ould Sidi, Abdeslam Kadrani, Bénédicte Quilot-Turion, Francoise F. Lescourret, Michel M. Génard. Compromising NSGA-II performances and stopping criteria: case of virtual peach design. International Conference on Metamaterials, Photonic Crystals and Plasmonics, Apr 2012, Paris, France. 2 p. ⟨hal-02807655⟩



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