A framework for multi-objective optimization of virtual tree pruning based on growth simulation

Abstract We present a framework for multi-objective optimization of fruit tree pruning within a simulated environment, where pruning is performed on a virtual tree model, and its effects on tree growth are observed. The proposed framework uses quantitative measures to express the short-term and long-term effects of pruning, for which potentially conflicting optimization objectives can be defined. The short-term objectives are evaluated on the pruned tree model directly, while the values of long-term objectives are estimated by executing a tree growth simulation. We demonstrate the concept by using a bi-objective case, where the estimated light interceptions of the pruned tree in the current and the next season are used to define separate optimization objectives. We compare the performance of the multi-objective simulated annealing and the NSGA-II method in building the sets of non-dominated pruning solutions. The obtained Pareto front approximations correspond to diverse pruning solutions that balance between optimizing either objective to different extents, which indicates a potential for new applications of the multi-objective pruning optimization concept.

[1]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[2]  Michael Fenner,et al.  Reproductive Allocation in Plants , 2012 .

[3]  Wojciech Palubicki,et al.  Self-organizing tree models for image synthesis , 2009, SIGGRAPH 2009.

[4]  D. H. Maggs,et al.  The Reduction in Growth of Apple Trees Brought About by Fruiting , 1963 .

[5]  Trevor Olesen,et al.  Pruning to control tree size, flowering and production of litchi , 2013 .

[6]  Bedrich Benes,et al.  IMapple — Functional structural model of apple trees , 2016, 2016 IEEE International Conference on Functional-Structural Plant Growth Modeling, Simulation, Visualization and Applications (FSPMA).

[7]  Long He,et al.  Sensing and Automation in Pruning of Apple Trees: A Review , 2018, Agronomy.

[8]  Long He,et al.  Development of a Robotic End Effector for Apple Tree Pruning , 2019 .

[9]  P. Siarry,et al.  Multiobjective Optimization: Principles and Case Studies , 2004 .

[10]  Radomír Mech,et al.  Visual models of plants interacting with their environment , 1996, SIGGRAPH.

[11]  Michel Génard,et al.  QualiTree, a virtual fruit tree to study the management of fruit quality. II. Parameterisation for peach, analysis of growth-related processes and agronomic scenarios , 2011, Trees.

[12]  Bikram Adhikari,et al.  Identification of pruning branches in tall spindle apple trees for automated pruning , 2014 .

[13]  C. Giulivo,et al.  Basic considerations about pruning of deciduous fruit trees , 2011 .

[14]  Hui Li,et al.  Research on 3D skeletal model extraction algorithm of branch based on SR4000 , 2019 .

[15]  Bedrich Benes,et al.  IMapple: a source-sink developmental model for ‘Golden Delicious’ apple trees , 2017, Acta Horticulturae.

[16]  Romeo Favreau,et al.  L-PEACH: a computer-based model to understand how peach trees grow. , 2010 .

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[18]  A. Ikinci,et al.  Effects of summer and dormant pruning time on the vegetative growth, yield, fruit quality and carbohydrate contents of two peach cultivars , 2013 .

[19]  P. Prusinkiewicz,et al.  Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH model. , 2005, The New phytologist.

[20]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[21]  J. P. Zoffoli,et al.  Pruning effects on vegetative growth and fruit quality of ‘Bing’/‘Gisela®5’ and ‘Bing’/‘Gisela®6’ sweet cherry trees (Prunus avium). , 2012 .

[22]  Lili Yang,et al.  Interactive Pruning Simulation of Apple Tree , 2015, CCTA.

[23]  Simon Kolmanič,et al.  EduAPPLE: Interactive Teaching Tool for Apple Tree Crown Formation , 2015 .

[24]  Avinash C. Kak,et al.  A novel framework for modeling dormant apple trees using single depth image for robotic pruning application , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[25]  Ersin Atay,et al.  A New Insight into Pruning Strategy in the Biennial Cycle of Fruiting: Vegetative Growth at Shoot and Whole-tree Level, Yield and Fruit Quality of Apple , 2017 .

[26]  Hervé Sinoquet,et al.  SIMWAL: A structural-functional model simulating single walnut tree growth in response to climate and pruning , 2000 .

[27]  G. A. Lang,et al.  VCHERRY â AN INTERACTIVE GROWTH, TRAINING AND FRUITING MODEL TO SIMULATE SWEET CHERRY TREE DEVELOPMENT, YIELD AND FRUIT SIZE , 2008 .

[28]  Stefan Kohek,et al.  Novel discrete differential evolution methods for virtual tree pruning optimization , 2015, Soft Computing.

[29]  Ning Xia,et al.  Virtual Apple Tree Pruning in Horticultural Education , 2009, Edutainment.

[30]  Christophe Godin,et al.  Competition-based Model of Pruning: Applications to Apple Trees , 2010 .

[31]  Michel Génard,et al.  QualiTree, a virtual fruit tree to study the management of fruit quality. I. Model development , 2011, Trees.

[32]  Bedřich Beneš An efficient estimation of light in simulation of plant development , 1996 .

[33]  Stefan Kohek,et al.  The computer‐aided teaching of apple tree pruning and training , 2017, Comput. Appl. Eng. Educ..

[34]  Radomír Mech,et al.  Self-organizing tree models for image synthesis , 2009, ACM Trans. Graph..

[35]  R. Rezaee,et al.  Vegetative and reproductive responses of some apple cultivars (Malus domestica Borkh.) to heading back prunning. , 2013 .

[36]  Jing Zhang,et al.  Branch detection for apple trees trained in fruiting wall architecture using depth features and Regions-Convolutional Neural Network (R-CNN) , 2018, Comput. Electron. Agric..