Methods for integrating machine learning and constrained optimization

In the framework of industrial problems, the application of Constrained Optimization is known to have overall very good modeling capability and performance and stands as one of the most powerful, explored, and exploited tool to address prescriptive tasks. The number of applications is huge, ranging from logistics to transportation, packing, production, telecommunication, scheduling, and much more. The main reason behind this success is to be found in the remarkable effort put in the last decades by the OR community to develop realistic models and devise exact or approximate methods to solve the largest variety of constrained or combinatorial optimization problems, together with the spread of computational power and easily accessible OR software and resources. On the other hand, the technological advancements lead to a data wealth never seen before and increasingly push towards methods able to extract useful knowledge from them; among the data-driven methods, Machine Learning techniques appear to be one of the most promising, thanks to its successes in domains like Image Recognition, Natural Language Processes and playing games, but also the amount of research involved. The purpose of the present research is to study how Machine Learning and Constrained Optimization can be used together to achieve systems able to leverage the strengths of both methods: this would open the way to exploiting decades of research on resolution techniques for COPs and constructing models able to adapt and learn from available data. In the first part of this work, we survey the existing techniques and classify them according to the type, method, or scope of the integration; subsequently, we introduce a novel and general algorithm devised to inject knowledge into learning models through constraints, Moving Target. In the last part of the thesis, two applications stemming from real-world projects and done in collaboration with Optit will be presented.

Evaluation of a 2D multileader training system for improving sustainability and precision orchard management applications in italian apple orchards

The presented study aimed to evaluate the productive and physiological behavior of a 2D multileader apple training systems in the Italian environment both investigating the possibility to increase yield and precision crop load management resolution. Another objective was to find valuable thinning thresholds guaranteeing high yields and matching fruit market requirements. The thesis consists in three studies carried out in a Pink Lady®- Rosy Glow apple orchard trained as a planar multileader training system (double guyot). Fruiting leaders (uprights) dimension, crop load, fruit quality, flower and physiological (leaf gas exchanges and fruit growth rate) data were collected and analysed. The obtained results found that uprights present dependence among each other and as well as a mutual support during fruit development. However, individual upright fruit load and upright’s fruit load distribution on the tree (~ plant crop load) seems to define both upright independence from the other, and single upright crop load effects on the final fruit quality production. Correlations between fruit load and harvest fruit size were found and thanks to that valuable thinning thresholds, based on different vegetative parameters, were obtained. Moreover, it comes out that an upright’s fruit load random distribution presents a widening of those thinning thresholds, keeping un-altered fruit quality. For this reason, uprights resulted a partially physiologically-dependent plant unit. Therefore, if considered and managed as independent, then no major problems on final fruit quality and production occurred. This partly confirmed the possibility to shift crop load management to single upright. The finding of the presented studies together with the benefits coming from multileader planar training systems suggest a high potentiality of the 2D multileader training systems to increase apple production sustainability and profitability for Italian apple orchard, while easing the advent of automation in fruit production.