Jovial Cheukam Ngouonou Thesis defense

To improve the efficiency of solution methods for many combinatorial optimisation problems in our daily lives, we use constraints programming to automatically generate conjectures. These conjectures characterise combinatorial objects used to model these optimisation problems. These include graphs, trees, forests, partitions and Boolean sequences. Unlike the state of the art, the system, called Bound Seeker, that we have developed not only generates conjectures independently, but it also points to links between conjectures. Thus, it groups the conjectures in the form of bounds of the same variable characterising the same combinatorial object. This grouping is called a bounds map of the combinatorial object considered. Then, a study
consisting of establishing links between generated maps is carried out. The goal of this study is to deepen knowledge on combinatorial objects and to develop the beginnings of automatic proofs of conjectures. Then, to show the consistency of the maps and the Bound Seeker, we develop some manual proofs of the conjectures discovered by the Bound Seeker. This allows us to demonstrate the usefulness of some new bound theorems that we have established. To illustrate one of its concrete applications, we introduce a method for semi automatic generation of filtering algorithms that reduce the search space for solutions to a combinatorial optimisation problem. This reduction is made thanks to the new bound theorems that we established after having automatically selected them from the conjectures generated by the Bound Seeker. To show the effectiveness of this technique, we successfully apply it to the problem of developing balanced academic courses for students.