Mission optimization for LEO space debris removal using graph theory

"The Kessler Run" is a competition in which participants would have to find the best way to reach and remove 123 debris in LEO orbit with a minimum cost. The starting point of the work was an already finished project that aimed to find one solution to the mentioned competition. Such solution involves the use of graphs method to develop the starting sequences of the solution. Those sequences are however uncompleted and require additional processing in order to get all the 123 debris. The goal of the work was to optimize this filling phase, already featured in the first finished project but needing improvements, in order to obtain better solutions. This purpose has been achieved via the implementation of 3 new methods of sequence-filling: a direct debris insertion method, that finds the possible spots in which new debris can be added to the sequence, a replacement-insertion method, that finds the best substitution of left debris with placed debris that can lead to a consequent additional placement, and a generated-spot insertion method, that creates, where possible, enough space to place a new debris in a sequence. All the starting solution, as well as the newly developed methods are all implemented in MATLAB. New results have then been found that are discussed at the end of the paper in comparison with the starting solution, highlighting advantages and potential improvements.