Improving Robustness of Spacecraft Downlink Schedules

Abstract

In the realm of scheduling problems different sources of uncertainty can invalidate the planned solutions: unpredictability of activity behaviors, machine breakdowns, new activities to be served, and so on. In this paper we are concerned with the generation of high quality downlink schedules in a spacecraft domain in presence of a high degree of uncertainty. In particular, we refer to a combinatorial optimization problem called MARS-EXPRESS Memory Dumping Problem (MEX-MDP), which arose in the European Space Agency program MARS-EXPRESS. A MEX-MDP consists in the generation of dumping commands to maximize the downloads of data sets from the satellite to the ground. The domain is characterized with several kinds of constraints -such as, bounded on-board memory capacities, limited communication windows over the downlink channels, deadlines and ready times imposed by the payload requirements -and different sources of uncertainty -e.g., the amount of data generated at each scientific observation or the channel data rate.In this paper we tackle this problem by using a reduction of the MEX-MDP to a Max-Flow problem: the former problem has a solution when the maximum flow in the latter equates the total amount of data to dump. Given this reduction, we introduce a novel definition of solution robustness based on the utilization of the on-board memory, as well as an iterative procedure to improve solution quality. The key idea behind this approach is that the lower the peaks in memory utilization, the higher the ability cope with unexpectedly large amount of data.

A Mathematical Programming Solution to the Mars Express Memory Dumping Problem

“…Computations experiments have been done on the benchmark instances provided by (Oddi and Policella 2004;2007), available on line. They have been produced from real data and some randomization, as described in the cited references.…”

“…Following (Oddi and Policella 2004;2007) we define the Mars Express memory dumping problem as follows.…”

“…The problem has been studied in several versions: a simplified version was initially considered in (Oddi and Policella 2004;2007). The objective is to compute a dumping schedule of maximum robustness in order to cope with uncertainty in the amount of incoming scientific data.…”

“…The objective is to compute a dumping schedule of maximum robustness in order to cope with uncertainty in the amount of incoming scientific data. The algorithm devised by (Oddi and Policella 2004;2007) to compute robust schedules is heuristic and iteratively improves the schedule robustness by solving a sequence of max-flow problems with classical polynomial-time specialized algorithms, such as the Ford and Fulkerson algorithm (Ahuja, Magnanti, and Orlin 1993).…”

“…In this paper we further elaborate on the formulation presented by (Oddi and Policella 2004;2007) and we present a linear programming algorithm to compute schedules of maximum robustness. The algorithm provides provably optimal solutions in a very short time.…”