On Formulating the Ground Scheduling Problem as a Multi-objective Bilevel Problem

Abstract

In this paper, a bilevel multi-objective formulation of the Ground Scheduling Problem is presented. First, the problem is formulated as a bilevel optimisation problem (BOP), wherein the upper level (UL) is a biobjective problem determining the pairs of Ground Station (GS) to Spacecraft (SC) and the starting time of each event with objectives the maximisation of the access windows and the minimisation of the communication clashes of each GS. These two objectives of the UL can be assumed as a measure of the violation of the feasibility of a schedule. The lower level (LL) consists of a single objective optimisation problem that determines the duration of each event, with objectives the communication time requirement of SCs with GS and the total ground station usage, combined together to a weighted sum function. The approach used to solve this multi-objective BOP is a nested approach, where the Pareto front of the upper level is obtained by a multi-objective optimisation algorithm (NSGA2) and the lower level is solved using a GA. The formulation is tested on one small test case from literature and the relevant results are reported.

Preferred Solutions of the Ground Station Scheduling Problem using NSGA-III with Weighted Reference Points Selection

“…As mentioned also in our earlier paper [11], the objectives FitAW and FitCS are a measure of the feasibility of the schedule. By solving the problem simultaneously and obtaining well-spread Pareto front, many of the solutions of the optimization will result in a different final schedule.…”

“…The formulation of GSP we adopt in this paper is the one used in [2], considering the following objectives: 1) maximizing the events that fall inside the available Access Windows of the ground stations, 2) minimizing the clashes when more than one satellite is communicating with the same ground station, 3) maximizing the time that is required to finalize specific telemetry tasks, such as the download of images, and finally, 4) taking advantage as much as possible from the ground station network by minimizing their idle time. As we have already noted in [11] and [12], the objectives of access windows and clashes are in fact constraints. By simultaneously solving this many-objective problem, it may lead to solutions of the Pareto front, that result in infeasible final schedules.…”

“…al [1], [2]. The mathematical notation is the same as presented in papers [11] and [12]. We assume that ground stations can communicate at most with one satellite at a time.…”

A Hybrid Genetic Algorithm for Ground Station Scheduling Problems

“…The genetic algorithm (GA) has the ability to customize coding modes, fitness functions, individual selection mechanisms, crossover strategies, and mutation strategies according to problem characteristics [7], and has excellent global search capability [8], which can effectively deal with the resource scheduling problem of ground stations [9,10].…”

Stochastic satellite tracking with constrained budget via structured-chromosome genetic algorithms

“…Optimisation-based approaches for operations planning and scheduling of ground stations have been proposed, e.g. using Genetic Algorithms (GA) (Soma et al 2004;Sun and Xhafa 2011), simulated annealing (Xhafa et al 2013), mixed integer programming (Spangelo et al 2015), a multi-objective bi-level formulation (Antoniou et al 2020;Petelin et al 2021), and dynamic programming for ESA's EPS (Damiani et al 2007). Specific approaches for low-cost stations have been investigated (Schmidt et al 2008) and compared (Kleinschrodt et al 2016).…”