Q2. What are the future works mentioned in the paper "A lagrangian heuristic for satellite range scheduling with resource constraints" ?
The authors also wish to thank Alessandro Donati from ESA for his helpful comments during the development of the project.
Q3. What is the common way to obtain a feasible schedule?
In case of Lagrangian relaxation, feasible schedules are typically obtained from pseudoschedules computed during the subgradient optimization by a combination of elementary moves such as swap, insertion, deletion, merge of pseudo-schedule, etc. (see, for instance, [1], [15]).
Q4. What is the key feature of Srsp-rc-rel?
Remark that, if satellites have infinite capacity and wj = 1 for all j ∈ J (i.e., all the services have the same revenue), then Srsp-rc-rel boils down to MuRRS.
Q5. What are the advantages of dualizing the assignment and the ground station capacity constraints?
Among them, the relaxation in which the assignment (2) and the ground station capacity constraints (3) are dualized shows two important advantages: it has the minimum number of multipliers and, at the same time, yields an efficiently solvable lagrangian subproblem.
Q6. What is the main drawback of fix-and-relax?
In general, fix-and-relax heuristics can have an important drawback: if at some iteration the relaxed MIP becomes infeasible, nothing can be inferred on the whole problem.
Q7. What is the heuristic for fixing a set of variables?
the set of variables to be fixed is determined exploiting the pseudo-schedule SC derived from the solution of the Lagrangian dual, as explained in the next subsection.
Q8. What is the problem with the Fix-and-Relax scheme?
the Fix-and-Relax scheme cannot be directly applied to {0, 1}- Srsp-rc-rel because even its linear relaxation (see §6) is too difficult to be solved.
Q9. What is the main problem of Srsp-rc-rel?
From a mathematical point of view, it is worthwhile to look also at the relaxation of Srsp-rc obtained eliminating precedence, set-up and on-board storage constraints.
Q10. What is the main problem with the installation of additional ground-stations?
This is becoming a critical task since the rapid increase in the number of satellites cannot be counterbalanced by installing additional, very expensive, ground-stations.