A Lagrangian heuristic for satellite range scheduling with resource constraints
The data exchange between ground stations and satellite constellations is becoming a challenging task, as more and more communication requests must be daily scheduled on a few, expensive stations located all around the Earth. Most of the scheduling procedures adopted in practice cannot cope with suc...
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| Vydáno v: | Computers & operations research Ročník 38; číslo 11; s. 1572 - 1583 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Kidlington
Elsevier Ltd
01.11.2011
Elsevier Pergamon Press Inc |
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| ISSN: | 0305-0548, 1873-765X, 0305-0548 |
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| Abstract | The data exchange between ground stations and satellite constellations is becoming a challenging task, as more and more communication requests must be daily scheduled on a few, expensive stations located all around the Earth. Most of the scheduling procedures adopted in practice cannot cope with such complexity, and the development of optimization-based tools is strongly spurred.
We show that the problem can be formulated as a multiprocessor task scheduling problem in which each job (communication) requires a time dependent pair of resources (ground station and satellite) to be processed, and the objective consists of maximizing the total revenue of on-time jobs. A time-indexed {0,1}-linear programming formulation is then introduced able to include all the complex technological constraints of current constellations. Unfortunately, relevant real-world scenarios yield integer programs with hundreds of thousands variables and a few million constraints, which cannot be tackled by standard integer programming (either exact or heuristic) techniques.
To overcome this difficulty, we developed a Lagrangian version of the Fix-and-Relax MIP heuristic. It is based on a Lagrangian relaxation of the problem which is shown to be equivalent to a sequence of maximum weighted independent set problems on interval graphs. The heuristic has been implemented in a tool used by the Italian reference operator for the GALILEO constellation, providing near optimal solutions to relevant large scale test problems. |
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| AbstractList | The data exchange between ground stations and satellite constellations is becoming a challenging task, as more and more communication requests must be daily scheduled on a few, expensive stations located all around the Earth. Most of the scheduling procedures adopted in practice cannot cope with such complexity, and the development of optimization-based tools is strongly spurred. We show that the problem can be formulated as a multiprocessor task scheduling problem in which each job (communication) requires a time dependent pair of resources (ground station and satellite) to be processed, and the objective consists of maximizing the total revenue of on-time jobs. A time-indexed {0,1}-linear programming formulation is then introduced able to include all the complex technological constraints of current constellations. Unfortunately, relevant real-world scenarios yield integer programs with hundreds of thousands variables and a few million constraints, which cannot be tackled by standard integer programming (either exact or heuristic) techniques. To overcome this difficulty, we developed a Lagrangian version of the Fix-and-Relax MIP heuristic. It is based on a Lagrangian relaxation of the problem which is shown to be equivalent to a sequence of maximum weighted independent set problems on interval graphs. The heuristic has been implemented in a tool used by the Italian reference operator for the GALILEO constellation, providing near optimal solutions to relevant large scale test problems. The data exchange between ground stations and satellite constellations is becoming a challenging task, as more and more communication requests must be daily scheduled on a few, expensive stations located all around the Earth. Most of the scheduling procedures adopted in practice cannot cope with such complexity, and the development of optimization-based tools is strongly spurred. We show that the problem can be formulated as a multiprocessor task scheduling problem in which each job (communication) requires a time dependent pair of resources (ground station and satellite) to be processed, and the objective consists of maximizing the total revenue of on-time jobs. A time-indexed {0,1}-linear programming formulation is then introduced able to include all the complex technological constraints of current constellations. Unfortunately, relevant real-world scenarios yield integer programs with hundreds of thousands variables and a few million constraints, which cannot be tackled by standard integer programming (either exact or heuristic) techniques. To overcome this difficulty, we developed a Lagrangian version of the Fix-and-Relax MIP heuristic. It is based on a Lagrangian relaxation of the problem which is shown to be equivalent to a sequence of maximum weighted independent set problems on interval graphs. The heuristic has been implemented in a tool used by the Italian reference operator for the GALILEO constellation, providing near optimal solutions to relevant large scale test problems. The data exchange between ground stations and satellite constellations is becoming a challenging task, as more and more communication requests must be daily scheduled on a few, expensive stations located all around the Earth. Most of the scheduling procedures adopted in practice cannot cope with such complexity, and the development of optimization-based tools is strongly spurred. We show that the problem can be formulated as a multiprocessor task scheduling problem in which each job (communication) requires a time dependent pair of resources (ground station and satellite) to be processed, and the objective consists of maximizing the total revenue of on-time jobs. A time-indexed {0,1}-linear programming formulation is then introduced able to include all the complex technological constraints of current constellations. Unfortunately, relevant real-world scenarios yield integer programs with hundreds of thousands variables and a few million constraints, which cannot be tackled by standard integer programming (either exact or heuristic) techniques. To overcome this difficulty, we developed a Lagrangian version of the Fix-and-Relax MIP heuristic. It is based on a Lagrangian relaxation of the problem which is shown to be equivalent to a sequence of maximum weighted independent set problems on interval graphs. The heuristic has been implemented in a tool used by the Italian reference operator for the GALILEO constellation, providing near optimal solutions to relevant large scale test problems. [PUBLICATION ABSTRACT] |
| Author | Nocella, Salvatore Smriglio, Stefano Rossi, Fabrizio Marinelli, Fabrizio |
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| Keywords | Multiprocessor scheduling Time-indexed scheduling formulation Lagrangian heuristic Applications Satellite communications Income Satellite telecommunication Temporal databases Satellite Time dependence Lagrange multiplier Zero one programming Independent set Relaxation method Large scale system Interval graph Script Lagrangian Task scheduling Graph theory Constrained optimization Integer programming Processor scheduling Resource constraint Optimal solution Heuristic method |
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| SubjectTerms | Applications Applied sciences Communication satellites Computer science; control theory; systems Computer systems and distributed systems. User interface Constellations Exact sciences and technology Ground stations Heuristic Integer programming Lagrange multiplier Lagrangian heuristic Linear programming Mathematical analysis Mathematical models Mathematical programming Multiprocessor scheduling Operational research and scientific management Operational research. Management science Optimization Satellite communications Satellites Scheduling Scheduling, sequencing Software Studies Time-indexed scheduling formulation |
| Title | A Lagrangian heuristic for satellite range scheduling with resource constraints |
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