A Constraint Programming Model for the Super-Agile Earth Observation Satellite Imaging Scheduling Problem

The gist The study presents an exact Constraint Programming formulation for the Super-Agile Earth Observation Satellite Imaging Scheduling Problem (SAEOS-ISP), which addresses new challenges introduced by variable observation durations, multiple imaging directions, and sequence-dependent transition times across multiple satellites.

Problem Context

The paper focuses on the Earth observation satellite imaging scheduling problem (EOS-ISP), which involves selecting and assigning imaging tasks to satellites to maximize mission performance under operational and physical constraints The growing scale and agility of satellite systems have made scheduling a highly complex and resource-constrained problem that requires fast and reliable decision-making Scheduling in Earth observation missions involves deciding when and how satellites acquire images of ground targets while respecting visibility, energy and memory constraints Targets can be transformed into a set of rectangular strips that cover the entire target (Lemaıitre et al., 2002) Each strip thus represents an individual imaging task The difficulty lies essentially in having to decide the start of the observation within a VTW.

SAEOS-ISP Complexity

The Super-Agile Earth Observation Satellite Imaging Scheduling Problem (SAEOS-ISP) is more complex than the Agile EOS-ISP because it introduces dynamic imaging capabilities and time-dependent transition constraints SAEOS can perform imaging in arbitrary directions, whereas AEOS can only acquire strips parallel to the sub-satellite track This high maneuverability expands the optimization search space and increases imaging flexibility, thereby posing new challenges to the scheduling problem and leading to substantially higher computational complexity. The SAEOS-ISP is considered largely unexplored, with no exact approaches yet proposed.

Proposed Methodology

The study proposes an exact optimization model based on Constraint Programming (CP), which is attractive for this problem because it can produce high-quality solutions within short computational times The proposed CP model accounts for three key features compared to previous exact methods for the AEOS-ISP: (1) variable-length observation windows, allowing imaging durations to vary for the same strip; (2) multiple imaging directions, making the pointing direction a decision variable; and (3) sequence-dependent transition times, which capture satellite maneuvers between consecutive observations. The model utilizes interval variables and sequence variables inherent to the CP Optimizer dedicated to scheduling

Model Formulation

The CP formulation aims to maximize total observation coverage revenue by maximizing the summed profits for observed spot targets and polygonal targets The objective function is defined as Maximize ∑j∈Js wj × presenceOf(Yj) + ∑r∈Rp wr × f 1 Ar Aj × presenceOf(Yj)! (4) The function f is defined by a piecewise linear function that penalizes partial observations while strongly encouraging complete coverage of each polygon Scheduling constraints utilize global constraints like alternative and noOverlap to define the scheduling logic.

Experimental Results

Computational experiments were conducted on a newly generated benchmark dataset composed of multiple multi-satellite scenarios and multi-type targets The model was evaluated against existing non-exact approaches, specifically referencing (Lu et al., 2023) For small to medium-sized instances, the CP model was able to find optimal solutions within short computational times The comparative analysis showed that the proposed approach attains higher computational performance than current state-of-the-art non-exact methods, while explicitly providing an evaluation of solution quality. For larger instances, near-optimal solutions can be obtained within just a few seconds.

Conclusion and Future Work

This work represents the first contribution in the literature that applies CP to the SAEOS-ISP, and the first exact approach proposed for this problem The experimental results show that the number of strips to be observed strongly affects the number of visible time windows and, consequently, the computational complexity of the problem As future work, it is intended to develop new methodologies to address the scalability of the model and to extend the formulation to incorporate additional challenges inherent to Earth observation satellite scheduling, namely energy and onboard memory constraints.

How it works

The scheduling process involves several key elements defined in the CP model:

1. Variables: Interval variables Xi jkl denote the time interval during which strip j is observed by satellite i in VTW vwi jkl These variables can be optional, existing only if strip j is observed by satellite i in VTW vwi jkl.

2. Sequence Variables: Si describes the order of the strips assigned to each satellite, ensuring that only one strip is observed at a time and embedding setup times, ∆(i jkl),(i j′k′l′), between each pair of consecutive observations

3. Constraints: The constraints (5) ensure that a satellite i is scheduled to observe strip j in VTW vwi jkl, and constraint (6) defines the sequence of the different strips assigned to satellite i, guaranteeing that only one strip is observed at a time and embedding setup times

4. Objective Function: The objective function aims to maximize total observation coverage revenue by summing profits for observed spot targets and polygonal targets

Key Findings

The results indicate the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP The lexicographic formulation, when imposing a short run time limit of only 10 seconds, still produced feasible solutions with optimality gaps below 1%. This performance suggests that our model has the potential to be more computationally efficient. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. For larger instances, near-optimal solutions can be obtained within just a few seconds. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. This work represents the first contribution in the literature that applies CP to the SAEOS-ISP, and the first exact approach proposed for this problem. The experimental results show that the number of strips to be observed strongly affects the number of visible time windows and, consequently, the computational complexity of the problem. This work represents the first contribution in the literature that applies CP to the SAEOS-ISP, and the first exact approach proposed for this problem. The experimental results show that our CP model was able to find optimal solutions within short computational times for instances of types A–E. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. This work represents the first contribution in the literature that applies CP to the SAEOS-ISP, and the first exact approach proposed for this problem. The experimental results show that our CP model was able to find optimal solutions within short computational times for instances of types A–E. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. This work represents the first contribution in the literature that applies CP to the SAEOS-ISP, and the first exact approach proposed for this problem. The experimental results show that our CP model was able to find optimal solutions within short computational times for instances of types A–E. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP. This work represents the first contribution in the literature that applies CP to the SAEOS-ISP, and the first exact approach proposed for this problem. The experimental results show that our CP model was able to find optimal solutions within short computational times for instances of types A–E. The obtained results highlight the efficiency and robustness of the proposed model for small to medium-sized instances, while also revealing the scalability challenges inherent to the SAEOS-ISP <ref:

1. Improved scheduling for super-agile Earth observation satellites (SAEOS) by proposing an exact Constraint Programming formulation that explicitly models variable imaging durations, multiple imaging directions, and sequence-dependent transition times. This allows AI systems to generate optimal observation schedules that account for the dynamic capabilities of SAEOSs while maximizing total observation coverage revenue.

2. Enhanced ability to handle complex target geometries through the integration of a piecewise linear function f(x) within the objective function, which penalizes partial observations while strongly encouraging complete coverage of polygonal targets. This allows AI systems to prioritize scheduling decisions that ensure full acquisition of large area targets over fragmented coverage.

3. Development of a lexicographic optimization framework that minimizes makespan while maximizing total observation profit, demonstrating the model's potential to produce high-quality feasible solutions within very short computational times (10 seconds) for near-optimal results. This enables AI systems to balance mission duration constraints with high data acquisition efficiency in real-time scenarios.

4. Scalability assessment capabilities by analyzing the structural growth of decision variables and constraints as the number of targets and strips increases, revealing the scalability challenges inherent to SAEOS-ISP. This allows AI researchers to predict when an exact CP model will become computationally inefficient for larger constellations.

5. Direct computational performance comparison against state-of-the-art non-exact methods, showing that the proposed exact model can achieve higher computational performance while explicitly providing a measure of solution quality (optimality gap). This enables AI systems to choose between fast, potentially suboptimal heuristic solutions and slower but provably better exact solutions based on required fidelity.