In this work, I address the mission planning problem for cleaning solar panels in large-scale photovoltaic plants using mobile cleaning robots. The presence of dust and sand in western China significantly reduces the power generation efficiency of solar panels. Timely cleaning is essential to maintain optimal performance. However, planning the cleaning sequence for hundreds or thousands of solar panel arrays is a complex combinatorial optimization problem. I propose a hierarchical zoning strategy that prioritizes areas based on environmental factors such as wind exposure and sunlight duration. The problem is formulated as a Traveling Salesman Problem (TSP) over the centroids of the zones. To solve this TSP efficiently, I develop an improved genetic algorithm (IGA) that incorporates a hybrid selection operator combining tournament and roulette wheel methods, a segment-based crossover operator, and a heuristic mutation operator. Experimental results demonstrate that the IGA outperforms the standard adaptive genetic algorithm (AGA) in terms of solution quality and convergence speed.
Photovoltaic (PV) plants in western China suffer from severe dust accumulation. The power output of a solar panel is strongly correlated with the cleanliness of its surface. Studies have shown that dust can reduce the efficiency by up to 30% within a few weeks. Therefore, regular cleaning is critical. Mobile cleaning robots offer a flexible and cost-effective solution, but they must navigate large plant areas containing many solar panel blocks. Determining the optimal order in which to clean these blocks is a key research challenge. Earlier works focused on path planning for single robots without considering the varying cleaning urgency of different solar panel zones. My approach introduces a priority-based zoning scheme and then solves the resulting sequencing problem using an enhanced genetic algorithm.
Problem Formulation and Zoning Strategy
Consider a large PV plant located in a windy, arid region. The plant is divided into multiple zones, each containing several solar panel arrays. The zones are defined based on geographical features: zones near wind gaps accumulate dust faster, and those with longer sunlight hours contribute more to total energy generation. Each zone is assigned a priority level (1 to 6, with 6 being highest). The cleaning robot must start from a depot, visit every zone exactly once, and return to the depot, while respecting that higher‑priority zones should be cleaned first. When priorities are equal, the robot seeks the shortest possible route. This is a classic TSP with a partial order constraint.
I model the PV plant as a complete undirected graph G = (V, E) where V is the set of zone centroids, and the edge weight between two nodes is the Manhattan distance between their centroids. The Manhattan distance is chosen because the robot moves along a grid‑like path within the plant. The objective is to find a Hamiltonian cycle that minimizes total travel distance while obeying the priority constraints. The priorities are predefined; for zones with the same priority, the TSP is solved only among those zones, and the order between different priority levels is fixed (higher first). In the case study, 30 zones are defined, with priorities as shown in Table 1.
| Zone | Priority | Zone | Priority | Zone | Priority |
|---|---|---|---|---|---|
| 1 | 1 | 11 | 1 | 21 | 1 |
| 2 | 1 | 12 | 1 | 22 | 1 |
| 3 | 1 | 13 | 1 | 23 | 1 |
| 4 | 1 | 14 | 1 | 24 | 1 |
| 5 | 1 | 15 | 1 | 25 | 1 |
| 6 | 1 | 16 | 1 | 26 | 1 |
| 7 | 1 | 17 | 1 | 27 | 3 |
| 8 | 1 | 18 | 1 | 28 | 3 |
| 9 | 1 | 19 | 1 | 29 | 4 |
| 10 | 1 | 20 | 1 | 30 | 6 |
The centroids of the 30 zones are calculated from the polygon geometry of each zone. The robot starts from a base station (zone 1, which is also the depot) and must visit all zones. The priority constraint forces the cleaning sequence to start with zone 30 (priority 6), then zones 29 (priority 4), then 27 and 28 (priority 3), and finally all priority‑1 zones in an optimized order. Thus the problem reduces to a TSP for the 26 zones of priority 1, with fixed high‑priority zones inserted at the beginning.
Improved Genetic Algorithm for TSP
Genetic algorithms are well‑suited for TSP, but they suffer from premature convergence and low efficiency. I introduce several improvements to enhance both exploration and exploitation.
Chromosome Encoding and Fitness Function
Each chromosome is a permutation of zone indices, using real‑number encoding (the order of visitation). For a route visiting n zones, the chromosome is a list [c₁, c₂, …, cₙ]. The objective function f is the total Manhattan distance along the route, including the return to the start.
To convert the minimization problem into a maximization fitness function, I apply a dynamic linear scaling:
$$F = f_{\max}^{(k)} – f + \xi^{(k)}$$
where \(f_{\max}^{(k)}\) is the maximum objective value in the current generation k, and \(\xi^{(k)}\) is a small positive adjustment that decreases over generations to maintain selection pressure. I set
$$\xi^{(0)} = M, \quad \xi^{(k)} = c \cdot \xi^{(k-1)}$$
with M = 600 and c = 0.99. This scaling prevents the fitness variance from shrinking too quickly.
Hybrid Selection Operator
Standard roulette wheel selection can lead to premature convergence, while tournament selection alone may lose diversity. I combine both: first, a tournament of size N = 10 selects a candidate pool; from this pool, one parent is chosen via roulette wheel (proportional to fitness) and the other parent is chosen randomly from the same pool. This mixed approach preserves high‑quality individuals while maintaining genetic diversity. The number of individuals directly passed to the next generation is floor(S / N), where S is the population size (100 in this study).
Segment‑Based Crossover Operator
Traditional Order Crossover (OX) is effective but can become stuck when the current best tour length is already low. I propose a dynamic crossover that switches between OX and a self‑crossover operation based on a threshold Q. The threshold Q is determined empirically from preliminary runs; I set Q = 900 km. If the best tour length in the current generation is greater than Q, OX is used to explore larger changes; otherwise, self‑crossover is applied to fine‑tune the solution.
Order Crossover (OX): Two parents are selected. A contiguous segment is chosen from each parent. The segment from parent 1 is copied to offspring 1, and the remaining cities are filled from parent 2 in the order they appear, skipping duplicates. For example:
Parent1: 1 2 | 3 4 5 6 | 7 8 9
Parent2: 4 6 | 1 8 2 9 | 5 3 7
Offspring1 inherits the segment [3,4,5,6]; the remaining cities from parent2 (starting after the segment) are [7,1,8,2,9] after removing duplicates. Offspring1 becomes: 2 9 3 4 5 6 7 1 8.
Self‑Crossover: On a single parent, two random cut points are selected, and the substring between them is reversed. For example:
Parent: 1 3 | 4 2 6 9 | 7 8 5 → Offspring: 1 3 | 9 6 2 4 | 7 8 5.
This operator helps escape local optima when the solution is already relatively good.
Heuristic Mutation Operator
I use a heuristic mutation operator that selects three random cities, explores all six possible permutations of their positions (only five new permutations, excluding the original), and keeps the one with the best fitness. This is a local search within the mutation step.
Algorithm Flow
The overall IGA procedure is as follows:
- Input zone coordinates and priorities. Sort zones by priority; fix the order of high‑priority zones.
- Initialize population S = 100 chromosomes randomly.
- Set parameters: dynamic scaling constants M, c; tournament size N = 10; crossover threshold Q = 900; crossover probability Pc = 0.8; mutation probability Pm = 0.05; maximum generation Tmax = 500.
- For each generation:
- Compute Manhattan distance for each chromosome and apply dynamic linear scaling to obtain fitness.
- Perform hybrid selection to create a mating pool.
- Apply crossover with probability Pc: if current best f > Q, use OX; else use self‑crossover.
- Apply heuristic mutation with probability Pm.
- Evaluate offspring and replace the population (elitism: keep the best individual).
- Update best‑found tour.
- Output the best route and its total distance.
Experimental Results and Analysis
I implemented both the IGA and a standard adaptive genetic algorithm (AGA) in MATLAB R2020a on a machine with AMD Ryzen 7 4800H, 2.90 GHz, 8 GB RAM. The problem instance involves 30 zones with the priorities listed in Table 1. The coordinates of the centroids were extracted from the geometry of the PV plant. The fixed order of high‑priority zones is: 30 → 29 → 28 → 27. The remaining 26 zones (priority 1) are optimized by the genetic algorithms. Both algorithms used population size 100, crossover probability 0.8, mutation probability 0.05, and 500 generations. The AGA employed adaptive crossover and mutation rates based on fitness, while the IGA used the improvements described above.
Table 2 compares the performance of the two algorithms over 10 independent runs.
| Algorithm | Best tour (km) | Worst tour (km) | Average tour (km) |
|---|---|---|---|
| AGA | 1200 | 1614 | 1461.2 |
| IGA | 760 | 832 | 796.8 |
The IGA consistently found tours shorter than 840 km, while the AGA often got stuck in local optima around 1200–1600 km. The best tour found by the IGA was 760 km, achieved in the 181st generation on one run. The corresponding optimal sequence for all 30 zones is: 30 → 29 → 28 → 27 → 6 → 24 → … → 7 → 20 → 4 → 22 → 30 (the full order of the 26 priority‑1 zones is omitted for brevity).
The convergence curves are also illustrative. In the IGA, the best fitness improved rapidly in the first 100 generations and stabilized near the optimum after about 180 generations. In contrast, the AGA showed slow progress and often plateaued at a much higher distance. The dynamic scaling and the segment‑based crossover were key in helping the IGA escape local optima.
Conclusion
In this study, I addressed the hierarchical mission planning problem for cleaning solar panels in large photovoltaic plants. By incorporating environmental priority factors and formulating the problem as a TSP, I developed an improved genetic algorithm that significantly outperforms a standard adaptive genetic algorithm. The hybrid selection operator, dynamic crossover threshold, and heuristic mutation contributed to faster convergence and better solution quality. The optimal cleaning sequence reduces the robot’s travel distance, thereby saving time and energy, which is critical for maintaining high power generation efficiency of solar panels. Future work will extend this approach to multiple cleaning robots and consider dynamic changes in solar panel dust accumulation.
This research provides a practical framework for scheduling cleaning operations in solar farms, especially in dusty regions. The methodology can be adapted to other combinatorial optimization problems in renewable energy infrastructure maintenance.