## Drone Path Optimization with DEAP (Genetic Algorithm Example)

**Drone path optimization** is an essential problem in various applications, including delivery systems, surveillance, and agricultural monitoring.

One common problem is to find the shortest or most efficient path for a drone to travel between several waypoints (points of interest), which is a variation of the well-known **Traveling Salesman Problem (TSP)**.

This example demonstrates how to solve a simplified version of the drone path optimization problem using the **DEAP** (Distributed Evolutionary Algorithms in $Python$) library with a genetic algorithm.

### Problem Definition

We will solve the problem of a drone needing to visit a set of predefined waypoints and return to the starting point.

The goal is to minimize the total travel distance while visiting each waypoint exactly once.

This is equivalent to solving the **TSP** but applied in a drone context, where each waypoint is a geographical coordinate (x, y).

### Genetic Algorithm Approach

A genetic algorithm ($GA$) is suitable for this type of optimization because of its ability to explore large search spaces.

In GA, we represent the possible solutions (paths) as individuals in a population.

The individuals evolve over generations based on their fitness, which in this case is the total travel distance of the path.

### Steps

**Representation**: Each individual in the population is a list of integers representing the order in which the drone visits the waypoints.**Fitness Function**: The fitness function calculates the total distance traveled by the drone. The shorter the total distance, the better the solution.**Selection**: Use tournament selection to choose the best individuals from the population.**Crossover**: Implement ordered crossover to combine two parent solutions and produce offspring.**Mutation**: Use a swap mutation to randomly change the order of the waypoints in an individual.**Evolution**: Repeat the selection, crossover, and mutation processes for multiple generations to evolve better solutions.

### Example Code with DEAP

1 | import random |

### Explanation of the Code

**Waypoints**: We generate random waypoints in a $2D$ space using`np.random.rand()`

.

These represent the locations the drone needs to visit.**Distance Calculation**: The function`distance()`

computes the Euclidean distance between two waypoints.**Fitness Function**: The`evaluate()`

function computes the total travel distance for a given order of waypoints (represented by an individual).

The individual starts at the first waypoint, visits all other waypoints, and returns to the starting point.**Genetic Algorithm Setup**:**Individuals**: Each individual represents a possible order in which the drone visits the waypoints.**Selection**: Tournament selection is used to choose individuals for crossover.**Crossover**: Ordered crossover (`cxOrdered`

) is used to combine two parents while maintaining valid waypoint orders.**Mutation**: The mutation function randomly swaps two waypoints in the path to introduce variation.

**Evolution**: The population evolves over $100$ generations, with crossover occurring $70$% of the time and mutation $20$% of the time.**Best Solution**: After the evolution, the best individual (path) is displayed, along with its total travel distance (fitness).

### Running the Code

When you run the code, the genetic algorithm evolves the population over generations, and you will see output showing the best and average fitness values for each generation. After the evolution completes, the best path and its corresponding total distance will be printed.

## Result

1 | gen nevals min avg |

The genetic algorithm ($GA$) has successfully found an optimized solution for the drone path optimization problem.

Let’s break down the results in detail:

### Generational Summary

**Generations (gen)**: The algorithm ran for a total of $100$ generations.

Each generation represents one iteration of the genetic algorithm, where the population of potential solutions evolves through selection, crossover, and mutation.**Evaluations (nevals)**: This column represents how many individuals were evaluated in each generation.

The typical number is around $220$-$250$ evaluations per generation.**Minimum Fitness (min)**: The “min” column represents the fitness of the best individual in each generation.

Fitness in this context is the total travel distance for the drone’s path (lower is better since we are minimizing distance).

The best fitness starts at $370.117$ in generation $0$ and improves steadily, eventually reaching the optimal value of $279.178$ around generation $11$.**Average Fitness (avg)**: The “avg” column shows the average fitness of all individuals in the population for that generation. This provides an indication of the overall quality of the population.

Initially, the average fitness starts around $613.888$, and as the generations progress, it improves significantly to about $318.160$ by the end.

### Key Observations

**Initial Population**: In the first generation, the best individual has a total distance of $370.117$, and the average distance of the population is much higher at $613.888$.

This suggests that the initial population was quite far from the optimal solution, which is typical in $GA$.**Rapid Improvement**: By generation $9$, the best individual already achieves a total distance of $280.492$.

From generation $11$ onwards, the best solution achieves a total distance of**279.178**, which remains the minimum for the rest of the evolution process.

This shows that the algorithm found an optimal or near-optimal solution early in the process.**Stabilization**: After generation $11$, the best individual does not improve further, and the population’s average fitness continues to improve but stabilizes.

This means that while many individuals in the population are becoming closer to the optimal solution, the algorithm is no longer finding a significantly better path.**Best Path**: The final result gives the best path found by the algorithm:1

[5, 9, 0, 2, 6, 1, 7, 4, 8, 3]

This is the sequence of waypoints the drone should visit to minimize its travel distance. The total distance traveled for this path is

**279.178 units**.

### Conclusion

The genetic algorithm performed well in solving the drone path optimization problem.

After $100$ generations, it found an optimal path with a total travel distance of **279.178**.

The algorithm quickly converged to this solution within the first $10$-$20$ generations, indicating efficient exploration of the solution space.

The result demonstrates how $GA$s can be an effective method for solving complex optimization problems like the **Traveling Salesman Problem** ($TSP$) applied to drone navigation.

If needed, this process can be extended to include additional constraints such as energy usage, obstacles, or even dynamic weather conditions, which would further challenge the optimization.

## Extensions

**Wind and Battery Constraints**: In more realistic drone optimization problems, you might need to incorporate constraints like wind speed, battery life, and no-fly zones.

These can be added as part of the fitness function or as additional constraints in the GA.**3D Coordinates**: If the drone operates in $3D$ space, the waypoints can be extended to include altitude $(x, y, z)$, and the distance function would need to account for this.

This example showcases how genetic algorithms, through $DEAP$, can be effectively applied to optimize complex path-planning problems such as drone navigation.