Genetic Algorithm to solve the Knapsack and Travelling Salesman problems.
In the App.py file please specify Knapsack problem or Travelling Salesman problem in the population creation [line 19].
Knapsack Problem:
Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. (Source: Wikipedia)
Specifically, each item can be selected multiple times to be put in the Knapsack.
The problem weights and values are given as follows:
| weight (Kg) | value ($) |
|---|---|
| 12 | 4 |
| 1 | 2 |
| 2 | 2 |
| 1 | 1 |
| 4 | 10 |
Travelling Salesman Problem:
Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits
each city exactly once and returns to the origin city? Source: Wikipedia
- Python=3.10
- Numpy
The Genetic Algorithm Implementation makes use of a binary encoding of the genotypes for both the Knapsack Problem and the Travelling Salesman problem.
The genome is encoded as a binary string.
Each three letter sub-string encodes for an item, resulting in a string of 15 characters fixed length.
Note: Correct the correct problem formulation would include a longer fixed length.
Generations: 1000
Population: 1000
Breeding Pool Size: 30
| Encoding (binary) | weight (Kg) | value ($) |
|---|---|---|
| 001 | 12 | 4 |
| 010 | 1 | 2 |
| 011 | 2 | 2 |
| 100 | 1 | 1 |
| 101 | 4 | 10 |
The genome is encoded as a binary string
Each three letter sub-string encodes for a connection to another city.
Each three letter substring 3-tuple index encodes for a home city.
Such that each three-tuple encodes for a home city, and a connection to the next city.
Considering 8 cities, the string length will be 24 characters
Generations: 1000
Population: 20
Breeding Pool Size: 10
Connection Encoding
| Encoding | Connection |
|---|---|
| 000 | City 0 |
| 001 | City 1 |
| 010 | City 2 |
| 011 | City 3 |
| 100 | City 4 |
| 101 | City 5 |
| 110 | City 6 |
| 111 | City 7 |
Every gene's (3-tuple) index in the genome represented a city, and the corresponding connection encoding represented to what city it was conencted to