In this assignment you will modify some provided Python code to implement a Simulated Annealing algorithm and also a Genetic Algorithm to solve the same instance of the knapsack problem. After implementing the code and solving the problem, please summarize your results in a table similar to Table 1.
Table 1: Example of results summary (numbers are not realistic)
Method
SA
t0
Cooling, tk
Mk
# of temps
Iterations
Items
Weight
Value
selected
1000
t0
10
900
2102
87
320
3180
1+0.9k
800
0.99tk−1
50
40
5333
27
230
1284
1200
0.99tk−1
50
40
5333
13
1250
2002
GA
Generations
Pop
Crossover
Mutation
Elitism
Items
Weight
Value
size
selected
1000
250
0.8
0.1
top 3
23
2650
1921
500
150
0.9
0.2
top 10%
39
1650
3914
etc.
1
Knapsack Problem Definition Given n different items, where each item i has an assigned value (vi) and weight (wi), select a combination of the items to maximize the total value without exceeding the weight limitations, W , of the knapsack.
IMPORTANT!: When generating random problem instance set n = 150 and use the provided seed value for the random number generator. The max weight is 2500.
Question 1: Simulated Annealing (40 points)
Using the provided Python code from the previous homework as a base, implement Simulated Annealing in code. Please address the following by including the associated Python code excerpts (as appropriate) and explanation of the code in the PDF file:
Logic to determine the initial temperature
At least two different temperature cooling schedules (the temperature update procedure) and ex-plore some options for the number of iterations performed at a given temperature (Mk)
• Python logic excerpt for computing the probabilities of accepting a non-improving move Stopping criterion
Apply the code to the random problem instance and determine the best solution and objective value using the multiple variations of your algorithm (e.g., different cooling schedules, different starting temperatures, different values for Mk).
Question 2: Genetic Algorithm (60 points)
Using the genetic algorithm Python code base provided as a starting point, implement a genetic algorithm to solve the knapsack problem. Please address the following by including the associated Python code excerpts (as appropriate) and explanation of the code in the PDF file:
createChromosome() logic
crossover() logic
Logic to compute chromosome fitness, e.g., any modifications to the evaluate() function
rouletteWheel() logic
• mutate() logic insert() logic
Apply the technique to the random problem instance and determine the best solution and objective value using your revised algorithm. Test multiple versions of the GA (e.g., different number of generations, population sizes, crossover rates, etc.)
Page 2
