Using a Population-based Algorithm (E.g. Genetic Algorithm or Ant Colony Optimisation algorithms) solve the following integer programming problem Maximize: f(x, y) = 52x+40y Subject to 6x-y-9 70x + 30y≤ 4731 x² + y² < 3893 x²-150x+80y≤ - 2832 x = [0,82], y ≤ [0,37] 1) Provide the python code 2) Answer the following: (i) Best solution found is (x,y)=(...,...) (ii) Objective function value f(x,y)=... (expected to be ≥3676) (iii) Checking all the constraints: 6x-y=... (expected to be >-9) 60x+20y=... (expected to be <4731) x2+y2=... (expected to be <3893) 109x2-110x+60y=... (expected to be <-2832)
Using a Population-based Algorithm (E.g. Genetic Algorithm or Ant Colony Optimisation algorithms) solve the following integer programming problem Maximize: f(x, y) = 52x+40y Subject to 6x-y-9 70x + 30y≤ 4731 x² + y² < 3893 x²-150x+80y≤ - 2832 x = [0,82], y ≤ [0,37] 1) Provide the python code 2) Answer the following: (i) Best solution found is (x,y)=(...,...) (ii) Objective function value f(x,y)=... (expected to be ≥3676) (iii) Checking all the constraints: 6x-y=... (expected to be >-9) 60x+20y=... (expected to be <4731) x2+y2=... (expected to be <3893) 109x2-110x+60y=... (expected to be <-2832)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
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![### Population-based Algorithm: Solving Integer Programming
#### Objective:
Maximize: \( f(x, y) = 52x + 40y \)
#### Constraints:
1. \( 6x - y \geq -9 \)
2. \( 70x + 30y \leq 4731 \)
3. \( x^2 + y^2 \leq 3893 \)
4. \( \frac{4}{3}x^2 - 150x + 80y \leq -2832 \)
5. \( x \in [0, 82] \), \( y \in [0, 37] \)
#### Tasks:
1. **Provide the python code**
2. **Answer the following**:
- **(i)** Best solution found is \((x, y) = (\cdots, \cdots)\)
- **(ii)** Objective function value \( f(x, y) = \cdots \) (expected to be ≥ 3676)
- **(iii)** Checking all the constraints:
- \( 6x - y = \cdots \) (expected to be ≥ -9)
- \( 70x + 30y = \cdots \) (expected to be ≤ 4731)
- \( x^2 + y^2 = \cdots \) (expected to be ≤ 3893)
- \( \frac{4}{3}x^2 - 150x + 80y = \cdots \) (expected to be ≤ -2832)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d77c7ac-5f9d-4c77-96d5-b6c0b2f44a3f%2Fc54ce64d-4549-4ebb-b597-80aec7c6234d%2Fzbdvmeb_processed.png&w=3840&q=75)
Transcribed Image Text:### Population-based Algorithm: Solving Integer Programming
#### Objective:
Maximize: \( f(x, y) = 52x + 40y \)
#### Constraints:
1. \( 6x - y \geq -9 \)
2. \( 70x + 30y \leq 4731 \)
3. \( x^2 + y^2 \leq 3893 \)
4. \( \frac{4}{3}x^2 - 150x + 80y \leq -2832 \)
5. \( x \in [0, 82] \), \( y \in [0, 37] \)
#### Tasks:
1. **Provide the python code**
2. **Answer the following**:
- **(i)** Best solution found is \((x, y) = (\cdots, \cdots)\)
- **(ii)** Objective function value \( f(x, y) = \cdots \) (expected to be ≥ 3676)
- **(iii)** Checking all the constraints:
- \( 6x - y = \cdots \) (expected to be ≥ -9)
- \( 70x + 30y = \cdots \) (expected to be ≤ 4731)
- \( x^2 + y^2 = \cdots \) (expected to be ≤ 3893)
- \( \frac{4}{3}x^2 - 150x + 80y = \cdots \) (expected to be ≤ -2832)
Expert Solution
Step 1
Answer:
Algorithms
Step1: we have initialize the answer and assign 0
Step2: then we have initialized X1 ,and Y1 and assign both as 0
Step3: we run the for loop up to 0 to 83 as x and inner loop run 0 to 38 as y
Step4: we have check the condition with the help of if condition and calculate the result and print it
Step by step
Solved in 4 steps with 1 images
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