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ISE 5113 Advanced Analytics and Metaheuristics
Homework #4
Instructor: Charles Nicholson
See course website for due date
Requirement details
1. Submit all of your well-documented (e.g. commented) Python code.
2. Provide appropriate output of your code. Please no more than 1 page of output per problem.
3. You may work in teams of 2 for this problem. Teams will not be assigned, you can ask around. You
may also work solo.
4. You cannot use available Python packages that do all of the work for you { you must code the logic to
receive a grade!
In this assignment for several problems you will modify some provided Python code to implement heuristic
algorithms to solve the same instance of the knapsack problem. After implementing all of the code and
solving the problem, you must provide a single table of all results similar to the following:
Algorithm Iterations Objective
Local Search (Best Improvement) 3102 117
Local Search (First Improvement) 951 112
Local Search (Random Restarts) 9,681 147
Local Search (Random Restarts) + allowed infeasible solutions 14,412 194
Simulated Annealing 2102 184
etc.
Knapsack Problem De nition
Given n di erent 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 = 100 and use a seed value (for the random
number generator) of 5113.
Question 1: Strategies for the problem (14 points)
(a) (2 points) De ne and explain a strategy for determining an initial solution to the this knapsack
problem for a neighborhood-based heuristic.
(b) (3 points) Recommend 3 neighborhood structure de nitions that you think would work well with
the example knapsack problem in this assignment.
(c) (3 points) What is the size of each of the neighborhoods you recommended?
1
(d) (4 points) Identify 2 neighborhood structure de nitions that you think would NOT work well with
the example knapsack problem in this assignment. Explain why.
(e) (2 points) In the evaluation of a given solution, an infeasible may be discovered. In this case,
provide 2 strategies for handling infeasibility.
Question 2: Local Search with Best Improvement (10 points)
space
Complete the original Python Local Search code provided to implement Hill Climbing with Best Im-
provement. Note you will need to implement your strategy for determining an initial solution, handling
infeasibility, and possible your neighborhood structures.
Apply the technique to the random problem instance and determine the best solution and objective
value using your revised algorithm.
Question 3: Local Search with First Improvement (5 points)
space
Modify the completed Python Local Search code to implement Hill Climbing with First Improvement.
Apply the technique to the random problem instance and determine the best solution and objective
value using your revised algorithm.
Question 4: Local Search with Random Restarts (8 points)
space
Modify the completed Python Local Search code to implement Hill Climbing with Random Restarts.
You may use Best Improvement or First Improvement (just clearly state your choice). Make sure to
include the following:
a136 Make the number of random restarts an easily modi able variable.
a136 Keep track of the best solution found across all of the restarts.
Apply the technique to the random problem instance and determine the best solution and objective
value using your revised algorithm.
Question 5: Local Search with Random Walk (8 points)
space
Modify the completed Python Local Search code to implement Hill Climbing with Random Walk. You
may use Best Improvement or First Improvement (just clearly state your choice). Make sure to include
the following:
a136 Make the probability of random walk an easily modi able variable.
Apply the technique to the random problem instance and determine the best solution and objective
value using your revised algorithm.
Question 6: Simulated Annealing (20 points)
space
Using the completed Python code as a base, implement Simulated Annealing. Make sure to include the
following:
a136 Explanation of how you determined the initial temperature.
a136 Well-de ned the temperature schedule (the temperature update procedure, the number of iterations
performed at a given temperature, etc.)
a136 Explanation of the stopping criterion.
Apply the technique to the random problem instance and determine the best solution and objective
value using your revised algorithm.
Page 2
Question 7: Tabu Search or Variable Neighborhood Search (30 points)
space
Using the completed Python code as a base, implement either a Tabu Search or Basic VNS to solve
the knapsack problem.
For TS, make sure to include the following:
a136 Explain the tabu criterion, tabu tenure, aspiration criterion, etc. and any other parameters you
include.
a136 Long-term memory is optional.
For Basic VNS, make sure to include the following:
a136 You must de ne and use at least 3 di erent neighborhood structures.
a136 De ne the local search component.
Apply the technique to the random problem instance and determine the best solution and objective
value using your revised algorithm.
Question 8: Summary (5 points)
space
What are your thoughts regarding the performance of the neighborhood-based heuristics that you im-
plemented? Which technique would you recommend for this problem? Did you try any variations (e.g.,
allowing infeasible moves, changing the initial solution strategy, di erent cooling processes, di erent
stopping criteria, etc.?) If so, what seemed to be most e ective?
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