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Optimization with Meta-Heuristics

Optimization with Meta-Heuristics. Question: Can you ever prove that a solution generated using a meta-heuristic is optimal? Answer: Yes, for a minimization problem, if the value of the solution equals a lower bound.

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Optimization with Meta-Heuristics

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  1. Optimization with Meta-Heuristics Question: Can you ever prove that a solution generated using a meta-heuristic is optimal? Answer: Yes, for a minimization problem, if the value of the solution equals a lower bound. Question: If the solution of a meta-heuristic for a minimization problem does not equal the lower bound, does that mean the solution is not optimal? Answer: Not necessarily, you just don’t know. Observation: Developing a good lower bound just as important as developing a good meta-heuristic algorithm.

  2. DOE for Meta-Heuristics Question: With all the seeming randomness, and choices of neighborhoods and algorithm parameters, how do you know you have developed a good approach or not? Answer: Design of Experiments

  3. DOE for Meta-Heuristics Recall the classic Johnson, et al. simulated annealing algorithm: 1. Get an initial solution S. 2. Get an initial temperature T > 0. 3. While not yet frozen do the following: 3.1 Perform the following loop l time. 3.1.1 Pick a random neighbor S’ of S. 3.1.2 Let D = cost(S’) – cost(S) 3.1.3 If D <= 0 (downhill move), Set S = S’. 3.1.4 If D > 0 (uphill move), Set S = S’ with probability e-D/T. 3.2 Set T = rT (reduce temperature). 4. Return S. What are potential experimental parameters?

  4. DOE for Meta-Heuristics Design parameters for simulated annealing algorithm include: • Problem instances • Cooling approach • Starting temperature • Number of iterations at temperature • Temperature reduction rate • Termination condition • Variance from Johnson’s classic algorithm • Neighborhoods • Acceptance probability function

  5. DOE for Meta-Heuristics Obtaining Problem Instances: • Benchmark problems • www.palette.ecn.purdue.edu/~uzsoy2/spssm.html • http://w.cba.neu.edu/~msolomon/problems.htm • many others • Problem generator • How many problems • Size of problem • Problem characteristics (unique for different problem types)

  6. www.palette.ecn.purdue.edu/~uzsoy2/spssm.html Shop Scheduling Benchmark Problems • General Information • C Programs For Problem Generation • Parameter Values For Problem Generation • J//Cmax Problems • J//Lmax Problems • J/2SETS/Cmax Problems • J/2SETS/Lmax Problems • F//Cmax Problems • F//Lmax Problems

  7. DOE for Meta-Heuristics How to report results: • Must evaluate to something (solution value – lower bound) • Compare solution versus run time • Compare over some problem generation parameter (due date range)

  8. DOE for Meta-Heuristics How to report results: different sized problem instances

  9. DOE for Meta-Heuristics How to report results: Comparison to benchmark problems

  10. DOE for Meta-Heuristics How to report results:

  11. DOE for Meta-Heuristics How to report results:

  12. DOE for Meta-Heuristics In class assignment: Develop a DOE for the traveling salesman problem.

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