Evaluation of modeling and solution techniques
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Evaluation of modeling and solution techniques. Theoretical worst case, average case, partial orders shortcomings: worst case seldom occurs unrealistic assumptions Empirical computational experiments. Principles. Results presented must be sufficient to justify claims

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Evaluation of modeling and solution techniques

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Evaluation of modeling and solution techniques

Evaluation of modeling and solution techniques

  • Theoretical

    • worst case, average case, partial orders

    • shortcomings:

      • worst case seldom occurs

      • unrealistic assumptions

  • Empirical

    • computational experiments


Principles

Principles

  • Results presented must be sufficient to justify claims

    • e.g., don’t confuse an algorithm with an implementation

  • Sufficient detail to allow reproducibility of results

    • give actual code

    • experimental notebook


Test problems

Test problems

  • Benchmark sets

    • from practice

    • specially constructed

  • Randomly generated

    • simple random

    • model a real problem


Advantages disadvantages

Advantages & disadvantages

  • Benchmark sets

    • sometimes representative of real world

    • expensive to collect, thus sets often small

    • biased

  • Randomly generated

    • can explore entire space of problems

    • allows statistically valid conclusions

    • lack of realism


Performance measures

Performance measures

  • Efficiency

    • CPU time

    • nodes visited

    • constraint checks

  • Robustness, scope

    • class of problems which can be effectively solved

  • Scalability

    • size of problems

  • Accuracy, solution quality


Performance claims

Performance claims

A claim that…

  • a new algorithm is feasible and promising

    • preliminary testing on several hand-picked problems

  • an algorithm/implementation is better

    • detailed comparison with prominent methods already available on broad range of problems


Pitfalls

Pitfalls

  • Straw algorithms

    • only compare against the “best”

  • Easy problems

  • Unfair comparisons

    • different languages, programmers, optimization efforts, machines, ...

  • Test set tuning

    • e.g., parameter tuning

    • solution: divide into “training” and test sets


Competitive testing vs scientific testing

Competitive testing vs Scientific testing

  • Drawbacks of competitive testing

    • enormous amount of work

    • dictates implementation language

    • tells us which algorithm is better but not why

    • negative results are considered uninteresting

  • Scientific testing

    • experiments designed to contribute to understanding


References

References

  • Crowder, H.P., Dembo, R.S., and Mulvey, J.M. “On reporting computational experiments with mathematical software,” ACM Transactions on Mathematical Software, 5:193-203, 1979.

  • Jackson, R.H.F., Boggs, P.T., Nash, S.G., and Powell, S. “Guidelines for reporting results of computational experiments,” Mathematical Programming, 49:413-426, 1990.

  • Hooker, J.N., “Needed: An empirical science of algorithms,” 1993.

  • Hooker, J.N., “Testing heuristics: We have it all wrong,” 1995.


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