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By Catherine C. McGeoch

"Computational experiments on algorithms can complement theoretical research through exhibiting what algorithms, implementations, and speed-up equipment paintings most sensible for particular machines or difficulties. This publication publications the reader throughout the nuts and bolts of the main experimental questions: What may still I degree? What inputs should still I attempt? How do I examine the knowledge? Answering those questions wishes rules from set of rules design Read more...

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321 and was subsequently repaired. 1. 7 Try a doubling experiment for a quick assessment of function growth. Cambridge Books Online © Cambridge University Press, 2012 34 2 A Plan of Attack Another question that arises early in some experimental studies is to determine when the algorithm has converged. In the context of iterative-improvement heuristics, convergence means, informally, that the probability of finding further improvements is too small to be worth continuing. Another type of convergence arises in stochastic algorithms, which step through sequences of states according to certain probabilities that change over time: here convergence means that the transition probabilities have reached steady state, so that algorithm performance is no longer affected by initial conditions.

Experimental designs for incremental and stochastic algorithms require stopping rules that can terminate trials soon after – but no sooner than – convergence occurs. A poorly chosen stopping rule either wastes time by letting the algorithm run longer than necessary or else stops the algorithm prematurely without giving it a chance to exhibit its best (or steady-state) performance. The latter type of error can create censored data, whereby a measurement of the (converged) cost of the algorithm is replaced by an estimate that depends on the stopping rule.

Experimental designs can be developed according to formal procedures from a subfield of statistics known as design of experiments (DOE). But the pure DOE framework is not always suitable for algorithmic questions – sometimes designs must be based upon problem-specific knowledge and common sense. The next section describes some basic goals of algorithmic experiments. 2 introduces concepts of DOE and shows how to apply them, formally and informally, to meet these goals. 1 Experimental Goals The immediate goal of the experiment is to answer the particular question being posed.

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