Online Optimization: Probabilistic Analysis and Algorithm Engineering

Hiller, Benjamin

doi:10.1007/978-3-642-20009-0_102

Cited by 4 publications

(2 citation statements)

References 55 publications

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“…Stochastic dominance (Müller and Stoyan 2002) origins from statistics where it is used to establish an order between distributions of two random variables. By interpreting the objective value obtained by an algorithm as a random variable, this concept has been transferred to online optimization (Hiller 2009) where the objective value distributions of two algorithms Alg 1 and Alg 2 are related to each other. Let F Alg : R → [0, 1] be the cumulative distribution function of the objective value of Alg: Alg 1 dominates Alg 2 stochastically at zeroth order if and only if…”

Section: Performance Measurement In Online Optimization With Lookaheadmentioning

confidence: 99%

Exact distributional analysis of online algorithms with lookahead

Dunke

Nickel

2020

4OR-Q J Oper Res

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In online optimization, input data is revealed sequentially. Optimization problems in practice often exhibit this type of information disclosure as opposed to standard offline optimization where all information is known in advance. We analyze the performance of algorithms for online optimization with lookahead using a holistic distributional approach. To this end, we first introduce the performance measurement method of counting distribution functions. Then, we derive analytical expressions for the counting distribution functions of the objective value and the performance ratio in elementary cases of the online bin packing and the online traveling salesman problem. For bin packing, we also establish a relation between algorithm processing and the Catalan numbers. The paper shows that an exact analysis is strongly interconnected to the combinatorial structure of the problem and algorithm under consideration. Results further indicate that the value of lookahead heavily relies on the problem itself. The analysis also shows that exact distributional analysis could be used in order to discover key effects and identify related root causes in relatively simple problem settings. These insights can then be transferred to the analysis of more complex settings where the introduced performance measurement approach has to be used on an approximative basis (e.g., in a simulation-based optimization).

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Section: Performance Measurement In Online Optimization With Lookaheadmentioning

confidence: 99%

Exact distributional analysis of online algorithms with lookahead

Dunke

Nickel

2020

4OR-Q J Oper Res

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“…to Bijective Analysis for a restricted class of sequences exhibiting locality of reference. For the more general analysis of stochastic dominance, Hiller and Vredeveld [23,24] showed that LRU is optimal with respect to probability distributions that model locality of reference.…”

Section: Other Measuresmentioning

confidence: 99%

Probabilistic alternatives for competitive analysis

Hiller

Vredeveld

2011

Comput Sci Res Dev

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In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: It sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior, or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.

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