Simulated annealing methods with general acceptance probabilities

Cache policies to minimize the content retrieval cost have been studied through competitive analysis when the miss costs are additive and the sequence of content requests is arbitrary. More recently, a cache utility maximization problem has been introduced, where contents have stationary popularities and utilities are strictly concave in the hit rates. This paper bridges the two formulations, considering linear costs and content popularities. We show that minimizing the retrieval cost corresponds to solving an online knapsack problem, and we propose new dynamic policies inspired by simulated annealing, including DynqLRU, a variant of qLRU. For such policies we prove asymptotic convergence to the optimum under the characteristic time approximation. In a real scenario, popularities vary over time and their estimation is very difficult. DynqLRU does not require popularity estimation, and our realistic, trace-driven evaluation shows that it significantly outperforms state-of-the-art policies, with up to 45% cost reduction. Notice: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

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“…The proof is in Appendix C and it follows from standard results for simulated annealing (see e.g. [23]). …”

Section: Convergencementioning

confidence: 99%

Cache policies for linear utility maximization

Neglia

Carra²,

Michiardi³

2017

IEEE INFOCOM 2017 - IEEE Conference on Computer Communications

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“…Geman and Geman (1984), Anily and Federgruen (1987), Mitra et al (1986), and Johnson and Jacobson (2002) determine various sufficient conditions on the cooling schedule for convergence in probability to a global minimum. Chiang and Chow (1988) and Holley and Stroock (1988) also provide convergence results.…”

Section: Penalty Methods and Annealingmentioning

confidence: 99%

Convergence in Probability of Compressed Annealing

2004

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We consider combinatorial optimization problems for which the formation of a neighborhood structure of feasible solutions is impeded by a set of constraints. Neighborhoods are recovered by relaxing the complicating constraints into the objective function within a penalty term. We examine a heuristic called compressed annealing that integrates a variable penalty multiplier approach within the framework of simulated annealing. We refer to the value of the penalty multiplier as "pressure." We analyze the behavior of compressed annealing by exploring the interaction between temperature (which controls the ability of compressed annealing to climb hills) and pressure (which controls the height of the hills). We develop a necessary and sufficient condition on the joint cooling and compression schedules for compressed annealing to converge in probability to the set of global minima. Our work generalizes the results of Hajek (1988) in the sense that when there are no relaxed constraints, our results reduce to his.

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“…Because the number of leaf nodes determines the number of interior nodes, the best possible BVH (as defined by global SAH cost) for a given set of leaves is always reachable from any other state. With this property, the probability of the simulated annealing algorithm coming across the best possible BVH approaches one as the annealing schedule grows [2]. While this will require an infeasible amount of computation in practice, the algorithm is nonetheless theoretically sound.…”

Section: Simulated Annealingmentioning

confidence: 97%

Tree rotations for improving bounding volume hierarchies

Kensler

2008

2008 IEEE Symposium on Interactive Ray Tracing

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Current top-down algorithms for constructing bounding volume hierarchies (BVHs) using the surface area heuristic (SAH) rely on an estimate of the cost of the potential subtrees to determine how to partition the primitives. After a tree has been fully built, however, the true cost value at each node can be computed. We present two related algorithms that use this information to reduce the tree's total cost through a series of local adjustments (tree rotations) to its structure. The first algorithm uses a fast and simple hill climbing method and the second uses simulated annealing to obtain greater improvements by avoiding local minima. Both algorithms are easy to add to existing BVH implementations and are suitable for preprocessing static geometry for interactive ray tracing.

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Simulated annealing methods with general acceptance probabilities

Cited by 124 publications

References 16 publications

Cache policies for linear utility maximization

Cache policies for linear utility maximization

Convergence in Probability of Compressed Annealing

Tree rotations for improving bounding volume hierarchies

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