Convergence of an annealing algorithm

Lundy, Margaret E.; Mees, A. I.

doi:10.1007/bf01582166

Cited by 596 publications

(190 citation statements)

References 7 publications

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“…SA is capable of surpassing local optima at high-medium temperatures and gradually converges as the temperature falls to zero. Asymptotically SA algorithm finds an optimal solution with probability one [25]; fortunately, a finite-time implementation of the algorithm returns near-optimal solutions for most problem instances [26]. The SA method requires calibrating the initial temperature, the length of the Markov chains and the cooling coefficient.…”

Section: Hybrid Simulated Annealing Algorithm With Mutation Operatormentioning

confidence: 99%

Design of prestressed concrete precast road bridges with hybrid simulated annealing

Martí

González-Vidosa

Yepes

et al. 2013

Engineering Structures

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ElsevierMartí Albiñana, JV.; Gonzalez Vidosa, F.; Yepes Piqueras, V.; Alcalá González, J. (2013 AbstractThis paper describes one approach to the analysis and design of prestressed concrete precast road bridges, with double U-shaped cross-section and isostatic spans. The procedure used to solve the combinatorial problem is a variant of simulated annealing with a neighborhood move based on the mutation operator from the genetic algorithms (SAMO). This algorithm is applied to the economic cost of these structures at different stages of manufacturing, transportation and construction. The problem involved 59 discrete design variables for the geometry of the beam and the slab, materials in the two elements, as well as active and passive reinforcement. The parametric study showed a good correlation for the cost, geometric and reinforcement characteristics with the span length, which can be useful for the day-to-day design of PC precast bridges. A cost sensitivity analysis first indicates that a maximum 20% rise in steel costs leads to an 11.82% increase in the cost, while a 20% rise in concrete costs increases the cost up to 4.20%, namely 2.8 times less. The analysis also indicated that the characteristics of the cost-optimized bridges are somewhat influenced by different economic scenarios for steel and concrete costs. Finally, there is a growth in the volume of concrete when the steel cost rises; surprisingly, the variation in the volume of concrete is almost insensitive to its rising price.

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Section: Hybrid Simulated Annealing Algorithm With Mutation Operatormentioning

confidence: 99%

Design of prestressed concrete precast road bridges with hybrid simulated annealing

Martí

González-Vidosa

Yepes

et al. 2013

Engineering Structures

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“…Between 1984 and 1986, several authors independently proved that it is possible to design a simulated annealing algorithm so that the probability to be in a state with the minimum cost approaches one as the temperature approaches zero [123,124,125,126,127]. This property is called convergence.…”

Section: Convergence To Optimummentioning

confidence: 99%

“…The stationary probability distribution for our instance of annealing can be derived from the result of Lundy and Mees [126]. They proved a formula for the stationary probability distribution given that a number of requirements are satisfied.…”

Section: Chapter 7 Simulated Annealing At And/invertermentioning

confidence: 99%

Integrated logic synthesis using simulated annealing

Färm

Dubrova

Kuehlmann

2011

Proceedings of the 21st Edition of the Great Lakes Symposium on Great Lakes Symposium on VLSI

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KTH School of Information andCommunication Technology SE-164 40 Kista SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen i elektronik fredagen den 26 januari 2007 klockan 9.00 i Sal E, Forumhuset, Kungl Tekniska högskolan, Isafjordsgatan 39, Kista. © Petra Färm, januari 2007Tryck: Universitetsservice US AB iii Abstract A conventional logic synthesis flow is composed of three separate phases: technology independent optimization, technology mapping, and technology dependent optimization. A fundamental problem with such a three-phased approach is that the global logic structure is decided during the first phase without any knowledge of the actual technology parameters considered during later phases. Although technology dependent optimization algorithms perform some limited logic restructuring, they cannot recover from fundamental mistakes made during the first phase, which often results in non-satisfiable solutions.We present a global optimization approach combining technology independent optimization steps with technology dependent objectives in an annealing-based framework. We prove that, for the presented move set and selection distribution, detailed balance is satisfied and thus the annealing process asymptotically converges to an optimal solution. Furthermore, we show that the presented approach can smoothly trade-off complex, multiple-dimensional objective functions and achieve competitive results. The combination of technology independent and technology dependent objectives is handled through dynamic weighting. Dynamic weighting reflects the sensitivity of the local graph structures with respect to the actual technology parameters such as gate sizes, delays, and power levels. The results show that, on average, the presented advanced annealing approach can improve the area and delay of circuits optimized using the Boolean optimization technique provided by SIS with 11.2% and 32.5% respectively.Furthermore, we demonstrate how the developed logic synthesis framework can be applied to two emerging technologies, chemically assembled nanotechnology and molecule cascades. New technologies are emerging because a number of physical and economic factors threaten the continued scaling of CMOS devices. Alternatives to silicon VLSI have been proposed, including techniques based on molecular electronics, quantum mechanics, and biological processes. We are hoping that our research in how to apply our developed logic synthesis framework to two of the emerging technologies might provide useful information for other designers moving in this direction.iv

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“…Work on SA has looked at the theory (Hajek, 1988), cooling schedules (Lundy and Mees, 1986), and applications of SA such as sequencing (Osman and Potts, 1989;Ogbu and Smith, 1990), timetabling (Abramson, 1991) and the Steiner problem in graphs (Downsland, 1991). Further information on SA can be found in a variety of sources (Collins et al, 1988;Van Laarhoven and Aarts, 1989;Aarts and Korst, 1989).…”

Section: Equationmentioning

confidence: 99%

Local search: A guide for the information retrieval practitioner

MacFarlane

Tuson

2009

Information Processing & Management

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThere are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in Information Retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a Query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The Query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR.

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Convergence of an annealing algorithm

Cited by 596 publications

References 7 publications

Design of prestressed concrete precast road bridges with hybrid simulated annealing

Design of prestressed concrete precast road bridges with hybrid simulated annealing

Integrated logic synthesis using simulated annealing

Local search: A guide for the information retrieval practitioner

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