A theoretical framework for simulated annealing

Romeo, F.; Sangiovanni-Vincentelli, A.

doi:10.1007/bf01759049

Cited by 149 publications

(57 citation statements)

References 38 publications

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“…The rate at which the SA reaches its global minimum is determined by the cooling schedule parameters, which include the starting temperature, cooling factor, number of transitions at each temperature [2] introduced the linear (or arithmetic) cooling schedule as given by Equation (1): [6] proposed the geometric cooling scheme described by the temperature-update scheme in Equation (2): [16]. In another related study, Gong, Lin, and Qian [17] proposed the quadratic cooling schedule to estimate the number of iterations of the algorithm using a fixed value of β selected from the interval (0, 1).…”

Section: Cooling Schemesmentioning

confidence: 99%

An Optimal Cooling Schedule Using a Simulated Annealing Based Approach

Peprah¹,

Appiah²,

Amponsah³

2017

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Simulated annealing (SA) has been a very useful stochastic method for solving problems of multidimensional global optimization that ensures convergence to a global optimum. This paper proposes a variable cooling factor (VCF) model for simulated annealing schedule as a new cooling scheme to determine an optimal annealing algorithm called the Powell-simulated annealing (PSA) algorithm. The PSA algorithm is aimed at speeding up the annealing process and also finding the global minima of test functions of several variables without calculating their derivatives. It has been applied and compared with the SA algorithm and Nelder and Mead Simplex (NMS) methods on Rosenbrock valleys in 2 dimensions and multiminima functions in 3, 4 and 8 dimensions. The PSA algorithm proves to be more reliable and always able to find the optimum or a point very close to it with minimal number of iterations and computational time. The VCF compares favourably with the Lundy and Mees, linear, exponential and geometric cooling schemes based on their relative cooling rates. The PSA algorithm has also been programmed to run on android smartphone systems (ASS) that facilitates the computation of combinatorial optimization problems.

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Section: Cooling Schemesmentioning

confidence: 99%

An Optimal Cooling Schedule Using a Simulated Annealing Based Approach

Peprah¹,

Appiah²,

Amponsah³

2017

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“…Neither the existence nor the uniqueness of a stationary probability distribution is guaranteed for a general transition matrix P. However, if the transition matrix P is irreducible and aperiodic, then there exists a unique stationary distribution π [128]. A transition matrix P(T ) is irreducible if its underlying search space graph is strongly connected and, for all s i ∈ S and s j ∈ Ω i , P i j (T ) > 0 [116]. The transition matrix is called aperiodic if its underlying search space graph has no state to which the search process will continually return with a fixed time period (greater that one).…”

Section: Convergence To Optimummentioning

confidence: 99%

“…The transition matrix is called aperiodic if its underlying search space graph has no state to which the search process will continually return with a fixed time period (greater that one). A sufficient condition for aperiodicity is that there exist a state s i ∈ S such that P ii = 0 [116].…”

Section: Convergence To Optimummentioning

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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“…Simulated annealing (Aarts et al 1997, Romeo andSangiovanni-Vincentelli 1991) represents an advancement over stochastic hill-climbing in that it is capable of avoiding entrapment in local minima and therefore has a better chance of approaching the global minimum. The basic idea for improvement is that solutions with an inferior fitness score have a non-zero probability of acceptance.…”

Section: Simulated Annealingmentioning

confidence: 99%