An Optimal Cooling Schedule Using a Simulated Annealing Based Approach

Abstract

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.

Simulated Annealing for volcano muography

“…which is very common in several other SAA implementations (Peprah et al, 2017;Mahdi et al, 2017;Cabrera et al, 2014;Khairuddin and Zainuddin, 2019).…”

Annealing Accelerator for Ising Spin Systems based on In-memory Complementary 2D FETs

“…Most of the work on optimization algorithms like SA is done in software [11,[13][14][15][16], with a few hardware demonstrations [18,19] based on von-Neumann architecture rendering them area and energy inefficient owing to the physical separation of memory and compute. Non-von Neumann hardware accelerators such as graphics processing units (GPUs) [20,21], and field-programmable gate arrays (FPGAs) [22] have become increasingly popular in the later years offering speedup, energy efficiency and smaller physical footprint [23].…”

“…It is similar to other optimization methods such as gradient descent [12] where transitions lowering are accepted. However, unlike the gradient descent method, it allows transitions increasing ("hill-climbing") determined by the annealing temperature [13][14][15][16]. This "hill-climbing" feature of SA makes it highly attractive for systems with multiple local minima in their energy landscape (Fig 1a).…”

Annealing Accelerator for Ising Spin Systems based on In-memory Complementary 2D FETs

“…It is similar to other optimization methods such as gradient descent [12] where transitions lowering are accepted. However, unlike the gradient descent method, it allows transitions increasing ("hill-climbing") determined by the annealing temperature [13][14][15][16]. This "hill-climbing" feature of SA makes it highly attractive for systems with multiple local minima in their energy landscape (Fig 1a).…”

“…Most of the work on optimization algorithms like SA is done in software [11,[13][14][15][16], with a few hardware demonstrations [18,19] based on von-Neumann architecture rendering them area and energy inefficient owing to the physical separation of memory and compute. Non-von Neumann hardware accelerators such as graphics processing units (GPUs) [20,21], and field-programmable gate arrays (FPGAs) [22] have become increasingly popular in the later years offering speedup, energy efficiency and smaller physical footprint [23].…”