Convergence and first hitting time of simulated annealing algorithms for continuous global optimization

2001 ◽  
Vol 54 (2) ◽  
pp. 171-199 ◽  
Author(s):  
M. Locatelli
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Hitting Time ◽  
First Hitting Time ◽  
Continuous Global Optimization ◽  
Annealing Algorithms

Convergence properties of simulated annealing for continuous global optimization

1996 ◽  
Vol 33 (4) ◽  
pp. 1127-1140 ◽  
Author(s):  
M. Locatelli
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Probability Distribution ◽  
Convergence Properties ◽  
Convergence Of Algorithms ◽  
Cooling Schedules ◽  
The Subject ◽  
Continuous Global Optimization ◽  
Annealing Algorithms ◽  
Candidate Point

In this paper conditions for the convergence of a class of simulated annealing algorithms for continuous global optimization are given. The previous literature about the subject gives results for the convergence of algorithms in which the next candidate point is generated according to a probability distribution whose support is the whole feasible set. A class of possible cooling schedules has been introduced in order to remove this restriction.

Convergence properties of simulated annealing for continuous global optimization

1996 ◽  
Vol 33 (04) ◽  
pp. 1127-1140 ◽  
Author(s):  
M. Locatelli
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Probability Distribution ◽  
Convergence Properties ◽  
Convergence Of Algorithms ◽  
Cooling Schedules ◽  
The Subject ◽  
Continuous Global Optimization ◽  
Annealing Algorithms ◽  
Candidate Point

In this paper conditions for the convergence of a class of simulated annealing algorithms for continuous global optimization are given. The previous literature about the subject gives results for the convergence of algorithms in which the next candidate point is generated according to a probability distribution whose support is the whole feasible set. A class of possible cooling schedules has been introduced in order to remove this restriction.

Convergence of a global stochastic optimization algorithm with partial step size restarting

2000 ◽  
Vol 32 (2) ◽  
pp. 480-498 ◽  
Author(s):  
G. Yin
Keyword(s):  
Monte Carlo ◽  
Global Optimization ◽  
Simulated Annealing ◽  
Weak Convergence ◽  
Stochastic Optimization ◽  
Optimization Algorithm ◽  
Step Size ◽  
Wide Range ◽  
Stochastic Optimization Algorithm ◽  
Annealing Algorithms

This work develops a class of stochastic global optimization algorithms that are Kiefer-Wolfowitz (KW) type procedures with an added perturbing noise and partial step size restarting. The motivation stems from the use of KW-type procedures and Monte Carlo versions of simulated annealing algorithms in a wide range of applications. Using weak convergence approaches, our effort is directed to proving the convergence of the underlying algorithms under general noise processes.

Simulated Annealing and Graph Colouring

2001 ◽  
Vol 10 (1) ◽  
pp. 29-40 ◽  
Author(s):  
ANDREAS NOLTE ◽  
RAINER SCHRADER
Keyword(s):  
Simulated Annealing ◽  
Combinatorial Optimization ◽  
Optimal Solution ◽  
Hitting Time ◽  
Graph Colouring ◽  
First Hitting Time ◽  
Exponential Time ◽  
Empirical Results ◽  
Exponential Size

Simulated annealing is a very successful heuristic for various problems in combinatorial optimization. In this paper an application of simulated annealing to the 3-colouring problem is considered. In contrast to many good empirical results we will show for a certain class of graphs that the expected first hitting time of a proper colouring, given an arbitrary cooling scheme, is of exponential size.These results are complementary to those in [13], where we prove the convergence of simulated annealing to an optimal solution in exponential time.

Simulated Annealing and Adaptive Search in Global Optimization

1994 ◽  
Vol 8 (4) ◽  
pp. 571-590 ◽  
Author(s):  
H. Edwin Romeijn ◽  
Robert L. Smith
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Probability Distributions ◽  
Global Optimum ◽  
Adaptive Search ◽  
Continuous Global Optimization ◽  
Definition Of ◽  
Cooling Schedule

Simulated annealing is a class of sequential search techniques for solving continuous global optimization problems. In this paper we attempt to help explain the success of simulated annealing for this class of problems by studying an idealized version of this algorithm, which we call adaptive search. The prototypical adaptive search algorithm generates a sequence of improving points drawn conditionally from samples from a corresponding sequence of probability distributions. Under the condition that the sequence of distributions stochastically dominate in objective function value the uniform distribution, we show that the expected number of improving points required to achieve the global optimum within a prespecified error grows at most linearly in the dimension of the problem for a large class of global optimization problems. Moreover, we derive a cooling schedule for simulated annealing, which follows in a natural way from the definition of the adaptive search algorithm.

Sign in / Sign up

Export Citation Format

Share Document