scholarly journals Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization

2004 ◽  
Vol 39 (4) ◽  
pp. 525-544 ◽  
Author(s):  
Stefan Droste ◽  
Thomas Jansen ◽  
Ingo Wegener
Keyword(s):  
Lower Bounds ◽  
Black Box ◽  
Upper And Lower Bounds ◽  
Randomized Search Heuristics ◽  
Search Heuristics ◽  
Randomized Search

scholarly journals Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions

2013 ◽  
Vol 22 (2) ◽  
pp. 294-318 ◽  
Author(s):  
CARSTEN WITT
Keyword(s):  
Polynomial Optimization ◽  
Linear Functions ◽  
Upper And Lower Bounds ◽  
Randomized Search Heuristics ◽  
Search Heuristics ◽  
Large Neighbourhood ◽  
Proof Techniques ◽  
Randomized Search ◽  
Remarkable Progress ◽  
Made In

The analysis of randomized search heuristics on classes of functions is fundamental to the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in bounding the expected optimization time of a simple evolutionary algorithm, called (1+1) EA, on the class of linear functions. We improve the previously best known bound in this setting from (1.39+o(1))en ln n to en ln n+O(n) in expectation and with high probability, which is tight up to lower-order terms. Moreover, upper and lower bounds for arbitrary mutation probabilities p are derived, which imply expected polynomial optimization time as long as p = O((ln n)/n) and p = Ω(n−C) for a constant C > 0, and which are tight if p = c/n for a constant c > 0. As a consequence, the standard mutation probability p = 1/n is optimal for all linear functions, and the (1+1) EA is found to be an optimal mutation-based algorithm. Furthermore, the algorithm turns out to be surprisingly robust since the large neighbourhood explored by the mutation operator does not disrupt the search.

Runtime analysis of discrete particle swarm optimization algorithms: A survey

2019 ◽  
Vol 61 (4) ◽  
pp. 177-185
Author(s):  
Moritz Mühlenthaler ◽  
Alexander Raß
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Upper And Lower Bounds ◽  
Swarm Optimization ◽  
Randomized Search Heuristics ◽  
Recent Developments ◽  
Randomized Search

Abstract A discrete particle swarm optimization (PSO) algorithm is a randomized search heuristic for discrete optimization problems. A fundamental question about randomized search heuristics is how long it takes, in expectation, until an optimal solution is found. We give an overview of recent developments related to this question for discrete PSO algorithms. In particular, we give a comparison of known upper and lower bounds of expected runtimes and briefly discuss the techniques used to obtain these bounds.

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