On the Computational Cost and Complexity of Stochastic Inverse Solvers

Faliszewski, Piotr; Smółka, Maciej; Schaefer, Robert; Paszyński, Maciej

doi:10.7494/csci.2016.17.2.225

Cited by 1 publication

(2 citation statements)

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…0; x t 2 K e ; x t 2 X l g being the first hitting time (FHT) of the set K e \ X l by the Markov chain modeling the stochastic search. It can be proven, that the expected hitting time E x 0 ðH e l Þ of reaching H e l starting from x 0 2 X l is the unique non-negative solution to the linear system [14,35]:…”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Understanding measure-driven algorithms solving irreversibly ill-conditioned problems

et al. 2021

View full text Add to dashboard Cite

The paper helps to understand the essence of stochastic population-based searches that solve ill-conditioned global optimization problems. This condition manifests itself by presence of lowlands, i.e., connected subsets of minimizers of positive measure, and inability to regularize the problem. We show a convenient way to analyze such search strategies as dynamic systems that transform the sampling measure. We can draw informative conclusions for a class of strategies with a focusing heuristic. For this class we can evaluate the amount of information about the problem that can be gathered and suggest ways to verify stopping conditions. Next, we show the Hierarchic Memetic Strategy coupled with Multi-Winner Evolutionary Algorithm (HMS/MWEA) that follow the ideas from the first part of the paper. We introduce a complex, ergodic Markov chain of their dynamics and prove an asymptotic guarantee of success. Finally, we present numerical solutions to ill-conditioned problems: two benchmarks and a real-life engineering one, which show the strategy in action. The paper recalls and synthesizes some results already published by authors, drawing new qualitative conclusions. The totally new parts are Markov chain models of the HMS structure of demes and of the MWEA component, as well as the theorem of their ergodicity.

show abstract

Section: Remarkmentioning

confidence: 99%

“…The hierarchic structure of the HMS search is especially effective if the computational cost of objective evaluation strongly decreases with its accuracy, which is typically the case when solving Inverse Parametric Problems (IPPs) [14].…”

Section: Hms Extended With Insensitivity Region Approximationmentioning

confidence: 99%