(1+1) Evolutionary Algorithm on Random Planted Vertex Cover Problems

Thumbnail Image

Persistent link to this item

View Statistics

Journal Title

Journal ISSN

Volume Title


(1+1) Evolutionary Algorithm on Random Planted Vertex Cover Problems

Published Date




Scholarly Text or Essay


Evolutionary Algorithms are powerful optimization tools that use the power of randomness and inspiration from biology to achieve results. A common combinatorial optimization problem is the recovery of a minimum vertex cover on some graph 𝐺 = (𝑉, 𝐸). In this work, an evolutionary algorithm will be employed on specific instances of the minimum vertex cover problem containing a random planted solution. This situation is common in data networks and translates to a core set of nodes and larger fringe set that are connected to the core. This study introduces a parameterized analysis of a standard (1+1) Evolutionary Algorithm applied to the random planted distribution of vertex cover problems. When the planted cover is at most logarithmic, restarting the (1+1) EA every 𝑂(𝑛 log 𝑛) steps will, within polynomial time, yield a cover at least as small as the planted cover for sufficiently dense random graphs (𝑝 > 0.71). For superlogarithmic planted covers, the (1+1) EA is proven to find a solution within fixed-parameter tractable time in expectation. To complement these theoretical investigations, a series of computational experiments were conducted, highlighting the intricate interplay between planted cover size, graph density, and runtime. A critical range of edge probability was also investigated.


A Plan B research project by Jack Kearney for a Master of Science degree.

Related to



Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Suggested citation

Kearney, Jack. (2024). (1+1) Evolutionary Algorithm on Random Planted Vertex Cover Problems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/261466.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.