Randomised Local Search Algorithm for the Clustering Problem

2000 ◽  
Vol 3 (4) ◽  
pp. 358-369 ◽  
Author(s):  
P. Fränti ◽  
J. Kivijärvi
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Local Search Algorithm ◽  
Clustering Problem

scholarly journals An exact algorithm for stable instances of the $ k $-means problem with penalties in fixed-dimensional Euclidean space

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fan Yuan ◽  
Dachuan Xu ◽  
Donglei Du ◽  
Min Li
Keyword(s):  
Euclidean Space ◽  
Local Search ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Dimensional Euclidean Space ◽  
Local Search Algorithm ◽  
Clustering Problem ◽  
Penalty Costs

<p style='text-indent:20px;'>We study stable instances of the <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem with penalties in fixed-dimensional Euclidean space. An instance of the problem is called <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>-stable if this instance exists a sole optimal solution and the solution keeps unchanged when distances and penalty costs are scaled by a factor of no more than <inline-formula><tex-math id="M4">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>. Stable instances of clustering problem have been used to explain why certain heuristic algorithms with poor theoretical guarantees perform quite well in practical. For any fixed <inline-formula><tex-math id="M5">\begin{document}$ \epsilon &gt; 0 $\end{document}</tex-math></inline-formula>, we show that when using a common multi-swap local-search algorithm, a <inline-formula><tex-math id="M6">\begin{document}$ (1+\epsilon) $\end{document}</tex-math></inline-formula>-stable instance of the <inline-formula><tex-math id="M7">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem with penalties in fixed-dimensional Euclidean space can be solved accurately in polynomial time.</p>

scholarly journals A Matheuristic Approach Combining Local Search and Mathematical Programming

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Carolina Lagos ◽  
Guillermo Guerrero ◽  
Enrique Cabrera ◽  
Stefanie Niklander ◽  
Franklin Johnson ◽  
...  
Keyword(s):  
Mathematical Programming ◽  
Local Search ◽  
Large Scale ◽  
Search Algorithm ◽  
Facility Location Problem ◽  
Specific Information ◽  
Local Search Algorithm ◽  
Capacitated Facility Location Problem ◽  
Capacitated Facility Location ◽  
Installation Cost

A novel matheuristic approach is presented and tested on a well-known optimisation problem, namely, capacitated facility location problem (CFLP). The algorithm combines local search and mathematical programming. While the local search algorithm is used to select a subset of promising facilities, mathematical programming strategies are used to solve the subproblem to optimality. Proposed local search is influenced by instance-specific information such as installation cost and the distance between customers and facilities. The algorithm is tested on large instances of the CFLP, where neither local search nor mathematical programming is able to find good quality solutions within acceptable computational times. Our approach is shown to be a very competitive alternative to solve large-scale instances for the CFLP.

A novel local search algorithm for the minimum capacitated dominating set

2018 ◽  
Vol 69 (6) ◽  
pp. 849-863 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Peng Zhao ◽  
Yupeng Zhou ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Local Search Algorithm

scholarly journals GASAT: A Genetic Local Search Algorithm for the Satisfiability Problem

2006 ◽  
Vol 14 (2) ◽  
pp. 223-253 ◽  
Author(s):  
Frédéric Lardeux ◽  
Frédéric Saubion ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Local Search ◽  
Hybrid Algorithm ◽  
State Of The Art ◽  
Search Algorithm ◽  
Satisfiability Problem ◽  
Local Search Algorithm ◽  
Overall Performance ◽  
Genetic Local Search ◽  
Search Stage

This paper presents GASAT, a hybrid algorithm for the satisfiability problem (SAT). The main feature of GASAT is that it includes a recombination stage based on a specific crossover and a tabu search stage. We have conducted experiments to evaluate the different components of GASAT and to compare its overall performance with state-of-the-art SAT algorithms. These experiments show that GASAT provides very competitive results.

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