Complexity of local search for the p-median problem
We study the complexity of finding local minima for the p-median problem. The relationship between Swap local optima, 0-1 local saddle points, and classical Karush-Kuhn-Tucker conditions is presented. It is shown that the local search problems with some neighborhoods are tight PLS-complete. Moreover, the standard local descent algorithm takes exponential number of iterations in the worst case regardless of the tie-breaking and pivoting rules used. To illustrate this property, we present a family of instances where some local minima may be hard to find. Computational results with different pivoting rules for random and Euclidean test instances are discussed. These empirical results show that the standard local descent algorithm is polynomial in average for some pivoting rules.
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- Orlin, James & Punnen, Abraham & Schulz, Andreas, 2004. "Approximate Local Search in Combinatorial Optimization," Working papers 4325-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Mladenovic, Nenad & Brimberg, Jack & Hansen, Pierre & Moreno-Perez, Jose A., 2007. "The p-median problem: A survey of metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 179(3), pages 927-939, June.
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