Hybrid Adaptive Large Neighborhood Search for the Optimal Statistic Median Problem

Authors:
Klemens Katterbauer;Ceyda Oguz;Sibel Salman
Affiliations:
College of Engineering, Koç University, 33450 Sariyer, Istanbul, Turkey;College of Engineering, Koç University, 33450 Sariyer, Istanbul, Turkey;College of Engineering, Koç University, 33450 Sariyer, Istanbul, Turkey
Venue:
Computers and Operations Research
Year:
2012

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Abstract

In this paper, the problem of maximizing the median of a convex combination of vectors having important applications in finance is considered. The objective function is a highly nonlinear, nondifferentiable function with many local minima and the problem was shown to be APX hard. We present two hybrid Large Neighborhood Search algorithms that are based on mixed-integer programs and include a time limit for their running times. We have tested the algorithms on three testbeds and showed their superiority compared to other state-of-the-art heuristics for the considered problem. Furthermore, we achieved a significant reduction in running time for large instances compared to solving it exactly while retaining high quality of the solutions returned.