Abstract
The solution of the Subproblem of the Cutting Angle Method of Global Optimization for problems of minimizing increasing positively homogeneous of degree one functions is proved to be NP-Complete. For the proof of this fact we formulate another problem which we call “Dominating Subset with Minimal Weight”. This problem is also NP-Complete. An O(n2)-time algorithm is presented for approximate solution of Dominant Subset with Minimal Weight Problem. This problem can be expressed as a kind of Assignment Problem in which it is allowed to assign multiple tasks to a single processor. Experimental analysis of the algorithm is performed using the program implemented in ANSI-C. The results of the analysis show the efficiency of the proposed algorithm.
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Mathematics Subject Classification (2000): 65K05, 90C27, 68Q25
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Nuriyev, U.G. An Approach to the Subproblem of the Cutting Angle Method of Global Optimization. J Glob Optim 31, 353–370 (2005). https://doi.org/10.1007/s10898-004-1687-x
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DOI: https://doi.org/10.1007/s10898-004-1687-x