On Producing Multiple Solutions Using Repeated Trials

Authors:
Frans M. Coetzee;Virginia L. Stonick
Affiliations:
Siemens Corporate Research, Princeton NJ 08540, USA/;ECE Department, Carnegie Mellon University, Pittsburgh PA 15213, USA
Venue:
Journal of Global Optimization
Year:
1998

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Abstract

The number of trials that is required by an algorithm to produce agiven fraction of the problem solutions with a specified level of confidenceis analyzed. The analysis indicates that the number of trials required tofind a large fraction of the solutions rapidly decreases as the number ofsolutions obtained on each trial by an algorithm increases. In applicationswhere multiple solutions are sought, this decrease in the number of trialscould potentially offset the additional computational cost of algorithmsthat produce multiple solutions on a single trial. The analysis frameworkpresented is used to compare the efficiency of a homotopy algorithm to thatof a Newton method by measuring both the number of trials and the number ofcalculations required to obtain a specified fraction of the solutions.