Genetic Optimization Using Derivatives^*

by

Jasjeet S. Sekhon $^{\mbox{\dag }}$
and

Walter R. Mebane, Jr. $^{\mbox{\ddag }}$


Draft: July 30, 1998

^* (1998) Political Analysis 7: 187-210.


$^{\mbox{\dag }}$ Assistant Professor, Department of Government, Harvard University, jsekhon@fas.harvard.edu, HTTP://data.fas.harvard.edu/jsekhon/. Jasjeet Sekhon's research is supported in part by the Social Sciences and Humanities Research Council of Canada grant number 752-95-0380.

$^{\mbox{\ddag }}$ Associate Professor, Department of Government, Cornell University, wrm1@cornell.edu, HTTP://macht.arts.cornell.edu/wrm1/.

Abstract:

To solve difficult optimization problems, we have developed a computer program called GENOUD (GENetic Optimization Using Derivatives) that combines evolutionary algorithm methods with a derivative-based, quasi-Newton method. GENOUD can work even when the most often used optimization methods completely fail. The objective function for a nonlinear model may not be globally concave, making it difficult for gradient-based optimization methods to find any optimum at all. Multiple local optima may exist so there is no guarantee that gradient-based methods will converge to the global optimum. We discuss the theoretical basis for expecting GENOUD to have a high probability of finding global optima. We conduct Monte Carlo experiments using scalar Normal mixture densities to illustrate this capability. We also use a real-data example (the four-dimensional Hopf model), which has many parameters and multiple local optima, to compare the performance of GENOUD to that of the Gauss-Newton algorithm in SAS's PROC MODEL.