Multimodal Objective Research Articles

A Bayesian Analysis of the Number of Cells of a Multinomial Distribution

Optimal Bayesian stopping rules are developed for a sequential sample from a multinomial distribution with an unknown number of cells. We consider both the case that the purpose of the sampling procedure is to identify all cells and the case that the purpose is simply to estimate their number. The approach can be applied to the termination of certain procedures for the global optimization of a multimodal objective function.

一変数多峰性関数に対する最適値探索法の研究

This paper attempts to explore the algorithm of a new method for solving non-linear optimization problems. The study focuses on the method for obtaining maximum or minimum value for one variable multi-modal function. It is shown that the algorithm developed here can be applied to solving the problem to optimize any objective function defined on a bounded closed interval which satisfies the Lipschitz's condition . The traditional optimizing methods deal primarily with the uni-modal objective function for obtaining optimum value. This paper studies the method to obtain the global solution for multi-modal objective function. This algorithm, through using the Lipschitz's constant, can determine the upper limit of the obtained solution and evaluate the relative error to the true optimum value. This algorithm makes use of the relative error stopping rule. The accuracy of the solution, therefore, does not depend on the form of the objective function. This method can also be applied to some of the separable objective functions in the fixed charge problem. Numerical tests with the algorithm produced fairly satisfactory results.