Multivariable monotonic optimization over multivalued logics and rectangular design lattices

Abstract

A minimum dichotomous direct search procedure is given for finding the optimum combination of N variables, each having M( n) possible values, when a certain monotonicity condition is satisfied. The least upper bound on the number of objective function evaluations is 1 + Σ N n=1 Q( n), where Q( n) is defined by 2 Q( n)-1 < M( n) < 2 Q( n) , whereas the total number of possibilities is Π N R=1 M( n). An example shows where the procedure applies to restricted problems in multivalued logic and engineering design.