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In this paper, we discuss the relevance and effectiveness of two com-mon methods for searching decision trees that represent design problems. When design problems are encoded in decision trees they are of-ten multimodal, capture a range of complexity in valid solutions, and have distinguishable internal locations. We propose the use of a simple Color Graph problem to represent these characteristics. The two methods evaluated are a genetic algorithm and a Monte Carlo tree search. Using the Color Graph problem, it is demonstrated that a genetic algorithm can perform exceptionally well on such unbounded and opaque design decision trees and that Monte Carlo tree searches are ineffective. Insights from this experiment are used to draw conclusions about the nature of design problems stored in decision trees and the need for new methods to search such trees and lead us to believe that exploitative methods are more effective than rigorously explorative methods.