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Exploring the bias of direct search and evolutionary optimization


There are many applications in science that yield the following optimization problem: given an objective function, which set of input decision variables produce the largest or smallest result? Optimization algorithms attempt to answer this question by searching for competitive solutions within an application's domain. But every search algorithm has some particular bias. Our results show that search algorithms are more effective when they cope with the features that make a particular application difficult. Evolutionary algorithms are stochastic population-based search methods that are often designed to perform well on problems containing many local optima. Although this is a critical feature, the number of local optima in the search space is not necessarily indicative of problem difficulty. The objective of this dissertation is to investigate how two relatively unexplored problem features, ridges and global structure, impact the performance of evolutionary parameter optimization. We show that problems containing these features can cause evolutionary algorithms to fail in unexpected ways. For example, the condition number of a problem is one way to quantify a ridge feature. When a simple unimodal surface has a high condition number, we show that the resulting narrow ridge can make many evolutionary algorithms extremely inefficient. Some even fail. Similarly, funnels are one way of categorizing a problem's global structure. A single-funnel problem is one where the local optima are clustered together such that there exists a global trend toward the best solution. This trend is less predicable on problems that contain multiple funnels. We describe a metric that distinguishes problems based on this characteristic. Then we show that the global structure of the problem can render successful global search strategies ineffective on relatively simple multi-modal surfaces. Our proposed strategy that performs well on problems with multiple funnels is counter-intuitive. These issues impact two real-world applications: an atmospheric science inversion model and a configurational chemistry problem. We find that exploiting ridges and global structure results in more effective solutions on these difficult real-world problems. This adds integrity to our perspective on how problem features interact with search algorithms, and more clearly exposes the bias of direct search and evolutionary algorithms.


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direct search
global structure
computer science


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