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On the analysis of interaction between decision variables

MANY real-world design and decision-making problems are characterized by the interactions between decision variables. In engineering optimization problems, the effects of one input variable on the performance measure may be influenced by one or several other input variables. In classification problems, one feature by itself may be irrelevant to the class label, however when combined with one or many feature(s), it may become highly relevant to the class label. Identifying variable interactions is important yet non-trivial. In this thesis, the overarching goals are (1) to identify and quantify variable interactions in a given optimization or classification problem and (2) to use this information to effectively solve the problem. The methodologies used to meet these goals are a combination of theoretical inquiry, computational modelling and experimental validation of the proposed methods. To identify and quantify variable interactions in a ‘Black-box’ Continuous Optimization Problem (BCOP), a novel Exploratory Landscape Analysis (ELA) measure is proposed based on the Maximal Information Coefficient (MIC). MIC can identify a wide range of functional relationships with high levels of accuracy. Then the proposed ELA measure is embedded into an algorithm design framework to effectively solve a BCOP. The experimental results confirm the effectiveness of the proposed ELA measure. The high computational cost is the main limitation of the proposed ELA measure, especially in large-scale BCOPs. Therefore I propose an eXtended Differential Grouping (XDG) method, which can be used to identify variable interactions based on non-linearity detection. The XDG method decomposes a large-scale BCOP into several sub-problems considering both direct and indirect variable interactions. When XDG is embedded into a Cooperative Co-evolution framework to solve large-scale BCOPs, it generates high qual-