The primary objective of this dissertation is to investigate research methods to answer the question: ``How (and why) does one measure, learn and optimize novelty and diversity of a set of items?" The computational models we develop to answer this question also provide foundational mathematical techniques to throw light on the following three questions:

1. How does one reliably measure the creativity of ideas?

2. How does one form teams to evaluate design ideas?

3. How does one filter good ideas out of hundreds of submissions?

Solutions to these questions are key to enable the effective processing of a large collection of design ideas generated in a design contest. In the first part of the dissertation, we discuss key qualities needed in design metrics and propose new diversity and novelty metrics for judging design products. We show that the proposed metrics have higher accuracy and sensitivity compared to existing alternatives in literature. To measure the novelty of a design item, we propose learning from human subjective responses to derive low dimensional triplet embeddings. To measure diversity, we propose an entropy-based diversity metric, which is more accurate and sensitive than benchmarks. In the second part of the dissertation, we introduce the bipartite b-matching problem and argue the need for incorporating diversity in the objective function for matching problems. We propose new submodular and supermodular objective functions to measure diversity and develop multiple matching algorithms for diverse team formation in offline and online cases. Finally, in the third part, we demonstrate filtering and ranking of ideas using diversity metrics based on Determinantal Point Processes as well as submodular functions. In real-world crowd experiments, we demonstrate that such ranking enables increased efficiency in filtering high-quality ideas compared to traditionally used methods.