In the last few decades computer systems and the underlying hardware have steadily become larger and more complex. The need to increase their efficiency through architectural innovation has not abated, but quantitatively evaluating the effect of various choices has become more difficult. Performance and resource consumption are determined by complex interactions between many modules, each with many possible alternative implementations. We need powerful computer programs to explore large design spaces, but the traditional approach of developing simulators, building prototypes, or writing heuristic-based algorithms in traditional programming languages is often tedious and slow. Fortunately mathematical optimization has made great advances in theory, and many fast commercial and academic solvers are now available. In this book we motivate and describe the use of mathematical modeling, specifically optimization based on mixed integer linear programming (MILP) as a way to design and...

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