P2: This problem is intended to provide you with an initial experience working through the EDO problem formulation cycle, and will be helpful in thinking about the process you need to use for your project. Please complete the following tasks and submit associated text, sketches, and figures as appropriate. This is intended to be a qualitative exercise. You do not need to derive in detail or implement the actual predictive models; rather, please describe at a high level what the models do (inputs, outputs, a description in words of how the models would be implemented). a) Select an engineering system to base the exercise on that 1) you have experience or interest in, 2) involves at least some element of physical system design, and 3) provides an opportunity to vary the fidelity of all three problem formulation dimensions (design representation, comparison metrics, and predictive model). Please provide a brief description of the system. You can include figures or images here if it helps to describe the system, but figures are not necessarily required. b) High-fidelity formulation: Please describe an EDO problem formulation that accurately represents overall design goals, even if the corresponding problem might not be solvable using EDO in practice. At this level, it may only make sense to describe each of the dimensions in words, but if it makes sense, please include figures that help to explain formulation elements. Please be sure to describe each of the three formulation elements separately. Offer a critique of your formulation regarding 1) how the fidelity of each formulation dimension might be improved further (e.g., more design DOFs in the representation, a broader perspective on comparison metrics, such as company or societal-level considerations), and 2) what challenges might be expected in actually attempting to implement and solve such a problem. c) Low-fidelity formulation: With the high-fidelity formulation now available that represents true design goals, create a simplified EDO problem formulation that would serve as a good starting point for a first numerical implementation and solution. This should be a formulation that is fairly simple (just a handful of design variables, simplified objective/constraint func- tions and models), while still capturing at least some important/interesting design tradeoffs. Include a sketch to depict the design representation and specify which parameters are the independent design variables. Define what the objective function(s) are (e.g., mass, deflection, other simpler proxy objective functions). Define the constraints (e.g., specific failure mode limits, such as stress, temperature, voltage, etc.). Describe what modeling strategy would be used to compute objective and constraint functions as a function of design variables. You do not need to provide actual model formulas, only the nature of the models (input/output, simplifying assumptions, model type, etc.). Perform a brief formulation analysis and discuss any potential shortcomings that the model might have, such as boundedness issues, model response smoothness, difficulty in model implementation, inaccuracy with respect to the high-fidelity formulation. d) Mid-fidelity formulation: Based on the previous two steps, including the analysis of the low-fidelity formulation, propose an improved-fidelity EDO problem formulation that en- hances formulation accuracy, while aiming to limit problem complexity sufficiently to enable practical implementation/solution (i.e., things that are computable, no magic profit functions). e) PFDS Sketch: Provide a conceptual sketch of the problem formulation decision space, and show how this space was traversed when moving from high to low to medium fidelity formulations.

P2: This problem is intended to provide you with an initial experience working through the EDO problem formulation cycle, and will be helpful in thinking about the process you need to use for your project. Please complete the following tasks and submit associated text, sketches, and figures as appropriate. This is intended to be a qualitative exercise. You do not need to derive in detail or implement the actual predictive models; rather, please describe at a high level what the models do (inputs, outputs, a description in words of how the models would be implemented). a) Select an engineering system to base the exercise on that 1) you have experience or interest in, 2) involves at least some element of physical system design, and 3) provides an opportunity to vary the fidelity of all three problem formulation dimensions (design representation, comparison metrics, and predictive model). Please provide a brief description of the system. You can include figures or images here if it helps to describe the system, but figures are not necessarily required. b) High-fidelity formulation: Please describe an EDO problem formulation that accurately represents overall design goals, even if the corresponding problem might not be solvable using EDO in practice. At this level, it may only make sense to describe each of the dimensions in words, but if it makes sense, please include figures that help to explain formulation elements. Please be sure to describe each of the three formulation elements separately. Offer a critique of your formulation regarding 1) how the fidelity of each formulation dimension might be improved further (e.g., more design DOFs in the representation, a broader perspective on comparison metrics, such as company or societal-level considerations), and 2) what challenges might be expected in actually attempting to implement and solve such a problem. c) Low-fidelity formulation: With the high-fidelity formulation now available that represents true design goals, create a simplified EDO problem formulation that would serve as a good starting point for a first numerical implementation and solution. This should be a formulation that is fairly simple (just a handful of design variables, simplified objective/constraint functions and models), while still capturing at least some important/interesting design tradeoffs. Include a sketch to depict the design representation and specify which parameters are the independent design variables. Define what the objective function(s) are (e.g., mass, deflection, other simpler proxy objective functions). Define the constraints (e.g., specific failure mode limits, such as stress, temperature, voltage, etc.). Describe what modeling strategy would be used to compute objective and constraint functions as a function of design variables. You do not need to provide actual model formulas, only the nature of the models (input/output, simplifying assumptions, model type, etc.). Perform a brief formulation analysis and discuss any potential shortcomings that the model might have, such as boundedness issues, model response smoothness, difficulty in model implementation, inaccuracy with respect to the high-fidelity formulation. d) Mid-fidelity formulation: Based on the previous two steps, including the analysis of the low-fidelity formulation, propose an improved-fidelity EDO problem formulation that enhances formulation accuracy, while aiming to limit problem complexity sufficiently to enable practical implementation/solution (i.e., things that are computable, no magic profit functions). e) PFDS Sketch: Provide a conceptual sketch of the problem formulation decision space, and show how this space was traversed when moving from high to low to medium fidelity formulations