A Nelder Mead Approach to Approximating Efficient Frontiers in Black-Box Simulation Optimization
Couche, Michael J.
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Nation-building models can lend powerful insights to decision makers and policy makers. One goal is to develop a set of policies to be considered for implementation. The tools of simulation help decision makers to arrive at a tangible model in a quick manner. However, the complexity of nations creates models that may be thought of as a black box. Black box models occur when the functional form of the interaction within a model is unknown. Policies most often will contain conflicting objectives with different preferences among them and can be represented as Multi-Criteria problems. Multi-Criteria problems are a class of optimization problems in which there are two or more objectives, often conflicting in nature. It is beneficial to explore iterative methods of solving these problems, which will result in the construction of efficient frontiers. An efficient frontier is a set of non-dominated points that give the most preferred solution to a multi-criteria problem. With these efficient frontiers, a decision maker can decide between several alternatives while trying to accomplish a set of policy goals without over sacrificing any part of the end result. The Nelder Mead Algorithm is used for the optimization of nonlinear functions in unconstrained spaces. It is very useful in solving Multi-Criteria Decision Making problems, and the nature of the simulation model is most likely nonlinear. This thesis makes several modifications to the Nelder Mead Algorithm that enhance the ability to solve this particular case of black box simulation multi-criteria optimization. These modifications include the use of the Tchebycheff Function for estimating efficient frontiers, incorporating penalty functions to insure realistic input and output values, and a "recursive" starting point process for the initialization of the algorithm.