An exploration and exploitation pareto approach to surrogate optimization

The experiments or simulations conducted by computers can be a tedious task, requiring substantial computational time. To find a global solution using a computer experiments process, we usually need to perform many function evaluations of the computer model. This research focuses on developing an optimization method to find a globally optimal solution efficiently using surrogates. The surrogates represent the computer model or the system that reads the inputs and generates the output responses of interest, so that these surrogate models can be used in place of time-consuming simulations runs. In surrogate based optimization, we iteratively build a surrogate model (a.k.a, approximate model or a metamodel) and conduct an optimization step, adding points in each iteration only as needed.;The proposed surrogate optimization method, Exploration and Exploitation Pareto Approach (EEPA), combines the notions of exploration and exploitation to seek the best solution with fewer function evaluations. Exploration is used to explore the points in an unexplored region. Exploration does not use the surrogate to look for new points. Four different exploration methods were used in this research, specifically maximin distance (Johnson, et. al.), cosine (Corley et.al.), Sobol&feet; (Sobol') sequence and Monte Carlo method (Niederreiter). Maximin looks for points that are at maximin distance from the existing points, cosine looks for the maximum angular distance between points, Sobol' looks for points that are evenly spaced and Monte Carlo looks for points randomly in the input space.;Exploitation is used to explore promising areas in the input space. Exploitation requires a surrogate or metamodel to be built in order to look for new points. Different surrogate or metamodel models, including multivariate adaptive regression splines, radial basis functions, and treed regression, are used in this study. The minimum response method (Regis and Shoemaker; Regis and Shoemaker) is used as the exploitation method in this study. Response metric helps to look for points that possibly give better solution.;Exploration and exploitation are combined in EEPA by obtaining a Pareto frontier. A Pareto frontier represents the non-dominating solutions given two or more solutions. The Pareto frontier is obtained by balancing the tradeoff between maximizing the exploration metric and minimizing the predicted response. Points are then chosen from this Pareto frontier at which additional function evaluations using the computer model are executed.;Various test functions were used to compare EEPA to pure exploitation and pure exploration methods. In addition, a green building test function is also considered. These test functions are of different dimensions and structure. The green building data is simulated from a computer model called eQUEST. The results showed that EEPA reached the best solution faster than pure exploration or exploitation methods. Also, among the exploration methods, the cosine method performed well.