Efficient Multi-Objective Surrogate Optimization Of Computationally Expensive Models With Application To Watershed Model Calibration
This thesis introduces efficient algorithms for multi-objective optimization of computationally expensive simulation optimization problems. Implementation of efficient algorithms and their advantage of use for calibration of complex and deterministic watershed simulation models is also analyzed. GOMORS, a novel parallel multi-objective optimization algorithm involving surrogate modeling via Radial Basis Function approximation, is introduced in Chapter 2. GOMORS is an iterative search algorithm where a multiobjective search utilizing evolution, local search, multi method search and non-dominated sorting is done on the surrogate function to select numerous points for simultaneous expensive evaluations in each algorithm iteration. A novel procedure, "multi-rule selection", is introduced that simultaneously selects evaluation points (which can be computed in parallel) within an algorithm iteration through different metrics. Results are compared against ParEGO and the widely used NSGA-II on numerous test problems including a hypothetical groundwater PDE problem. The results indicate that GOMORS outperforms ParEGO and NSGA-II within a budget of 400 function evaluations. The superiority of performance of GOMORS is more evident for problems involving a large number of decision variables (15-25 decision variables). The second contribution (Chapter 3) to the thesis is a comparative analysis of algorithms for multi-objective calibration of complex watershed models. Since complex watershed models can be computationally expensive, we analyze and compare performance of various algorithms within a limited evaluation budget of 1000 evaluations. The primary aim of the analysis is to assess effectiveness of algorithms in identifying "meaningful trade-offs" for multi-objective watershed model calibration problems within a limited evaluation budget. A new metric, referred as the Distributed Cardinality index, is introduced for quantifying the relative effectiveness of different algorithms in identifying "meaningful tradeoffs". Our results indicate that GOMORS (the algorithm introduced in Chapter 2), outperforms various other algorithms, including ParEGO and AMALGAM, in computing good and meaningful trade-off solutions, within a limited simulation evaluation budget. The third and final contribution (see Chapter 4) to the thesis is MOPLS, a Multi-Objective Parallel Local Stochastic Search algorithm for efficient optimization of computationally expensive problems. MOPLS is an iterative algorithm which incorporates simultaneous local candidate search on response surface models within a synchronous parallel framework to select numerous evaluation points in each iteration. MOPLS was applied to various test problems and multi-objective watershed calibration problems with 4, 8 and 16 synchronous parallel processes and results were compared against GOMORS, ParEGO and AMALGAM. The results indicate that within a limited evaluation budget, MOPLS outperforms ParEGO and AMALGAM for computationally expensive watershed calibration problems, when comparison is made in function evaluations. When parallel speedup is taken into consideration and comparison is made in wall clock time, the results indicate that overall performance of MOPLS is better than GOMORS, ParEGO and AMALGAM.
Diamessis,Peter J.; Frazier,Peter
Civil and Environmental Engineering
Ph. D., Civil and Environmental Engineering
Doctor of Philosophy
dissertation or thesis