Mode pursuing sampling (MPS) was developed as a global optimization algorithm for design optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for design problems of low dimensionality, i.e., the number of design variables is less than 10. This work integrates the concept of trust regions into the MPS framework to create a new algorithm, trust region based mode pursuing sampling (TRMPS2), with the aim of dramatically improving performance and efficiency for high dimensional problems. TRMPS2 is benchmarked against genetic algorithm (GA), dividing rectangles (DIRECT), efficient global optimization (EGO), and MPS using a suite of standard test problems and an engineering design problem. The results show that TRMPS2 performs better on average than GA, DIRECT, EGO, and MPS for high dimensional, expensive, and black box (HEB) problems.
Expensive constraints are commonly seen in real-world engineering design. However, metamodel based design optimization (MBDO) approaches often assume inexpensive constraints. In this work, the situational adaptive Kreisselmeier and Steinhauser (SAKS) method was employed in the development of a hybrid adaptive aggregation-based constraint handling strategy for expensive black-box constraint functions. The SAKS method is a novel approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The SAKS strategy was integrated with a modified trust region-based mode pursuing sampling (TRMPS) algorithm to form the SAKS-trust region optimizer (SAKS-TRO) for single-objective design optimization problems with expensive black-box objective and constraint functions. SAKS-TRO was benchmarked against five popular constrained optimizers and demonstrated superior performance on average. SAKS-TRO was also applied to optimize the design of an industrial recessed impeller.
Mode Pursing Sampling (MPS) was developed as a global optimization algorithm for design problems involving expensive black-box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of variables is less than 10. This work integrates the concept of the trust region into the MPS framework so that MPS can be applied to solve high dimensional optimization problems. Two trust regions are defined and their sizes are dynamically adjusted. Within each trust region, the search follows the traditional MPS process. Preliminary testing shows encouraging results. Nomenclature= metamodel weights = quadratic model coefficients = generic function = generic number of dimensions = number of variables = speed control factor = points obtained from the metamodel = points evaluated using the objective function
Metamodel based design optimization (MBDO) algorithms have attracted considerable interests in recent years due to their special capability in dealing with complex optimization problems with computationally expensive objective and constraint functions and local optima. Conventional unimodal-based optimization algorithms and stochastic global optimization algorithms either miss the global optimum frequently or require unacceptable computation time. In this work, a generic testbed/platform for evaluating various MBDO algorithms has been introduced. The purpose of the platform is to facilitate quantitative comparison of different MBDO algorithms using standard test problems, test procedures, and test outputs, as well as to improve the efficiency of new algorithm testing and improvement. The platform consists of a comprehensive test function database that contains about 100 benchmark functions and engineering problems. The testbed accepts any optimization algorithm to be tested, and only requires minor modifications to meet the test-bed requirements. The testbed is useful in comparing the performance of competing algorithms through execution of same problems. It allows researchers and practitioners to test and choose the most suitable optimization tool for their specific needs. It also helps to increase confidence and reliability of the newly developed MBDO tools. Many new MBDO algorithms, including Mode Pursuing Sampling (MPS), Pareto Set Pursuing (PSP), and Space Exploration and Unimodal Region Elimination (SEUMRE), were tested in this work to demonstrate its functionality and benefits.
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