A new constraint-handling method based on Pareto-optimality and niching concepts for multi-objective multiconstraint evolutionary optimization is proposed. The proposed method does not require any constants to be tuned for constraint-handling. In addition, the present method does not use the weighted-sum of constraints and thus does not require tuning of weight coefficients and is efficient even when all individuals in the initial population are infeasible or the amount of violation of each constraint is significantly different. The proposed approach is demonstrated to be remarkably more robust than the dynamic penalty approach and other dominance-based approaches through the optimal design of a welded beam and conceptual design optimization of a two-stage-to-orbit spaceplane.
The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use of expensive computer simulations are required, metamodels are widely used to speed up the process of global sensitivity analysis. In this paper, a multi-fidelity framework for global sensitivity analysis using polynomial chaos expansion (PCE) is presented. The goal is to accelerate the computation of Sobol sensitivity indices when the deterministic simulation is expensive and simulations with multiple levels of fidelity are available. This is especially useful in cases where a partial differential equation solver computer code is utilized to solve engineering problems. The multi-fidelity PCE is constructed by combining the lowfidelity and correction PCE. Following this step, the Sobol indices are computed using this combined PCE. The PCE coefficients for both low-fidelity and correction PCE are computed with spectral projection technique and sparse grid integration. In order to demonstrate the capability of the proposed method for sensitivity analysis, several simulations are conducted. On the aerodynamic example, the multi-fidelity approach is able to obtain an accurate value of Sobol indices with 36.66% computational cost compared to the standard single-fidelity PCE for a nearly similar accuracy.
Computationally expensive multiobjective optimization problems are difficult to solve using solely evolutionary algorithms (EA) and require surrogate models, such as the Kriging model. To solve such problems efficiently, we propose infill criteria for appropriately selecting multiple additional sample points for updating the Kriging model. These criteria correspond to the expected improvement of the penalty-based boundary intersection (PBI) and the inverted PBI. These PBI-based measures are increasingly applied to EAs due to their ability to explore better nondominated solutions than those that are obtained by the Tchebycheff function. In order to add sample points uniformly in the multiobjective space, we assign territories and niche counts to uniformly distributed weight vectors for evaluating the proposed criteria. We investigate these criteria in various test problems and compare them with established infill criteria for multiobjective surrogate-based optimization. Both of the proposed criteria yield better diversity and convergence than those obtained with other criteria for most of the test problems.
Index Terms-Efficient global optimization (EGO), expected improvement (EI), penalty-based boundary intersection (PBI), expensive optimization, multiobjective optimization.1089-778X (c)
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