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The proposed algorithms are suboptimal due to the approximate objective function and the constraint relaxation steps.
Response Surface Methodology (RSM) was, firstly, applied to approximate objective functions.
In the meta-modeling module, the extreme learning machine (ELM) is used as a meta-model to estimate the approximate objective value of a design.
To approximate objective functions by means of experimental data, the MLP (Multi-Layer Perceptron) neural network modeling is separately executed in each objective function.
From the obtained results, we conclude that the objective value (GNI) is dependent on the maximum permitted value of environmental pollution cost (UB); therefore, it is meaningful to examine the sensitivity of approximate objective value with respect to UB.
In this approach, the optimum design is obtained by solving a sequence of sub-programming problems that usually consist of an approximate objective function subjected to a set of approximate constraint functions.
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Sequential quadratic programming was used to obtain the optimal design variables with the minimum value of the approximated objective function.
The creative writer unwittingly manages to make a mess of the ordinary thinking process: memory, imagination, and something approximating objective reality are all mooshed together into a dark, rich stew.
It explains the use of the multidimensional Hermite polynomial, differing to the Taylor polynomial approximation, to approximate the objective function to replace the finite element computation in optimization.
Response surface approximation was used to approximate the objective function to reduce computing time.
However, relatively few of these multi-objective algorithms handle constraints, and even fewer, use surrogates to approximate the objective or constraint functions when these functions are computationally expensive.
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