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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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Wavelet multi-resolution approximation for multiobjective optimal control.

Wen Zou1, Qingbin Zhang2, Qingyu Gao2

  • 1College of Computer and Information Engineering, Hunan University of Commerce, Changsha, P.R.China.

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|August 3, 2018
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Summary
This summary is machine-generated.

This study introduces a novel sequential method using wavelet multi-resolution approximation for computationally expensive multi-objective optimization problems. The approach efficiently approximates the Pareto front (PF) with fewer weights, demonstrating effectiveness on complex optimization tasks.

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Area of Science:

  • Computational Mathematics
  • Optimization Theory
  • Numerical Analysis

Background:

  • Multi-objective optimization problems (MOOPs) are often computationally expensive.
  • Traditional methods involve decomposing MOOPs into single-objective problems, treating the Pareto front (PF) as a weight function.
  • Existing techniques can be resource-intensive for complex problems.

Purpose of the Study:

  • To propose a new sequential method for solving computationally expensive MOOPs.
  • To leverage wavelet multi-resolution approximation for efficient Pareto front approximation.
  • To reduce the number of weights required for accurate PF representation.

Main Methods:

  • A sequential approach utilizing multi-resolution approximation based on wavelets.
  • Initial sampling on a coarse grid with few collocation points.
  • Adaptive wavelet collocation for automatic point refinement and Pareto front approximation.

Main Results:

  • The proposed method approximates the Pareto front (PF) effectively.
  • Achieved approximation with a relatively small number of weights.
  • Demonstrated efficiency on a typical MOOP and an expensive optimal control problem.

Conclusions:

  • The sequential wavelet-based method offers an efficient solution for computationally demanding MOOPs.
  • The adaptive refinement strategy significantly reduces computational cost.
  • The method shows promise for practical applications in complex optimization scenarios.