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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

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Runtime analysis of an evolutionary algorithm for stochastic multi-objective combinatorial optimization.

Walter J Gutjahr¹

¹Department of Statistics and Operations Research, University of Vienna, Vienna, A-1010, Austria. walter.gutjahr@univie.ac.at

Evolutionary Computation

|October 19, 2011

Summary

This summary is machine-generated.

The adaptive Pareto sampling (APS) framework requires ε-dominance when using the simple evolutionary multi-objective optimizer (SEMO) for stochastic multi-objective combinatorial optimization. This ensures fast convergence to the Pareto front and aids in runtime analysis.

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Area of Science:

Optimization Theory
Computational Intelligence
Algorithm Analysis

Background:

Stochastic multi-objective combinatorial optimization (SMOCO) problems present significant computational challenges.
The adaptive Pareto sampling (APS) framework offers a method for tackling these problems by integrating sampling with deterministic subproblem solutions.

Purpose of the Study:

To investigate the effectiveness of the simple evolutionary multi-objective optimizer (SEMO) within the APS framework for SMOCO problems.
To determine the necessary conditions for achieving fast convergence to the Pareto front when using SEMO in APS.
To establish a theoretical basis for analyzing the runtime complexity of evolutionary SMOCO algorithms.

Main Methods:

Integration of the simple evolutionary multi-objective optimizer (SEMO) as a subprocedure within the adaptive Pareto sampling (APS) framework.
Application of ε-dominance to ensure efficient convergence properties.
Development of general theorems to relate the runtime complexity of APS to that of SEMO.

Main Results:

The use of ε-dominance is essential for achieving fast convergence to the Pareto front when SEMO is employed within the APS framework for SMOCO.
Two general theorems are established, providing a method to derive runtime complexity results for APS based on SEMO's performance.
This work lays the groundwork for future runtime analyses of evolutionary algorithms applied to SMOCO.

Conclusions:

The combination of APS and SEMO, with the crucial addition of ε-dominance, provides an effective approach for solving SMOCO problems.
The established theorems facilitate the theoretical analysis of evolutionary SMOCO algorithms, advancing the field of optimization.
This research contributes to the development of more efficient and theoretically grounded algorithms for complex optimization tasks.