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A tutorial on multiobjective optimization: fundamentals and evolutionary methods.

Michael T M Emmerich1, André H Deutz1

  • 1LIACS, Leiden University, Leiden, The Netherlands.

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Summary
This summary is machine-generated.

Bio-inspired algorithms are highly effective for solving complex multiobjective optimization problems. This tutorial reviews foundational concepts and state-of-the-art evolutionary multiobjective optimization methods.

Keywords:
Decomposition-based MOEAsIndicator-based MOEAsMultiobjective evolutionary algorithmsMultiobjective optimizationPareto-based MOEAsPerformance assessment

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Optimization

Background:

  • Bio-inspired search paradigms are exceptionally useful for multiobjective optimization problems.
  • Population-based approaches, mimicking natural evolution, immune systems, and swarm intelligence, effectively approximate Pareto fronts.
  • Established algorithms like NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D are standard solvers in this domain.

Purpose of the Study:

  • To provide a comprehensive tutorial on evolutionary multiobjective optimization (EMO).
  • To review fundamental concepts and introduce representative state-of-the-art EMO algorithms.
  • To guide readers in understanding algorithm principles, application scope, performance assessment, and emerging research trends.

Main Methods:

  • Review of fundamental mathematical principles in multiobjective optimization.
  • Introduction and illustration of working principles for representative EMO algorithms (e.g., NSGA-II, SPEA2, MOPSO).
  • Discussion on statistical methods for performance assessment of optimization algorithms.

Main Results:

  • Overview of widely adopted EMO algorithms and their underlying mechanisms.
  • Explanation of how these algorithms approximate Pareto fronts using populations of agents.
  • Identification of current trends and related research areas within EMO.

Conclusions:

  • This tutorial serves as a foundational resource for understanding EMO.
  • It aims to equip readers with basic knowledge and a starting point for research in this active field.
  • It also assists advanced researchers in identifying potential open research topics.