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A Survey of Decomposition-Based Evolutionary Multi-Objective Optimization: Part I-Past and Future

Ke Li

TL;DR

This two-part survey series uses MOEA/D as the representative of decomposition-based EMO to review the up-to-date development in this area, and systematically and comprehensively analyze its research landscape.

Abstract

Decomposition has been the mainstream approach in classic mathematical programming for multi-objective optimization and multi-criterion decision-making. However, it was not properly studied in the context of evolutionary multi-objective optimization (EMO) until the development of multi-objective evolutionary algorithm based on decomposition (MOEA/D). In this two-part survey series, we use MOEA/D as the representative of decomposition-based EMO to review the up-to-date development in this area, and systematically and comprehensively analyze its research landscape. In the first part, we present a comprehensive survey of the development of MOEA/D from its origin to the current state-of-the-art approaches. In order to be self-contained, we start with a step-by-step tutorial that aims to help a novice quickly get onto the working mechanism of MOEA/D. Then, selected major developments of MOEA/D are reviewed according to its core design components including weight vector settings, subproblem formulations, selection mechanisms and reproduction operators. Besides, we also overview some selected advanced topics for constraint handling, optimization in dynamic and uncertain environments, computationally expensive objective functions, and preference incorporation. In the final part, we shed some light on emerging directions for future developments.

A Survey of Decomposition-Based Evolutionary Multi-Objective Optimization: Part I-Past and Future

TL;DR

This two-part survey series uses MOEA/D as the representative of decomposition-based EMO to review the up-to-date development in this area, and systematically and comprehensively analyze its research landscape.

Abstract

Decomposition has been the mainstream approach in classic mathematical programming for multi-objective optimization and multi-criterion decision-making. However, it was not properly studied in the context of evolutionary multi-objective optimization (EMO) until the development of multi-objective evolutionary algorithm based on decomposition (MOEA/D). In this two-part survey series, we use MOEA/D as the representative of decomposition-based EMO to review the up-to-date development in this area, and systematically and comprehensively analyze its research landscape. In the first part, we present a comprehensive survey of the development of MOEA/D from its origin to the current state-of-the-art approaches. In order to be self-contained, we start with a step-by-step tutorial that aims to help a novice quickly get onto the working mechanism of MOEA/D. Then, selected major developments of MOEA/D are reviewed according to its core design components including weight vector settings, subproblem formulations, selection mechanisms and reproduction operators. Besides, we also overview some selected advanced topics for constraint handling, optimization in dynamic and uncertain environments, computationally expensive objective functions, and preference incorporation. In the final part, we shed some light on emerging directions for future developments.
Paper Structure (43 sections, 13 equations, 7 figures)

This paper contains 43 sections, 13 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Background Knowledge
  3. Basic Concepts
  4. Tutorial of Vanilla MOEA/D
  5. Decomposition
  6. Collaboration
  7. Selected Developments on Major Components of MOEA/D
  8. Weight Vector Setting
  9. Fixed methods
  10. Model-based adaptation methods
  11. Delete-and-add methods
  12. Subproblem Formulations
  13. TCH variants
  14. PBI variants
  15. Constrained Decomposition
  16. ...and 28 more sections

Figures (7)

  • Figure 1: A pragmatic history of decomposition-based EMO algorithms from the past till the development of MOEA/D.
  • Figure 3: The left panel provides an illustrative example of the weight vector distribution and the neighborhood structure in MOEA/D. The right panel gives the working mechanism of MOEA/D as a three-step process.
  • Figure 4: MOEA/D obtains evenly distributed solutions by using evenly distributed weight vectors merely when the PF is a simplex. Otherwise, some weight vectors do not have Pareto-optimal solutions like PF2; or the distribution of the corresponding Pareto-optimal solutions is highly biased like PF3 and PF4.
  • Figure 5: Contour lines of the Tchebycheff approach and its three variants.
  • Figure 6: Contour lines of the PBI approach and its three variants.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5