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Metaheuristics for (Variable-Size) Mixed Optimization Problems: A Unified Taxonomy and Survey

El-Ghazali Talbi

TL;DR

A unified taxonomy for metaheuristic solutions for solving (V)MVOPs is presented in an attempt to provide a common terminology and classification mechanisms and identifies the various solving methodologies than can be applied in metaheuristics.

Abstract

Many real world optimization problems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a variable-size search space. Depending on the values of dimensional variables, the number and type of the variables of the problem can vary dynamically. MVOPs and variable-size MVOPs (VMVOPs) are difficult to solve and raise a number of scientific challenges in the design of metaheuristics. Standard metaheuristics have been first designed to address continuous or discrete optimization problems, and are not able to tackle (V)MVOPs in an efficient way. The development of metaheuristics for solving such problems has attracted the attention of many researchers and is increasingly popular. However, to our knowledge there is no well established taxonomy and comprehensive survey for handling this important family of optimization problems. This paper presents a unified taxonomy for metaheuristic solutions for solving (V)MVOPs in an attempt to provide a common terminology and classification mechanisms. It provides a general mathematical formulation and concepts of (V)MVOPs, and identifies the various solving methodologies than can be applied in metaheuristics. The advantages, the weaknesses and the limitations of the presented methodologies are discussed. The proposed taxonomy also allows to identify some open research issues which needs further in-depth investigations.

Metaheuristics for (Variable-Size) Mixed Optimization Problems: A Unified Taxonomy and Survey

TL;DR

A unified taxonomy for metaheuristic solutions for solving (V)MVOPs is presented in an attempt to provide a common terminology and classification mechanisms and identifies the various solving methodologies than can be applied in metaheuristics.

Abstract

Many real world optimization problems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a variable-size search space. Depending on the values of dimensional variables, the number and type of the variables of the problem can vary dynamically. MVOPs and variable-size MVOPs (VMVOPs) are difficult to solve and raise a number of scientific challenges in the design of metaheuristics. Standard metaheuristics have been first designed to address continuous or discrete optimization problems, and are not able to tackle (V)MVOPs in an efficient way. The development of metaheuristics for solving such problems has attracted the attention of many researchers and is increasingly popular. However, to our knowledge there is no well established taxonomy and comprehensive survey for handling this important family of optimization problems. This paper presents a unified taxonomy for metaheuristic solutions for solving (V)MVOPs in an attempt to provide a common terminology and classification mechanisms. It provides a general mathematical formulation and concepts of (V)MVOPs, and identifies the various solving methodologies than can be applied in metaheuristics. The advantages, the weaknesses and the limitations of the presented methodologies are discussed. The proposed taxonomy also allows to identify some open research issues which needs further in-depth investigations.
Paper Structure (22 sections, 7 equations, 7 figures)

This paper contains 22 sections, 7 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Mixed-variable optimization problems
  3. Fixed-size mixed-variable optimization problems
  4. Variable-size mixed-variable optimization problems
  5. Main metaheuristic components
  6. A taxonomy of metaheuristics for MVOPs
  7. Global approaches for MVOPs
  8. Encodings adaptation
  9. Variation operators adaptation
  10. Decomposition-based approaches for MVOPs
  11. Sequential approaches for MVOPs
  12. Nested approaches for MVOPs
  13. Co-evolutionary approaches for MVOPs
  14. A taxonomy of metaheuristics for VMVOPs
  15. Global approaches for VMVOPs
  16. ...and 7 more sections

Figures (7)

  • Figure 1: A taxonomy of metaheuristic methodologies for solving MVOPs.
  • Figure 4: Building blocks for decomposition-based sequential approaches in handling MVOPs.
  • Figure 5: Nested decomposition-based approaches for handling MVOPs.
  • Figure 7: A taxonomy of metaheuristic methodologies to solve VMVOPs.
  • Figure 8: Hidden genes representation and variation operators for VMVOPs.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Definition 1
  • Definition 2