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

TL;DR

This paper introduces a unified taxonomy and comprehensive survey of metaheuristics designed for variable-size mixed-variable optimization problems, addressing a significant gap in classification and understanding of solution approaches.

Contribution

It provides the first well-established taxonomy and mathematical formulation for metaheuristics tackling (V)MVOPs, along with an analysis of methodologies and open research challenges.

Findings

Unified taxonomy for (V)MVOP metaheuristics

Analysis of advantages and limitations of methodologies

Identification of open research issues

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.