Continuous Metaheuristics for Binary Optimization Problems: An Updated Systematic Literature Review

Abstract

For years, extensive research has been in the binarization of continuous metaheuristics for solving binary-domain combinatorial problems. This paper is a continuation of a previous review and seeks to draw a comprehensive picture of the various ways to binarize this type of metaheuristics; the study uses a standard systematic review consisting of the analysis of 512 publications from 2017 to January 2022 (5 years). The work will provide a theoretical foundation for novice researchers tackling combinatorial optimization using metaheuristic algorithms and for expert researchers analyzing the binarization mechanism’s impact on the metaheuristic algorithms’ performance. Structuring this information allows for improving the results of metaheuristics and broadening the spectrum of binary problems to be solved. We can conclude from this study that there is no single general technique capable of efficient binarization; instead, there are multiple forms with different performances.

Binarization of Metaheuristics: Is the Transfer Function Really Important?

“…The binarization techniques used in continuous MHs involve transferring continuous domain values to binary domains, with the aim of maintaining the quality of moves and generating high-quality binary solutions. While some MHs operate on binary domains without a binary scheme, studies have demonstrated that continuous MHs supported by a binary scheme perform exceptionally well on multiple NP-hard combinatorial problems [ 1 ]. Examples of such MHs include the binary bat algorithm [ 28 , 29 ], particle swarm optimization [ 30 ], binary sine cosine algorithm [ 2 , 31 , 32 , 33 ], binary salp swarm algorithm [ 34 , 35 ], binary grey wolf optimizer [ 32 , 36 , 37 ], binary dragonfly algorithm [ 38 , 39 ], the binary whale optimization algorithm [ 2 , 32 , 40 ], and the binary magnetic optimization algorithm [ 41 ].…”

“…In the scientific community, two-step binarization schemes are very relevant [ 1 ]. They have been widely used to solve a variety of combinatorial problems [ 47 ].…”

“…In this sense, the application of metaheuristic optimization algorithms has become a valuable tool for finding efficient and effective solutions to these problems. Furthermore, the use of continuous metaheuristics to solve binary problems has become increasingly relevant due to their ability to find optimal solutions in a short period of time [ 1 ]. These techniques are capable of efficiently exploring and exploiting the search space, making them ideal for optimization problems in fields such as engineering, data science, and industry.…”

Qubit Efficient Quantum Algorithms for the Vehicle Routing Problem on Noisy Intermediate‐Scale Quantum Processors

“…algorithms [86][87][88] amongst others, [89][90][91][92][93][94][95] with many of these having been adapted for the vehicle routing problem. [96][97][98][99][100][101][102][103][104] To find solutions to the QUBO problem using traditional quantum approaches, the cost function is first mapped to an Ising Hamiltonian:…”

“…The QUBO problem is a binary optimization problem consisting of finding a binary vector $$\vec{x}^*$$ such that: $$$$\begin{equation} \vec{x}^* = \underset{\vec{x}}{\textrm {arg min}}\, \vec{x}^{\top } \mathcal {A} \vec{x} \end{equation}$$$$where $$\vec{x}\in \lbrace 0,1\rbrace ^{n_c}$$ is a vector of $$n_c$$ classical binary variables and $$\mathcal {A}^{n_c\times n_c}$$ is a real and symmetric matrix constructed from our optimization problem. Classical methods of finding solutions to QUBO problems involve a range of metaheuristic algorithms such as simulated annealing, [ 76–81 ] TABU search [ 82–85 ] or genetic algorithms [ 86–88 ] amongst others, [ 89–95 ] with many of these having been adapted for the vehicle routing problem. [ 96–104 ]…”