## 1 Introduction
Some metaheuristic procedures supply better results in solving specific problems, whereas other metaheuristics are limited to certain domains of the decision variables; however, all of them are successful in solving optimization challenges [2]. Among these classic population-based methods, evolutionary algorithms (EAs) [7; 20] constitute a set of algorithms based on [PERSON]'s evolutionary theory, where they start from an initial randomly generated population, which is improved over generations through recombination and mutation operators. Genetic algorithms (GAs) [21] are a subset of EAs, where the individuals in the population are in the form of an array or chromosome. Other important population-based metaheuristics are the gravitational search algorithm (GSA) [2] (it is based on the Newtonian law of gravity), the black hole (BH) algorithm [22] (where the best solution of a population is treated as a black hole that attracts other solutions or normal stars around it during the search), ant colony optimization (ACO) [23] (an ant colony searches for food according to the concentration of a chemical substance called a pheromone that ants deposit during the search), particle swarm optimization (PSO) [24] (it simulates bird behaviour using a simplified social model), the bat algorithm (BA) [25] (it is inspired by how bats look for their prey using echolocation), the artificial bee colony (ABC) algorithm [26] (it is inspired by the behaviour of honeybee swarms), and the artificial chemical reaction optimization algorithm (ACROA) [27] (it is inspired by some types and frequencies of certain chemical reactions). In the last five years, several optimization algorithms have been developed that consider novel search strategies and provide significant results. An important fraction of these methods is based on the social behaviour of a group of individuals of a determined live species. One of them considers, as a source of inspiration, human reasoning to make decisions when faced with fuzzy data [28]. Some of these techniques are: grey wolf optimizer (GWO) [29] (it imitates the command hierarchy and hunting strategy of grey wolves), the pity beetle algorithm (PBA) [30] (it was inspired by the grouping behaviour of the beetle _Pityogenes chalcogenplus_, looking for food and nests), shark smell optimization (SSO) [31] (it simulates the skill of a shark for finding their prey by using its sense of smell and moving toward the source of the odour), symbiotic organisms search (SOS) [32] (mimics the symbiotic interaction strategies followed by organisms to survive and propagate in the ecosystem), dolphin echolocation (DOE) [33] (it considers the echolocation system used by dolphins in searching for food), the whale optimization algorithm (WOA) [34] (it mimics the social behaviour of humpback whales), and the emperor penguin optimizer (EPO) [35] (it simulates the huddling behaviour of emperor penguins (_Aptenodytes forsteri_)). This paper proposes a novel metaheuristic for continuous domains inspired by a physical-chemical process, i.e., the thermodynamic equilibrium between two fluid phases of a mixture composed by two chemical species: the vapour-liquid equilibrium (VLE) metaheuristic. The algorithm is based on the distribution of the most volatile component of a binary chemical mixture, between the liquid phase and the gas phase constituted by the vapour [36]. Thus, the search process of the metaheuristic is guided by the state changes of binary systems and uses the mathematical concept of the total differential. The behaviour of each binary system represents the movements or changes of a decision variable of an individual of a population. The metaheuristic also considers stochastic components to include diversity during the search process to avoid being trapped in local optima. Some examples of these components are found when generating new individuals, applying mutation operators, and enabling the exploration around worse solutions instead of better solutions.