Bio-inspired computing is an emerging paradigm which is based on the basics and inspiration of natural phenomena to design new and robust competing techniques. Various nature science areas have motivated the inspiration for the design of new intelligent systems. Chemical engineering is one of them. In Chemistry, the vapor-liquid equilibrium process describes the distribution of chemical species combining two essential phases: vapor phase and liquid phase. Using a binary system of compounds is possible to simulate a search process based on the equilibrium between both phases. In this paper, we propose a new algorithm inspired by this chemical phenomenon for solving a new patient bed assignment problem. This problem consists of assigning patients to beds by considering relevant medical requirements trying to maximize the most covered soft constraints. For that, we take a traditional model, and we transform it by using the constraint optimization paradigm. We test our algorithm on 30 benchmarks taken of Chilean health services. To verify results, we perform statistical comparatives with artificial bee algorithm, ant colony optimization, the bat method, cuckoo search, genetic algorithm, particle swarm optimization, and a random strategy. Computational experiments illustrate that the VLE algorithm properly solved 30 instances, finding all global optimal. In nineteen instances, VLE converged towards the best solution in its median value. In ten instances, the median, the average and the best value, all of them achieved the global optimal. Now, when comparing VLE against other techniques, we can note that VLE is surpassed by the artificial bee colony in two instances only. The rest of the results show VLE as a robust algorithm able to suppress classical, such as genetic algorithm and particle swarm optimization.