Abstract
In this article, a novel optimization metaheuristic based on the vapour-liquid equilibrium is described to solve highly nonlinear optimization problems in continuous domains. During the search for the optimum, the procedure truly simulates the vapour-liquid equilibrium state of multiple binary chemical systems. Each decision variable of the optimization problem behaves as the molar fraction of the lightest component of a binary chemical system. The equilibrium state of each system is modified several times, independently and gradually, in two opposite directions and at different rates. The best thermodynamic conditions of equilibrium for each system are searched and evaluated to identify the following step towards the solution of the optimization problem. While the search is carried out, the algorithm randomly accepts inadequate solutions. This process is done in a controlled way by setting a minimum acceptance probability to restart the exploration in other areas to prevent becoming trapped in local optimal solutions. Moreover, the range of each decision variable is reduced autonomously during the search. The algorithm reaches competitive results with those obtained by other stochastic algorithms when testing several benchmark functions, which allows us to conclude that our metaheuristic is a promising alternative in the optimization field.
Highlights
Over the past decades, conventional search methods have been applied to solve optimization problems, providing promising results in many cases
Among single solution-based metaheuristics, we focus on simulated annealing (SA) [5], variable neighbourhood search (VNS) [6], greedy randomized adaptive search procedure (GRASP) [7], guided local search (GLS) [8], iterated local search (ILS) [9]
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
Summary
Conventional search methods have been applied to solve optimization problems, providing promising results in many cases These methods may fail in more complex real-world problems where nonlinearity and multimodality are fundamental issues. In most situations such problems are nonlinear, hindering the solution Another difficulty arises when the problem is non-convex, the gradient is unknown, or the first derivatives do not exist. In these cases, it is not possible to apply gradient-based optimization methods, which is common in real-world problems. It is not possible to apply gradient-based optimization methods, which is common in real-world problems Another challenge arises when the number of decision variables is large, affecting the search space. Most real-world problems cannot be handled by conventional
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