The performance of simulated annealing in parameter estimation for vapor-liquid equilibrium modeling

Abstract

-In this paper we report the application and evaluation of the simulated annealing (SA) optimization method in parameter estimation for vapor-liquid equilibrium (VLE) modeling. We tested this optimization method using the classical least squares and error-in-variable approaches. The reliability and efficiency of the data-fitting procedure are also considered using different values for algorithm parameters of the SA method. Our results indicate that this method, when properly implemented, is a robust procedure for nonlinear parameter estimation in thermodynamic models. However, in difficult problems it still can converge to local optimums of the objective function.

On the capabilities and limitations of harmony search for parameter estimation in vapor–liquid equilibrium modeling

“…It is important to note that the global minimization of least squares objective function can be done as an unconstrained optimization problem using these thermodynamic models. However, several studies have shown that, even for relatively simple thermodynamic equations such as those given in Table 1, multiple local optima can occur in non-linear parameter estimation for VLE data modeling [8,[11][12][13]. This is because the highly non-linear form of the thermodynamic models makes F obj potentially non-convex.…”

“…However, this type of optimization problems is complex and difficult to solve using traditional local optimization methods due to [7][8][9]: (a) the presence of several local minima for the objective function used as optimization criterion, (b) the objective function may be flat or with discontinuities in some regions of solution domain, and (c) the model parameters may vary over a wide range of values. In fact, results reported by several studies [4,[7][8][9][10][11][12][13][14][15][16] indicate that the parameter estimation problem has complex non-linear objective functions even using thermodynamic models with a relatively small number of adjustable parameters. In addition, we have to face both large-scale and non-convex optimization problems if the error-in-variable formulation is used.…”

“…On the other hand, several studies have shown the potential of stochastic (or meta-heuristic) optimization methods to solve non-linear parameter estimation problems for modeling phase equilibrium data [11][12][13][14][15]. A meta-heuristic method is a high-level algorithm that combines rules (or heuristics) and randomness to imitate natural phenomena and to solve optimization problems.…”

“…These methods offer several advantages for solving global optimization problems such as generality, robust performance, few information requirements of the optimization problem to be solved, easy implementation, and a reasonable computational time. To date, different stochastic methods have been studied and tested for parameter estimation using VLE data, and they include: Simulated Annealing, Genetic Algorithm, Differential Evolution, and Particle Swarm Optimization, among others [4,[11][12][13][14][15]. These strategies usually show a robust performance but, in some challenging problems, they may fail to locate the global optimum [4,13].…”

Novel bare-bones particle swarm optimization and its performance for modeling vapor–liquid equilibrium data

“…Parameter estimation based on both least squares (LS) and error-in-variable (EIV) approaches are considered. Of these, 10 problems are based on LS approach and another 6 problems are based on VLE-EIV approach; both these approaches minimize an objective function subject to constraints arising from model equations [2][3][4]17,18]. Recently, our group solved these parameter estimation problems by PSO and other stochastic global optimization algorithms [6,19].…”