Reliability vs. Efficiency When Solving Multiphase Equilibrium Problems with Hybrid Optimization Codes

Summary The computational problems in reservoir fluid systems are mainly in the critical region and in liquid-liquid (LL), vapor-liquid-liquid (VLL), and higher-phase equilibria. The conventional methods to perform phase-equilibrium calculations with the equality of chemical potentials cannot guarantee a correct solution. In this study, we propose a simple method to calculate the equilibrium state by direct minimization of the Gibbs free energy of the system at constant temperature and pressure. We use the simulated annealing (SA) algorithm to perform the global minimization. Estimates of key parameters of the SA algorithm are also made for phase-behavior calculations. Several examples, including (1) VL equilibria in the critical region, (2) VLL equilibria for reservoir fluid systems, (3) VLL equilibria for an H2S-containing mixture, and (4) VL-multisolid equilibria for reservoir fluids, show the reliability of the method.

Non-convex optimization problems are prevalent in scientific and engineering applications, often characterized by multiple local minima that challenge standard optimization techniques. Global optimization methods, such as Genetic Algorithms (GA) (1992) [4] and Particle Swarm Optimization (PSO) (1995) [6], provide robust global exploration but tend to converge slowly. Conversely, local search methods, such as Newton’s method (2004) [1], (2006) [7], and the Conjugate Gradient (CG) (1964) [3] method, offer rapid convergence but are susceptible to local minima. In this paper, we present four hybrid optimization algorithms that integrate the exploratory strength of global algorithms with the refinement ability of local methods. The proposed hybrids, Genetic Algorithms (GA) + Newton, GA + CG, PSO + Newton, and PSO + CG, are evaluated against their standalone counterparts on standard benchmark functions (2013) [5], including Rosenbrock, Rastrigin, Ackley, and Himmelblau. This work builds upon our previous research on the hybridization of two global search algorithms, the Nelder–Mead (simplex) algorithm and the Bat algorithm, which resulted in the Hybrid Simplex Bat Algorithm (HSBA) [2], recently Published. Results demonstrate that the hybrid approaches consistently outperform traditional methods in terms of accuracy, convergence rate, and computational efficiency.

Harmony Search (HS) algorithm is a new meta-heuristic global search algorithm. To solve the algorithm easily fall into the local optimal problem, this paper proposes an adaptive novel global harmony search (ANGHS) algorithm based on NGHS algorithm. First, a new location update strategy is given using the adjustment parameter F. Then, the mutation operation is introduced in the case of excluding the small probability Pm. In order to avoid blind adjustment of the step size in the late search and effectively adjust the structure of the solution, the definition of the norm is introduced to adjust parameter bw dynamically. In this paper, 7 standard Benchmark functions are used to simulate the experiment. The results show that the algorithm avoids the premature problem of the algorithm and enhances the global search ability of the algorithm, with obvious improvement in convergence speed and stability, and has good optimize performance.

A powerful idea for deterministic global optimization is the use of global feasible search, namely, algorithms that guarantee finding feasible solutions of nonconvex problems or prove that none exists. In this article, a set of conditions for global feasible search algorithms is established. The utility of these conditions is demonstrated on two algorithms that solve special problem classes globally. Also, a new model transformation is shown to convert a generalized polynomial problem into one of the special classes above. A flywheel design example illustrates the approach. A sequel article provides further computational details and design examples.

Energy Systems Engineering

ABSTRACTEngineering design often involves different types of simulation, which results in expensive computational costs. Variable fidelity approximation-based design optimization approaches can realize effective simulation and efficiency optimization of the design space using approximation models with different levels of fidelity and have been widely used in different fields. As the foundations of variable fidelity approximation models, the selection of sample points of variable-fidelity approximation, called nested designs, is essential. In this article a novel nested maximin Latin hypercube design is constructed based on successive local enumeration and a modified novel global harmony search algorithm. In the proposed nested designs, successive local enumeration is employed to select sample points for a low-fidelity model, whereas the modified novel global harmony search algorithm is employed to select sample points for a high-fidelity model. A comparative study with multiple criteria and an engineering application are employed to verify the efficiency of the proposed nested designs approach.

The paper presents the application of the Taguchi's global optimisation algorithm to analyse the self-excited induction generator performances. The analysis is based essentially on finding the root of the equivalent circuit's admittance (or the impedance) being equated to zero. This equation has two unknowns the magnetizing reactance and the frequency. The two variables depend strongly on the equivalent circuit parameters and the external parameters which are the load, the excitation capacitance and the prime mover rotor speed. Previous work on the subject have used either gradient based or global search algorithms. In this work, a new global search technique is used to solve this equation. Besides its global search features, this optimization algorithm is superior in terms of accuracy and ease of implementation. A study of some simulations results carried out using Matlab software has been done to corroborate the above advantages.

Imposing suitably designed nonconvex regularization is effective to enhance sparsity, but the corresponding global search algorithm has not been well established. In this article, we propose a global search algorithm for the nonconvex two-level l1 penalty based on its piecewise linear property and apply it to machine learning tasks. With the search capability, the optimization performance of the proposed algorithm could be improved, resulting in better sparsity and accuracy than most state-of-the-art global and local algorithms. Besides, we also provide an approximation analysis to demonstrate the effectiveness of our global search algorithm in sparse quantile regression.

This work aims on method development for obtaining initial designs for ultraviolet (UV) and deep-ultraviolet (DUV) objectives through global search algorithm. We studied a global search based algorithm tending to obtain the feasible local minima of lens design landscape. One of the major challenges of our work is writing macro input related to a number of lenses, the length of objective, and glass material. The obtained results show the main advantages and efficiency of the design approach based on the global search algorithm. As an output, we developed a method and criteria for successful selection of the starting point of micro-lithographic objectives

This paper proposed a new hybrid method combining genetic algorithm(GA) and coordinate search method (CSM). Genetic algorithm is good at global exploration but bad at accuracy and local search. Whereas, coordinate search method is good at local exploitation, and its accuracy is reliable when searching in a local area. Thus we combine those two methods in this paper to design a hybrid method called genetic algorithm with coordinate search (GACS). Experimental tests shows that this method are good at both global search and local accuracy. © 2012 IEEE.

This article presents a new multidimensional descent method for solving global optimization problems with box-constraints. This is a hybrid method where local search method is used for a local descent and global search is used for further multidimensional search on the subsets of intersection of cones generated by the local search method and the feasible region. The discrete gradient method is used for local search and the cutting angle method is used for global search. Two- and three-dimensional cones are used for the global search. Such an approach allows one, as a rule, to escape local minimizers which are not global ones. The proposed method is local optimization method with strong global search properties. We present results of numerical experiments using both smooth and non-smooth global optimization test problems. These results demonstrate that the proposed algorithm allows one to find a global or a near global minimizer.

This paper addresses the problem of global optimization by means of a monotonic transformation. With an observation on global optimality of functions under such a transformation, we show that a simple and effective algorithm can be derived to search within possible regions containing the global optima. Numerical experiments are performed to compare this algorithm with one that does not incorporate transformed information using several benchmark problems. These results are also compared to best known global search algorithms in the literature. In addition, the algorithm is shown to be useful for several neural network learning problems, which possess much larger parameter spaces.

High dimensional global optimization problems arise frequently in process systems engineering. This is a result of the complex mechanistic relationships that describe process systems, and/or their large-scale nature. High dimensional optimization problems can often be more easily solved by instead solving a sequence of reduced-dimension subproblems. Surrogate models can allow the formulation of reduced-dimension subproblems by approximating the key features of the original model. Surrogate-based optimization (SBO) is to use surrogate modeling to solve a sequence of approximate reduced-dimension subproblems, in order to converge to a high quality solution to the original high dimensional problem. Here we review the key characteristics of SBO frameworks and their application to process systems optimization problems.

Summary Increasing oil recovery technology is crucial for the sustainable growth of the petroleum industry and the assurance of energy security. Dimethyl ether (DME) has emerged as a potential candidate to further enhance the efficiency of water/CO2 flooding processes. However, developing a reliable and accurate multiphase equilibrium calculation package that meets the high efficiency and robustness standards required for reservoir simulation in DME-enhanced water/CO2 flooding remains a significant challenge. This study presents a comprehensive multiphase equilibrium calculation framework specifically designed for H2O/brine-CO2-DME-hydrocarbon systems. The Peng-Robinson (PR) equation of state (EOS) combined with the Huron-Vidal (HV) mixing rule is used to predict phase behavior accurately. The framework incorporates several key components: (1) an improved model for saline systems to enhance computational efficiency; (2) innovative stability analysis strategies to ensure robustness; (3) a salt precipitation module to address water vaporization scenarios; and (4) a numerical solver that integrates successive substitution iteration (SSI) with the trust region (TR) method to secure computational efficiency. Extensive testing involving millions of data points has demonstrated the accuracy, robustness, and efficiency of our algorithm. This framework serves as a powerful tool for phase equilibrium calculations in complex reservoir systems, facilitating more effective simulation and optimization of DME-enhanced water/CO2 flooding operations.

State-of-the-art antenna design and optimization (D/O) is increasingly being done using Global Search and Optimization (GSO) algorithms such as Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Differential Evolution (DE), and a plethora of other evolutionary algorithms, among them Central Force Optimization (CFO), which is the subject of this note. CFO analogizes real gravity in the real Universe so that its gravity is usually attractive in nature, that is, “positive”. But in metaphorical CFO space the algorithm designer is free to turn gravity on its head by making it negative, and doing so to a small extent can improve CFO’s exploration of the search space thus providing even better results. This extension is discussed in some detail and applied to a 6-element Yagi-Uda array as an example.