Hybrid gradient particle swarm optimization for dynamic optimization problems of chemical processes

Xu, Chunxiao; Du, Wenli; Qi, Rongbin; Qian, Feng; Tianfield, Huaglory

doi:10.1002/apj.1712

Cited by 24 publications

(21 citation statements)

References 36 publications

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“…This system has been studied, among others, by Jacobson and Lele 20 , Mekarapiruk and Luus 14 , Chen et al 24 , Shelokar et al 6 and Chen et al 3 . The system equations are…”

Section: Example 1 Mathematical System With Nonlinear Inequality Conmentioning

confidence: 99%

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Two-Step Method for Dynamic Optimization of Inequality State Constrained Systems Using Iterative Dynamic Programming

Sundaralingam¹

2015

Ind. Eng. Chem. Res.

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A two step method for the solution of dynamic optimization problems with state inequality constraints using Iterative dynamic programming (IDP) is presented. In the first step, a preliminary control policy along with approximate values for the start and end points of the state constrained arc is obtained. The final solution is obtained in the second step by using the preliminary control policy as an input along with an analytical expression for the control during the constrained portion of the state trajectory. The use of flexible stage lengths in IDP helps in locating the start and end points of the state constrained arc accurately. For the examples considered, the method results in better values of the performance index than previously reported in the literature. It also results in a significant reduction in computation time as compared to the existing method, for the solution of problems with a single active state constraint and a single control, using IDP.

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“…This system has been studied, among others, by Jacobson and Lele 20 , Mekarapiruk and Luus 14 , Chen et al 24 , Shelokar et al 6 and Chen et al 3 . The system equations are…”

Section: Example 1 Mathematical System With Nonlinear Inequality Conmentioning

confidence: 99%

“…Chen et al3 using gradient based PSO. The total computation time for the two steps is 1063 secs whereas the two successive 23 grid point runs ofMekarapiruk and Luus 14 to obtain their answer will take 3770 secs.…”

mentioning

confidence: 99%

Two-Step Method for Dynamic Optimization of Inequality State Constrained Systems Using Iterative Dynamic Programming

Sundaralingam¹

2015

Ind. Eng. Chem. Res.

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“…To enhance the performance of common PSO, we proposed a PSO variant named HGPSO for solving DOPs [16], in which two strategies were employed.…”

Section: B Hgpsomentioning

confidence: 99%

“…Since stochastic methods can obtain global optimum for multimodal problems, stochastic methods, such as genetic algorithm (GA) [6], [7], DE [5], [8], particle swam optimization (PSO) [9], ant colony algorithm [10], simulated annealing [11], have been employed to solve DOPs. In our earlier work [16], PSO and GBA were hybridized to constitute an optimization method, named hybrid gradient particle swarm optimization (HGPSO), for DOPs. HGPSO combines the strong global search ability of PSO and the strong local search ability of GBA.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Optimization of Industrial Processes With Nonuniform Discretization-Based Control Vector Parameterization

Tianfield

et al. 2014

IEEE Trans. Automat. Sci. Eng.

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This paper proposes a novel scheme of nonuniform discretizetion-based control vector parameterization (ndCVP, for short) for dynamic optimization problems (DOPs) of industrial processes. In our ndCVP scheme, the time span is partitioned into a multitude of uneven intervals, and incremental time parameters are encoded, along with the control parameters, into the individual to be optimized. Our coding method can avoid handling complex ordinal constraints. It is proved that ndCVP is a natural generalization of uniform discretization-based control vector parameterization (udCVP). By integrating ndCVP into hybrid gradient particle swarm optimization (HGPSO), a new optimization method, named ndCVP-HGPSO for short, is formed. By application in four classic DOPs, simulation results show that ndCVP-HGPSO is able to achieve similar or even better performances with a small number of control intervals; while the computational overheads are acceptable. Furthermore, ndCVP and udCVP are compared in terms of two situations: given the same number of control intervals and given the same number of optimization variables. The results show that ndCVP can achieve better performance in most cases.Note to Practitioners-This paper was motivated by the problems of operational optimization in industrial processes. Most problems in industrial processes are dynamic optimization problems, and the aim is to optimize control variables like feeding rates, heating/cooling for reaction over a time span. Most of existing optimization methods use uniform discretization-based control vector parameterization (udCVP for short), in which the time span for optimization is partitioned into a multitude of even intervals and thus merely the control parameters need to be optimized. In this paper, we propose a novel scheme of nonuniform-based discretization control vector parameterization (ndCVP), in which the time span is unevenly partitioned, and the incremental time parameters are encoded into the individual to be optimized as well. It is proved that ndCVP is a natural generalization of udCVP. Moreover, by integrating ndCVP into hybrid gradient particle swarm optimization (HGPSO), a new Manuscript optimization method, named ndCVP-HGPSO for short, is formed for DOPs. Numeric simulations show that ndCVP-HGPSO is a highly competitive method for DOPs, because ndCVP can adjust the time intervals to generate high precision results in compliance with the shape of control trajectories.Index Terms-Dynamic optimization, hybrid gradient particle swarm optimization, nonuniform discretizetion-based control vector parameterization.

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A hybrid gradient‐based and differential evolution algorithm for infinite impulse response adaptive filtering

Yuenyong

Nishihara

2013

Adaptive Control & Signal

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Global optimization algorithms (GO) had been applied to solve the adaptive infinite impulse response filtering problem, which is known to have multimodal error surface under certain conditions. However, although GO may be able to search multimodal surfaces, they have certain disadvantages. They may not converge to any minimum point, the convergence speed is reduced as the solution vectors move closer, and tracking ability for non-stationary environment is lacking. The traditional gradient descent method does not have these limitation but is not able to search multimodal surfaces. In this work, we propose a hybrid algorithm combining gradient descent and differential evolution (DE) for adapting the coefficients of infinite impulse response adaptive filters. DE is run in a block-based manner. The coefficient vector with the lowest error surface value (the best member) of the current block is updated via gradient descent for the duration of the next block. Thus combining the ability to search multimodal surface of DE and fast local search of gradient descent. As with all GO, global search capacity is gradually lost as the coefficient vectors converge together. Thus, re-initialization is also incorporated into the hybrid algorithm to provide continuous global search capacity for non-stationary environment. All the coefficient vectors except the best member are reinitialized when the normalized mean Euclidean distance between each pair of vectors falls below a threshold value. Simulation results show that the proposed algorithm achieves better solution quality and convergence speed than classic DE and GO for stationary and non-stationary environments. The poor performance of ABC compared with other algorithm is not due to bad choice of parameter, the algorithm seem to be sensitive to small block length, and hence noisy cost function than others. ABC becomes comparable with others when L is significantly larger than 30 Further work includes incorporating adaptive parameters for DE and adaptive stepsize for gradient descent, experimenting with block gradient update, and testing other measures that may be more appropriate than the normalized mean Euclidean distance for re-initialization checking.

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Hybrid gradient particle swarm optimization for dynamic optimization problems of chemical processes

Cited by 24 publications

References 36 publications

Two-Step Method for Dynamic Optimization of Inequality State Constrained Systems Using Iterative Dynamic Programming

Two-Step Method for Dynamic Optimization of Inequality State Constrained Systems Using Iterative Dynamic Programming

Dynamic Optimization of Industrial Processes With Nonuniform Discretization-Based Control Vector Parameterization

A hybrid gradient‐based and differential evolution algorithm for infinite impulse response adaptive filtering

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