Alopex-based Evolutionary Algorithm Research Articles

Multi-plant direct heat integration based on the risk-based Shapley value and Alopex-based evolutionary algorithm

Current heat exchanger network (HEN) synthesis is mainly focused on minimizing the total annual cost (TAC), and then allocating the minimized TAC among plants. However, the obtained HENs usually have complex inter-plant heat matches, and if unplanned shutdowns occur, connected plants will suffer huge economic losses. Consequently, some plants may be unsatisfied with their allocated costs and prefer not to join this multi-plant coalition. In this study, a natural risk-based Shapley value curve is used to represent the variation of cost allocation under shutdown risks between 0% and 100%. Alopex-based optimization strategies are proposed to optimize the modified HEN model with core constraints that can restrict the Shapley value curve to the core range as feasible cost allocation solutions. Therefore, HEN configurations and acceptable cost allocation plans under any shutdown risks are determined simultaneously. Two cases demonstrate that the proposed methodology can reduce shutdown-induced economic losses and facilitate multi-plant cooperation.

A simultaneous optimization of a flexible heat exchanger network under uncertain conditions

Heat exchanger networks are important for energy recovery and cost reduction. Flexible networks can handle environmental disturbances, and is more practical for industrial processes than the conventional HEN design with fixed parameters. Previous research on flexible HEN synthesis has mainly applied sequential synthesis, in which the structure determination and area optimization are conducted separately, or other multi-period methods in which only a few extreme operating conditions are selected; however, these methods are not sufficiently accurate for solving nonconvex problems. In this study, a bi-level simultaneous optimization strategy is proposed for the synthesis of flexible HENs under the nominal and all the extreme operating conditions. A binary particle swarm optimization is used in the outer layer to optimize the structural variables, and an Alopex-based evolutionary algorithm is used in the inner layer to determine the heat exchanger areas. Via this method, the result of a convex problem can be directly obtained. Furthermore, to deal with nonconvex problems, a flexibility analysis is conducted to adjust the heat exchanger areas on each critical point. The results of two cases with lower total annual costs than those reported previously are included to demonstrate the efficiency of the proposed method.

BP neural network modeling with sensitivity analysis on monotonicity based Spearman coefficient

This paper proposes a new monotonicity extraction method which is used to constrain the modeling process of a neural network. The main contributions of this paper are the sensitivity analysis on monotonicity based on Spearman coefficient, and the application of monotonicity on neural network modeling. This study uses scatter plots of bivariate variables and the Spearman coefficient to extract the monotonic information. To weaken the influence of noise, binary 0–1 integer linear program is applied to filter the scatter diagram. Based on the monotonicity information, a constraint optimization problem is proposed to obtain the BP neural network model and an Alopex-based evolutionary algorithm (AEA) is used to search for the optimal weights and thresholds. The results of a numeral example and an ethylene cracking furnace show that the proposed approach can achieve a good predicting performance in the two cases.

Multi-plant indirect heat integration based on the Alopex-based evolutionary algorithm

Multi-plant indirect heat integration via an intermediate fluid loop is an effective and energy-saving method of heat recovery. It is most suitable in practical applications because it requires fewer inter-plant pipelines and has the advantages of a simple heat exchanger network. A well-designed heat exchanger network will significantly increase economic efficiency and reduce energy consumption in plants. In this paper, a multi-plant indirect heat exchanger network model is developed for recycling heat using intermediate fluid. This model aims to minimize the total annual cost, including utility cost, number of units and heat transfer area cost. An Alopex-based evolutionary algorithm is used to optimize the model and obtain the heat capacity flow rate of intermediate fluids, the temperature of the heat transfer medium and the configuration of the superstructure simultaneously. Results from three examples demonstrate that the proposed model can perform well in multi-plant heat exchanger network synthesis.

Improved Alopex-based evolutionary algorithm by Gaussian copula estimation of distribution algorithm and its application to the Butterworth filter design

ABSTRACTThe application of evolutionary algorithms (EAs) is becoming widespread in engineering optimisation problems because of their simplicity and effectiveness. The Alopex-based evolutionary algorithm (AEA) possesses the basic characteristics of heuristic search algorithms but is lacking in adequate information about the fitness landscape of the input domain, reducing the convergence speed. To improve the performance of AEA, the Gaussian copula estimation of distribution algorithm (EDA) is embedded into the original AEA in this paper. With the help of Gaussian copula EDA, precise probability models are built utilising the best solutions, which can increase the convergence speed, and at the same time, keep the population diversity as much as possible. The simulation results on the benchmark functions and the application to the Butterworth filter design demonstrate the efficiency and effectiveness of the proposed algorithm, compared with several other EAs.

Improved Alopex-based evolutionary algorithm (AEA) by quadratic interpolation and its application to kinetic parameter estimations

The Algorithm of Pattern Extraction (Alopex)-based evolutionary algorithm (AEA) is an intelligent optimization algorithm that combines the Alopex with the evolution algorithm. It has high exploratory ability due to its especial searching mechanism. However, the AEA is poor at exploitation to some extent. To improve the performance of AEA, quadratic interpolation (QI) method is introduced to the AEA in this paper. The improved algorithm chooses three individuals to fit a quadratic function to approximate the objective function in each iterative of the AEA and uses the extreme point of the quadratic function to generate new individuals. The QI method can help the algorithm to converge rapidly near optimal solutions, which can greatly improve the exploitation ability of AEA. The traditional and CEC 2013 benchmark functions are both used to test the performance of the improved algorithm (QIAEA); the experimental results show that the QIAEA has better convergent speed and higher accuracy than the AEA. The QIAEA is also compared with several state-of-the-art algorithms and the results show that the QIAEA is an effective and efficient algorithm. Furthermore, its applications to parameter estimation for a model of sulfur dioxide (SO2) oxidation with a cesium–rubidium–vanadium (Cs–Rb–V) sulfuric acid catalyst and a heavy oil thermal cracking three-lump model demonstrate that QIAEA can forecast more accurately than other methods tested.

A modeling method based on artificial neural network with monotonicity knowledge as constraints

This paper proposes a new strategy to model a nonlinear industrial process. The proposed approach is based on Back-Propagation Neural Network (BPNN) models combined with monotonicity knowledge from mechanism analysis or expertise. The main contribution is to construct a unified framework for the modeling process by integrating the BPNN, monotonicity detection, constraint optimization problem, and Evolutionary Algorithm (EA). Initially, a BPNN structure is chosen to describe the input–output relationship. In the training process of the BPNN, the monotonicity knowledge is used as constraint condition for modeling. Thus, the training process changes to a Constraint Optimization Problem (COP). Finally, a new EA, namely Alopex-based EA (AEA), is used to search for the optimal weights and thresholds. This novel approach can avoid the over-fitting problem to some extent, especially when modeling a system with a small quantity of samples. In addition, we explain this method by the Bayesian inference and apply the method to model the acetylene concentration at the outlet of an acetylene hydrogenation reactor.

An improved AEA using local search and its application to parameter estimation for homogeneous mercury oxidation

The Alopex-based evolutionary algorithm (AEA) possesses the basic characteristics of evolutionary algorithms as well as the advantages of the simulated annealing algorithm and gradient descent methods. The AEA is good at exploration but poor at exploitation, which results to some extent in poor convergence. To improve the performance of the basic AEA, we propose a local search algorithm in this paper to generate the subsequent population when the results for the best individual have not improved after several consecutive iterations. Furthermore, we modify the annealing temperature in the AEA. Numerical simulation results of 20 benchmark functions show that this improved AEA algorithm (LAEA) can generate solutions of higher quality. Furthermore, we used LAEA to estimate reaction kinetic parameters for homogeneous mercury oxidation, and the satisfactory result shows its suitability for practical applications.

A new constraint handling method based on the modified Alopex-based evolutionary algorithm

In this paper, a new constraint handling method based on a modified AEA (Alopex-based evolutionary algorithm) is proposed. Combined with a new proposed ranking and selecting strategy, the algorithm gradually converges to a feasible region from a relatively feasible region. By introduction of an adaptive relaxation parameter μ, the algorithm fully takes into account different functions corresponding to different sizes of feasible region. In addition, an adaptive penalty function method is employed, which adaptively adjust the penalty coefficient so as to guarantee a moderate penalty. By solving 11 benchmark test functions and two engineering problems, experiment results indicate that the proposed method is reliable and efficient for solving constrained optimization problems. Also, it has great potential in handling many engineering problems with constraints, even with equations.

An improved AEA algorithm with Harmony Search(HSAEA) and its application in reaction kinetic parameter estimation

Alopex-based evolutionary algorithm (AEA) is one kind of evolutionary algorithm. It possesses the basic characteristics of evolutionary algorithms as well as the advantages of gradient descent methods and simulation anneal algorithm, but it is also easy to trap into a local optimum. For the AEA algorithm, the unreasonably settings of compared population and step length are two typical drawbacks, which lead to the lack of communication between individuals in each generation. In this paper, estimation of distribution algorithm (EDA) is employed to generate the compared population. Then the moving step length in AEA is improved to vary with different phases of the iteration during the actual operation process. And more importantly, harmony search algorithm (HS) is introduced to improve the quality of population of every generation. By compared with original AEA, the performance of the improved algorithm (HSAEA) was tested on 22 unconstrained benchmark functions. The testing results show that HSAEA clearly outperforms original AEA for almost all the benchmark functions. Furthermore, HSAEA is used to estimate reaction kinetic parameters for a heavy oil thermal cracking three lumps model and Homogeneous mercury (Hg) oxidation, and satisfactory results are obtained.

A new improved Alopex-based evolutionary algorithm and its application to parameter estimation

In this work, focusing on the demerit of AEA (Alopex-based evolutionary algorithm) algorithm, an improved AEA algorithm (AEA-C) which was fused AEA with clonal selection algorithm was proposed. Considering the irrationality of the method that generated candidate solutions at each iteration of AEA, clonal selection algorithm could be applied to improve the method. The performance of the proposed new algorithm was studied by using 22 benchmark functions and was compared with original AEA given the same conditions. The experimental results show that the AEA-C clearly outperforms the original AEA for almost all the 22 benchmark functions with 10, 30, 50 dimensions in success rates, solution quality and stability. Furthermore, AEA-C was applied to estimate 6 kinetics parameters of the fermentation dynamics models. The standard deviation of the objective function calculated by the AEA-C is 41.46 and is far less than that of other literatures’ results, and the fitting curves obtained by AEA-C are more in line with the actual fermentation process curves.

Alopex-based evolutionary algorithm and its application to reaction kinetic parameter estimation

In this paper, a novel Alopex-based evolutionary algorithm (AEA) is proposed, whose distinguished features are stochastic selection and self-adaptive evolutionary computation. The AEA not only inherits the primary characteristics of basic evolutionary algorithms (EAs), but also possesses the merits of gradient methods and simulated annealing algorithm. It can efficiently maintain the population diversity and improve the capabilities of escaping from local optima. The numerical simulation results of 22 benchmark functions demonstrate that the performance of the proposed AEA is superior to that of the basic EAs. Finally, the new algorithm is applied to estimate the kinetic parameters of 2-chlorophenol oxidation of supercritical water. The promising results illustrate the efficiency of the proposed method and show that it could be used as a reliable tool for engineering applications.