Robust Evolutionary Optimization Research Articles

A multi-objective robust evolutionary optimization approach applied to the multivariate helical milling process of super duplex steel

This work presents an approach for multivariate modeling and multi-objective robust evolutionary optimization for processes presenting as inputs control and noise variables and as outputs a set of correlated responses regarding process performance and product quality. Factor analysis is applied to obtain a transformed output set that is uncorrelated and retains most part of the information of the original outputs. Models that are robust regarding noise variables relating this transformed output set with the control variables are obtained through robust parameter design. Response models in the function of process and noise variables are obtained through the least squares method. Mean and variance models as a function of process variables are obtained through error propagation. Robust mean square error models are obtained to model the bias and variance of each latent variable. Finally, multi-objective evolutionary optimization is performed. Three evolutionary algorithms were applied and compared through hypervolume. The approach is applied in the helical milling of super duplex stainless steel UNS S32760. Tool overhang length, hole depth, and lubri-cooling flow rate were set as noise factors. Cutting forces were monitored, while roughness and roundness were measured to evaluate process performance and product quality. The three factors, obtained to represent the six outputs, guaranteed dimensionality reduction and minimized the redundancy in output space. The mean square error models obtained to these three factors as a function of control variables minimize both bias and variance regarding noise factors. The AGE-MOEA multi-objective evolutionary algorithm obtained the best performance considering the hypervolume. Some solutions with high trade-off were selected through pseudo-weights to aid the decision-making.

Parameter estimation in non-linear chemical processes: an opposite point-based differential evolution (OPDE) approach

Abstract In recent years, evolutionary algorithms have been gaining popularity for finding optimal solutions to non-linear multimodal problems encountered in many engineering disciplines. Differential evolution (DE), an evolutionary algorithm, is a novel optimization method capable of handling nondifferentiable, non-linear, and multimodal objective functions. DE is an efficient, effective, and robust evolutionary optimization method. Still, DE takes large computational time to optimize the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This paper introduces a modification to the original DE that enhances the convergence rate without compromising solution quality. The proposed opposite point-based differential evolution (OPDE) algorithm utilizes opposite point-based population initialization, in addition to random initialization. Such an improvement reduces computational effort. The OPDE has been applied to benchmark test functions and high-dimensional non-linear chemical engineering problems. The proposed method of population initialization accelerates the convergence speed of DE, as indicated by the results obtained using benchmark test functions and non-linear chemical engineering problems.

Convex-hull based robust evolutionary optimization approach for ROC maximization under label noise

Convex-hull based receiver operating characteristic (ROC) maximization has become a hot research topic due to its significance in the study of imbalance binary classification. Recently, a series of multi-objective evolutionary algorithms (MOEAs) have been proposed to maximize ROC convex hull by regarding it as a multi-objective optimization problem. However, in real applications, the ubiquitous label noises degrade the performance of the existing MOEAs. To address this issue, in this paper, we propose a robust evolutionary optimization approach, named REO, to enhance the robustness of the existing MOEAs. In the proposed approach, we firstly design a distance-based samples selection method to extract a “clean” data subset, aiming to obtain an ideal individual. Second, with the ideal individual, a problem-oriented two-stage adaptive updating strategy is designed to guide the population evolution and enhance the robustness of MOEAs. Specifically, in the first stage, based on the achieved ideal individual, a bi-level evolution direction is constructed to provide the guidance for the evolution of population. In the second stage, we utilize the cosine similarity to assign different step sizes to adaptively update the inferior individuals. Experimental results on 19 complicated datasets with different noise levels show that the proposed REO approach can effectively enhance the robustness of the existing MOEAs for ROC convex hull maximization under the label noises.

PGFLibPy: An Open-Source Parallel Python Toolbox for Genetic Folding Algorithm

Genetic folding (GF) is a robust evolutionary optimization algorithm. For efficient hyper-scale GFs, a hybrid parallel approach based on CPU architecture Parallel GF (PGF) is proposed. It aids in resolving kernel tricks that are difficult to predict using conventional optimization approaches. The regression and classification problems are solved using PGF. Four concurrent CPUs are formed to parallelize the GF, and each executes eight threads. It is also easily scalable to multi-core CPUs. PGFLibPy is a Python-based machine learning framework for classification and regression problems. PGFLibPy was used to build a model of the UCI dataset that reliably predicts regression values. The toolbox activity is used for binary and multiclassification datasets to classify UCI. PGFLibPy’s has 25 Python files and 18 datasets. Dask parallel implementation is being considered in the toolbox. According to this study, this toolbox can categorize and predict models on any other dataset. The source code, binaries, and dataset are available for download at https://github.com/mohabedalgani/PGFLibPy.

Multi-objective robust evolutionary optimization of the boring process of AISI 4130 steel

Boring is widely applied to enlarge holes. The high L/D ratio of boring bars enables self-excited vibration, deteriorating the quality of the hole. Therefore, this work aims the multi-objective evolutionary robust optimization of the boring process. Robust parameter design is employed to achieve robust models for roughness and roundness concerning tool overhang length and borehole depth, set as noise variables. These models aid the attainment of control factors’ levels, i.e., feed, cutting speed, and fixture position, which turn the responses less sensitive to noise. The robust models together with the material removal rate deterministic model are optimized through evolutionary multi-objective methods. The effects of process and noise factors are discussed considering literature. The multi-objective evolutionary optimization of the robust models helps to achieve these robust levels of process factors besides balancing the trade-off between the outcomes. The multi-objective robust evolutionary results outperform the scalarization approach considered for comparison purposes.

Introducing Robust Evolutionary Optimization in Noisy Fractional-Order Systems

This paper investigates the problem of searching for the robust initial values of noisy fractional-order chaotic systems when the desired output is given. The problem is addressed under the framework of robust evolutionary optimization. Two different ways of adding noise are considered: (1) the noise is added to the initial point; (2) the noise is added to the orbit of the system. A series of experiments are conducted to validate the effectiveness of robust evolutionary optimization. The experimental results reveal that robust initial values of noisy fractional-order chaotic systems can be obtained in an efficient way by introducing robust evolutionary optimization.

Robust evolutionary shape optimization for ergonomic excellence based on contact pressure distribution

The aim of this paper is the development of a robust evolutionary shape optimization procedure for ergonomic excellence based on contact pressure distribution. FEM - based numerical analysis is implemented to obtain the resulting contact pressure distribution. An example of person-seat interaction is analysed in this paper since plenty of experimental data set exists on this topic. A simplified geometrical model of the human body and seat is used and partly parameterized using a generic B-spline surface. The impact of the changes in geometry on the pressure distribution is analysed by the optimizer, and the seat geometry is steered into a shape with minimal high contact pressure areas. The procedure is general and can be adapted (with changes in geometry and boundary conditions) to distinct ergonomic problems such as footwear, therapeutic beds, automotive or aeronautical seating. The developed procedure can aid in virtual testing during the seat development phase in cases when the seat is designed for a selected population or for a single person and expected postural variations.

Optimization of Dynamic Systems: A Comparative Study of Two Modified Differential Evolution Algorithms

Differential Evolution (DE) is a novel, efficient, effective and robust evolutionary optimization technique. DE algorithm is gaining popularity for solving complex optimization problems encountered in many engineering disciplines. This paper deals with the application and performance evaluation of two modified versions of DE [named as Modified Differential Evolution (MDE) and Trigonometric Differential Evolution (TDE)]. Three algorithms have been used for solving five dynamic optimization problems encountered in chemical engineering. Results indicate that MDE algorithm outperformed DE and TDE algorithms for solving problems with small number of control stages. But TDE algorithm is found to be faster and efficient than MDE and DE algorithms particularly for problems involving large number of control stages.

A local mesh free numerical method with automatic parameter optimization

The concern of the paper is a local mesh free numerical method, implemented with automatic optimization of the discretization parameters, to solve problems of two-dimensional linear elasticity.For a nodal discretization, the mesh free local method uses a node-by-node process to generate the global system of equilibrium equations; in the local domain of each node, the respective equilibrium equations are generated with a reduced numerical integration and used as the formulation basis of the numerical method.Application of the local numerical method, to each node of a mesh free discretization, requires the use of two arbitrary parameters which specify the size of, respectively the compact support and the local domain of integration. In this paper, these parameters are automatically defined by means of a multi-objective optimization process, based on genetic algorithms, which is the novelty of the present numerical method. For the sake of efficiency a comparison between genetic algorithms and another robust evolutionary optimization method, the symbiotic organism search algorithm, is carried out.A benchmark problem was analyzed to assess the accuracy and efficiency of these techniques. The results presented in the paper are in perfect agreement with those of analytical solutions and therefore, make reliable and robust this mesh free numerical method, implemented with automatic parameter optimization.

Global Robust Control Model of Friction Stir Welding of Aluminum Alloy Based on Main Motor Power Output Prediction

Aiming at the softening problem of 7075 superhard aluminium welded joints such as hot cracks and gas holes in traditional fusion welding process, a dynamic robust control model based on the relationship between friction stir welding process parameters and welded joint strength is established. According to the non-linear relationship between global motion estimation and welded strength parameters, a dynamic robust control model of stirring needle motion is established, and the physical parameters such as elongation after fracture, tensile strength and hardness are calculated. A robust dynamic evolutionary optimization model of welding process parameters is established in the future to realize real-time optimization control of process parameters. On the basis of global motion control, the electric power output of the friction stir welding main motor is predicted according to the required line energy input of the stirring needle motion characteristics, and the real-time optimal control method of the motor electric power based on the expected thermal energy input of the welding process is established. A series of strength tests of welded joints based on the model show that the predicted results of the model can meet the needs of engineering and have practical value in engineering.

High-Dimensional Robust Multi-Objective Optimization for Order Scheduling: A Decision Variable Classification Approach

This paper tackles the high-dimensional robust order scheduling problem. A multi-objective evolutionary algorithm called constrained nondominated sorting differential evolution based on decision variable classification is developed to search for robust order schedules. The decision variables are classified into highly and weakly robustness-related variables according to their contributions to the robustness of candidate solutions. The experimental results reveal that the performance of robust evolutionary optimization can be greatly improved via analyzing the properties of decision variables and then decomposing the high-dimensional robust optimization problem. It is also unveiled that the order scheduling is greatly affected by the uncertain daily production quantities. The robust order schedules are able to provide more information on earliness/tardiness of the orders, which enhances the flexibility of the production.

Reservoir operation using a robust evolutionary optimization algorithm

In this research, a significant improvement in reservoir operation was achieved using a state-of-the-art evolutionary algorithm named Borg MOEA. A real-world multipurpose dam was used to test the algorithm's performance, and the target of the reservoir operation policy was to fulfil downstream water demands in drought condition while maintaining a sustainable quantity of water in the reservoir for the next year. The reservoir's performance was improved by increasing the maximum reservoir storage by 14.83 million m3. Furthermore, sustainable water storage in the reservoir was achieved for the next year, for the simulated low flow condition considered, while the total annual imbalance between the monthly reservoir releases and water demands was reduced by 64.7%. The algorithm converged quickly and reliably, and consistently good results were obtained. The methodology and results will be useful to decision makers and water managers for setting the policy to manage the reservoir efficiently and sustainably.

Enhanced lipase recovery through RSM integrated differential evolutionary approach from the fermented biomass

The aim of this work was to apply a modeling integrated optimisation approach for a complex, highly nonlinear system for an extracellular lipase extraction process. The model was developed using mutation, crossover and selection variables of Differential Evolution (DE) based on central composite design of Response Surface Methodology. The experimentally validated model was optimized by DE, a robust evolutionary optimization tool. A maximum lipase activity of 134.13 U/gds (more than 36.28 U/gds compared to one variable at a time approach) was observed with the DE-stated optimum values of 25.01% dimethyl sulfoxide concentration, 40 mM buffer, 128.52 min soaking time and 35oC with the DE control parameters, namely number of population, generations, crossover operator and scaling factor as 20, 50, 0.5 and 0.25, respectively. The use of DE approach improved the optimization capability and decision speed, resulting in an improved yield of 36.28 U/gds compared to the one variable at a time approach for the extracellular lipase activity under the non-optimized conditions. The developed mathematical model and optimization were generic in nature, which seemed to be useful for the scale-up studies of maximum recovery of lipase from the fermented biomass.

Novel Approach of Designing Multiplier-less Finite Impulse Response Filter using Differential Evolution Algorithm

Reduction of computational complexity of digital hardware has drawn the special attention of researchers in recent past. Proper emphasis is needed in this regard towards the settlement of computationally efficient as well as functionally competent design of digital systems. In this communication, we have made one novel attempt for designing multiplier-free Finite duration Impulse Response (FIR) digital filter using one robust evolutionary optimization technique, called Differential Evolution (DE). The search has been directed through two sequentially opposite paths which include quantization and optimization as fundamental operations. Besides performing a detailed comparative analysis between these two proposed approaches; the performance evaluation of the designed filter with other existing discrete coefficient FIR models has also been carried out. Finally, the optimum search method for realizing the required set of specifications has been suggested.

Time-stamped resampling for robust evolutionary portfolio optimization

Traditional mean–variance financial portfolio optimization is based on two sets of parameters, estimates for the asset returns and the variance–covariance matrix. The allocations resulting from both traditional methods and heuristics are very dependent on these values. Given the unreliability of these forecasts, the expected risk and return for the portfolios in the efficient frontier often differ from the expected ones. In this work we present a resampling method based on time-stamping to control the problem. The approach, which is compatible with different evolutionary multiobjective algorithms, is tested with four different alternatives. We also introduce new metrics to assess the reliability of forecast efficient frontiers.

A strength Pareto evolutionary algorithm-based conflict assessment framework of electricity market participants' objectives in generation maintenance scheduling

SUMMARY Conflicts between independent system operators (ISOs) and power producers, each preferring the annual maintenance plans based on their own objectives, have resulted from power system restructuring. Therefore, the ISO needs to specify how much the producers are free to adjust their maintenance programs on their own, without violating reliability criteria. In this article, a conflict assessment framework is described to characterize the degree of conflict among the electricity market participants' (ISO and producers) objectives. Four steps, namely, information gathering, mathematical modeling of the objectives, conflict front discovery, and finally the sensitivity analysis, were proposed as the basic steps of the framework. In this way, a multiobjective optimization problem was introduced by which a set of compromise solutions, denoted as a Pareto-optimal front, can be found. To discover the front, the strength Pareto evolutionary algorithm was used as a robust evolutionary optimization technique. For the sensitivity analysis, two parameters, namely, the front curve relative change and its degree of linearity, were used. The proposed framework was tested on IEEE-RTS, and its capabilities were assessed and appreciated. Copyright © 2011 John Wiley & Sons, Ltd.

Application of a hybrid evolutionary technique for efficiency determination of a submersible induction motor

Electric motors are the largest consumers of electricity in plants and induction motors constitute nearly two-thirds of them. The replacement of in-service induction motors with more efficient ones is a very important strategy for energy savings and consequently nearly 30 different methods have been used to determine the efficiency of induction motors in the last 2 decades. This paper aims to develop the efficiency determination of a 20 Hp submersible induction motor. Due to getting perfect efficiency of the submersible induction motor, a robust hybrid evolutionary optimization technique, which consists of a genetic algorithm and simulated annealing, is used. The obtained results are compared with genetic algorithm and torque gauge result values and dramatically significant results of our proposed algorithm are observed.

An investigation on noise-induced features in robust evolutionary multi-objective optimization

Multi-objective (MO) optimization is a challenging research topic because it involves the simultaneous optimization of several complex and conflicting objectives that requires researchers to address many issues which are unique to MO problems. However multi-objectivity is only one aspect of real-world applications and there is a growing interest in the optimization of solutions that are insensitive to parametric variations as well. In order to evaluate the capability of MO evolutionary algorithms (MOEAs) to find robust solutions, it is important to employ suitable test functions. In this paper, empirical studies are conducted to examine the suitability of existing robust test functions. Results suggest that these test functions have a bias towards the region where the robust solutions lie, rendering it difficult to assess the true capability of MOEAs. Motivated by such a finding, we present a framework for the construction of robust continuous MO test functions characterized by different noise-induced features. These noise-induced features can pose different difficulties to the optimization algorithms. A fitness-inheritance scheme is also presented and incorporated into two well-known MOEAs. Empirical analysis of the proposed robust MO test functions reveals that some noise-induced features present greater challenges to robust MOEAs as compared to existing robust test functions. In addition, the vehicle routing problem with stochastic demand (VRPSD) is presented as a practical example of robust combinatorial MO optimization problems. The work presented in this paper should encourage further studies and the development of more effective algorithms for robust MO optimization.

Parallelization strategies for rapid and robust evolutionary multiobjective optimization in water resources applications

This study uses a formal metrics-based framework to demonstrate the Master–Slave (MS) and the Multiple-Population (MP) parallelization schemes for the Epsilon-Nondominated Sorted Genetic Algorithm-II ( ε-NSGAII). The MS and MP versions of the ε-NSGAII generalize the algorithm’s auto-adaptive population sizing, ε-dominance archiving, and time continuation to a distributed processor environment using the Message Passing Interface. This study uses three test cases to compare the MS and MP versions of the ε-NSGAII: (1) an extremely difficult benchmark test function termed DTLZ6 drawn from the computer science literature, (2) an unconstrained, continuous hydrologic model calibration test case for the Leaf River near Collins, Mississippi, and (3) a discrete, constrained four-objective long-term groundwater monitoring (LTM) application. The MP version of the ε-NSGAII is more effective than the MS scheme when solving DTLZ6. Both the Leaf River and the LTM test cases proved to be more appropriately suited to the MS version of the ε-NSGAII. Overall, the MS version of the ε-NSGAII exhibits superior performance on both of the water resources applications, especially when considering its simplicity and ease-of-implementation relative to the MP scheme. A key conclusion of this study is that a simple MS parallelization strategy can exploit time-continuation and parallel speedups to dramatically improve the efficiency and reliability of evolutionary multiobjective algorithms in water resources applications.

Modified differential evolution (MDE) for optimization of non-linear chemical processes

In recent years, evolutionary algorithms (EAs) are gaining popularity for finding the optimal solution of non-linear multimodal problems encountered in many engineering disciplines. Differential evolution (DE), one of the evolutionary algorithms, is a novel optimization method capable of handling nondifferentiable, non-linear and multimodal objective functions. Previous studies have shown that differential evolution is an efficient, effective and robust evolutionary optimization method. Still, DE takes large computational time for optimizing the computationally expensive objective functions. And therefore, an attempt to speed up DE is considered necessary. This paper introduces a modification to original DE that enhances the convergence rate without compromising on solution quality. Our modified differential evolution (MDE) algorithm utilizes only one set of population as against two sets in original DE at any given point of time in a generation. Such an improvement reduces the memory and computational efforts. The proposed MDE is applied to benchmark test functions and five non-linear chemical engineering problems. Results obtained are compared with those obtained using DE by considering the convergence history (CPU time and the number of runs converged to global optimum) and the established statistical techniques, taking into account the variability in the results, such as t-test. As compared to DE, MDE is found to perform better in locating the global optimal solution for all the problems considered.