Multi-objective Differential Evolution Approach Research Articles

Multiobjective Differential Evolution for Feature Selection in Classification.

Feature selection aims to reduce the number of features and improve the classification accuracy, which is an essential step in many real-world problems. Multiple feature subsets with different features selected can achieve similar or even the same objective values (e.g., maximize the classification accuracy and minimize the number of selected features). This means the optimal feature subsets of a classification problem may not be unique. However, most existing feature selection methods do not take into consideration finding multiple optimal feature subsets. In this article, a multiobjective differential evolution approach is developed to search for multiple optimal feature subsets. The contributions are three-fold. First, to provide a good starting point, an initialization method considering feature relevance is proposed. Second, a clustering method is used to divide the whole population into multiple subpopulations. In each of these subpopulations, a subarchive utilizes a developed crowding distance to ensure diversity by considering both the search space and the objective space. Finally, the nondominated solutions from all the subarchives are retained in another archive to guide the evolutionary feature selection process, together with an improved hypervolume contribution indicator. The experiments on 14 datasets of varying difficulty show that the proposed approach can evolve a better Pareto front of feature subsets compared with seven other state-of-the-art methods as well as find different feature subsets with similar or the same classification performance.

Feature Selection Using Diversity-Based Multi-objective Binary Differential Evolution

By identifying relevant features from the original data, feature selection methods can maintain or improve the classification accuracy and reduce the dimensionality. Recently, many multi-objective evolutionary methods have been proposed for feature selection. However, effectively handling the trade-offs between convergence and diversity of the non-dominated solutions remains a major challenge, especially for high-dimensional datasets. To cover this issue, this work studies a diversity-based multi-objective differential evolution approach to feature selection. During the environmental selection process, each of the solutions in the candidate pool will have a diversity score, and solutions with large diversity score values will be preferred so as to improve the population diversity. To reduce the search space, irrelevant and weakly relevant features are detected and removed in the proposed method. A new binary mutation operator using the neighborhood information of individuals is also proposed, aiming to produce better feature subsets. Experimental results on 14 datasets with varying difficulties show that the proposed feature selection method can obtain significantly better feature selection performance than current popular multi-objective feature selection methods.

Multiobjective Differential Evolution with Discrete Elite Guide in Internet of Vehicles Roadside Unit Deployment

In a vehicular ad hoc network (VANET), roadside units (RSUs) are installed at roadside and intersections to process vehicle-to-infrastructure communication, collect and analyse intelligent vehicle traffic data, send information to vehicles, and achieve early warning of safe driving of vehicles. Owning to the high cost of implementing and maintaining RSUs, it is of vital importance to determine where and how many RSUs to deploy. Optimal RSU deployment requires both a small number of RSUs and the maximum coverage of vehicle running process, which constitutes a conflicting multiobjective problem. Nevertheless, existing works do not explicitly utilize multiobjective algorithm to solve the RSU deployment problem. Therefore, a multiobjective differential evolution approach is proposed in this work to solve the problem. Firstly, to conquer the complexity of urban road RSU deployment, the static model is established. Secondly, in the proposed multiobjective differential evolution with discrete elitist guide (MODE-deg), the sigmoid function is applied to discrete individual values. Finally, elitist individuals are selected based on crowding distance ranking and nondominated ranking to generate new individuals, which further improve the convergence speed and population performance. Experimental results show that MODE-deg can generate the optimal nondominant solution set with good convergence and diversity, in contrast to other multiobjective evolutionary algorithms in five test functions of ZDT.

An efficient generalised opposition-based multi-objective optimisation method for factory cranes with time-space constraints

In order to improve the performance of large manufacturing enterprises, besides the adoption of new technologies, it is also feasible to efficiently schedule logistics equipment such as cranes, which costs much less since only software changes are involved. In this research, the objectives of minimising total waiting cost and total delay cost are optimised simultaneously when executing crane-delivery tasks in factories. Given the time-space constraints and NP-hard nature of the problem, a generalised opposition-based learning (GOBL) mechanism and two problem-based searching strategies are developed and fused into the multi-objective differential evolution approach, namely GOMODE. The introduction of GOBL mechanism enables the proposed algorithm to search in a more extensive solution space, which improves the population diversity and avoids the premature problem. The performance of the GOMODE has been compared with classical multi-objective optimisation algorithms. The experimental results indicate that the GOMODE achieves a better performance both on solutions' quality and diversity. [Received: 11 December 2018; Accepted: 23 December 2019]

An efficient generalised opposition-based multi-objective optimisation method for factory cranes with time-space constraints

In order to improve the performance of large manufacturing enterprises, besides the adoption of new technologies, it is also feasible to efficiently schedule logistics equipment such as cranes, which costs much less since only software changes are involved. In this research, the objectives of minimising total waiting cost and total delay cost are optimised simultaneously when executing crane-delivery tasks in factories. Given the time-space constraints and NP-hard nature of the problem, a generalised opposition-based learning (GOBL) mechanism and two problem-based searching strategies are developed and fused into the multi-objective differential evolution approach, namely GOMODE. The introduction of GOBL mechanism enables the proposed algorithm to search in a more extensive solution space, which improves the population diversity and avoids the premature problem. The performance of the GOMODE has been compared with classical multi-objective optimisation algorithms. The experimental results indicate that the GOMODE achieves a better performance both on solutions' quality and diversity. [Received: 11 December 2018; Accepted: 23 December 2019]

A new multi-objective differential evolution approach for simultaneous clustering and feature selection

Today’s real-world data mostly involves incomplete, inconsistent, and/or irrelevant information that causes many drawbacks to transform it into an understandable format. In order to deal with such issues, data preprocessing is a proven discipline in data mining. One of the typical tasks in data preprocessing, feature selection aims to reduce the dimensionality in the data and thereby contributes to further processing. Feature selection is widely used to enhance the performance of a supervised learning algorithm (e.g., classification) but is rarely used in unsupervised tasks (e.g., clustering). This paper introduces a new multi-objective differential evolution approach in order to find relatively homogeneous clusters without the prior knowledge of cluster number using a smaller number of features from all available features in the data. To analyze the goodness of the introduced approach, several experiments are conducted on a various number of real-world and synthetic benchmarks using a variety of clustering approaches. From the analyzes through several different criteria, it is suggested that our method can significantly improve the clustering performance while reducing the dimensionality at the same time.

Automatic Scientific Document Clustering Using Self-organized Multi-objective Differential Evolution

Document clustering is the partitioning of a given collection of documents into various K- groups based on some similarity/dissimilarity criterion. This task has applications in scope detection of journals/conferences, development of some automated peer-review support systems, topic-modeling, latest cognitive-inspired works on text summarization, and classification of documents based on semantics, etc. In the current paper, a cognitive-inspired multi-objective automatic document clustering technique is proposed which is a fusion of self-organizing map (SOM) and multi-objective differential evolution approach. The variable number of cluster centers are encoded in different solutions of the population to determine the number of clusters from a data set in an automated way. These solutions undergo various genetic operations during evolution. The concept of SOM is utilized in designing new genetic operators for the proposed clustering technique. In order to measure the goodness of a clustering solution, two cluster validity indices, Pakhira-Bandyopadhyay-Maulik index, and Silhouette index, are optimized simultaneously. The effectiveness of the proposed approach, namely self-organizing map based multi-objective document clustering technique (SMODoc_clust) is shown in automatic classification of some scientific articles and web-documents. Different representation schemas including tf, tf-idf and word-embedding are employed to convert articles in vector-forms. Comparative results with respect to internal cluster validity indices, namely, Dunn index and Davies-Bouldin index, are shown against several state-of-the-art clustering techniques including three multi-objective clustering techniques namely MOCK, VAMOSA, NSGA-II-Clust, single objective genetic algorithm (SOGA) based clustering technique, K-means, and single-linkage clustering. Results obtained clearly show that our approach is better than existing approaches. The validation of the obtained results is also shown using statistical significant t tests.

Harmonic multi-objective differential evolution approach for multi-objective optimization of fed-batch bioreactor

ABSTRACTLysine as one of the essential amino acids is often used as a chemical agent, medicament, food material, and human and animals feed additive. Microbial fermentation is one of the most economical processes to produce lysine. Batch or fed-batch fermentation processes are often used to produce lysine. The use of fed-batch operation improves the productivity, reduces the fermentation time, and increases the yield of the reaction. Using a mathematical modeling approach, it is possible to obtain a deeper insight of biochemical-based processes. In this manuscript, an optimal feeding profile for fed-batch bioreactor is obtained for the multi-objective optimization (MOO) of conflicting objectives, i.e., the yield (with two different expressions) and the productivity. MODE-III and Harmonic MODE algorithms are used for the MOO study. Pareto optimal fronts are also reported for constant feeding rate, singular feeding rates, and for the different feeding rates in a given range. With the increase in the value of the feed rate, the productivity increases while the yield decreases. Both versions of the MODE algorithm result in the smooth Pareto front; however, the Harmonic MODE algorithm results in a good and diverse set of solutions.

Design optimization of ferrite assisted synchronous reluctance motor using multi-objective differential evolution algorithm

PurposeThe purpose of this paper is performance enhancement of ferrite-assisted synchronous reluctance (FASR) motor using multi-objective differential evolution (MODE) algorithm, considering the significant geometric design parameters.Design/methodology/approachThis work illustrates the optimization of FASR motor using MODE algorithm to enhance the performance of the motor considering barrier angular positions, magnet height, magnet axial length, flux barrier angles of the rotor and air gap length. In the optimization routine to determine the performance parameters, generalized regression neural network-based interpolation is used. The results of MODE are validated with multi-objective particle swarm optimization algorithm and multi-objective genetic algorithm.FindingsThe design optimization procedure developed in this work for FASR motor aims at achieving multiple objectives, namely, average torque, torque ripple and efficiency. With multiple objectives, it is essential to give the designer the tradeoff between different objectives so as to arrive at the best design suitable for the application. The results obtained in this work justify the application of the MODE approach for FASR motor to determine the various feasible solutions within the bounds of the design.Research limitations/implicationsAnalysis, design and optimization of synchronous reluctance motor has been explored in detail to establish its potential for variable speed applications. In recent years, the focus is toward the electromagnetic design of hybrid configurations such as FASR motor. It is in this preview this work aims to achieve optimal design of FASR motor using multi-objective optimization approach.Practical/implicationsThe results of this work will supplement and encourage the application of FASR motor as a viable alternate for variable speed drive applications. In addition, the application of MODE to arrive at better design solutions is demonstrated.Originality/valueThe approach presented in this work focuses on obtaining enhanced design of FASR motor considering average torque, torque ripple and efficiency as performance measures. The posteriori analysis of optimization provides an insight into the choice of parameters involved and their effects on the design of FASR motor. The efficacy of the optimization routine is justified in comparison with other multi-objective algorithms.

A multi-objective differential evolution approach based on ε-elimination uniform-diversity for mechanism design

In this paper, a new multi-objective uniform-diversity differential evolution (MUDE) algorithm is proposed and used for Pareto optimum design of mechanisms. The proposed algorithm uses a diversity preserving mechanism called the ?-elimination algorithm to improve the population diversity among the obtained Pareto front. The proposed algorithm is firstly tested on some constrained and unconstrained benchmarks proposed for the special session and competition on multi-objective optimizers held under IEEE CEC 2009. The inverted generational distance (IGD) measure is used to assess the performance of the algorithm. Secondly, the proposed algorithm has been used for multi-objective optimization of two different combinatorial case studies. The first case contains a two-degree of freedom leg mechanism with springs. Three conflicting objective functions that have been considered for Pareto optimization are namely, leg size, vertical actuating force, and the peak crank torque. The second case is a two-finger robot gripper mechanism with two conflicting objectives which are the difference between the maximum and minimum gripping force and the transmission ratio of actuated and experienced gripper forces. Comparisons of obtained Pareto fronts using the method of this work with those obtained in other references show significant improvements.

Multi Objective Differential Evolution approach for voltage stability constrained reactive power planning problem

This paper presents the application of Multi Objective Differential Evolution (MODE) algorithm to solve the Voltage Stability Constrained Reactive Power Planning (VSCRPP) problem. Minimization of total cost of energy loss and reactive power production cost of capacitors and maximization of voltage stability margin are taken as the objectives in the Reactive Power Planning (RPP) problem. The L-index of the load buses is taken as the indicator of voltage stability. In the proposed approach, generator bus voltage magnitudes, transformer tap settings and reactive power generation of capacitor bank are taken as the control variables and are represented as the combination of floating point numbers and integers. The MODE emphasizes the non dominated solutions and simultaneously maintains diversity in the non dominated solutions. DE/randSF/1/bin strategy scheme of Differential Evolution with self tuned parameter which employs binomial crossover and difference vector based mutation is used for the VSCRPP problem. A fuzzy based mechanism is employed to get the best compromise solution from the pareto front to aid the decision maker. The proposed reactive power planning model is implemented on two test systems, IEEE 30 bus and IEEE 57 bus test systems. The simulation results of the proposed optimization approach show that MODE is better in maintaining diversity and optimality of solutions.

Multiobjective optimization design of concentric ring arrays with 3D beam scanning using differential evolution algorithm

AbstractThis paper presents a multiobjective differential evolution (MODE) algorithm for designing concentric ring arrays with three‐dimensional (3D) beam scanning. The problem formulation of the concentric ring arrays with 3D beam scanning based on the optimization of the array geometry is a constrained multiobjective optimization problem. To obtain 3D beam scanning, concentric ring array geometries are optimized. The design tradeoffs, namely, the directivity, peak sidelobe level, and the total number of elements of the concentric ring array, are captured by using MODE. MODE adopts an external archive to retain nondominated solutions that are found during the evolutionary process. The method yields the distribution of the objective function values and the corresponding array configurations. In addition, the nondominated sorting genetic algorithm‐II (NSGA‐II), which is a well‐known multiobjective evolutionary algorithm, is also employed to optimize the proposed problems. The comparison with the results of NSGA‐II reveals the superiority of the MODE approach and confirms its potential for the array synthesis problems. Copyright © 2012 John Wiley & Sons, Ltd.

Environmental/economic power dispatch problem using multi-objective differential evolution algorithm

This paper presents a multi-objective differential evolution (MODE) algorithm for environmental/economic power dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multi-objective problem with competing and non-commensurable objectives of fuel cost, emission and system loss. The proposed MODE approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed approach have been carried out on the IEEE 30- and 118-bus test system. The results demonstrate the capability of the proposed MODE approach to generate well-distributed Pareto optimal non-dominated solutions of multi-objective EED problem. The comparison with reported results of other MOEAs reveals the superiority of the proposed MODE approach and confirms its potential for solving other power systems multi-objective optimization problems.

Multi-objective balancing of assembly lines by population heuristics

This paper is concerned with the solution of the multi-objective single-model deterministic assembly line balancing problem (ALBP). Two bi-criteria objectives are considered: 1. Minimising the cycle time of the assembly line and the balance delay time of the workstations. 2. Minimising the cycle time and the smoothness index of the workload of the line. A new population heuristic is proposed to solve the problem based on the general differential evolution (DE) method. The main characteristics of the proposed multi-objective DE (MODE) heuristic are: a. It formulates the cost function of each individual ALB solution as a weighted-sum of multiple objectives functions with self-adapted weights. b. It maintains a separate population with diverse Pareto-optimal solutions. c. It injects the actual evolving population with some Pareto-optimal solutions. d. It uses a new modified scheme for the creation of the mutant vectors. Moreover, special representation and encoding schemes are developed and discussed which adapt MODE on ALBPs. The efficiency of MODE is measured over known ALB benchmarks taken from the open literature and compared to that of two other previously proposed population heuristics, namely, a weighted-sum Pareto genetic algorithm (GA), and a Pareto-niched GA. The experimental comparisons showed a promising high quality performance for MODE approach.