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The purpose of this paper is to design an improved multi-objective algorithm with better spread and convergence than some current algorithms. The proposed application is for engineering design problems.

This study proposes two novel approaches which focus on faster convergence to the Pareto front (PF) while adopting the advantages of Strength Pareto Evolutionary Algorithm-2 (SPEA2) for better spread. In first method, decision variables corresponding to the optima of individual objective functions (Utopia Point) are strategically used to guide the search toward PF. In second method, boundary points of the PF are calculated and their decision variables are seeded to the initial population.

The proposed methods are tested with a wide range of constrained and unconstrained multi-objective test functions using standard performance metrics. Performance evaluation demonstrates the superiority of proposed algorithms over well-known existing algorithms (such as NSGA-II and SPEA2) and recent ones such as NSLS and E-NSGA-II in most of the benchmark functions. It is also tested on an engineering design problem and compared with a currently used algorithm.

The algorithms are intended to be used for practical engineering design problems which have many variables and conflicting objectives. A complex example of Welded Beam has been shown at the end of the paper.

The algorithm would be useful for many design problems and social/industrial problems with conflicting objectives.

This paper presents two novel hybrid algorithms involving SPEA2 based on: local search; and Utopia point directed search principles. This concept has not been investigated before.

The paper formulates a bi-objective mixed-integer nonlinear programming model, aimed at minimizing the total labor hours and the workload unfairness for the multi-skilled worker assignment problem in Seru production system (SPS).

Three approaches, namely epsilon-constraint method, non-dominated sorting genetic algorithm 2 (NSGA-II) and improved strength Pareto evolutionary algorithm (SPEA2), are designed for solving the problem.

Numerous experiments are performed to assess the applicability of the proposed model and evaluate the performance of algorithms. The merged Pareto-fronts obtained from both NSGA-II and SPEA2 were proposed as final solutions to provide useful information for decision-makers.

SPS has the flexibility to respond to the changing demand for small amount production of multiple varieties products. Assigning cross-trained workers to obtain flexibility has emerged as a major concern for the implementation of SPS. Most enterprises focus solely on measures of production efficiency, such as minimizing the total throughput time. Solutions based on optimizing efficiency measures alone can be unacceptable by workers who have high proficiency levels when they are achieved at the expense of the workers taking more workload. Therefore, study the tradeoff between production efficiency and fairness in the multi-skilled worker assignment problem is very important for SPS.

The study investigates a new mixed-integer programming model to optimize worker-to-seru assignment, batch-to-seru assignment and task-to-worker assignment in SPS. In order to solve the proposed problem, three problem-specific solution approaches are proposed.

The purpose of this paper is to address a multiobjective FAP (frequency assignment problem) formulation. More precisely, two conflicting objectives – the interference cost and the separation cost – are considered to characterize FAP as an MO (multiobjective optimization) problem.

The contribution to this specific telecommunication problem in a real scenario follows a recent approach, for which the authors have already accomplished some preliminary results. In this paper, a much more complete analysis is performed, including two well‐known algorithms (such as the NSGA‐II and SPEA2), with new results, new comparisons and statistical studies. More concretely, in this paper five different algorithms are presented and compared. The popular multiobjective algorithms, NSGA‐II and SPEA2, are compared against the Differential Evolution with Pareto Tournaments (DEPT) algorithm, the Greedy Multiobjective Variable Neighborhood Search (GMO‐VNS) algorithm and its variant Greedy Multiobjective Skewed Variable Neighborhood Search (GMO‐SVNS). Furthermore, the authors also contribute with a new design of multiobjective metaheuristic named Multiobjective Artificial Bee Colony (MO‐ABC) that is included in the comparison; it represents a new metaheuristic that the authors have developed to address FAP. The results were analyzed using two complementary indicators: the hypervolume indicator and the coverage relation. Two large‐scale real‐world mobile networks were used to validate the performance comparison made among several multiobjective metaheuristics.

The final results show that the multiobjective proposal is very competitive, clearly surpassing the results obtained by the well‐known multiobjective algorithms (NSGA‐II and SPEA2).

The paper provides a comparison among several multiobjective metaheuristics to solve FAP as a real‐life telecommunication engineering problem. A new multiobjective metaheuristic is also presented. Preliminary results were enhanced with two well‐known multiobjective algorithms. To the authors' knowledge, they have never been investigated for FAP.

In recent decades, development of effective methods for optimizing a set of conflicted objective functions has been absorbing an increasing interest from researchers. This refers to the essence of real-life engineering systems and complex natural mechanisms which are generally multi-modal, non-convex and multi-criterion. Until now, several deterministic and stochastic methods have been proposed to cope with such complex systems. Advanced soft computational methods such as evolutionary games (cooperative and non-cooperative), Pareto-based techniques, fuzzy evolutionary methods, cooperative bio-inspired algorithms and neuro-evolutionary systems have effectively come to the aid of researchers to build up efficient paradigms with application to vector optimization. The paper aims to discuss this issue.

A novel hybrid algorithm called synchronous self-learning Pareto strategy (SSLPS) is presented for the sake of vector optimization. The method is the ensemble of evolutionary algorithms (EA), swarm intelligence (SI), adaptive version of self-organizing map (CSOM) and a data shuffling mechanism. EA are powerful numerical optimization algorithms capable of finding a global extreme point over a wide exploration domain. SI techniques (the swarm of bees in our case) can improve both intensification and robustness of exploration. CSOM network is an unsupervised learning methodology which learns the characteristics of non-dominated solutions and, thus, enhances the quality of the Pareto front.

To prove the effectiveness of the proposed method, the authors engage a set of well-known benchmark functions and some well-known rival optimization methods. Additionally, SSLPS is employed for optimal design of shape memory alloy actuator as a nonlinear multi-modal real-world engineering problem. The experiments show the acceptable potential of SSLPS for handling both numerical and engineering multi-objective problems.

To the author’s best knowledge, the proposed algorithm is among the rare multi-objective methods which fosters the use of automated unsupervised learning for increasing the intensity of Pareto front (while preserving the diversity). Also, the research evaluates the power of hybridization of SI and EA for efficient search.

In the development of electromagnetic devices, multiobjective topology optimisation is effective to obtain diverse design candidates for production models. However, multiobjective topology optimisation has not widely been performed because it is difficult to obtain resultant shapes for engineering realisation due to large search spaces. The purpose of this paper is to present a new multiobjective topology optimisation method.

This paper presents a new multiobjective topology optimisation method in which the Immune Algorithm is modified for multiobjecrive optimisation and a shape modification process based on spatial filtering is employed.

The present method shows that better Pareto solutions can be found in comparison with the conventional methods.

A new effective multiobjective topology optimisation is presented. This method enables to diverse design candidates for production models.

One of the main components of multi-objective, and therefore, many-objective evolutionary algorithms, is the selection mechanism. It is responsible for performing two main tasks simultaneously. First, it has to promote convergence by selecting solutions which are as close as possible to the Pareto optimal set. And second, it has to promote diversity in the solution set provided. In the current work, an exhaustive study that involves the comparison of several selection mechanisms with different features is performed. Particularly, Pareto-based and indicator-based selection schemes, which belong to well-known multi-objective optimisers, are considered. The paper aims to discuss these issues.

Each of those mechanisms is incorporated into a common multi-objective evolutionary algorithm framework. The main goal of the study is to measure the diversity preserved by each of those selection methods when addressing many-objective optimisation problems. The Walking Fish Group test suite, a set of optimisation problems with a scalable number of objective functions, is taken into account to perform the experimental evaluation.

The computational results highlight that the the reference-point-based selection scheme of the Non-dominated Sorting Genetic Algorithm III and a modified version of the Non-dominated Sorting Genetic Algorithm II, where the crowding distance is replaced by the Euclidean distance, are able to provide the best performance, not only in terms of diversity preservation, but also in terms of convergence.

The performance provided by the use of the Euclidean distance as part of the selection scheme indicates this is a promising line of research and, to the best of the knowledge, it has not been investigated yet.

In this work, the multi-objective optimization shuffled complex evolution is proposed. The algorithm is based on the extension of shuffled complex evolution, by incorporating two classical operators into the original algorithm: the rank ordering and crowding distance. In order to accelerate the convergence process, a Local Search strategy based on the generation of potential candidates by using Latin Hypercube method is also proposed.

The multi-objective optimization shuffled complex evolution is used to accelerate the convergence process and to reduce the number of objective function evaluations.

In general, the proposed methodology was able to solve a classical mechanical engineering problem with different characteristics. From a statistical point of view, we demonstrated that differences may exist between the proposed methodology and other evolutionary strategies concerning two different metrics (convergence and diversity), for a class of benchmark functions (ZDT functions).

The development of a new numerical method to solve multi-objective optimization problems is the major contribution.

The purpose of this paper is to improve and to extend the use of original rank‐niche evolution strategy (RNES) algorithm to solve constrained and unconstrained multiobjective optimization problems.

A new mutation step size is developed for evolution strategy. A mixed ranking procedure is used to improve the quality of the fitness function. A self‐adaptive sharing radius is developed to save computational time. Four constraint‐treating methods are developed to solve constrained optimization problems. Two of them do not use penalty function approach.

The improved RNES algorithm finds better quality Pareto‐optimal solutions more efficiently than the previous version. For most test problems, the solutions obtained by improved RNES are better than, or at least can be compared with, results from other papers.

The application of any evolutionary algorithm to real structural optimization problems would face a problem of spending huge computational time. Some approximate analysis method needs to be incorporated with RNES to solve practical problems.

This paper provides an easier approach to find Pareto‐optimal solutions using an evolutionary algorithm. The algorithm can be used to solve both unconstrained and constrained problems.

The purpose of this paper is to improve the accuracy of the facial expression recognition by using genetic algorithm (GA) with an appropriate fitness evaluation function and Pareto optimization model with two new objective functions.

To achieve facial expression recognition with high accuracy, the Haar-like features representation approach and the bilateral filter are first used to preprocess the facial image. Second, the uniform local Gabor binary patterns are used to extract the facial feature so as to reduce the feature dimension. Third, an improved GA and Pareto optimization approach are used to select the optimal significant features. Fourth, the random forest classifier is chosen to achieve the feature classification. Subsequently, some comparative experiments are implemented. Finally, the conclusion is drawn and some future research topics are pointed out.

The experiment results show that the proposed facial expression recognition algorithm outperforms ones in the existing literature in terms of both the actuary and computational time.

The GA and Pareto optimization algorithm are combined to select the optimal significant feature. To improve the accuracy of the facial expression recognition, the GA is improved by adjusting an appropriate fitness evaluation function, and a new Pareto optimization model is proposed that contains two objective functions indicating the achievements in minimizing within-class variations and in maximizing between-class variations.

Although the multi-criteria technique analytic hierarchy process (AHP) has successfully been applied in many areas, either selecting or ranking alternatives or to derive priority vector (weights) for a set of criteria, there is a significant drawback in using this technique if the pairwise comparison matrix (PCM) has inconsistent comparisons, in other words, a consistency ratio (CR) above the value of 0.1, the final solution cannot be validated. Many studies have been developed to treat the inconsistency problem, but few of them tried to satisfy different quality measures, which are minimum inconsistency (fMI), the total number of adjusted pairwise comparisons (fNC), original rank preservation (fKT), minimum average weights adjustment (fWA) and finally, minimum L1 matrix norm between the original PCM and the adjusted PCM (fLM).

The approach is defined in four steps: first, the decision-maker should choose which quality measures she/he wishes to use, ranging from one to all quality measures. In the second step, the authors encode the PCM to be used in a many-objective optimization algorithm (MOOA), and each pairwise comparison can be adjusted individually. The authors generate consistent solutions from the obtained Pareto optimal front that carry the desired quality measures in the third step. Lastly, the decision-maker selects the most suitable solution for her/his problem. Remarkably, as the decision-maker can choose one (mono-objective), two (multi-objective), three or more (many-objectives) quality measures, not all MOOAs can handle or perform well in mono- or multi-objective problems. The unified non-sorting algorithm III (U-NSGA III) is the most appropriate MOOA for this type of scenario because it was specially designed to handle mono-, multi- and many-objective problems.

The use of two quality measures should not guarantee that the adjusted PCM is similar to the original PCM; hence, the decision-maker should consider using more quality measures if the objective is to preserve the original PCM characteristics.

For the first time, a many-objective approach reduces the CR to consistent levels with the ability to consider one or more quality measures and allows the decision-maker to adjust each pairwise comparison individually.