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The purpose of this paper is to extend a (μ/ρ, λ) evolution strategy to perform remarkably more globally and to detect as many solutions as possible close to the Pareto optimal front.

A C‐link cluster algorithm is used to group the parameter configurations of the current population into more or less independent clusters. Following this procedure, recombination (a classical operator of evolutionary strategies) is modified. Recombination within a cluster is performed with a higher probability than recombination of individuals coming from detached clusters.

It is shown that this new method ends up virtually always in the global solution of a multi‐modal test function. When applied to a real‐world application, several solutions very close to the front of Pareto optimal solutions are detected.

Stochastic optimization strategies need a very large number of function calls to exhibit their ability to reach very good local if not the global solution. Therefore, the application of such methods is still limited to problems where the forward solutions can be obtained with a reasonable computational effort.

The main improvement is the usage of approximate number of isolated clusters to dynamically update the size of the population in order to save computation time, to find the global solution with a higher probability and to use more than one objective function to cover a larger part of the Pareto optimal front.

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.

The goal of this study is to carry out multi‐objective optimization by considering minimization of surface roughness (Ra) and build time (T) in selective laser sintering (SLS) process, which are functions of “build orientation”. Evolutionary algorithms are applied for this purpose. The performance comparison of the optimizers is done based on statistical measures. In order to find truly optimal solutions, local search is proposed. An important task of decision making, i.e. the selection of one solution in the presence of multiple trade‐off solutions, is also addressed. Analysis of optimal solutions is done to gain insight into the problem behavior.

The minimization of Ra and T is done using two popular optimizers – multi‐objective genetic algorithm (non‐dominated sorting genetic algorithm (NSGA‐II)) and multi‐objective particle swarm optimizers (MOPSO). Standard measures from evolutionary computation – “hypervolume measure” and “attainment surface approximator” have been borrowed to compare the optimizers. Decision‐making schemes are proposed in this paper based on decision theory.

The objects are categorized into groups, which bear similarity in optimal solutions. NSGA‐II outperforms MOPSO. The similarity of spread and convergence patterns of NSGA‐II and MOPSO ensures that obtained solutions are (or are close to) Pareto‐optimal set. This is validated by local search. Based on the analysis of obtained solutions, general trends for optimal orientations (depending on the geometrical features) are found.

A novel and systematic way to address multi‐objective optimization decision‐making post‐optimal analysis is shown. Simulations utilize experimentally derived models for roughness and build time. A further step could be the experimental verification of findings provided in this study.

This study provides a thorough methodology to find optimal build orientations in SLS process. A route to decipher valuable problem information through post‐optimal analysis is shown. The principles adopted in this study are general and can be extended to other rapid prototyping (RP) processes and expected to find wide applicability.

This paper is a distinct departure from past studies in RP and demonstrates the concepts of multi‐objective optimization, decision‐making and related issues.

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.

Real-world applications in engineering and other fields usually involve simultaneous optimization of multiple objectives, which are generally non-commensurable and conflicting with each other. This paper aims to treat the transformer design optimization (TDO) as a multiobjective problem (MOP), to minimize the manufacturing cost and the total owing cost, taking into consideration design constraints.

To deal with this optimization problem, a new method is proposed that combines the unrestricted population-size evolutionary multiobjective optimization algorithm (UPS-EMOA) with differential evolution, also applying lognormal distribution for tuning the scale factor and the beta distribution to adjust the crossover rate (UPS-DELFBC). The proposed UPS-DELFBC is useful to maintain the adequate diversity in the population and avoid the premature convergence during the generational cycle. Numerical results using UPS-DELFBC applied to the transform design optimization of 160, 400 and 630 kVA are promising in terms of spacing and convergence criteria.

Numerical results using UPS-DELFBC applied to the transform design optimization of 160, 400 and 630 kVA are promising in terms of spacing and convergence criteria.

This paper develops a promising UPS-DELFBC approach to solve MOPs. The TDO problems for three different transformer specifications, with 160, 400 and 630 kVA, have been addressed in this paper. Optimization results show the potential and efficiency of the UPS-DELFBC to solve multiobjective TDO and to produce multiple Pareto solutions.

The purpose of this paper is to present a modified version of the non-dominated sorted genetic algorithm with an application in the design optimization of a power inductor for magneto-fluid hyperthermia (MFH).

The proposed evolutionary algorithm is a modified version of migration-non-dominated sorting genetic algorithms (M-NSGA) that now includes the self-adaption of migration events- non-dominated sorting genetic algorithms (SA-M-NSGA). Moreover, a criterion based on the evolution of the approximated Pareto front has been activated for the automatic stop of the computation. Numerical experiments have been based on both an analytical benchmark and a real-life case study; the latter, which deals with the design of a class of power inductors for tests of MFH, is characterized by finite element analysis of the magnetic field.

The SA-M-NSGA substantially varies the genetic heritage of the population during the optimization process and allows for a faster convergence.

The proposed SA-M-NSGA is able to find a wider Pareto front with a computational effort comparable to a standard NSGA-II implementation.

The fatigue, thermal and wear-based bearing lives are the most important factors in the design of spherical roller bearings (SRBs). The main novelty of the present work is consideration of thermal effects as an additional objective function. The dynamic capacity (Cd), the elasto-hydrodynamic minimum film thickness (h_min) and the maximum bearing temperature (T_max) are related directly with overall lives of the bearing, and these constitute the multiple tasking operating requirements for the design of bearings.

These tasks depend upon various bearing design variables and associated constraints to help in formulating the realistic design optimization problem and in the present work these have been used to get optimal designs of SRBs in the form of Pareto-optimum fronts by using genetic algorithms.

The optimized lives show higher values as compared to the standard lives and better design choices as compared to that are available in the literature. The robustness of obtained designs are shown by conducting the sensitivity analysis of optimized operating requirements by perturbing optimum bearing variables.

The robustness of the design could be improved by optimizing tolerances of design variables based on desired variation in multiple tasking operating requirements.

For the aerospace and space applications such critical design of bearings are required based on multiple tasking operating requirements. For example for higher temperature application in gearboxes, turbines and drilling equipment.

In critical applications, multiple tasking operating requirements are essential and often bearings put limit to the life of satellites and aircraft, and bearing design methodology proposed and implemented in the present paper addresses these issues, especially addition of thermal issue in bearing design.

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize an objective vector into a single objective by a weight vector. In these cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands a user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto‐optimal points, instead of a single point. In this paper, Pareto‐based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. These algorithms are based on Continuous Evolutionary Algorithms, which were developed by the authors to solve single‐objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche‐formation method for fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Pareto‐optimal tradeoff surface. Finally, the validity of this method has been demonstrated through some numerical examples.

This paper presents a methodology based on Multiobjective Genetic Algorithms (MOGAs) for the design of electrical engineering systems. MOGAs allow one to optimize multiple heterogeneous criteria in complex systems, but also simplify couplings and sensitivity analysis by determining the evolution of design variables along the Pareto‐optimal front.

To illustrate the use of MOGAs in electrical engineering, the optimal design of an electromechanical system has been investigated. A rather simplified case study dealing with the optimal dimensioning of an inverter – permanent magnet motor – reducer – load association is carried out to demonstrate the interest of the approach. The purpose is to simultaneously minimize two objectives: the global losses and the mass of the system. The system model is described by analytical model and we use the MOGA called NSGA‐II.

From the extraction of Pareto‐optimal solutions, MOGAs facilitate the investigation of parametric sensitivity and the analysis of couplings in the system. Through a simple but typical academic problem dealing with the optimal dimensioning of a inverter – permanent magnet motor – reducer – load association, it has been shown that this multiobjective a posteriori approach could offer interesting outlooks in the global optimization and design of complex heterogeneous systems. The final choice between all Pareto‐optimal configurations can be a posteriori done in relation to other issues which have not been considered in the optimization process. In this paper, we illustrate this point by considering the cogging torque for the final decision.

We have proposed an original quantitative methodology based on correlation coefficients to characterize the system interactions.

This study aims to propose a complete and powerful methodology that allows the optimization of the passive suspension system of vehicles, which simultaneously takes comfort and safety into account and provides a set of optimal solutions through a Pareto-optimal front, in a low computational time.

Unlike papers that consider simple vehicle models (quarter vehicle model or half car model) and/or simplified road profiles (harmonic excitation, for example) and/or perform a single-objective optimization and/or execute the dynamic analysis in the time domain, this paper presents an effective and fast methodology for the multi-objective optimization of the suspension system of a full-car model (including the driver seat) traveling on an irregular road profile, whose dynamic response is determined in the frequency domain, considerably reducing computational time.

The results showed that there was a reduction of 28% in the driver seat vertical acceleration weighted root mean square (RMS) value of the proposed model, which is directly related to comfort, and, simultaneously, an improvement or constancy concerning safety, with low computational cost. Hence, the proposed methodology can be indicated as a successful tool for the optimal design of the suspension systems, considering, simultaneously, comfort and safety.

Despite the extensive literature on optimizing vehicle passive suspension systems, papers combining multi-objective optimization presenting a Pareto-optimal front as a set of optimal results, a full-vehicle model (including the driver seat), an irregular road profile and the determination of the dynamic response in the frequency domain are not found.