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Real-world optimization problems are often subject to several constraints which are expensive to evaluate in terms of cost or time. Although a lot of effort is devoted to make use of surrogate models for expensive optimization tasks, not many strong surrogate-assisted algorithms can address the challenging constrained problems. Efficient Global Optimization (EGO) is a Kriging-based surrogate-assisted algorithm. It was originally proposed to address unconstrained problems and later was modified to solve constrained problems. However, these type of algorithms still suffer from several issues, mainly: (1) early stagnation, (2) problems with multiple active constraints and (3) frequent crashes. In this work, we introduce a new EGO-based algorithm which tries to overcome these common issues with Kriging optimization algorithms. We apply the proposed algorithm on problems with dimension d < 4from the G-function suite [16] and on an airfoil shape example.

Purpose – A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a tight coupling between the optimization and uncertainty procedures, use all of the possible probabilistic information to drive the optimizer, and leverage high-performance parallel computing. Design/methodology/approach – This algorithm is a generalization of a classical genetic algorithm for multi-objective optimization (NSGA-II) by Deb et al. The proposed algorithm relies on the use of all possible information in the probabilistic domain summarized by the cumulative distribution functions (CDFs) of the objective functions. Several analytic test functions are used to benchmark this algorithm, but only the results of the Fonseca-Fleming test function are shown. An industrial application is presented to show that P-NSGA can be used for multi-objective shape optimization of a Formula 1 tire brake duct, taking into account the geometrical uncertainties associated with the rotating rubber tire and uncertain inflow conditions. Findings – This algorithm is shown to have deterministic consistency (i.e. it turns back to the original NSGA-II) when the objective functions are deterministic. When the quality of the CDF is increased (either using more points or higher fidelity resolution), the convergence behavior improves. Since all the information regarding uncertainty quantification is preserved, all the different types of Pareto fronts that exist in the probabilistic framework (e.g. mean value Pareto, mean value penalty Pareto, etc.) are shown to be generated a posteriori. An adaptive sampling approach and parallel computing (in both the uncertainty and optimization algorithms) are shown to have several fold speed-up in selecting optimal solutions under uncertainty. Originality/value – There are no existing algorithms that use the full probabilistic distribution to guide the optimizer. The method presented herein bases its sorting on real function evaluations, not merely measures (i.e. mean of the probabilistic distribution) that potentially do not exist.

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of statistical moments as deterministic attributes that define the objectives of the optimization process, the inverse cumulative distribution function allows for the use of all the possible information available in the probabilistic domain. Furthermore, the use of a quantile based approach leads naturally to a multi-objective methodology which allows an a-posteriori selection of the candidate design based on risk/opportunity criteria defined by the designer.

An optimization procedure aimed at the design of multicomponent airfoils for high-lift applications is described. The procedure is based on a multiobjective genetic algorithm; two flow solvers have been coupled with the genetic algorithm: a viscous–inviscid interaction method, based on an Euler flow solver and an integral boundary layer routine, and a method based on a full potential flow solver. The first model is used for high-lift configurations, whereas the second is used to optimize transonic performances for cruise configurations. The applications described include both single and multiobjective design of a high-lift multicomponent airfoil, and a multipoint design where the transonic and high-lift requirements are taken into account simultaneously.

Real-world design problems need robust and effective system-level optimization tools inasmuch as they are ruled by several criteria, most often in multidisciplinary environments. In this work a hybrid optimization algorithm has been obtained by adding a gradient-based technique to the set of operators of a multiobjective genetic algorithm. This makes it possible to increase the computational efficiency of the genetic algorithm while preserving its favorable features of robustness, problem independence, and multiobjective optimization capabilities. Aerodynamic shape design problems, including both airfoil and wing designs, are considered

Some of the advantages and drawbacks of genetic algorithms applications to aerodynamic design are demonstrated. A numerical procedure for the aerodynamic design of transonic airfoils by means of genetic algorithms, with single-point, multipoint, and multiobjective optimization capabilities, is presented. In the ® rst part, an investigation on the relative ef® ciency of different genetic operators combinations is carried out on an aerodynamic inverse design problem. It is shown how an appropriate tuning of the algorithm can provide improved performances, better adaption to design space size and topology, and variables cross correlation. In the second part, the multiobjective approach to design is introduced. The problem of the optimization of the drag rise characteristics of a transonic airfoil is addressed and dealt with using a single point, a multipoint, and a multiobjective approach. A comparison between the results obtained using the three different strategies is ® nally established, showing the advantages of multiobjective optimization.

A numerical procedure for the aerodynamic design of transonic airfoils by means of genetic algorithms, with single point, multipoint and multiobjective optimization capabilities, is presented. Both direct and inverse design problems can be faced. In the first part of the work, some results of an investigation on the relative efficiency of different genetic operators combinations are reported; the test problems used to this end consist in the search of the maximum of a mathematical function, and in an aerodynamic inverse design problem. It is shown how different optimization problems are better faced by different genetic algorithms, depending on design space size and topology, and variables cross-correlation. In the second part of the paper, the multiobjective approach to design is introduced, with the aid of two mathematical tests. Afterwards, the problem of the optimization of the drag rise characteristics of a transonic airfoil is addressed; this problem is faced using a single point, a multipoint and a multiobjective approach, and a comparison is established between the results obtained using the three different strategies.

This paper presents a new approach to robustness analysis in multi-objective optimization problems aimed at obtaining the most robust Pareto front solutions and also at distributing solutions along the most robust regions of the optimal Pareto set. The methodology proposed is applied to a single screw polymer extrusion with the aim of obtaining the most robust solutions for the optimization of the extruder geometry. The non-dominated solutions obtained take into account their degree of robustness and the distribution of such solutions along the Pareto front accordingly with specific algorithm parameter values. The results obtained have physical meaning and are in accordance with the practical knowledge about the industrial process studied.

Nash equilibrium and evolutionary algorithm are used to optimize a wing of a regional turboprop aircraft, with the aim to compare different optimization strategies in the aircraft design field. Since the aircraft design field is very complex in terms of number of involved variables and space of analysis, it is not possible to perform an optimization process accounting for all possible parameters. This leads to the need to reduce the number of the variables to the most significant ones. A multi-objective optimization approach is here performed, paying attention to the variables which mainly influence the objective functions. Results of Nash-Genetic algorithm are compared against those of both a typical Pareto front and a scalarization, showing that the proposed approach locates almost all solutions on the Pareto front, while the scalarization results are confined only in a zone of this front. The optimization elapsed time for a single optimization point is less than 32% of an entire Pareto front, but the designer must initially choose the players’ cards assignment.

An interactive version of the inverse modeling based multiobjective evolutionary algorithm is presented. Instead of generating a representation of the whole Pareto optimal front, the algorithm aims at producing solutions in the regions where the decision maker is interested in. This is facilitated through an interactive solution process where the decision maker iteratively evaluates a set of solutions shown to her/him and the preference information obtained is used to adapt the search process of the algorithm. peerReviewed

Both the pressure drop and the cut-off diameter are important performance parameters in the design of the cyclone separator. In this paper, a multi-objective optimization study of the gas cyclone separator is performed. In order to predict accurately the complex non linear relationships between the performance parameters (pressure drop and cut-off diameter) and the geometrical dimensions, two radial basis neural networks (RBFNN) are developed and employed to model the pressure drop and cut-off diameter for cyclone separators. The artificial neural networks have been trained and tested by the experimental data available in literatures for pressure drop and the Iozia and Leith model for the cut-off diameter. The results demonstrate that artificial neural networks can offer an alternative and powerful approach to model the cyclone pressure drop and cut-off diameter. The two trained artificial neural networks have been used as two objective functions to get new optimal ratios for minimum pressure drop and minimumcut-off diameter using the multi-objective genetic algorithm optimization technique. Sometimes, the main concern is minimizing the pressure drop, so a single objective optimization study has been performed to obtain the cyclone geometrical ratio for minimum pressure drop. The comparison of numerical simulation for the new optimal design and for the Stairmand design confirms the superior performance of the new design.