Evolutionary Multi-Objective Optimization Under Uncertainty Through Adaptive Kriging in Augmented Input Space

This paper presents an engine sizing and cycle selection study of ultra high bypass ratio engines applied to a subsonic commercial aircraft in the N+2 (2025) timeframe. NASA has created the Environmentally Responsible Aviation (ERA) project to serve as a technology transition bridge between fundamental research (TRL 1–4) and potential commercial application (TRL 7). Specifically, ERA is focused on subsonic transport technologies that could reach TRL 6 by 2020 and can be integrated into an advanced vehicle concept to simultaneously meet the ERA project metrics for noise, emissions, and fuel burn. An important variable in exploring the technology trade space is the selection of the optimal engine cycle for use on the advanced aircraft. Previous literature demonstrated the cycle optimization using a design of experiments (DOE) to explore the engine cycle design space for a pre-defined technology package. However, since the optimal engine cycle is dependent upon the specific technology package, this process would have to be repeated to ensure optimal performance for each technology package. With more than 80 technologies to be analyzed, the combinatorial space of technology packages is enormous. As a result, executing a DOE to find the optimum engine cycle for each technology package is infeasible. To address this issue, it is proposed to use surrogate models that encompass the engine cycle and technology design space to enable fast and accurate optimization of the engine cycle for any given technology package. This paper describes the generation and analysis of surrogate models used for technology assessment and cycle optimization of an ultra high bypass geared turbofan engine architecture. The first study in the paper shows that a single surrogate model can be used to accurately simulate both a technology and cycle design space. To demonstrate the proposed surrogate modeling approach, the cycle design space for three different technology packages was analyzed. This study demonstrated that when an optimal cycle is found within the constrained interior of a design space, the surrogate modeling approach is quite accurate. The study also established that the surrogate models can also be used to assess potential cycles at the boundaries or even outside of the region for which they were trained.

Evolutionary Multi-objective Optimization(EMO) is becoming a hot research area and quite a few aspects of Multi-objective Evolutionary algorithms(MOEAs) have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by a representative combinatorial Multi-objective Problem(MOP): Multi-objective TSP. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two kinds of selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using Finite Markov Chain and proved that it could converge to Pareto Front with probability 1.We also find that the convergence property of MOEAs has much relationship with search and selection operators.

The increasing use of surrogate models has widened the range of application of classical reliability-based design optimization (RBDO) techniques to industrial problems. In this paper, we consider such an approach to the lightweight design of an automotive body structure. Solving this problem while approximating the complex models (nonlinear, noisy and high-dimensional) with a single metamodel would require a very large and non affordable design of experiments (DOE). We thus investigate and propose a methodology of adaptive Kriging based RBDO where an initial DOE is iteratively updated so as to improve the Kriging models only in regions that actually matter. The nested reliability analysis is expressed in terms of quantiles assessment. Two stages of enrichment are performed. The first one seeks to gradually improve the accuracy of the metamodels where the probabilistic constraints are likely to be violated. The second one is embedded in an evolution strategy optimization scheme where, at each iteration, the accuracy of the quantile estimation is improved if necessary. The methodology is applied on an analytical and crashworthiness design problems showing good performance by enhancing accuracy and efficiency with respect to a traditional approach.

In evolutionary multi-objective optimization, it has been illuminated that guide search with neighboring solutions improve the quality of new trial solutions and accelerate algorithms convergence by the regularity property of the continuous multi-objective optimization problems (MOPs). Very recently, clustering learning-based mating strategies have been popular for establishing reproduction operators with neighboring solutions. However, the existing mating strategies may be more reasonable with the full consideration and utilization of the regularity property. The current mating restrictions excessively emphasize algorithm convergence and ignore population diversity. In addition, the selected clustering algorithms in mating restrictions are not conducive for solving MOPs, which have complex Pareto sets (PSs) and\or Pareto fronts (PFs). To solve above problems and address both the algorithm convergence and the population diversity of multi-objective evolutionary algorithms (MOEAs), the spectral clustering based multi-source mating selection strategy (SMMS) is designed to detect regularity properties and balance population diversity while accelerating algorithm convergence. Consequently, a spectral clustering based multi-source mating selection multi-objective evolutionary algorithms is proposed, teamed SMMEA. SMMEA is applied to a number of test suites with a complex PS or PF, and compared with six state-of-the-art MOEAs. The results demonstrate that the proposed algorithm outperforms over the other approaches.

An Enhanced multi-objective evolutionary optimization algorithm based on decomposition (E-MOEA-D) proposed for optimal placement of Distributed Generation (DG) and Electric Vehicle (EV) Fast Charging Station (FCS) in distribution system. The diversity of the evolutionary algorithm improves the convergence and diverse solution in the process of evolutionary optimization. The proposed algorithm is improved using enhanced diversity algorithm, which yield diverse candidate solutions in population. The optimal placement of DGs and FCS are formulated using three objective functions as i) Active power loss ii) Voltage deviation iii) DG cost. The proposed algorithm is simulated on IEEE-33 bus distribution system. The proposed algorithm is compared with other competitive multi-objective evolutionary algorithms such as decomposition based multi-objective evolutionary algorithm (MOEA-D) and Non-dominated sorting multi-objective evolutionary algorithm (NSGA-II).

An efficient combination of multi-objective evolutionary optimization and reliability analysis for reliability-based design optimization of truss structures

Broad learning approach to Surrogate-Assisted Multi-Objective evolutionary fuzzy clustering algorithm based on reference points for color image segmentation

A computationally efficient procedure for multiobjective design optimization with variable-fidelity models and response surface surrogates is presented. The proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model, obtained with kriging interpolation of the low-fidelity model data enhanced by space-mapping correction exploiting a few high-fidelity training points. The initial Pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model. The latter are realized with a space-mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The proposed method allows us to obtain, at a low computational cost, a set of designs representing tradeoffs between the conflicting objectives. The current approach is illustrated using examples of airfoil design: one in transonic flow, involving aerodynamics tradeoffs; and another one in low-speed flow, involving tradeoffs between the aerodynamic and the aeroacoustic performances.

Hybrid-Game Strategies for multi-objective design optimization in engineering

Adaptive surrogate-assisted multi-objective evolutionary algorithm using an efficient infill technique

Modeling the speed-based vessel schedule recovery problem using evolutionary multiobjective optimization

Many real-world optimization problems involve multiple, typically conflicting objectives. Often, it is very difficult to weigh the different criteria exactly before alternatives are known. Evolutionary multi-objective optimization usually solves this predicament by searching for the whole Pareto-optimal front of solutions. However, often the user has at least a vague idea about what kind of solutions might be preferred. In this chapter, we argue that such knowledge should be used to focus the search on the most interesting (from a user’s perspective) areas of the Paretooptimal front. To this end, we present and compare two methods which allow to integrate vague user preferences into evolutionary multi-objective algorithms. As we show, such methods may speed up the search and yield a more fine-grained selection of alternatives in the most relevant parts of the Pareto-optimal front.

The Hausdorff distance d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> is a widely used tool to measure the distance between different objects in several research fields. Possible reasons for this might be that it is a natural extension of the well-known and intuitive distance between points and/or the fact that d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> defines in certain cases a metric in the mathematical sense. In evolutionary multiobjective optimization (EMO) the task is typically to compute the entire solution set-the so-called Pareto set-respectively its image, the Pareto front. Hence, d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> should, at least at first sight, be a natural choice to measure the performance of the outcome set in particular since it is related to the terms spread and convergence as used in EMO literature. However, so far, d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> does not find the general approval in the EMO community. The main reason for this is that d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> penalizes single outliers of the candidate set which does not comply with the use of stochastic search algorithms such as evolutionary strategies. In this paper, we define a new performance indicator, Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , which can be viewed as an “averaged Hausdorff distance” between the outcome set and the Pareto front and which is composed of (slight modifications of) the well-known indicators generational distance (GD) and inverted generational distance (IGD). We will discuss theoretical properties of Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> (as well as for GD and IGD) such as the metric properties and the compliance with state-of-theart multiobjective evolutionary algorithms (MOEAs), and will further on demonstrate by empirical results the potential of Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> as a new performance indicator for the evaluation of MOEAs.

Network robustness optimization is crucial for enhancing the resilience of industrial networks and social systems against malicious attacks. Existing studies typically evaluate the robustness by simulating the sequential removal of nodes or edges and recording the residual connectivity at each step. However, the attack simulation is computationally expensive and becomes impractical for large-scale networks. Therefore, this paper proposes a multiobjective evolutionary algorithm assisted by a graph isomorphism network (GIN)-based surrogate model to efficiently optimize network robustness. First, the robustness optimization task is formulated as a multiobjective problem that simultaneously considers network robustness against attacks and the structural modification cost. Then, a GIN-based surrogate model is constructed to approximate the robustness, replacing the expensive simulation assessments. Finally, the multiobjective evolutionary algorithm is employed to explore promising network structures guided by the surrogate model, which is continuously updated via online learning to improve both prediction accuracy and optimization performance. Experimental results in various synthetic and real-world networks demonstrate that the proposed algorithm reduces the computational cost of the robustness evaluation by about 65% while achieving comparable or even superior robustness optimization performance compared with those of baseline algorithms. These results indicate that the proposed method is practical and scalable and can be applied to enhance the robustness of industrial and social networks.

Surrogate-assisted multi-objective evolutionary feature selection of generation-based fixed evolution control for time series forecasting with LSTM networks