Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

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A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

In solving many real-world optimization problems, neither mathematical functions nor numerical simulations are available for evaluating the quality of candidate solutions. Instead, surrogate models must be built based on historical data to approximate the objective functions and no new data will be available during the optimization process. Such problems are known as offline data-driven optimization problems. Since the surrogate models solely depend on the given historical data, the optimization algorithm is able to search only in a very limited decision space during offline data-driven optimization. This paper proposes a new offline data-driven evolutionary algorithm to make the full use of the offline data to guide the search. To this end, a surrogate management strategy based on ensemble learning techniques developed in machine learning is adopted, which builds a large number of surrogate models before optimization and adaptively selects a small yet diverse subset of them during the optimization to achieve the best local approximation accuracy and reduce the computational complexity. Our experimental results on the benchmark problems and a transonic airfoil design example show that the proposed algorithm is able to handle offline data-driven optimization problems with up to 100 decision variables.

Offline Data-Driven Evolutionary Optimization Using Selective Surrogate Ensembles

AK-MCSi: A Kriging-based method to deal with small failure probabilities and time-consuming models

A novel non-probabilistic reliability-based design optimization algorithm using enhanced chaos control method

Traditional structural uncertainty analysis is mainly based on probability models and requires the establishment of accurate parametric probability distribution functions using large numbers of experimental samples. In many actual engineering problems, the probability distributions of some parameters can be established due to sufficient samples available, whereas for some parameters, due to the lack or poor quality of samples, only their variation intervals can be obtained, or their probability distribution types can be determined based on the existing data while some of the distribution parameters such as mean and standard deviation can only be given interval estimations. This thus will constitute an important type of probability-interval hybrid uncertain problem, in which the aleatory and epistemic uncertainties both exist. The probability-interval hybrid uncertainty analysis provides an important mean for reliability analysis and design of many complex structures, and has become one of the research focuses in the field of structural uncertainty analysis over the past decades. This paper reviews the four main research directions in this area, i.e., uncertainty modeling, uncertainty propagation analysis, structural reliability analysis, and reliability-based design optimization. It summarizes the main scientific problems, technical difficulties, and current research status of each direction. Based on the review, this paper also provides an outlook for future research in probability-interval hybrid uncertainty analysis.

Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review

We extended variable fidelity optimization framework to include multiple surrogates.Build multiple Kriging models by using k-means clustering algorithm.More reliably solve the large sample size surrogate-modeling problem.Accelerate surrogate-assisted multi-objective genetic algorithm.Results converge closely to the high-fidelity Pareto front. Surrogate-assisted evolutionary optimization has proved to be effective in reducing optimization time, as surrogates, or meta-models can approximate expensive fitness functions in the optimization run. While this is a successful strategy to improve optimization efficiency, challenges arise when constructing surrogate models in higher dimensional function space, where the trade space between multiple conflicting objectives is increasingly complex. This complexity makes it difficult to ensure the accuracy of the surrogates. In this article, a new surrogate management strategy is presented to address this problem. A k-means clustering algorithm is employed to partition model data into local surrogate models. The variable fidelity optimization scheme proposed in the author's previous work is revised to incorporate this clustering algorithm for surrogate model construction. The applicability of the proposed algorithm is illustrated on six standard test problems. The presented algorithm is also examined in a three-objective stiffened panel optimization design problem to show its superiority in surrogate-assisted multi-objective optimization in higher dimensional objective function space. Performance metrics show that the proposed surrogate handling strategy clearly outperforms the single surrogate strategy as the surrogate size increases.

Yan Liu

Papers

Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm

Efficient optimization of reliability-constrained structural design problems including interval uncertainty

Probabilistic risk, sustainability, and utility associated with ship grounding hazard

Risk-informed structural repair decision making for service life extension of aging naval ships

Time-dependent reliability assessment of ship structures under progressive and shock deteriorations