A Surrogate Model Assisted Evolutionary Algorithm for Computationally Expensive Design Optimization Problems with Discrete Variables

Real-world computationally expensive design optimization problems with discrete variables pose challenges to surrogate-based optimization methods in terms of both efficiency and search ability. In this paper, a new method is introduced, called surrogate model-aware differential evolution with neighbourhood exploration, which has two phases. The first phase adopts a surrogate-based optimization method based on efficient surrogate model-aware search framework, the goal of which is to reach at least the neighbourhood of the global optimum. In the second phase, a neighbourhood exploration method for discrete variables is developed and collaborates with the first phase to further improve the obtained solutions. Empirical studies on various benchmark problems and a real-world network-on-chip design optimization problem show the combined advantages in terms of efficiency and search ability: when only a very limited number of exact evaluations are allowed, the proposed method is not slower than one of the most efficient methods for the targeted problem; when more evaluations are allowed, the proposed method can obtain results with comparable quality compared to standard differential evolution, but it requires only 1% to 30% of exact function evaluations

A Surrogate Model Assisted Evolutionary Algorithm for Computationally Expensive Design Optimization Problems with Discrete Variables

Real-world computationally expensive design optimization problems with discrete variables pose challenges to surrogate-based optimization methods in terms of both efficiency and search ability. In this paper, a new method is introduced, called surrogate model-aware differential evolution with neighbourhood exploration, which has two phases. The first phase adopts a surrogate-based optimization method based on efficient surrogate model-aware search framework, the goal of which is to reach at least the neighbourhood of the global optimum. In the second phase, a neighbourhood exploration method for discrete variables is developed and collaborates with the first phase to further improve the obtained solutions. Empirical studies on various benchmark problems and a real-world network-on-chip design optimization problem show the combined advantages in terms of efficiency and search ability: when only a very limited number of exact evaluations are allowed, the proposed method is not slower than one of the most efficient methods for the targeted problem; when more evaluations are allowed, the proposed method can obtain results with comparable quality compared to standard differential evolution, but it requires only 1% to 30% of exact function evaluations

A Random Forest Assisted Evolutionary Algorithm for Data-Driven Constrained Multi-Objective Combinatorial Optimization of Trauma Systems for publication

Many real-world optimization problems can be solved by using the data-driven approach only, simply because no analytic objective functions are available for evaluating candidate solutions. In this work, we address a class of expensive datadriven constrained multi-objective combinatorial optimization problems, where the objectives and constraints can be calculated only on the basis of large amount of data. To solve this class of problems, we propose to use random forests and radial basis function networks as surrogates to approximate both objective and constraint functions. In addition, logistic regression models are introduced to rectify the surrogate-assisted fitness evaluations and a stochastic ranking selection is adopted to further reduce the influences of the approximated constraint functions. Three variants of the proposed algorithm are empirically evaluated on multi-objective knapsack benchmark problems and two realworld trauma system design problems. Experimental results demonstrate that the variant using random forest models as the surrogates are effective and efficient in solving data-driven constrained multi-objective combinatorial optimization problems

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems

Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems, the performance of these surrogate-assisted multi-objective evolutionary algorithms deteriorate drastically. In this work, a novel Classifier-assisted rank-based learning and Local Model based multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional expensive multi-objective optimization problems. The proposed algorithm consists of three parts: classifier-assisted rank-based learning, hypervolume-based non-dominated search, and local search in the relatively sparse objective space. Specifically, a probabilistic neural network is built as classifier to divide the offspring into a number of ranks. The offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for real function evaluations. Then, radial basis function networks are built as surrogates to approximate the objective functions. After searching non-dominated solutions assisted by the surrogate model, the candidates with higher hypervolume improvement are selected for real evaluations. Subsequently, in order to maintain the diversity of solutions, the most uncertain sample point from the non-dominated solutions measured by the crowding distance is selected as the guided parent to further infill in the uncertain region of the front. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate that the proposed algorithm shows superior performance compared with the state-of-the-art surrogate-assisted multi-objective evolutionary algorithms. The source code for this work is available at https://github.com/JellyChen7/CLMEA

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

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.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.The research of Tinkle Chugh was funded by the COMAS Doctoral Program (at the University of Jyväskylä) and FiDiPro Project DeCoMo (funded by Tekes, the Finnish Funding Agency for Innovation), and the research of Dr. Karthik Sindhya was funded by SIMPRO project funded by Tekes as well as DeCoMo

Surrogate-Assisted Artificial Immune Systems for Expensive Optimization Problems

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Synthesis of a discrete-action thermo-bimetallic actuator with a tongue

The selection of suitable parameters, by experimental or intuitive processes for snap-through actuation of a bimetallic actuator at a prescribed temperature is an extremely time-consuming task. This paper describes a new methodology for the optimization of a discrete action thermo-bimetallic actuator with a tongue. This methodology makes it possible to solve the optimization task with higher efficiency. The requirement is to find optimal parameters values so that the actuator will make a snap-through at a given temperature. The constrained optimization task was performed using an evolutional algorithm and surrogate modelling and this was coded in Matlab. Functional relationships between the criteria and parameters were not set explicitly, but they were calculated using finite element method, each simulation of which was performed in Abaqus

Bayesian Quality-Diversity approaches for constrained optimization problems with mixed continuous, discrete and categorical variables

Complex engineering design problems, such as those involved in aerospace, civil, or energy engineering, require the use of numerically costly simulation codes in order to predict the behavior and performance of the system to be designed. To perform the design of the systems, these codes are often embedded into an optimization process to provide the best design while satisfying the design constraints. Recently, new approaches, called Quality-Diversity, have been proposed in order to enhance the exploration of the design space and to provide a set of optimal diversified solutions with respect to some feature functions. These functions are interesting to assess trade-offs. Furthermore, complex engineering design problems often involve mixed continuous, discrete, and categorical design variables allowing to take into account technological choices in the optimization problem. In this paper, a new Quality-Diversity methodology based on mixed continuous, discrete and categorical Bayesian optimization strategy is proposed. This approach allows to reduce the computational cost with respect to classical Quality - Diversity approaches while dealing with discrete choices and constraints. The performance of the proposed method is assessed on a benchmark of analytical problems as well as on an industrial design optimization problem dealing with aerospace systems