Building a surrogate model of an objective function has shown to be effective to assist evolutionary algorithms (EAs) to solve real-world complex optimisation problems which involve either computationally expensive numerical simulations or costly physical experiments. However, their effectiveness mostly focuses on small-scale problems with less than 10 decision variables. The scalability of surrogate assisted EAs (SAEAs) have not been well studied yet. In this paper, we propose a Gaussian process surrogate model assisted EA for medium-scale expensive multi-objective optimisation problems with up to 50 decision variables. There are three distinctive features of our proposed SAEA. First, instead of using all decision variables in surrogate model building, we only use those correlated ones to build the surrogate model for each objective function. Second, rather than directly optimising the surrogate objective functions, the original multi-objective optimisation problem is transformed to a new one based on the surrogate models. Last but not the least, a subset selection method is developed to choose a couple of promising candidate solutions for actual objective function evaluations thus to update the training dataset. The effectiveness of our proposed algorithm is validated on benchmark problems with 10, 20, 50 variables, comparing with three state-of-the-art SAEAs.
The installed amount of renewable energy has expanded massively in recent years. Wave energy, with its high capacity factors has great potential to complement established sources of solar and wind energy. This study explores the problem of optimising the layout of advanced, three-tether wave energy converters in a size-constrained farm in a numerically modelled ocean environment. Simulating and computing the complicated hydrodynamic interactions in wave farms can be computationally costly, which limits optimisation methods to have just a few thousand evaluations. For dealing with this expensiv…
In this paper, we propose a novel approach (SAPEO) to support the survival selection process in multi-objective evolutionary algorithms with surrogate models - it dynamically chooses individuals to evaluate exactly based on the model uncertainty and the distinctness of the population. We introduce variants that differ in terms of the risk they allow when doing survival selection. Here, the anytime performance of different SAPEO variants is evaluated in conjunction with an SMS-EMOA using the BBOB bi-objective benchmark. We compare the obtained results with the performance of the regular SMS-EMO…
Chemical plant design and optimisation have proven challenging due to the complexity of these real-world systems. The resulting complexity translates into high computational costs for these systems' mathematical formulations and simulation models. Research has illustrated the benefits of using machine learning surrogate models as substitutes for computationally expensive models during optimisation. This paper extends recent research into optimising chemical plant design and operation. The study further explores Surrogate Assisted Genetic Algorithms (SA-GA) in more complex variants of the origi…
Stochastic, iterative search methods such as Evolutionary Algorithms (EAs) are proven to be efficient optimizers. However, they require evaluation of the candidate solutions which may be prohibitively expensive in many real world optimization problems. Use of approximate models or surrogates is being explored as a way to reduce the number of such evaluations. In this paper we investigated three such methods. The first method (DAFHEA) partially replaces an expensive function evaluation by its approximate model. The approximation is realized with support vector machine (SVM) regression models. T…
By remarkably reducing real fitness evaluations, surrogate-assisted evolutionary algorithms (SAEAs), especially hierarchical SAEAs, have been shown to be effective in solving computationally expensive optimization problems. The success of hierarchical SAEAs mainly profits from the potential benefit of their global surrogate models known as "blessing of uncertainty" and the high accuracy of local models. However, their performance leaves room for improvement on highdimensional problems since now it is still challenging to build accurate enough local models due to the huge solution space. Direct…
Surrogate assisted evolutionary algorithms (EA) are rapidly gaining popularity where applications of EA in complex real world problem domains are concerned. Although EAs are powerful global optimizers, finding optimal solution to complex high dimensional, multimodal problems often require very expensive fitness function evaluations. Needless to say, this could brand any population-based iterative optimization technique to be the most crippling choice to handle such problems. Use of approximate model or surrogates provides a much cheaper option. However, naturally this cheaper option comes with…
EXPObench: Benchmarking Surrogate-based Optimisation Algorithms on Expensive Black-box Functions
School of Industrial Engineering, Eindhoven University of Technology（埃因霍温理工大学工业工程学院）；Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology（代尔夫特理工大学电气工程、数学与计算机科学学院）
Very expensive problems are very common in practical system that one fitness evaluation costs several hours or even days. Surrogate assisted evolutionary algorithms (SAEAs) have been widely used to solve this crucial problem in the past decades. However, most studied SAEAs focus on solving problems with a budget of at least ten times of the dimension of problems which is unacceptable in many very expensive real-world problems. In this paper, we employ Voronoi diagram to boost the performance of SAEAs and propose a novel framework named Voronoi-based efficient surrogate assisted evolutionary al…
Institute for Intelligent Systems, University of Johannesburg（约翰内斯堡大学智能系统研究所）；Faculty of Engineering and the Built Environment, University of Johannesburg（约翰内斯堡大学工程与建筑环境学院）；Department of Statistical Sciences, University of Cape Town（开普敦大学统计科学系）
Portfolio management is a multi-period multi-objective optimisation problem subject to a wide range of constraints. However, in practice, portfolio management is treated as a single-period problem partly due to the computationally burdensome hyper-parameter search procedure needed to construct a multi-period Pareto frontier. This study presents the \gls{ParDen-Sur} modelling framework to efficiently perform the required hyper-parameter search. \gls{ParDen-Sur} extends previous surrogate frameworks by including a reservoir sampling-based look-ahead mechanism for offspring generation in \glspl{E…
The integration of Reinforcement Learning (RL) and Evolutionary Algorithms (EAs) aims at simultaneously exploiting the sample efficiency as well as the diversity and robustness of the two paradigms. Recently, hybrid learning frameworks based on this principle have achieved great success in various challenging robot control tasks. However, in these methods, policies from the genetic population are evaluated via interactions with the real environments, limiting their applicability in computationally expensive problems. In this work, we propose Surrogate-assisted Controller (SC), a novel and effi…
Deep convolutional neural networks have demonstrated promising performance on image classification tasks, but the manual design process becomes more and more complex due to the fast depth growth and the increasingly complex topologies of convolutional neural networks. As a result, neural architecture search has emerged to automatically design convolutional neural networks that outperform handcrafted counterparts. However, the computational cost is immense, e.g. 22,400 GPU-days and 2,000 GPU-days for two outstanding neural architecture search works named NAS and NASNet, respectively, which moti…
Real-world optimisation problems typically have objective functions which cannot be expressed analytically. These optimisation problems are evaluated through expensive physical experiments or simulations. Cheap approximations of the objective function can reduce the computational requirements for solving these expensive optimisation problems. These cheap approximations may be machine learning or statistical models and are known as surrogate models. This paper introduces a simulation of a well-known batch processing problem in the literature. Evolutionary algorithms such as Genetic Algorithm (G…
Significant effort has been made to solve computationally expensive optimization problems in the past two decades, and various optimization methods incorporating surrogates into optimization have been proposed. However, most optimization toolboxes do not consist of ready-to-run algorithms for computationally expensive problems, especially in combination with other key requirements, such as handling multiple conflicting objectives or constraints. Thus, the lack of appropriate software packages has become a bottleneck for solving real-world applications. The proposed framework, pysamoo, addresse…
In the paper, a multi-objective evolutionary surrogate-assisted approach for the fast and effective generative design of coastal breakwaters is proposed. To approximate the computationally expensive objective functions, the deep convolutional neural network is used as a surrogate model. This model allows optimizing a configuration of breakwaters with a different number of structures and segments. In addition to the surrogate, an assistant model was developed to estimate the confidence of predictions. The proposed approach was tested on the synthetic water area, the SWAN model was used to calcu…
Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationall…
In NeuroEvolution, the topologies of artificial neural networks are optimized with evolutionary algorithms to solve tasks in data regression, data classification, or reinforcement learning. One downside of NeuroEvolution is the large amount of necessary fitness evaluations, which might render it inefficient for tasks with expensive evaluations, such as real-time learning. For these expensive optimization tasks, surrogate model-based optimization is frequently applied as it features a good evaluation efficiency. While a combination of both procedures appears as a valuable solution, the definiti…
Multi-Objective Optimization (MOO) is very difficult for expensive functions because most current MOO methods rely on a large number of function evaluations to get an accurate solution. We address this problem with surrogate approximation and parallel computation. We develop an MOO algorithm MOPLS-N for expensive functions that combines iteratively updated surrogate approximations of the objective functions with a structure for efficiently selecting a population of $N$ points so that the expensive objectives for all points are simultaneously evaluated on $N$ processors in each iteration. MOPLS…
We present an algorithm for multi-objective optimization of computationally expensive problems. The proposed algorithm is based on solving a set of surrogate problems defined by models of the real one, so that only solutions estimated to be approximately Pareto-optimal are evaluated using the real expensive functions. Aside of the search for solutions, our algorithm also performs a meta-search for optimal surrogate models and navigation strategies for the optimization landscape, therefore adapting the search strategy for solutions to the problem as new information about it is obtained. The com…
When generating content for video games using procedural content generation (PCG), the goal is to create functional assets of high quality. Prior work has commonly leveraged the feasible-infeasible two-population (FI-2Pop) constrained optimisation algorithm for PCG, sometimes in combination with the multi-dimensional archive of phenotypic-elites (MAP-Elites) algorithm for finding a set of diverse solutions. However, the fitness function for the infeasible population only takes into account the number of constraints violated. In this paper we present a variant of FI-2Pop in which a surrogate mo…
Electric machine design optimization is a computationally expensive multi-objective optimization problem. While the objectives require time-consuming finite element analysis, optimization constraints can often be based on mathematical expressions, such as geometric constraints. This article investigates this optimization problem of mixed computationally expensive nature by proposing an optimization method incorporated into a popularly-used evolutionary multi-objective optimization algorithm - NSGA-II. The proposed method exploits the inexpensiveness of geometric constraints to generate feasibl…
University of New South Wales（新南威尔士大学）；University of Sydney（悉尼大学）；SRM Institute of Science and Technology（SRM科学技术研究所）
The complex and computationally expensive nature of landscape evolution models pose significant challenges in the inference and optimisation of unknown parameters. Bayesian inference provides a methodology for estimation and uncertainty quantification of unknown model parameters. In our previous work, we developed parallel tempering Bayeslands as a framework for parameter estimation and uncertainty quantification for the Badlands landscape evolution model. Parallel tempering Bayeslands features high-performance computing with dozens of processing cores running in parallel to enhance computatio…
Convolutional neural networks (CNNs) have gained remarkable success in recent years. However, their performance highly relies on the architecture hyperparameters, and finding proper hyperparameters for a deep CNN is a challenging optimization problem owing to its high-dimensional and computationally expensive characteristics. Given these difficulties, this study proposes a surrogate-assisted highly cooperative hyperparameter optimization (SHCHO) algorithm for chain-styled CNNs. To narrow the large search space, SHCHO first decomposes the whole CNN into several overlapping sub-CNNs in accordanc…
East China University of Science and Technology（华东理工大学）；University of Surrey（萨里大学）
Data-driven optimization has found many successful applications in the real world and received increased attention in the field of evolutionary optimization. Most existing algorithms assume that the data used for optimization is always available on a central server for construction of surrogates. This assumption, however, may fail to hold when the data must be collected in a distributed way and is subject to privacy restrictions. This paper aims to propose a federated data-driven evolutionary multi-/many-objective optimization algorithm. To this end, we leverage federated learning for surrogat…
Large Language Model-Driven Surrogate-Assisted Evolutionary Algorithm for Expensive Optimization
Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University（香港理工大学电子与电气工程系）；College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机科学与软件工程学院）；School of Automation and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学自动化与智能制造学院）；Academy of Artificial Intelligence, College of Mathematics Science, Inner Mongolia Normal University（内蒙古师范大学数学科学学院人工智能学院）；Key Laboratory of Collaborative Intelligence Systems, Ministry of Education, Xidian University（西安电子科技大学教育部协同智能系统重点实验室）
This paper describes the N-Tuple Bandit Evolutionary Algorithm (NTBEA), an optimisation algorithm developed for noisy and expensive discrete (combinatorial) optimisation problems. The algorithm is applied to two game-based hyper-parameter optimisation problems. The N-Tuple system directly models the statistics, approximating the fitness and number of evaluations of each modelled combination of parameters. The model is simple, efficient and informative. Results show that the NTBEA significantly outperforms grid search and an estimation of distribution algorithm.
Hyperparameter optimisation is a crucial process in searching the optimal machine learning model. The efficiency of finding the optimal hyperparameter settings has been a big concern in recent researches since the optimisation process could be time-consuming, especially when the objective functions are highly expensive to evaluate. In this paper, we introduce an intelligent evolutionary optimisation algorithm which applies machine learning technique to the traditional evolutionary algorithm to accelerate the overall optimisation process of tuning machine learning models in classification probl…
University of Exeter（埃克塞特大学）；Swansea University（斯旺西大学）
Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an $ε$-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our $ε$-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a…
It is typical for a machine learning system to have numerous hyperparameters that affect its learning rate and prediction quality. Finding a good combination of the hyperparameters is, however, a challenging job. This is mainly because evaluation of each combination is extremely expensive computationally; indeed, training a machine learning system on real data with just a single combination of hyperparameters usually takes hours or even days. In this paper, we address this challenge by trying to predict the performance of the machine learning system with a given combination of hyperparameters …
In complex, expensive optimization domains we often narrowly focus on finding high performing solutions, instead of expanding our understanding of the domain itself. But what if we could quickly understand the complex behaviors that can emerge in said domains instead? We introduce surrogate-assisted phenotypic niching, a quality diversity algorithm which allows to discover a large, diverse set of behaviors by using computationally expensive phenotypic features. In this work we discover the types of air flow in a 2D fluid dynamics optimization problem. A fast GPU-based fluid dynamics solver is …
Multi-objective optimisation is a popular approach for finding solutions to complex problems with large search spaces that reliably yields good optimisation results. However, with the rise of cyber-physical systems, emerges a new challenge of noisy fitness functions, whose objective value for a given configuration is non-deterministic, producing varying results on each execution. This leads to an optimisation process that is based on stochastically sampled information, ultimately favouring solutions with fitness values that have co-incidentally high outlier noise. In turn, the results are unfa…
Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究中心）；Leiden University Medical Center（莱顿大学医学中心）；TU Delft（代尔夫特理工大学）
We propose a novel surrogate-assisted Evolutionary Algorithm for solving expensive combinatorial optimization problems. We integrate a surrogate model, which is used for fitness value estimation, into a state-of-the-art P3-like variant of the Gene-Pool Optimal Mixing Algorithm (GOMEA) and adapt the resulting algorithm for solving non-binary combinatorial problems. We test the proposed algorithm on an ensemble learning problem. Ensembling several models is a common Machine Learning technique to achieve better performance. We consider ensembles of several models trained on disjoint subsets of a …
Enhancing SAEAs with Unevaluated Solutions: A Case Study of Relation Model for Expensive Optimization
Shanghai Jiao Tong University（上海交通大学）；Shanghai Frontiers Science Center of Molecule Intelligent Syntheses（上海分子智能合成前沿科学中心）；East China Normal University（华东师范大学）
