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

Despite the success of Evolutionary Algorithms in solving complex problems, they may require many function evaluations. This becomes an issue when dealing with costly problems. Surrogate models may overcome this difficulty, though their use in problems with medium to large dimensionality is underexplored in the literature. Problems with multiple conflicting objectives can be formulated as Multi-objective Optimization Problems (MOPs). MOPs have received a great attention lately, mainly with Multi-objective Evolutionary Algorithms (MOEAs). This paper proposes ELMOEA/D-DE, a surrogate-assisted MOEA, for solving expensive MOPs in small evaluation budgets. ELMOEA/D-DE encompasses a state-of-the-art MOEA based on decomposition, Differential Evolution (DE) operators and Extreme Learning Machines. This paper tests three variants of ELMOEA/D-DE, using different DE operators, for solving five known benchmark MOPs with 10 to 60 decision variables. All variants achieve good results in terms of hyper volume metric and the best variant with operator DE/rand/1/bin is compared with two state-of-the-art approaches (MOEA/D-RBF and a non-surrogate-based MOEA), achieving the best results in all but one problems instances.

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

A surrogate-assisted multi-objective evolutionary algorithm with dimension-reduction for production optimization

Many real-world applications can be formulated as expensive multimodal optimization problems (EMMOPs). When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face the problem of selecting surrogate models but also need to tackle the problem of discovering and updating multiple modalities. Different optimization problems and different stages of evolutionary algorithms (EAs) generally require different types of surrogate models. To address this issue, in this article, we present a multisurrogate-assisted multitasking particle swarm optimization algorithm to seek multiple optimal solutions of EMMOPs at a low computational cost. The proposed algorithm first transforms an EMMOP into a multitasking optimization problem by integrating various surrogate models, and designs a multitasking niche particle swarm algorithm to solve it. Following that, a surrogate model management strategy based on the skill factor and clustering is developed to effectively balance the number of real function evaluations and the prediction accuracy of candidate optimal solutions. In addition, an adaptive local search strategy based on the trust region is proposed to enhance the capability of swarm in exploiting potential optimal modalities. We compare the proposed algorithm with five state-of-the-art SAEAs and seven multimodal EAs on 19 benchmark functions and the building energy conservation problem and experimental results show that the proposed algorithm can obtain multiple highly competitive optimal solutions.

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields resulting from some computational mechanics simulations. Within a design context, a surrogate takes a vector of design variables that describe a current design and returns an approximation of the design’s response through a pseudo-time variable. To compare various radial basis function (RBF) surrogate modeling approaches, the prediction of a load displacement path of a snap-through structure is used as an example numerical problem. This work specifically considers the scenario where analytical sensitivities are available directly from the computational mechanics’ solver and therefore gradient enhanced surrogates are constructed. In addition, the gradients are used to perform a domain transformation preprocessing step to construct surrogate models in a more isotropic domain, which is conducive to RBFs. This work demonstrates that although the gradient-based domain transformation scheme offers a significant improvement to the performance of the space-time surrogate models (STSMs), the network surrogate model (NSM) is far more robust. This research offers explanations for the improved performance of NSMs over STSMs and recommends future research to improve the performance of STSMs.

The use of computer simulations has become a viable alternative for real-life controlled experiments. Due to the computational cost of these high fidelity simulations, surrogate models are often employed as an approximation for the original simulator. Because of their compact formulation and negligible evaluation time, global surrogate models are very useful tools for exploring the design space, optimization, visualization and sensitivity analysis. Additionally, multiple surrogate models can be chained together to model large scale systems where the direct use of the original expensive simulators would be too cumbersome. Many surrogate model types, such as neural networks, support vector machines and rational models have been proposed, and many more techniques have been developed to minimize the number of expensive simulations required to train a sufficiently accurate surrogate model. In this chapter, we present a fully automated and integrated global surrogate modeling methodology for regression modeling and active learning that readily enables the adoption of advanced global surrogate modeling methods by application scientists. The work brings together insights from distributed systems, artificial intelligence, and modeling & simulation, and has applications in a very wide range of fields. The merits of this approach are illustrated with several examples, and several surrogate model types.

Enhancing the maintenance strategy and cost in systems with surrogate assisted multiobjective evolutionary algorithms

In the field of energy system modelling, increasing complexity and optimization analysis are essential for understanding the most effective decarbonization options. However, the growing need for intricate models leads to increased computational time, which can hinder progress in research and policy-making. This study aims to address this issue by integrating machine learning algorithms with EnergyPLAN and EPLANopt, a coupling of EnergyPLAN software and a multi-objective evolutionary algorithm, to expedite the optimization process while maintaining accuracy. By saving computational time, we can increase the number of evaluations, thereby enabling deeper exploration of uncertainty in energy system modelling. Although machine learning models have been widely employed as surrogate models to accelerate optimization problems, their application in energy system modeling at the national scale, while preserving high temporal resolution and extensive sector-coupling, remains scarce. Several machine learning models were evaluated, and an artificial neural network was selected as the most effective surrogate model. The findings demonstrate that incorporating this surrogate model within the optimization process reduces computational time by 64 % compared to the conventional EPLANopt approach, while maintaining an accuracy level close to that obtained by running EPLANopt without the surrogate model.

In this paper we propose a methodology based on an evolutionary multiobjective optimization algorithm for the problem of up-grading (expansion) the physical topology of transparent optical networks. The aim is to define the new topology layout and the specification of the new optical devices that should be deployed in an existing network in order to improve its performance, considering simultaneously the total installation cost (capital cost) and the total network blocking probability (performance criteria). To accomplish that, we propose a capital cost model for the network. We considered the following physical layer impairments: losses in optical devices, amplified spontaneous emission in optical amplifier and homodyne crosstalk in optical cross connect. The multiobjective optimization evolutionary algorithm used in the optimization process is the NSGA-II. Our proposed methodology can solve the expand physical topology design problem taking into account the physical layer impairments and the capital costs simultaneously. We also present a case study to show the effectiveness of our methodology.

High-dimensional expensive optimization by Kriging-assisted multiobjective evolutionary algorithm with dimensionality reduction

Surrogate-assisted evolutionary algorithms (SAEAs) have been widely developed to solve complex and computationally expensive multiobjective optimization problems (EMOPs) in recent years. However, when dealing with high-dimensional optimization problems in decision space, the performance of these surrogate-assisted multiobjective evolutionary algorithms (MOEAs) deteriorates drastically. In this work, a novel classifier-assisted rank-based learning and local model-based multiobjective evolutionary algorithm (CLMEA) is proposed for high-dimensional EMOPs. CLMEA makes full use of the uncertainty of solutions in the decision space and objective space to explore the uncertain but informative space toward high-dimensional problems. Specifically, the offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for function evaluations (FEs). To reduce the search region of high-dimensional problems and maintain the diversity of solutions, the most uncertain sample point from the nondominated solutions measured by the crowding distance is selected as the center to conduct local search. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate superior performance of CLMEA compared with the state-of-the-art surrogate-assisted MOEAs. The source code for this work is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/JellyChen7/CLMEA</uri>

As a branch of frequent pattern mining, the task-oriented pattern mining has received increasing attention due to its broad application scenarios. The lexicographic subset tree based algorithm and the multiobjective evolutionary algorithm are two effective approaches for finding the most frequent and complete pattern in task-oriented applications. However, both suffer from heavy computational cost since their runtime increases rapidly as the transaction dataset is scaled up. To address this issue, this paper regards the task-oriented pattern mining as a data-driven optimization problem and solves it by using a surrogate-assisted multiobjective evolutionary algorithm. Based on the framework of our previous multiobjective evolutionary algorithm for task-oriented pattern mining, the proposed algorithm estimates the objective values of most solutions using an ensemble of surrogates instead of the real objective functions, thereby highly improving the efficiency of the algorithm. Experimental results on three task-oriented applications indicate that the proposed algorithm has better efficiency than state-of-the-art algorithms.

The shelter location is very important for evacuation planning in natural disasters, and evolutionary algorithms (EAs) have demonstrated their effectiveness in solving this challenging problem. However, few EAs have been reported focusing on the shelter location problem under uncertainty of road networks due to the expensive cost of calculating the evacuation distance for individual evaluation. To address this issue, in this article, we propose a clustering-based surrogate-assisted multiobjective EA, termed AR-MOEA+SA, in the framework of a recently developed EA AR-MOEA. In AR-MOEA+SA, a surrogate model, the radial basis function (RBF), is adopted to approximately calculate the evacuation distance under uncertainty of road networks. Due to the fact that there often exist a large number of communities needing to be considered in shelter location, a clustering strategy is suggested to convert the surrogate of high-dimensional problem into the one of low-dimensional problem in the proposed AR-MOEA+SA for efficiently building the RBF network. A population initialization strategy is also suggested in AR-MOEA+SA to enhance the quality of training data in the early stages of evolution. Experimental results on a variety of test instances demonstrate the superiority of the proposed AR-MOEA+SA over the original version of AR-MOEA in terms of both computational efficiency and solution quality.

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

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).