Inverted Generational Distance (IGD) has been widely considered as a reliable performance indicator to concurrently quantify the convergence and diversity of multi- and many-objective evolutionary algorithms. In this paper, an IGD indicator-based evolutionary algorithm for solving many-objective optimization problems (MaOPs) has been proposed. Specifically, the IGD indicator is employed in each generation to select the solutions with favorable convergence and diversity. In addition, a computationally efficient dominance comparison method is designed to assign the rank values of solutions along with three newly proposed proximity distance assignments. Based on these two designs, the solutions are selected from a global view by linear assignment mechanism to concern the convergence and diversity simultaneously. In order to facilitate the accuracy of the sampled reference points for the calculation of IGD indicator, we also propose an efficient decomposition-based nadir point estimation method for constructing the Utopian Pareto front which is regarded as the best approximate Pareto front for real-world MaOPs at the early stage of the evolution. To evaluate the performance, a series of experiments is performed on the proposed algorithm against a group of selected state-of-the-art many-objective optimization algorithms over optimization problems with $8$-, $15$-, and $20$-objective. Experimental results measured by the chosen performance metrics indicate that the proposed algorithm is very competitive in addressing MaOPs.
Subset selection is an interesting and important topic in the field of evolutionary multi-objective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive, subset selection is an essential post-processing procedure to select a pre-specified number of solutions as the final result. In this paper, we discuss the efficiency of greedy subset selection for the hypervolume, IGD and IGD+ indicators. Greedy algorithms usually efficiently handle subset selection. However, when a large number of solutions are given (e.g., subset selection from tens of thousands of solutio…
The algorithms of multi-objective optimisation had a relative growth in the last years. Thereby, it's requires some way of comparing the results of these. In this sense, performance measures play a key role. In general, it's considered some properties of these algorithms such as capacity, convergence, diversity or convergence-diversity. There are some known measures such as generational distance (GD), inverted generational distance (IGD), hypervolume (HV), Spread($Δ$), Averaged Hausdorff distance ($Δ_p$), R2-indicator, among others. In this paper, we focuses on proposing a new indicator to mea…
In solving multi-modal, multi-objective optimization problems (MMOPs), the objective is not only to find a good representation of the Pareto-optimal front (PF) in the objective space but also to find all equivalent Pareto-optimal subsets (PSS) in the variable space. Such problems are practically relevant when a decision maker (DM) is interested in identifying alternative designs with similar performance. There has been significant research interest in recent years to develop efficient algorithms to deal with MMOPs. However, the existing algorithms still require prohibitive number of function e…
Dominance move (DoM) is a binary quality indicator to compare solution sets in multiobjective optimization. The indicator allows a more natural and intuitive relation when comparing solution sets. It is Pareto compliant and does not demand any parameters or reference sets. In spite of its advantages, the combinatorial calculation nature is a limitation. The original formulation presents an efficient method to calculate it in a biobjective case only. This work presents an assignment formulation to calculate DoM in problems with three objectives or more. Some initial experiments, in the biobject…
Subset selection is an important component in evolutionary multiobjective optimization (EMO) algorithms. Clustering, as a classic method to group similar data points together, has been used for subset selection in some fields. However, clustering-based methods have not been evaluated in the context of subset selection from solution sets obtained by EMO algorithms. In this paper, we first review some classic clustering algorithms. We also point out that another popular subset selection method, i.e., inverted generational distance (IGD)-based subset selection, can be viewed as clustering. Then, …
Evolutionary diversity optimization aims to compute a diverse set of solutions where all solutions meet a given quality criterion. With this paper, we bridge the areas of evolutionary diversity optimization and evolutionary multi-objective optimization. We show how popular indicators frequently used in the area of multi-objective optimization can be used for evolutionary diversity optimization. Our experimental investigations for evolving diverse sets of TSP instances and images according to various features show that two of the most prominent multi-objective indicators, namely the hypervolume…
Southern University of Science and Technology（南方科技大学）
In general, a multi-objective optimization problem does not have a single optimal solution but a set of Pareto optimal solutions, which forms the Pareto front in the objective space. Various evolutionary algorithms have been proposed to approximate the Pareto front using a pre-specified number of solutions. Hundreds of solutions are obtained by their single run. The selection of a single final solution from the obtained solutions is assumed to be done by a human decision maker. However, in many cases, the decision maker does not want to examine hundreds of solutions. Thus, it is needed to sele…
RDEx-MOP: Indicator-Guided Reconstructed Differential Evolution for Fixed-Budget Multiobjective Optimization
Department of Engineering, University of Toyama（富山大学工学部）；Cyberscience Center, Tohoku University（东北大学网络科学中心）；Faculty of Science and Technology, Hirosaki University（弘前大学理工学部）；Sino-German College of Applied Sciences, Tongji University（同济大学中德工程学院）；School of Mechanical Engineering, Tongji University（同济大学机械工程学院）；Department of Information Engineering, Yantai Vocational College（烟台职业学院信息工程系）
In this paper we propose a novel methodology to assist in identifying vulnerabilities in a real-world complex heterogeneous industrial control systems (ICS) using two evolutionary multiobjective optimisation (EMO) algorithms, NSGA-II and SPEA2. Our approach is evaluated on a well known benchmark chemical plant simulator, the Tennessee Eastman (TE) process model. We identified vulnerabilities in individual components of the TE model and then made use of these to generate combinatorial attacks to damage the safety of the system, and to cause economic loss. Results were compared against random at…
TRUST-TAEA: A trustworthiness-guided two-archive evolutionary algorithm with variable-grouping sparse search for large-scale multi-objective optimization
Southwest Petroleum University（西南石油大学）；Jagiellonian University in Krakow（克拉科夫雅盖隆大学）
Most optimization-based community detection approaches formulate the problem in a single or bi-objective framework. In this paper, we propose two variants of a three-objective formulation using a customized non-dominated sorting genetic algorithm III (NSGA-III) to find community structures in a network. In the first variant, named NSGA-III-KRM, we considered Kernel k means, Ratio cut, and Modularity, as the three objectives, whereas the second variant, named NSGA-III-CCM, considers Community score, Community fitness and Modularity, as three objective functions. Experiments are conducted on fou…
Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionary algorithms for multi-modal multi-objective optimization have been proposed in the literature. However, there is no efficient method for multi-modal many-objective optimization, where the number of objectives is more than three. To address this issue, this paper proposes a niching indicator-based multi-modal multi- and many-objective optimization algorithm. In the proposed method, the fitness calculation is performed among a child and its closest individuals …
Technical indicators use graphic representations of data sets by applying various mathematical formulas to financial time series of prices. These formulas comprise a set of rules and parameters whose values are not necessarily known and depend on many factors: the market in which it operates, the size of the time window, and others. This paper focuses on the real-time optimization of the parameters applied for analyzing time series of data. In particular, we optimize the parameters of technical and financial indicators and propose other applications, such as glucose time series. We propose the…
Assessing the empirical performance of Multi-Objective Evolutionary Algorithms (MOEAs) is vital when we extensively test a set of MOEAs and aim to determine a proper ranking thereof. Multiple performance indicators, e.g., the generational distance and the hypervolume, are frequently applied when reporting the experimental data, where typically the data on each indicator is analyzed independently from other indicators. Such a treatment brings conceptual difficulties in aggregating the result on all performance indicators, and it might fail to discover significant differences among algorithms if…
This paper proposes non-dominated sorting genetic algorithm-II (NSGA-II ) in the context of technical indicator-based stock trading, by finding optimal combinations of technical indicators to generate buy and sell strategies such that the objectives, namely, Sharpe ratio and Maximum Drawdown are maximized and minimized respectively. NSGA-II is chosen because it is a very popular and powerful bi-objective evolutionary algorithm. The training and testing used a rolling-based approach (two years training and a year for testing) and thus the results of the approach seem to be considerably better i…
Although quality indicators play a crucial role in benchmarking evolutionary multi-objective optimization algorithms, their properties are still unclear. One promising approach for understanding quality indicators is the use of the optimal distribution of objective vectors that optimizes each quality indicator. However, it is difficult to obtain the optimal distribution for each quality indicator, especially when its theoretical property is unknown. Thus, optimal distributions for most quality indicators have not been well investigated. To address these issues, first, we propose a problem form…
An evolutionary search space can be smoothly transformed via a suitable change of basis; however, it can be difficult to determine an appropriate basis. In this paper, a method is proposed to select an optimum basis can be used to simplify an evolutionary search space in a binary encoding scheme. The basis search method is based on a genetic algorithm and the fitness evaluation is based on the epistasis, which is an indicator of the complexity of a genetic algorithm. Two tests were conducted to validate the proposed method when applied to two different evolutionary search problems. The first s…
In this paper, we proposed a multi-objective approach for the EEG Inverse Problem. This formulation does not need unknown parameters that involve empirical procedures. Due to the combinatorial characteristics of the problem, this alternative included evolutionary strategies to resolve it. The result is a Multi-objective Evolutionary Algorithm based on Anatomical Restrictions (MOEAAR) to estimate distributed solutions. The comparative tests were between this approach and 3 classic methods of regularization: LASSO, Ridge-L and ENET-L. In the experimental phase, regression models were selected to…
Multiobjective Optimization of Classifiers by Means of 3-D Convex Hull Based Evolutionary Algorithm
Xidian University（西安电子科技大学）；Polytechnic Institute of Leiria（莱里亚理工学院）；Leiden University（莱顿大学）；Microsoft Research Asia（微软亚洲研究院）；Newcastle University（纽卡斯尔大学）
The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is a popular algorithm for solving Multi-Objective Problems (MOPs). The main component of MOEA/D is to decompose a MOP into easier sub-problems using a set of weight vectors. The choice of the number of weight vectors significantly impacts the performance of MOEA/D. However, the right choice for this number varies, given different MOPs and search stages. Here we adaptively change the number of vectors by removing unnecessary vectors and adding new ones in empty areas of the objective space. Our MOEA/D variant uses the C…
A preference based multi-objective evolutionary algorithm is proposed for generating solutions in an automatically detected knee point region. It is named Automatic Preference based DI-MOEA (AP-DI-MOEA) where DI-MOEA stands for Diversity-Indicator based Multi-Objective Evolutionary Algorithm). AP-DI-MOEA has two main characteristics: firstly, it generates the preference region automatically during the optimization; secondly, it concentrates the solution set in this preference region. Moreover, the real-world vehicle fleet maintenance scheduling optimization (VFMSO) problem is formulated, and a…
Parent selection in evolutionary algorithms for multi-objective optimisation is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points. We propose to refine the parent selection on evolutionary multi-objective optimisation with diversity-based metrics. The aim is to focus on individuals with a high diversity contribution located in poorly explored areas of the search space, so the chances of creating new non-dominated individuals are better than in highly populated areas. We show by means of rigorous runtime analysis that the use of diversity-based pa…
We propose the cone epsilon-dominance approach to improve convergence and diversity in multiobjective evolutionary algorithms (MOEAs). A cone-eps-MOEA is presented and compared with MOEAs based on the standard Pareto relation (NSGA-II, NSGA-II*, SPEA2, and a clustered NSGA-II) and on the epsilon-dominance (eps-MOEA). The comparison is performed both in terms of computational complexity and on four performance indicators selected to quantify the quality of the final results obtained by each algorithm: the convergence, diversity, hypervolume, and coverage of many sets metrics. Sixteen well-known…
We propose an algorithm and a new method to tackle the classification problems. We propose a multi-output neural tree (MONT) algorithm, which is an evolutionary learning algorithm trained by the non-dominated sorting genetic algorithm (NSGA)-III. Since evolutionary learning is stochastic, a hypothesis found in the form of MONT is unique for each run of evolutionary learning, i.e., each hypothesis (tree) generated bears distinct properties compared to any other hypothesis both in topological space and parameter-space. This leads to a challenging optimisation problem where the aim is to minimise…
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…
College of Computer Science, Sichuan University（四川大学计算机学院）；Zhizhe Information Technology Services Company Limited（智哲信息技术服务有限公司）；School of Electrical and Computer Engineering, Oklahoma State University（俄克拉荷马州立大学电气与计算机工程学院）
Evolutionary Neural Architecture Search (ENAS) can automatically design the architectures of Deep Neural Networks (DNNs) using evolutionary computation algorithms. However, most ENAS algorithms require intensive computational resource, which is not necessarily available to the users interested. Performance predictors are a type of regression models which can assist to accomplish the search, while without exerting much computational resource. Despite various performance predictors have been designed, they employ the same training protocol to build the regression models: 1) sampling a set of DNN…
Multiobjective Evolutionary Pruning of Deep Neural Networks with Transfer Learning for improving their Performance and Robustness
University of Granada（格拉纳达大学）；Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI)（安达卢西亚数据科学与计算智能研究所（DaSCI））；TECNALIA（泰克纳利亚）；Basque Research & Technology Alliance (BRTA)（巴斯克研究与技术联盟（BRTA））；University of the Basque Country (UPV/EHU)（巴斯克大学（UPV/EHU））
When is global evolutionary search useful for variational quantum algorithms? A landscape-first study
VSB - Technical University of Ostrava（俄斯特拉发理工大学）；IT4Innovations National Supercomputing Center, VSB - Technical University of Ostrava（俄斯特拉发理工大学 IT4创新国家超算中心）；Klaipeda University（克莱佩达大学）
Optimal sensor placement (SP) usually minimizes an impact measure, such as the amount of contaminated water or the number of inhabitants affected before detection. The common choice is to minimize the minimum detection time (MDT) averaged over a set of contamination events, with contaminant injected at a different location. Given a SP, propagation is simulated through a hydraulic software model of the network to obtain spatio-temporal concentrations and the average MDT. Searching for an optimal SP is NP-hard: even for mid-size networks, efficient search methods are required, among which evolut…
