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Metrics to guide a multi-objective evolutionary algorithm for ordinal classification

NEUROCOMPUTING 2014年 135卷 21-31页

作者： Cruz-Ramirez, M. Hervas-Martinez, C. Sanchez-Monedero, J. Gutierrez, P. A. Univ Cordoba Dept Numer Anal & Comp Sci E-14071 Cordoba Spain

Ordinal classification or ordinal regression is a classification problem in which the labels have an ordered arrangement between them. Due to this order, alternative performance evaluation metrics are need to be used in order to consider the magnitude of errors. This paper presents a study of the use of a multi-objective optimization approach in the context of ordinal classification. We contribute a study of ordinal classification performance metrics, and propose a new performance metric, the maximum mean absolute error (MMAE). MMAE considers per-class distribution of patterns and the magnitude of the errors, both issues being crucial for ordinal regression problems. In addition, we empirically show that some of the performance metrics are competitive objectives, which justify the use of multi-objective optimization strategies. In our case, a multi-objective evolutionary algorithm optimizes an artificial neural network ordinal model with different pairs of metric combinations, and we conclude that the pair of the mean absolute error (MAE) and the proposed MMAE is the most favourable. A study of the relationship between the metrics of this proposal is performed, and the graphical representation in the two-dimensional space where the search of the evolutionary algorithm takes place is analysed. The results obtained show a good classification performance, opening new lines of research in the evaluation and model selection of ordinal classifiers. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Mean absolute error multi-objective evolutionary algorithm Ordinal measures Ordinal classification Ordinal regression Proportional odds model

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Study on the performance and efficiency of multi-objective evolutionary algorithms for trimaran outrigger layout seakeeping optimization problem

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OCEAN ENGINEERING 2024年第Part2期309卷

作者： Wang, Shangming Duan, Fei Wang, Enhao Shanghai Jiao Tong Univ State Key Lab Ocean Engn 800 Dongchuan Rd Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Sch Ocean & Civil Engn 800 Dongchuan Rd Shanghai 200240 Peoples R China Tsinghua Univ Inst Ocean Engn Shenzhen Int Grad Sch Shenzhen 518055 Guangdong Peoples R China

Trimaran as a high-performance vessel, possesses excellent characteristics such as high speed, low wave -making resistance, and good seakeeping performance. Different from conventional monohull ship, the design of a trimaran requires additional consideration of the outrigger layout, as the position of two outriggers can affect its hydrodynamic performance. In this study, high-speed slender body potential flow theory (also named the 2D+t theory or the 2.5D method) was employed to calculate the heave and pitch motion in order to evaluate the seakeeping performance of trimarans with different outrigger layouts at varying speeds. Model experiments were subsequently conducted to validate the effectiveness of the 2.5D method in simulating the motion of trimarans under different outrigger layouts. Three multi -objective evolutionary algorithms, including Non -dominated sorting genetic algorithm II (NSGA-II), Non -dominated sorting genetic algorithm III (NSGA-III), and multi -objective evolutionary algorithm based on decomposition (MOEA/D), as well as their applications in the optimization of trimaran outrigger layouts were introduced. Utilizing the 2.5D method based computational program as the solver, the efficiency and performance of these multi -objective evolutionary algorithms were compared. Discuss the advantages and disadvantages of three multi -objective evolutionary algorithms in solving trimaran outrigger layout optimization problem by comparing the optimization results from two aspects: optimization efficiency, and optimal solution performance. The results indicate that for optimization efficiency, the weighted sum approach based MOEA/D exhibits best optimization efficiency. NSGA-II and NSGA-III show a good advantage in terms of optimal solution performance, and compared to NSGA-II, NSGA-III can obtain more Pareto solutions.

关键词： Trimaran Seakeeping multi-objective optimization multi-objective evolutionary algorithm Model tests

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What Performance Indicators to Use for Self-Adaptation in multi-objective evolutionary algorithms

What Performance Indicators to Use for Self-Adaptation in Mu...

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Genetic and evolutionary Computation Conference (GECCO)

作者： Ye, Furong Neumann, Frank de Nobel, Jacob Neumann, Aneta Back, Thomas Chinese Acad Sci ISCAS Beijing Peoples R China Univ Adelaide Adelaide SA Australia Leiden Univ LIACS Leiden Netherlands

ISBN: (纸本)9798400704949

Parameter control has succeeded in accelerating the convergence process of evolutionary algorithms. While empirical and theoretical studies have shed light on the behavior of algorithms for single-objective optimization, little is known about how self-adaptation influences multi-objective evolutionary algorithms. In this work, we contribute (1) extensive experimental analysis of the Global Simple evolutionary multi-objective algorithm (GSEMO) variants on classic problems, such as OneMinMax, LOTZ, COCZ, and (2) a novel version of GSEMO with self-adjusting mutation rates. To enable self-adaptation in GSEMO, we explore three techniques from single-objective optimization for self-adjusting mutation rates and use various performance metrics, such as hypervolume and inverted generational distance, to guide the adaptation. Our experiments show that adapting the mutation rate based on single-objective optimization and hypervolume can speed up the convergence of GSEMO. Moreover, we demonstrate that a GSEMO with self-adjusting mutation rates, which focuses on optimizing one of the objectives alternatively and adjusts the mutation rate for each solution individually, can outperform the GSEMO with static mutation rates across the tested problem. This work provides a comprehensive benchmarking study for MOEAs and complements existing theoretical runtime analysis. Our proposed algorithm addresses interesting issues for designing MOEAs for future practical applications.

关键词： multi-objective evolutionary algorithm self-adjusting mutation benchmarking

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A Mixed-Factor evolutionary algorithm for multi-objective Knapsack Problem 1

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18th International Conference on Intelligent Computing (ICIC)

作者： Du, Yanlian Feng, Zejing Shen, Yijun Hainan Univ Sch Informat & Commun Engn Haikou 570228 Hainan Peoples R China Hainan Univ State Key Lab Marine Resources Utilizat South Chi Haikou 570228 Hainan Peoples R China Hainan Univ Coll Appl Sci & Technol Danzhou 571737 Peoples R China

ISBN: (数字)9783031138706

ISBN: (纸本)9783031138706;9783031138690

Nondominated-sorting plays an important role in multi-objective evolutionary algorithm in recent decades. However, it fails to work well when the target multi-objective problem has a complex Pareto front, brusque nondominated-sorting virtually steers by the conflicting nature of objectives, which leads to irrationality. In this paper, a novel mixed-factor evolutionary algorithm is proposed. A normalization procedure, i.e. mixed-factor, is introduced in the objective space, which links all the objectives for all the solutions of the problem to ease the conflicting nature. In the process of nondominated-sorting, the mixed factors of individual substitute the raw objectives. In order to ensure that the population are thoroughly steered through the normalized objective space, hybrid ageing operator and static hypermutation with first constructive mutation are used to guide the searching agents converge towards the true Pareto front. The algorithm proposed is operated on multi-objective knapsack problem. The effectiveness of MFEA is compared with five state-of-the-art algorithms, i.e., NSGA-II, NSGA-III, MOEA/D, SPEA2 and GrEA, in terms of five performance metrics. Simulation results demonstrate that MFEA achieves better performance.

关键词： multi-objective evolutionary algorithm Mixed-factor evolutionary algorithm multi-objective Knapsack Problem Normalization procedure

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A co-evolutionary algorithm based on sparsity clustering for sparse large-scale multi-objective optimization

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2024年第PartB期133卷

作者： Zhang, Yajie Wu, Chengming Tian, Ye Zhang, Xingyi Anhui Univ Sch Comp Sci & Technol Hefei Peoples R China Anhui Univ Sch Artificial Intelligence Hefei Peoples R China Anhui Univ Inst Phys Sci & Informat Technol Hefei Peoples R China Anhui Univ Informat Mat & Intelligent Sensing Lab Anhui Prov Hefei Peoples R China

Sparse large-scale multi -objective optimization problems (LSMOPs), which are characterized by high dimensional search space and sparse Pareto optimal solutions, have a widespread existence in academic research and practical applications. While the high dimensional decision space poses challenges to multi -objective evolutionary algorithms (MOEAs), the difficulty of solving sparse LSMOPs can be alleviated by utilizing the prior knowledge that the optimal solutions are sparse. In this paper, a co -evolutionary algorithm based on sparsity clustering, namely SCEA, is proposed, where the prior knowledge of sparse optimal solutions is utilized explicitly. At each generation, SCEA first calculates the current optimal sparsity by sparsity clustering. Then, SCEA divides the population into a winner subpopulation and two loser subpopulations. While the winner subpopulation reproduces offspring solutions by conventional genetic operators, the loser subpopulations generate offspring solutions along two competitive directions under the guidance of current optimal sparsity and variable importance. In the experiments, four state-of-the-art MOEAs are selected as the comparative algorithms. Experimental results show that the proposed algorithm is superior to the four competitors on both benchmark problems and practical applications, which include the sparse signal reconstruction problem, the community detection problem, and the instance selection problem.

关键词： multi-objective evolutionary algorithm Large-scale multi-objective optimization Signal reconstruction Community detection Instance selection

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Last-mile drone delivery combinatorial double auction model using multi-objective evolutionary algorithms

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SOFT COMPUTING 2022年第22期26卷 12355-12384页

作者： Lee, Chen-Wei Wong, Wai-Peng Univ Sains Malaysia Sch Management George Town 11800 Penang Malaysia Monash Univ Sch Informat Technol Malaysia CampusJalan Lagoon Selatan Subang Jaya 47500 Selangor Malaysia

This study proposes a combinatorial double auction bi-objective winner determination problem for last-mile delivery using drone. Prior studies are limited on solving mixed integer model, which are not efficient for large-scale scenario. However, this is not practical in real cases as the computation time to obtain the solution is longer due to number of combinations of packages and participants anticipated in the last-mile delivery platform. Four multi-objective evolutionary algorithms (MOEAs) with the decomposed winner determination problem model are experimented. This study is able to yield Pareto optimal solutions from multiple runs of mixed linear integer programming (MILP) using different objectives weights in the model. Unmanned aerial vehicle, or drone, has potential to reduce cost and save time for last-mile logistic operations. The result positively shows MOEAs are more efficient than MILP in yielding a set of feasible solutions for undertaking complex winner determination problem models. The percentage of improvement in terms of time spent identifying the best option is almost 100%. This is likely an unprecedented research in drone where combinatorial double auction is applied to complex drone delivery services and MOEAs are used to solve the associated winner determination problem model.

关键词： Combinatorial double auction Decomposed problem Drone delivery multi-objective evolutionary algorithm Winner determination problem

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A new adaptive decomposition-based evolutionary algorithm for multi- and many-objective optimization

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EXPERT SYSTEMS WITH APPLICATIONS 2023年第PartC期213卷

作者： Bao, Chunteng Gao, Diju Gu, Wei Xu, Lihong Goodman, Erik D. Shanghai Maritime Univ Key Lab Marine Technol & Control Engn Minist Transport Shanghai 201306 Peoples R China Tongji Univ Coll Elect & Informat Engn Shanghai 201804 Peoples R China Michigan State Univ BEACON Ctr Study Evolut Act E Lansing MI 48824 USA

In decomposition-based multi-objective evolutionary algorithms (MOEAs), a set of uniformly distributed refer-ence vectors (RVs) is usually adopted to decompose a multi-objective optimization problem (MOP) into several single-objective sub-problems, and the RVs are fixed during evolution. When it comes to multi-objective opti-mization problems (MOPs) with complex Pareto fronts (PFs), the effectiveness of the multi-objective evolu-tionary algorithm (MOEA) may degrade. To solve this problem, this article proposes an adaptive decomposition -based evolutionary algorithm (ADEA) for both multi-and many-objective optimization. In ADEA, the candidate solutions themselves are used as RVs, so that the RVs can be automatically adjusted to the shape of the Pareto front (PF). Also, the RVs are successively generated one by one, and once a reference vector (RV) is generated, the corresponding sub-objective space is dynamically decomposed into two sub-spaces. Moreover, a variable metric is proposed and merged with the proposed adaptive decomposition approach to assist the selection operation in evolutionary many-objective optimization (EMO). The effectiveness of ADEA is compared with several state-of-the-art MOEAs on a variety of benchmark MOPs with up to 15 objectives. The empirical results demonstrate that ADEA has competitive performance on most of the MOPs used in this study.

关键词： multi-objective evolutionary algorithm Many-objective optimization Pareto front Adaptive decomposition

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A computation offloading algorithm based on multi-objective evolutionary optimization in mobile edge computing

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2023年第1期121卷

作者： Chai, Zheng-Yi Liu, Xu Li, Ya-Lun Tiangong Univ Sch Comp Sci & Technol Tianjin 300387 Peoples R China Tiangong Univ Sch Software Tianjin 300387 Peoples R China Tiangong Univ Tianjin Key Lab Autonomous Intelligence Technol & Tianjin 300387 Peoples R China Tiangong Univ Sch Elect & Informat Engn Tianjin 300387 Peoples R China

For computation offloading problem (COP) in mobile edge computing (MEC), the energy consumption of terminal equipments(TEs) and the delay of mobile equipment applications are two optimization goals. In real life, terminal equipment is dynamic, and their number, mobility, and continuous changes in wireless channels will affect the balance between the mentioned energy consumption and delay. Different from available works, we model the COP in MEC as a dynamic multi-objective problem (DMOP) in this paper, and propose an improved dynamic multi-objective evolutionary optimization based on decomposition (DMOEA/D) to solve it, namely DMOEA/D-COPMEC. In the proposed algorithm, the environmental change is detected by a fixed detector, and whether the current change is similar to the historical change is determined. If so, the difference prediction is used to re-locate the population individual in the new MEC environment, otherwise, the memory -based strategy is used to response environmental change. In MOEA/D, an adaptive weight adjustment strategy based on chain segmentation (CS) is adopted to generate a set of uniformly distributed weight vectors. The simulation results show that the proposed algorithm can better balance the application delay and the terminal energy consumption if there is environment change. The solution set is closer to reality and better than the related algorithms.

关键词： Computation offloading Dynamic multi-objective optimization Mobile edge computing multi-objective evolutionary algorithm (MOEA)

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An Adaptive Formulation-based Many-objective evolutionary algorithm for multi-Scenario Optimization in Data Enrichment

An Adaptive Formulation-based Many-Objective Evolutionary Al...

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IEEE Congress on evolutionary Computation (IEEE CEC)

作者： Fan, Liang Feng, Xudong Wang, Handing Xidian Univ Sch Artificial Intelligence Xian Peoples R China AECC Sichuan Gas Turbine Estab Sci & Technol Altitude Simulat Lab Mianyang Sichuan Peoples R China

ISBN: (纸本)9781728183923

In many practical applications, data enrichment can generate a large amount of accurate data to alleviate the problem of data scarcity. In order to make the fake data generated in data enrichment as close to the real data as possible, the data enriching model must be tuned to meet the loss requirements of multiple objectives in different scenarios, which makes it a multi-scenario many-objective optimization problem. However, due to the curse of the dimensionality of the scenario space and the objective space, the existing many-objective evolutionary algorithms cannot solve the problem in data enrichment well. To effectively handle this problem, we propose an adaptive formulation-based multi-objective evolutionary algorithm, where the aggregation function is used to reduce the dimension of the scenario space to one and the multiple objectives into three objectives through the adaptive formulation of the original problem. In this way, a multi-scenario many-objective problem is converted into a multi-objective problem which could be solved by existing multi-objective evolutionary algorithms. The proposed algorithm is applied to the practical data enrichment problem to solve the multi-scenario many-objective optimization problem and compared with NSGA-III. The experimental results demonstrate the remarkable superiority of the proposed algorithm over NSGA-III.

关键词： Data enrichment adaptive formulation scenario reduction multi-scenario optimization many-objective optimization multi-objective evolutionary algorithm

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Two infill criteria driven surrogate-assisted multi-objective evolutionary algorithms for computationally expensive problems with medium dimensions

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SWARM AND evolutionary COMPUTATION 2021年 60卷

作者： Li, Fan Gao, Liang Garg, Akhil Shen, Weiming Huang, Shifeng Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Sch Mech Sci & Engn Natl CNC Engn Technol Res Ctr Wuhan 430074 Peoples R China

This paper proposed a surrogate-assisted dominance-based multi-objective evolutionary algorithm to solve multi-objective computationally expensive problems with medium dimensions. Two infill criteria are collaboratively used to select promising individuals for exact evaluations. The convergence-based criterion is used to promote the exploitation of current promising areas. This criterion also considers the dispersion of selected solutions to exploit current non-dominant front. The diversity-based criterion is used to enhance the exploration of the population and enhance the accuracy of surrogate models. The feedback information from the convergence-based criterion is used to adjust the frequency of using the diversity-based criterion in order to reduce the consumed function evaluations. Benchmark functions with dimensions varying from 8 to 30 and a reactive power optimization problem are used to test the proposed algorithm. The experimental results demonstrate that the proposed algorithm significantly outperforms some state-of-the-art evolutionary algorithms on most problems.

关键词： Computationally expensive problem multi-objective evolutionary algorithm Infill criterion Surrogate model

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