In multiobjective optimisation, a set of scalable test problems with a variety of features allow researchers to investigate and evaluate the abilities of different optimisation algorithms, and thus can help them to design and develop more effective and efficient approaches. Existing test problem suites mainly focus on situations where all the objectives are fully conflicting with each other. In such cases, an m-objective optimisation problem has an (m-1)-dimensional Pareto front in the objective space. However, in some optimisation problems, there may be unexpected characteristics among objectives, e.g., redundancy. The redundancy of some objectives can lead to the multiobjective problem having a degenerate Pareto front, i.e., the dimension of the Pareto front of the $m$-objective problem be less than (m-1). In this paper, we systematically study degenerate multiobjective problems. We abstract three general characteristics of degenerate problems, which are not formulated and systematically investigated in the literature. Based on these characteristics, we present a set of test problems to support the investigation of multiobjective optimisation algorithms under situations with redundant objectives. To the best of our knowledge, this work is the first one that explicitly formulates these three characteristics of degenerate problems, thus allowing the resulting test problems to be featured by their generality, in contrast to existing test problems designed for specific purposes (e.g., visualisation).
Training-Free Diffusion-Driven Modeling of Pareto Set Evolution for Dynamic Multiobjective Optimization
Institute of Artificial Intelligence, Xiamen University（厦门大学人工智能研究所）；Department of Artificial Intelligence, School of Informatics, Xiamen University（厦门大学信息学院人工智能系）；Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education（教育部多媒体可信感知与高效计算重点实验室）；Key Laboratory of Digital Protection and Intelligent Processing of Intangible Cultural Heritage of Fujian and Taiwan, Ministry of Culture and Tourism（文化和旅游部闽台非物质文化遗产数字化保护与智能处理重点实验室）；Department of Artificial Intelligence, Sichuan University（四川大学人工智能系）
A Large-Scale Sparse Multiobjective Optimization Algorithm Based on Optimal Performance Scores
School of Computer Science, South China Normal University（华南师范大学计算机学院）；National-local Joint Engineering Laboratory for Digitalize Eletrical Design Technology, Wenzhou University（温州大学数字电气设计技术国家地方联合工程实验室）；Institute of Science and Technology Innovation, Dongguan University of Technology（东莞理工学院科技创新研究院）；College of Cyber Security, Guangzhou University（广州大学网络空间安全学院）
Proven Advantage of Multiobjective Evolutionary Algorithms for Problems with Different Degrees of Conflict
School of Computer Science and Technology, International Research Institute for Artificial Intelligence, Harbin Institute of Technology, Shenzhen, China（哈尔滨工业大学深圳，计算机科学与技术学院，人工智能国际研究院）
Benchmark for CEC 2024 Competition on Multiparty Multiobjective Optimization
School of Computer Science and Technology, Harbin Institute of Technology（哈尔滨工业大学计算机科学与技术学院）；School of Artificial Intelligence, Nanjing University of Information Science and Technology（南京信息工程大学人工智能学院）；Department of Computer Science and Engineering, Southern University of Science and Technology（南方科技大学计算机科学与工程系）
An Ontology of Preference-Based Multiobjective Metaheuristics
National University of Defense Technology（国防科技大学）；Leiden University（莱顿大学）；De Montfort University（德蒙福特大学）；Instituto Universitário de Lisboa (ISCTE-IUL)（里斯本大学学院）；Polytechnic Institute of Leiria（莱里亚理工学院）；University of Münster（明斯特大学）
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）
