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Tutorial on

Multiobjective Optimization in the Presence of Constraints

by Bogdan Filipič and Aljoša Vodopija


Until recently, it has been generally believed that constraint handling techniques (CHTs) developed for single-objective optimization can be easily adapted for multiobjective optimization. As the evolutionary computation community is now realizing this is more difficult than expected, increasingly more research is focusing on constraint handling in multiobjective optimization. This tutorial provides an overview of the state of the art in the field. It starts with the motivation for dealing with constrained multiobjective optimization problems (CMOPs), gives their formal definition, and describes the prerequisites for and challenges in solving CMOPs. Next, it discusses CHTs for both single- and multiobjective optimization with an emphasis on the recently proposed techniques for multiobjective optimization. It further presents the test problems, contrasts the artificial and real-world ones, and characterizes the problems from the perspective of constraints. It also discusses the means for assessing the performance of algorithms solving CMOPs. The tutorial concludes with a summary of the state of the art and a discussion of open issues and future research directions.


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[PHOTO] Bogdan Filipič is a senior researcher and head of Computational Intelligence Group at the Department of Intelligent Systems of the Jožef Stefan Institute, Ljubljana, Slovenia, and associate professor of Computer Science at the Jožef Stefan International Postgraduate School. He received his Ph.D. degree in Computer Science from the University of Ljubljana. His research interests are in computational intelligence, evolutionary computation and stochastic optimization. He focuses on evolutionary multiobjective optimization, including result visualization, constraint handling and use of surrogate models. He is also active in promoting evolutionary computation in practice and has led optimization projects for steel industry, car manufacturing and energy management. He was the general chair of PPSN 2014, organized several special sessions and tracks at major international conferences, and served as program chair at BIOMA 2020. He was a guest lecturer at the University of Oulu, Finland, and the VU University Amsterdam, The Netherlands, and was giving tutorials at recent CEC and GECCO conferences.

[PHOTO] Aljoša Vodopija is a research assistant at the Department of Intelligent Systems of the Jožef Stefan Institute, Ljubljana, Slovenia, and a final-year Ph.D. student of Information and Communication Technologies at the Jožef Stefan International Postgraduate School. In 2017, he received his M.Sc. degree in Mathematics from the University of Ljubljana, Faculty of Mathematics and Physics. He joined the Department of Intelligent Systems in 2016. He initially spent two years working on European projects H2020. His research involved optimization, machine learning and model-driven decision support systems. Within his current doctoral research, he focuses on constrained multiobjective optimization with evolutionary algorithms. Besides, he is involved in international projects developing solutions for engineering optimization problems, including optimization of elevator systems and finding optimal landing sites for lunar landers.