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1. Managing Objective Archives for Solution Set Reduction in Many-Objective Optimization

   https://doi.org/10.1109/SSCI52147.2023.10372007  

   Peerlinck, Amy; Sheppard, John (December 2023, IEEE Symposium Series on Computational Intelligence)

   As objectives increase in many-objective optimization (MaOO), often so do the number of non-dominated solutions, potentially resulting in solution sets with thousands of non-dominated solutions. Such a larger final solution set increases difficulty in visualization and decision-making. This raises the question: how can we reduce this large solution set to a more manageable size? In this paper, we present a new objective archive management (OAM) strategy that performs post-optimization solution set reduction to help the end-user make an informed decision without requiring expert knowledge of the field of MaOO. We create separate archives for each objective, selecting solutions based on their fitness as well as diversity criteria in both the objective and variable space. We can then look for solutions that belong to more than one archive to create a reduced final solution set. We apply OAM to NSGA-II and compare our approach to environmental selection finding that the obtained solution set has better hypervolume and spread. Furthermore, we compare results found by OAM-NSGA-II to NSGA-III and get competitive results. Additionally, we apply OAM to reduce the solutions found by NSGA-III and find that the selected solutions perform well in terms of overall fitness, successfully reducing the number of solutions. 

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2. A Novel Objective Reduction Algorithm for Nonlinear Many-Objective Optimization Problems

   https://doi.org/10.69997/sct.108915  

   Wang, Hongxuan; Allman, Andrew (July 2025, Systems & Control Transactions)

   Sustainability is increasingly recognized as a critical global issue. Multi-objective optimization is an important approach for sustainable decision-making, but problems with four or more objectives are hard to interpret due to its high dimensions. In our groups previous work, an algorithm capable of systematically reducing objective dimensionality for (mixed integer) linear Problem has been developed. In this work, we will extend the algorithm to tackle nonlinear many-objective problems. An outer approximation-like method is employed to systematically replace nonlinear objectives and constraints. After converting the original nonlinear problem to linear one, previous linear algorithm can be applied to reduce the dimensionality. The benchmark DTLZ5(I, M) problem set is used to evaluate the effectiveness of this approach. Our algorithm demonstrates the ability to identify appropriate objective groupings on benchmark problems of up to 20 objectives when algorithm hyperparameters are appropriately chosen. We also conduct extensive testing on the hyperparameters to determine their optimal settings. Additionally, we analyze the computation time required for different components of the algorithm, ensuring efficiency and practical applicability. 

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3. Federated Multi-Objective Learning

   Yang, Haibo; Liu, Zhuqing; Liu, Jia; Dong, Chaosheng; Momma, Michinari (December 2024, NeurIPS)
4. Multi-Objective PSO-PINN

   Davi, Caio; Braga-Neto, Ulisses (July 2023, 1st workshop on Synergy of Scientific and Machine Learning Modeling, SynS & ML - ICML, Honolulu, Hawaii, USA. July, 2023.)

   PSO-PINN is a class of algorithms for training physics-informed neural networks (PINN) using particle swarm optimization (PSO). PSO-PINN can mitigate the well-known difficulties presented by gradient descent training of PINNs when dealing with PDEs with irregular solutions. Additionally, PSO-PINN is an ensemble approach to PINN that yields reproducible predictions with quantified uncertainty. In this paper, we introduce Multi-Objective PSO-PINN, which treats PINN training as a multi-objective problem. The proposed multi-objective PSO-PINN represents a new paradigm in PINN training, which thus far has relied on scalarizations of the multi-objective loss function. A full multi-objective approach allows on-the-fly compromises in the trade-off among the various components of the PINN loss function. Experimental results with a diffusion PDE problem demonstrate the promise of this methodology. 

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5. Federated Multi-Objective Learning

   Yang, Haibo: Liu; Liu, Jia; Dong, Chaosheng; Momma, Michinari (December 2023, Proc. NeurIPS)