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This paper brings forward an infeasible proximal bundle method designed for nonsmooth convex multiobjective optimization problems that involve constraints. The method is flexible as it does not require initial feasible points. It directly handles constrained multiobjective functions without scalarization. An aggregation technique is introduced to avoid excessive elements and accelerate convergence. Under reasonable assumptions, the method converges to a global Pareto optimal solution.

Real-world sequential decision-making tasks are generally complex, requiring trade-offs between multiple, often conflicting, objectives. Despite this, the majority of research in reinforcement learning and decision-theoretic planning either assumes only a single objective, or that multiple objectives can be adequately handled via a simple linear combination. Such approaches may oversimplify the underlying problem and hence produce suboptimal results. This paper serves as a guide to the application of multi-objective methods to difficult problems, and is aimed at researchers who are already familiar with single-objective reinforcement learning and planning methods who wish to adopt a multi-objective perspective on their research, as well as practitioners who encounter multi-objective decision problems in practice. It identifies the factors that may influence the nature of the desired solution, and illustrates by example how these influence the design of multi-objective decision-making systems for complex problems.

In the last two decades, the fast and elitist non-dominated sorting genetic algorithm (NSGA-II) has attracted extensive research interests, and it is still one of the hottest research methods to deal with multi-objective optimization problems. Considering the importance and wide applications of NSGA-II method, we believe it is the right time to provide a comprehensive survey of the research work in this area, and also to discuss the potential in the future research. The purpose of this paper is to summarize and explore the literature on NSGA-II and another version called NSGA-III, a reference-point based many-objective NSGA-II approach. In this paper, we first introduce the concept of multi-objective optimization and the foundation of NSGA-II. Then we review the family of NSGA-II and their modifications, and classify their applications in engineering community. Finally, we present several interesting open research directions of NSGA-II for multi-objective optimization.

With the continuous development of aviation technology, the design of airborne system architectures has become increasingly complex and requires trade-offs among multiple objectives. Traditional design methods often fail to optimize multiple objectives simultaneously, leading to limitations in system performance. To address this issue, this paper proposes an AI-assisted multi-objective trade-off method for airborne system architecture, which aims to achieve efficient optimization and trade-off of multiple objectives through AI technology. Combined with a dynamic constraint handling mechanism, this method addresses the pain points of low search efficiency in high-dimensional design spaces and difficulty in balancing multi-objective conflicts in traditional methods.

In this paper, a practical model structure capable of being a non-contact system is derived and investigated. A magnetoresistance model is established. By analysing several influencing factors affecting the transformer core, and on the basis of the traditional transformer according to the design formula of the transformer, according to the electromagnetic geometric relationship and the multi-objective optimization algorithm, the design process of the ipt system is improved by using electromagnetic simulation analysis.

This work proposes a new multi-objective algorithm inspired from the navigation of grass hopper swarms in nature. A mathematical model is first employed to model the interaction of individuals in the swam including attraction force, repulsion force, and comfort zone. A mechanism is then proposed to use the model in approximating the global optimum in a single-objective search space. Afterwards, an archive and target selection technique are integrated to the algorithm to estimate the Pareto optimal front for multi-objective problems. To benchmark the performance of the algorithm proposed, a set of diverse standard multi-objective test problems is utilized. The results are compared with the most well-regarded and recent algorithms in the literature of evolutionary multi-objective optimization using three performance indicators quantitatively and graphs qualitatively. The results show that the proposed algorithm is able to provide very competitive results in terms of accuracy of obtained Pareto optimal solutions and their distribution.

Practitioners often encounter challenging real-world problems that involve a simultaneous optimization of multiple objectives in a complex search space. To address these problems, we propose a practical multiobjective Bayesian optimization algorithm. It is an extension of the widely used Tree-structured Parzen Estimator (TPE) algorithm, called Multiobjective Tree-structured Parzen Estimator (MOTPE). We demonstrate that MOTPE approximates the Pareto fronts of a variety of benchmark problems and a convolutional neural network design problem better than existing methods through the numerical results. We also investigate how the configuration of MOTPE affects the behavior and the performance of the method and the effectiveness of asynchronous parallelization of the method based on the empirical results.

By simultaneously considering the supported truss configuration optimization and optimal attitude–vibration control in rigid–flexible coupling (RFC) structure, this study proposes a novel integrated uncertain optimal structure-control design strategy with interval uncertainties. Based on the principle of energy equivalence, the flexible support truss of the RFC structure is simplified using an equivalent beam model, which can significantly reduce the degree of freedom of the model and improve design efficiency on the premise of satisfying the analysis accuracy of the static and dynamic characteristics of the complete truss structure. The Lagrangian method is applied to establish an RFC structure model including a central rigid body, equivalent flexible truss and free end mass. Given the difficulty of quantifying the multi-source uncertainty encountered by actual RFC structures, the structural optimization and control system design in this study considers them as interval uncertainty. As long as the uncertainty bounds are known, the uncertainty propagation in the integrated design strategy can be quantified using interval dimension-wise analysis. The time-independent interval reliability-based frequency constraint and time-dependent interval reliability-based dynamic response constraint are both constituted for the proposed integrated uncertain optimal design strategy, which is solved using an advanced multi-objective optimization algorithm. One numerical example is applied to verify the proposed method. An optimum integrated design layout with a lightweight truss configuration and a low energy consumption control system is obtained.

The proposed dynamic multi-objective evolutionary algorithm, DMOEA/D-HP, addresses temporal variations in both the Pareto Front (PF) and Pareto Set (PS) for dynamic multi-objective optimization problems (DMOPs). Utilizing a hybrid prediction approach, the algorithm adapts to the dynamic nature of the problem. The population is divided into three segments for prediction: individuals with a distance greater than a threshold in PS for central prediction, those with a distance less than a threshold in PS for differential evolutionary prediction, and the remaining individuals for cross-mutation to maintain diversity. To assess DMOEA/D-HP’s effectiveness, it is compared with three advanced algorithms in DMOP by using the DF test set. Experimental results demonstrate that DMOEA/D-HP outperforms in terms of distribution and convergence when solving DMOPs.

Hyperparameter optimization (HPO) is a necessary step to ensure the best possible performance of Machine Learning (ML) algorithms. Several methods have been developed to perform HPO; most of these are focused on optimizing one performance measure (usually an error-based measure), and the literature on such single-objective HPO problems is vast. Recently, though, algorithms have appeared that focus on optimizing multiple conflicting objectives simultaneously. This article presents a systematic survey of the literature published between 2014 and 2020 on multi-objective HPO algorithms, distinguishing between metaheuristic-based algorithms, metamodel-based algorithms and approaches using a mixture of both. We also discuss the quality metrics used to compare multi-objective HPO procedures and present future research directions.