Related papers: ROM-based multiobjective optimization of elliptic …
For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming…
Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty…
Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…
Multi-objective optimization (MOO) arises in many real-world applications where trade-offs between competing objectives must be carefully balanced. In the offline setting, where only a static dataset is available, the main challenge is…
Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be…
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…
Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond…
Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic…
In this paper, we propose a simple yet efficient strategy for improving the multi-objective steepest descent method proposed by Fliege and Svaiter (Math Methods Oper Res, 2000, 3: 479--494). The core idea behind this strategy involves…
According to the published papers and books since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems treated by population-based optimizers like Evolutionary…
A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization…
The decomposition-based method has been recognized as a major approach for multi-objective optimization. It decomposes a multi-objective optimization problem into several single-objective optimization subproblems, each of which is usually…
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
In this paper, we deal with the Front Steepest Descent algorithm for multi-objective optimization. We point out that the algorithm from the literature is often incapable, by design, of spanning large portions of the Pareto front. We thus…
For general multi-objective optimization problems, we propose a novel performance metric called domination measure to measure the quality of a solution, which can be intuitively interpreted as the size of the portion of the solution space…
Multi-task learning solves multiple correlated tasks. However, conflicts may exist between them. In such circumstances, a single solution can rarely optimize all the tasks, leading to performance trade-offs. To arrive at a set of optimized…
In the context of the optimization of rotating electric machines, many different objective functions are of interest and considering this during the optimization is of crucial importance. While evolutionary algorithms can provide a Pareto…
Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is…
While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…