Related papers: Transforming Design Spaces Using Pareto-Laplace Fi…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the $p$-Laplace operator is utilized to approximate a descent method for Lipschitz shapes.…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
Since the rise of Large Language Models (LLMs) a couple of years ago, researchers in metaheuristics (MHs) have wondered how to use their power in a beneficial way within their algorithms. This paper introduces a novel approach that…
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
Traditionally, researchers in decision making have focused on attempting to reach Pareto Optimality using horizontal approaches, where optimality is calculated taking into account every participant at the same time. Sometimes, this may…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
Transmission system operators need to adapt their decision-making tools to the technological evolutions of the twenty first century. A computation inherent to most tools seeks to find alternating-current power flows that minimize power loss…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans,…
Modern cyber-physical systems (e.g., robotics systems) are typically composed of physical and software components, the characteristics of which are likely to change over time. Assumptions about parts of the system made at design time may…
Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and…
Multi-objective optimization (MOO) problems require balancing competing objectives, often under constraints. The Pareto optimal solution set defines all possible optimal trade-offs over such objectives. In this work, we present a novel…
Learning to Optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine learning to enhance conventional optimization techniques. As real-world optimization problems…
An important challenge in multi-objective reinforcement learning is obtaining a Pareto front of policies to attain optimal performance under different preferences. We introduce Iterated Pareto Referent Optimisation (IPRO), which decomposes…
We advance a combined filtered/phase-field approach to topology optimization in the setting of linearized elasticity. Existence of minimizers is proved and rigorous parameter asymptotics are discussed by means of variational convergence…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
Nanophotonics finds ever broadening applications requiring complex component designs with a large number of parameters to be simultaneously optimized. Recent methodologies employing optimization algorithms commonly focus on a single design…
Optimization has found numerous applications in engineering, particularly since 1960s. Many optimization applications in engineering have more than one objective (or performance criterion). Such applications require multi-objective (or…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…