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Query plans are compared according to multiple cost metrics in multi-objective query optimization. The goal is to find the set of Pareto plans realizing optimal cost tradeoffs for a given query. So far, only algorithms with exponential…
To date, the multi-objective optimization literature has mainly focused on conflicting objectives, studying the Pareto front, or requiring users to balance tradeoffs. Yet, in machine learning practice, there are many scenarios where such…
Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
In solving multi-modal, multi-objective optimization problems (MMOPs), the objective is not only to find a good representation of the Pareto-optimal front (PF) in the objective space but also to find all equivalent Pareto-optimal subsets…
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved…
In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses according to some meta-goal. For example, in physics-informed…
Multi-objective optimization (MOO) is a prevalent challenge for Deep Learning, however, there exists no scalable MOO solution for truly deep neural networks. Prior work either demand optimizing a new network for every point on the Pareto…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
The NSGA-II is the most prominent multi-objective evolutionary algorithm (cited more than 50,000 times). Very recently, a mathematical runtime analysis has proven that this algorithm can have enormous difficulties when the number of…
In this paper we develop two goal-oriented adaptive strategies for a posteriori error estimation within the generalized multiscale finite element framework. In this methodology, one seeks to determine the number of multiscale basis…
In multiobjective optimisation, a set of scalable test problems with a variety of features allow researchers to investigate and evaluate the abilities of different optimisation algorithms, and thus can help them to design and develop more…
Deep neural networks suffer from storing millions and billions of weights in memory post-training, making challenging memory-intensive models to deploy on embedded devices. The weight-sharing technique is one of the popular compression…
We introduce a novel multiobjective optimization algorithm based on the conformational space annealing (CSA) algorithm, MOCSA. It has three characteristic features: (a) Dominance relationship and distance between solutions in the objective…
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…
Ultrathin meta-optics offer unmatched, multifunctional control of light. Next-generation optical technologies, however, demand unprecedented performance. This will likely require design algorithms surpassing the capability of human…
In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary…
We propose a general topology optimization framework for metasurface inverse design that can automatically discover highly complex multi-layered meta-structures with increased functionalities. In particular, we present topology-optimized…
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…
Adaptive optimization methods are well known to achieve superior convergence relative to vanilla gradient methods. The traditional viewpoint in optimization, particularly in convex optimization, explains this improved performance by arguing…