Related papers: Data-Driven Analysis of Pareto Set Topology
We consider the problem of computing the topology and describing the geometry of a parametric curve in $\mathbb{R}^n$. We present an algorithm, PTOPO, that constructs an abstract graph that is isotopic to the curve in the embedding space.…
Multi-task learning (MTL), which aims to improve performance by learning multiple tasks simultaneously, inherently presents an optimization challenge due to multiple objectives. Hence, multi-objective optimization (MOO) approaches have been…
A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…
Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first…
Normalization of objectives plays a crucial role in evolutionary multi-objective optimization (EMO) to handle objective functions with different scales, which can be found in real-world problems. Although the effect of normalization methods…
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…
Model compression plays a vital role in the practical deployment of deep neural networks (DNNs), and evolutionary multi-objective (EMO) pruning is an essential tool in balancing the compression rate and performance of the DNNs. However, due…
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the…
Knowledge transfer-based evolutionary optimization has garnered significant attention, such as in multi-task evolutionary optimization (MTEO), which aims to solve complex problems by simultaneously optimizing multiple tasks. While this…
This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to…
The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…
We present an approach utilizing Topological Data Analysis to study the structure of face poses used in affective computing, i.e., the process of recognizing human emotion. The approach uses a conditional comparison of different emotions,…
In general, a multi-objective optimization problem does not have a single optimal solution but a set of Pareto optimal solutions, which forms the Pareto front in the objective space. Various evolutionary algorithms have been proposed to…
Problems defined on binary decision spaces have been intensively studied in the theory of multi-objective evolutionary algorithms (MOEAs). In contrast, no mathematical runtime analyses exist so far for MOEAs dealing with decision variables…
The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot…
Multi-objective probabilistic model checking provides a way to verify several, possibly conflicting, quantitative properties of a stochastic system. It has useful applications in controller synthesis and compositional probabilistic…
Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions…
Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…
Computing diverse sets of high quality solutions for a given optimization problem has become an important topic in recent years. In this paper, we introduce a coevolutionary Pareto Diversity Optimization approach which builds on the success…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…