Related papers: Bezier Simplex Fitting: Describing Pareto Fronts o…
The Bezier simplex fitting is a novel data modeling technique which exploits geometric structures of data to approximate the Pareto front of multi-objective optimization problems. There are two fitting methods based on different sampling…
B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto…
We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…
In many real-world applications, the Pareto Set (PS) of a continuous multiobjective optimization problem can be a piecewise continuous manifold. A decision maker may want to find a solution set that approximates a small part of the PS and…
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…
Efficiently solving multi-objective optimization problems for simulation optimization of important scientific and engineering applications such as materials design is becoming an increasingly important research topic. This is due largely to…
We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of…
In smooth and convex multiobjective optimization problems the set of Pareto optima is diffeomorphic to an $m-1$ dimensional simplex, where $m$ is the number of objective functions. The vertices of the simplex are the optima of the…
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…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives…
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is…
This article introduces an expansion within SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) suite, now extended to single, multiple, and many objective optimization problems. The newly developed…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…