Related papers: Small Approximate Pareto Sets for Bi-objective Sho…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose…
Expensive multi-objective optimization problems can be found in many real-world applications, where their objective function evaluations involve expensive computations or physical experiments. It is desirable to obtain an approximate Pareto…
This work studies the behavior of three elitist multi- and many-objective evolutionary algorithms generating a high-resolution approximation of the Pareto optimal set. Several search-assessment indicators are defined to trace the dynamics…
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…
This paper investigates the problem of computing the shortest path between two states under resource constraints in environments with resource-replenishment regions. Namely, the length of the path is limited by a budget that can be restored…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
This paper deals with approximate Pareto solutions of a nonsmooth interval-valued multiobjective optimization problem with data uncertainty in constraints. We first introduce some kinds of approximate Pareto solutions for the robust…
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…
We are interested in the existence of Pareto solutions to the vector optimization problem $$\text{Min}_{\,\mathbb{R}^m_+} \{f(x) \,|\, x\in \mathbb{R}^n\},$$ where $f\colon\mathbb{R}^n\to \mathbb{R}^m$ is a polynomial map. By using the {\em…
We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…
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…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
Smoothed analysis of multiobjective 0-1 linear optimization has drawn considerable attention recently. The number of Pareto-optimal solutions (i.e., solutions with the property that no other solution is at least as good in all the…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
Recently, it has been shown that the enumeration of Minimal Correction Subsets (MCS) of Boolean formulas allows solving Multi-Objective Boolean Optimization (MOBO) formulations. However, a major drawback of this approach is that most MCSs…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is…