Related papers: Approximation of a Pareto Set Segment Using a Line…
Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be…
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…
Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to…
The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…
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…
Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…
Recently, Pareto Set Learning (PSL) has been proposed for learning the entire Pareto set using a neural network. PSL employs preference vectors to scalarize multiple objectives, facilitating the learning of mappings from preference vectors…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
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…
Papadimitriou and Yannakakis show that the polynomial-time solvability of a certain singleobjective problem determines the class of multiobjective optimization problems that admit a polynomial-time computable $(1+\varepsilon, \dots ,…
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…
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…
Pareto set learning (PSL) is an emerging approach for acquiring the complete Pareto set of a multi-objective optimization problem. Existing methods primarily rely on the mapping of preference vectors in the objective space to Pareto optimal…
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…
We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{\mathbf{x} \in \mathbf{S}}\{ (f_1(\mathbf{x}), f_2(\mathbf{x})) \}$, where $f_1$ and $f_2$ are two…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
Pareto front learning is a technique that introduces preference vectors in a neural network to approximate the Pareto front. Previous Pareto front learning methods have demonstrated high performance in approximating simple Pareto fronts.…
The objective of this paper is to provide a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems for which the objective space is not necessarily convex. Our approach is…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality. The core of the algorithm is a new selection criterion based on a…