Related papers: One-Exact Approximate Pareto Sets
In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to…
An NP-hard combinatorial optimization problem $\Pi$ is said to have an {\em approximation threshold} if there is some $t$ such that the optimal value of $\Pi$ can be approximated in polynomial time within a ratio of $t$, and it is NP-hard…
Many-objective optimisation, a subset of multi-objective optimisation, involves optimisation problems with more than three objectives. As the number of objectives increases, the number of solutions needed to adequately represent the entire…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
In many environmental monitoring scenarios, the sampling robot needs to simultaneously explore the environment and exploit features of interest with limited time. We present an anytime multi-objective informative planning method called…
The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows.…
The Next Release Problem consists in selecting a subset of requirements to develop in the next release of a software product. The selection should be done in a way that maximizes the satisfaction of the stakeholders while the development…
The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+eps)-approximations in f(k,eps)n^{O(1)} time where k is some parameter of the input. We obtain the following results on…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
This paper addresses the problem of constrained multi-objective optimization over black-box objective functions with practitioner-specified preferences over the objectives when a large fraction of the input space is infeasible (i.e.,…
In multi-criteria optimization problems, several objective functions have to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as the optimal…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
$ \newcommand{\eps}{\epsilon} \newcommand{\NP}{\mathsf{NP}} \newcommand{\YES}{\mathsf{YES}} \newcommand{\NO}{\mathsf{NO}} \newcommand{\myminus}{\text{-}}\newcommand{\Bsat}{{\mathsf{B}}} \newcommand{\threesat}{\rm{3}\myminus\mathsf{SAT}}…
Recently, the property of connectedness has been claimed to give a strong motivation on the design of local search techniques for multiobjective combinatorial optimization (MOCO). Indeed, when connectedness holds, a basic Pareto local…
We present an extremely simple polynomial-space exponential-time $(1-\varepsilon)$-approximation algorithm for MAX-k-SAT that is (slightly) faster than the previous known polynomial-space $(1-\varepsilon)$-approximation algorithms by Hirsch…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…