11 papers · ranked by Valyu relevance
Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
Approximate integer programming is the following: For a given convex body $K \subseteq{\mathbb{R}}^n$, either determine whether $K \cap{\mathbb{Z}}^n$ is empty, or find an integer point in the convex body $2\cdot K - c +c$ which is K, scaled by 2 from its center of gravity c. Approximate integer programming can be…
Zhi-Cheng Wang, Xiao-Bei Wu
Biogeography-based optimization (BBO) is a relatively new bioinspired heuristic for global optimization based on the mathematical models of biogeography. By investigating the applicability and performance of BBO for integer programming, we find that the original BBO algorithm does not perform well on a set of benchmark…
Ahmed F. Ali, Mohamed A. Tawhid
Cuckoo search algorithm is a promising metaheuristic population based method. It has been applied to solve many real life problems. In this paper, we propose a new cuckoo search algorithm by combining the cuckoo search algorithm with the Nelder-Mead method in order to solve the integer and minimax optimization…
Gennadiy Averkov, Matthias Schymura
For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called the relaxation complexity ${{\,\mathrm{rc}\,}}X$. This parameter, introduced by Kaibel & Weltge (2015), captures the complexity of linear descriptions of X without using…
Ulrich Pferschy, Rostislav Staněk
The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph $G = V, E$ and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with respect to the distances d. The method of choice for solving the TSP to…
Ritchie Lee, Susmit Jha, Anastasia Mavridou, Dimitra Giannakopoulou + 4 more
'Ralph Bottesch' 'Max W. Haslbeck' 'Alban Reynaud' 'René Thiemann'] We implement a decision procedure for linear mixed integer arithmetic and formally verify its soundness in Isabelle/HOL. We further integrate this procedure into one application, namely into CeTA, a formally verified certifier to check untrusted…
Elisabeth Gaar, Markus Sinnl
The discrete -neighbor -center problem (d--CP) is an emerging variant of the classical -center problem which recently got attention in literature. In this problem, we are given a discrete set of points and we need to locate facilities on these points in such a way that the maximum distance between each point where no…
Martin Gonzalez, Jose J. López-Espín, Juan Aparicio, El-Ghazali Talbi + 1 more
'El-Ghazali Talbi' 'Nicholas Higham'] Mixed Integer Linear Programs (MILPs) are usually NP-hard mathematical programming problems, which present difficulties to obtain optimal solutions in a reasonable time for large scale models. Nowadays, metaheuristics are one of the potential tools for solving this type of problems…
Albert No
The size of the largest binary single deletion code has been unknown for more than 50 years. It is known that Varshamov-Tenengolts (VT) code is an optimum single deletion code for block length $n\leq10$; however, only a few upper bounds of the size of single deletion code are proposed for larger n. We provide improved…
Ahmad Abdi, Gérard Cornuéjols, Bertrand Guenin, Levent Tunçel
A rational number is dyadic if it has a finite binary representation $p/2^k$, where p is an integer and k is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in floating-point arithmetic on a computer. A vector is dyadic if all its entries are…
Daniel Molina-Pérez, Edgar Alfredo Portilla-Flores, Efrén Mezura-Montes, Eduardo Vega-Alvarado + 2 more
'Efrén Mezura-Montes' 'Eduardo Vega-Alvarado' 'María Bárbara Calva-Yañez' 'Thomas Stützle'] Mixed integer nonlinear programming (MINLP) addresses optimization problems that involve continuous and discrete/integer decision variables, as well as nonlinear functions. These problems often exhibit multiple discontinuous…