13 papers · ranked by Valyu relevance
Demétrios Araújo Magalhães Coutinho, Samuel Xavier‐de‐Souza, Daniel Aloise
'Daniel Aloise'] The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the conception of this algorithm. In this paper, we present a…
Henry W. Robbins, Samuel C Gutekunst, Frans Schalekamp, David B. Shmoys + 1 more
'David B. Shmoys' 'David P. Williamson'] The Simplex algorithm for solving linear programs—one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century—is an important topic in many algorithms courses. While the algorithm relies on intuitive geometric ideas, the…
Daniel Gibor
In this paper, we present a randomized polynomial-time simplex algorithm with higher probability and tighter bounds for linear programming by applying improved quasi-convex properties, a logarithmic rounding on a given polytope and its logarithmic perturbation. We base our work on the first randomized polynomial-time…
Alexander Black, Jesús A. De Loera, Sean Kafer, Laura Sanità
We present new pivot rules for the Simplex method for LPs over 0/1 polytopes. We show that the number of non-degenerate steps taken using these rules is strongly polynomial and even linear in the dimension or in the number of variables. Our bounds on the number of steps are asymptotically optimal on several well-known…
Kirill Kukharenko, Laura Sanità
The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better extreme point along an improving edgedirection of the underlying polyhedron.
Seid Miad Zandavi, Yuk Ying Chung, Ali Anaissi
The scheduling of multi-user remote laboratories is modeled as a multimodal function for the proposed optimization algorithm. The hybrid optimization algorithm, hybridization of the Nelder-Mead Simplex algorithm and Non-dominated Sorting Genetic Algorithm (NSGA), is proposed to optimize the timetable problem for the…
Alberto Del Pia, Carla Michini
The goal of this paper is to design a simplex algorithm for linear programs on lattice polytopes that traces 'short' simplex paths from any given vertex to an optimal one. We consider a lattice polytope P contained in [0, k] n and defined via m linear inequalities. Our first contribution is a simplex algorithm that…
Birgit Rudloff, Fırdevs Ulus, Robert J. Vanderbei
In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (the Evans-Steuer) algorithm [15]. Different from it, the proposed algorithm works in the parameter space and does not aim to find…
Denis Kleverov, Ekaterina Aladyeva, Alexey Serdyukov, Maxim N. Artyomov
Non-negative matrix factorization (NMF) is one of the most powerful linear algebra tools, which has found application in various areas of data analysis, including computational biology. Despite numerous optimization methods devised for NMF, our comprehension of the inherent topological structure within factorizable…
Colin Lynch, Kaitlin Baudier, Douglas Montgomery, Meghan Barrett
Animal nutritionists seek to understand how animals regulate the intake and balance of multiple nutrients, yet the design and analysis of such experiments are often limited by how nutrient spaces are represented. The geometric framework for nutrition (GFN) provides a powerful means to visualize nutrient interactions…
Michael W. Reimann, Daniela Egas-Santander
Neuronal connectivity has been characterized at various scales and with respect to various structural aspects. In models of connectivity, it has so far remained difficult to match all of them at once, in particular the higher-order structure appears to be elusive. Here we introduce a new type of graph model that…
Prasad U. Bandodkar, Razeen R. Shaikh, Gregory T. Reeves
Model development is essential to gain a mathematical understanding of the underlying phenomena in systems biology. In most models, it is typically hard to estimate the values of the biophysical/phenomenological parameters that characterize the model. The parameters are estimated by minimizing a function that reduces a…
Changin Oh, Kathleen P. Wilkie
We present the Toroidal Search Algorithm (TSA), a novel population-based metaheuristic optimization method inspired by the topology of a torus. Conventional metaheuristics frequently suffer from boundary stagnation, a phenomenon that severely degrades performance in bounded and high-dimensional search spaces. TSA…