16 papers · ranked by Valyu relevance
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…
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.
Eleon Bach, Sophie Huiberts
Smoothed analysis is a method for analyzing the performance of algorithms, used especially for those algorithms whose running time in practice is significantly better than what can be proven through worst-case analysis. Spielman and Teng (STOC '01) introduced the smoothed analysis framework of algorithm analysis and…
Yann Disser, Nils Mosis
The existence of a polynomial-time pivot rule for the simplex method is a fundamental open question in optimization. While many super-polynomial lower bounds exist for individual or very restricted classes of pivot rules, there currently is little hope for an unconditional lower bound that addresses all pivot rules. We…
Rutinaldo Aguiar Nascimento, Álvaro Barroca Neto, Yuri Shalom de Freitas Bezerra, Hugo Alexandre Dantas do Nascimento + 3 more
'Yuri Shalom de Freitas Bezerra' 'Hugo Alexandre Dantas do Nascimento' 'Liacir dos Santos Lucena' 'Joaquim Elias de Freitas' 'Seyedali Mirjalili'] The FWI is formulated as a nonlinear optimization problem that traditionally uses local (derivative-based) minimization to find the scalar field of properties that best…
Liming Wei, Fengyang Zhang, Vedik Basetti
To accelerate energy efficiency improvement and green transition in industrial parks while addressing energy utilization and carbon reduction requirements, this study proposes a low-carbon economic dispatch model for integrated energy systems (IES) based on an enhanced multi-objective artificial hummingbird algorithm…
Tianhao Liu, Shanwen Pu, Dongdong Ge, Yinyu Ye
Linear programming has been practically solved mainly by simplex and interior point methods. Compared with the weakly polynomial complexity obtained by the interior point methods, the existence of strongly polynomial bounds for the length of the pivot path generated by the simplex methods remains a mystery. In this…
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 edge-direction of the underlying polyhedron. A key…
Hassan Musafer, Emre Tokgoz, Ausif Mahmood, Jingbo Wang
This article provides a new tool for examining the efficiency and robustness of derivative-free optimization algorithms based on high-dimensional normalized data profiles that test a variety of performance metrics. Unlike the traditional data profiles that examine a single dimension, the proposed data profiles require…
Jan Schröder, Yair Censor, Philipp Süss, Karl-Heinz Küfer
Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Qianxiang Ai, Joshua Schrier
In a recent paper in this journal (Chem. Mater. 2022, 34, 2545-2552), Twyman et al. studied the environmental stability of crystals by introducing a greedy heuristic algorithm for determining possible oxidation reactions. We show how the problem can be solved exactly, with less code and comparable computational time by…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Killian Hong-Minh, Paul Sheehan
In this report we apply the algorithm for measuring the volume of polytopes described by Jim Lawrence [1], to Polytropes [2]. By using a tropical form of Cramer's rule we found an efficient way to find all pseudovertices which are necessary for computing the volume. Due to the limited possibilities for hyperplanes of…
Authors not listed
Identifying synthesis routes from knowledge graphs poses challenges beyond retrosynthesis, including path–finding artifacts and data issues. We introduce “SynGPS”, a novel algorithm that overcomes these limitations by identifying viable routes even with common artifacts. SynGPS can resolve nonsensical cycles…