A new non-monotonic infeasible simplex-type algorithm for Linear Programming

PeerJ Computer Science ◽

10.7717/peerj-cs.265 ◽

2020 ◽

Vol 6 ◽

pp. e265

Author(s):

Charalampos P. Triantafyllidis ◽

Nikolaos Samaras

Keyword(s):

Linear Programming ◽

State Of The Art ◽

The State ◽

Feasible Direction ◽

Type Algorithm ◽

Basic Solutions ◽

Interior Points ◽

Number Of Iterations

This paper presents a new simplex-type algorithm for Linear Programming with the following two main characteristics: (i) the algorithm computes basic solutions which are neither primal or dual feasible, nor monotonically improving and (ii) the sequence of these basic solutions is connected with a sequence of monotonically improving interior points to construct a feasible direction at each iteration. We compare the proposed algorithm with the state-of-the-art commercial CPLEX and Gurobi Primal-Simplex optimizers on a collection of 93 well known benchmarks. The results are promising, showing that the new algorithm competes versus the state-of-the-art solvers in the total number of iterations required to converge.

Download Full-text

The State of the Art of Linear Programming on Personal Computers

INFORMS Journal on Applied Analytics ◽

10.1287/inte.18.4.49 ◽

1988 ◽

Vol 18 (4) ◽

pp. 49-58 ◽

Cited By ~ 5

Author(s):

Ramesh Sharda

Keyword(s):

Linear Programming ◽

State Of The Art ◽

The State ◽

Personal Computers

Download Full-text

Solving Delete Free Planning with Relaxed Decision Diagram Based Heuristics

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.11659 ◽

2020 ◽

Vol 67 ◽

pp. 607-651

Author(s):

Margarita Paz Castro ◽

Chiara Piacentini ◽

Andre Augusto Cire ◽

J. Christopher Beck

Keyword(s):

Linear Programming ◽

Empirical Analysis ◽

State Of The Art ◽

The State ◽

Decision Diagrams ◽

Binary Decision ◽

Admissible Heuristics ◽

The Cost ◽

Construction Algorithms ◽

Diagram Representation

We investigate the use of relaxed decision diagrams (DDs) for computing admissible heuristics for the cost-optimal delete-free planning (DFP) problem. Our main contributions are the introduction of two novel DD encodings for a DFP task: a multivalued decision diagram that includes the sequencing aspect of the problem and a binary decision diagram representation of its sequential relaxation. We present construction algorithms for each DD that leverage these different perspectives of the DFP task and provide theoretical and empirical analyses of the associated heuristics. We further show that relaxed DDs can be used beyond heuristic computation to extract delete-free plans, find action landmarks, and identify redundant actions. Our empirical analysis shows that while DD-based heuristics trail the state of the art, even small relaxed DDs are competitive with the linear programming heuristic for the DFP task, thus, revealing novel ways of designing admissible heuristics.

Download Full-text

Practical Picture Processing

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051700 ◽

1974 ◽

Vol 32 ◽

pp. 338-339

Author(s):

T. A. Welton

Keyword(s):

Radiation Damage ◽

Coherence Length ◽

Spatial Information ◽

State Of The Art ◽

Coherent Radiation ◽

The State ◽

Energy Spread ◽

Electron Micrograph ◽

Picture Processing ◽

Molecular Skeleton

Various authors have emphasized the spatial information resident in an electron micrograph taken with adequately coherent radiation. In view of the completion of at least one such instrument, this opportunity is taken to summarize the state of the art of processing such micrographs. We use the usual symbols for the aberration coefficients, and supplement these with £ and 6 for the transverse coherence length and the fractional energy spread respectively. He also assume a weak, biologically interesting sample, with principal interest lying in the molecular skeleton remaining after obvious hydrogen loss and other radiation damage has occurred.

Download Full-text