A local search based restart evolutionary algorithm for finding triple product property triples

2018 ◽  
Vol 48 (9) ◽  
pp. 2894-2911 ◽  
Author(s):  
Yi Xiang ◽  
Yuren Zhou ◽  
Zefeng Chen
Keyword(s):  
Local Search ◽  
Evolutionary Algorithm ◽  
Triple Product ◽  
Product Property ◽  
Triple Product Property

scholarly journals A fast search algorithm for 〈m,m,m〉 Triple Product Property triples and an application for 5×5 matrix multiplication

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Sarah Hart ◽  
Ivo Hedtke ◽  
Matthias Müller-Hannemann ◽  
Sandeep Murthy
Keyword(s):  
Search Algorithm ◽  
Matrix Multiplication ◽  
Triple Product ◽  
Product Property ◽  
Fast Search ◽  
Fast Search Algorithm ◽  
Triple Product Property

AbstractWe present a new fast search algorithm for 〈

scholarly journals A note on the triple product property for subsets of finite groups

2011 ◽  
Vol 14 ◽  
pp. 232-237 ◽  
Author(s):  
Peter M. Neumann
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Abelian Subgroup ◽  
Matrix Multiplication ◽  
Triple Product ◽  
Product Property ◽  
Simple Observation ◽  
A Finite Group ◽  
Triple Product Property

AbstractThe triple product property (TPP) for subsets of a finite group was introduced by Henry Cohn and Christopher Umans in 2003 as a tool for the study of the complexity of matrix multiplication. This note records some consequences of the simple observation that if (S1,S2,S3) is a TPP triple in a finite group G, then so is (dS1a,dS2b,dS3c) for any a,b,c,d∈G.Let si:=∣Si∣ for 1≤i≤3. First we prove the inequality s1(s2+s3−1)≤∣G∣ and show some of its uses. Then we show (something a little more general than) that if G has an abelian subgroup of index v, then s1s2s3 ≤v2 ∣G∣.

New Evolutionary Algorithm Based on 2-Opt Local Search to Solve the Vehicle Routing Problem with Private Fleet and Common Carrier

2012 ◽  
pp. 125-148
Author(s):  
Jalel Euchi ◽  
Habib Chabchoub ◽  
Adnan Yassine
Keyword(s):  
Local Search ◽  
Evolutionary Algorithm ◽  
Vehicle Routing ◽  
Cost Savings ◽  
Alternative Mode ◽  
Cost Of Transport ◽  
Routing Problem ◽  
The Cost ◽  
Specific Assignment ◽  
Selection Of

Mismanagement of routing and deliveries between sites of the same company or toward external sites leads to consequences in the cost of transport. When shipping alternatives exist, the selection of the appropriate shipping alternative (mode) for each shipment may result in significant cost savings. In this paper, the authors examine a class of vehicle routing in which a fixed internal fleet is available at the warehouse in the presence of an external transporter. The authors describe hybrid Iterated Density Estimation Evolutionary Algorithm with 2-opt local search to determine the specific assignment of each tour to a private vehicle (internal fleet) or an outside carrier (external fleet). Experimental results show that this method is effective, allowing the discovery of new best solutions for well-known benchmarks.

scholarly journals Markov Chain Analyses of Random Local Search and Evolutionary Algorithm

2014 ◽  
Vol 1 (3) ◽  
pp. 220 ◽  
Author(s):  
Hiroshi Furutani ◽  
Hiroki Tagami ◽  
Makoto Sakamoto ◽  
Yifei Du
Keyword(s):  
Markov Chain ◽  
Local Search ◽  
Evolutionary Algorithm
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