Some Linear Minimax Problems Over an Ordered Field

1955 ◽  
Vol 77 (3) ◽  
pp. 541
Author(s):  
R. J. Levit
Keyword(s):  
Minimax Problems ◽  
Ordered Field

scholarly journals A Shuffle-Based Artificial Bee Colony Algorithm for Solving Integer Programming and Minimax Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1211
Author(s):  
Ivona Brajević
Keyword(s):  
Integer Programming ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Minimax Problems ◽  
Abc Algorithm ◽  
Bee Colony ◽  
Effective Performance ◽  
Complex Optimization ◽  
Overall Performance ◽  
Integer Programming Problems

The artificial bee colony (ABC) algorithm is a prominent swarm intelligence technique due to its simple structure and effective performance. However, the ABC algorithm has a slow convergence rate when it is used to solve complex optimization problems since its solution search equation is more of an exploration than exploitation operator. This paper presents an improved ABC algorithm for solving integer programming and minimax problems. The proposed approach employs a modified ABC search operator, which exploits the useful information of the current best solution in the onlooker phase with the intention of improving its exploitation tendency. Furthermore, the shuffle mutation operator is applied to the created solutions in both bee phases to help the search achieve a better balance between the global exploration and local exploitation abilities and to provide a valuable convergence speed. The experimental results, obtained by testing on seven integer programming problems and ten minimax problems, show that the overall performance of the proposed approach is superior to the ABC. Additionally, it obtains competitive results compared with other state-of-the-art algorithms.

Scale, Landscape and Indigenous Bedouin Land Use: Spatial Order and Agricultural Sedentarisation in the Negev Highland

2021 ◽  
Vol 25 (1) ◽  
pp. 4-35
Author(s):  
Ariel Meraiot ◽  
Avinoam Meir ◽  
Steve Rosen
Keyword(s):  
Large Scale ◽  
Small Scale ◽  
Scale Analysis ◽  
Structure Development ◽  
British Mandate ◽  
Field Surveys ◽  
Ordered Field ◽  
Modern Period ◽  
Ordered Space ◽  
Sustainable Planning

By taking a small-scale perspective, Bedouin pastoral space in the Israeli Negev in the modern period has been misinterpreted as chaotic by various Israeli institutions. In critiquing this ontology we suggest that a knowledge gap with regard to an appropriate scale of understanding Bedouin settlement patterns and mechanisms of sedentarisation is at its root, and that a larger-scale analysis indicates that their space is in fact highly ordered. Field surveys and interviews with the local Bedouin showed that household cultivation plots in the Negev Highland during the period of the British Mandate were organised at a large scale through natural and man-made landscape features reflecting their structure, development and deployment in a highly ordered space. This analysis carries significant implications for understanding pastoral spaces at the local scale, particularly offering better comprehension of various sedentary forms and suggesting new approaches to sustainable planning and development for the Bedouin.

Making the hyperreal line both saturated and complete

1991 ◽  
Vol 56 (3) ◽  
pp. 1016-1025 ◽  
Author(s):  
H. Jerome Keisler ◽  
James H. Schmerl
Keyword(s):  
Set Theory ◽  
Nonempty Intersection ◽  
Finite Intersection ◽  
Second Order Arithmetic ◽  
Ordered Field ◽  
Finite Intersection Property ◽  
Regular Cardinals ◽  
Hyperreal Numbers ◽  
Order Arithmetic ◽  
Internal Sets

AbstractIn a nonstandard universe, the κ-saturation property states that any family of fewer than κ internal sets with the finite intersection property has a nonempty intersection. An ordered field F is said to have the λ-Bolzano-Weierstrass property iff F has cofinality λ and every bounded λ-sequence in F has a convergent λ-subsequence. We show that if κ < λ are uncountable regular cardinals and βα < λ whenever α < κ and β < λ then there is a κ-saturated nonstandard universe in which the hyperreal numbers have the λ-Bolzano-Weierstrass property. The result also applies to certain fragments of set theory and second order arithmetic.

Sign in / Sign up

Export Citation Format

Share Document