scholarly journals Solving Interval Quadratic Programming Problems by Using the Numerical Method and Swarm Algorithms

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
M. A. Elsisy ◽  
D. A. Hammad ◽  
M. A. El-Shorbagy
Keyword(s):  
Quadratic Programming ◽  
Numerical Method ◽  
Programming Problem ◽  
Numerical Solutions ◽  
Quadratic Programming Problem ◽  
New Approach ◽  
Swarm Algorithms ◽  
Quadratic Programming Problems ◽  
Chaotic Particle Swarm Optimization ◽  
Interval Quadratic Programming

In this paper, we present a new approach which is based on using numerical solutions and swarm algorithms (SAs) to solve the interval quadratic programming problem (IQPP). We use numerical solutions for SA to improve its performance. Our approach replaced all intervals in IQPP by additional variables. This new form is called the modified quadratic programming problem (MQPP). The Karush–Kuhn–Tucker (KKT) conditions for MQPP are obtained and solved by the numerical method to get solutions. These solutions are functions in the additional variables. Also, they provide the boundaries of the basic variables which are used as a start point for SAs. Chaotic particle swarm optimization (CPSO) and chaotic firefly algorithm (CFA) are presented. In addition, we use the solution of dual MQPP to improve the behavior and as a stopping criterion for SAs. Finally, the comparison and relations between numerical solutions and SAs are shown in some well-known examples.

scholarly journals A method of redundant constraint elimination in the problem of body recovery based on support function measurements

2015 ◽  
pp. 348-359
Author(s):  
И.А. Палачев
Keyword(s):  
Quadratic Programming ◽  
Programming Problem ◽  
Support Function ◽  
New Method ◽  
Quadratic Programming Problem ◽  
New Approach ◽  
Recovery Algorithm ◽  
Redundant Constraint ◽  
Order Of Magnitude ◽  
Recovery Methods

Предложен новый алгоритм восстановления тел по измерениям их опорных функций, который представляет собой алгоритм квадратичного или линейного программирования в форме Гарднера-Кидерлена с меньшим числом ограничений. Уменьшение числа ограничений достигается за счет нового метода, который позволяет исключить из исходной системы ограничений часть ограничений как избыточные. Предложен новый подход, позволяющий применять методы восстановления тел по измерениям опорной функции к задаче восстановления тел по теневым контурам. Представлено описание реализации алгоритма, а также результаты его тестирования на реальных промышленных теневых контурах. Предложенный метод в рассмотренном примере позволил сократить число ограничений на 80% и ускорить исходный алгоритм Гарднера-Кидерлена на порядок. A new body recovery algorithm based on support function measurements is proposed. The proposed algorithm represents a linear or quadratic programming problem in Gardner-Kiderlen form with smaller number of constraints. The reduction of constraint number is based on a new method that allows one to eliminate a part of initial constraints as redundant. A new approach of body recovery based on shadow contours is proposed. It allows one to reuse body recovery methods based on support function measurements. The implementation of the algorithm is described and some results of its testing on real industrial contours are discussed. The proposed method ensures the reduction of constraint number by 80% in the discussed example and also enables to speedup the initial Gardner-Kiderlen algorithm by an order of magnitude.

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