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Explicit solution of a tropical optimization problem with application to project scheduling. / Krivulin, Nikolai.
Mathematical Methods and Optimization Techniques in Engineering: Proc. 1st Intern. Conf. on Optimization Techniques in Engineering (OTENG '13), Antalya, Turkey, October 8-10, 2013. WSEAS - World Scientific and Engineering Academy and Society, 2013. стр. 242 стр., 39-45.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная
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TY - CHAP
T1 - Explicit solution of a tropical optimization problem with application to project scheduling
AU - Krivulin, Nikolai
PY - 2013
Y1 - 2013
N2 - A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate transposition operator. A special case of the problem, which arises in just-in-time scheduling, serves as a motivation for the study. To solve the general problem, we derive a sharp lower bound for the objective function and then find vectors that yield the bound. Under general conditions, an explicit solution is obtained in a compact vector form. This result is applied to provide new solutions for scheduling problems under consideration. To illustrate, numerical examples are also presented.
AB - A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate transposition operator. A special case of the problem, which arises in just-in-time scheduling, serves as a motivation for the study. To solve the general problem, we derive a sharp lower bound for the objective function and then find vectors that yield the bound. Under general conditions, an explicit solution is obtained in a compact vector form. This result is applied to provide new solutions for scheduling problems under consideration. To illustrate, numerical examples are also presented.
KW - idempotent semifield
KW - tropical optimization problem
KW - nonlinear objective function
KW - span seminorm
KW - project scheduling
M3 - Chapter
SN - 978-960-474-339-1
SP - 242 стр., 39-45
BT - Mathematical Methods and Optimization Techniques in Engineering: Proc. 1st Intern. Conf. on Optimization Techniques in Engineering (OTENG '13), Antalya, Turkey, October 8-10, 2013
PB - WSEAS - World Scientific and Engineering Academy and Society
ER -
ID: 4651297