Explicit solution of a tropical optimization problem with application to project scheduling
Abstract
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.
Cite
@article{arxiv.1303.5457,
title = {Explicit solution of a tropical optimization problem with application to project scheduling},
author = {Nikolai Krivulin},
journal= {arXiv preprint arXiv:1303.5457},
year = {2013}
}
Comments
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 Press, 2013, pp. 39-45. ISBN 978-960-474-339-1