Algebraic solution to bi-criteria tropical optimization problems

Результат исследований: Материалы конференцийтезисырецензирование


We consider constrained tropical optimization problems in which two objective functions are minimized simultaneously in the linear space of vectors over idempotent semifield. The objective functions in the problems take a form that includes both the unknown vector and its conjugate transpose, and are sometimes called tropical pseudo-linear and pseudo-quadratic functions. The feasible solution set is defined by linear vector inequalities and box constraints. To solve such a bi-objective problem, we follow an approach that involves the introduction of two parameters to represent the minimum values of the objective functions and thereby describe the Pareto frontier for the problem. The optimization problem then reduces to a system of parametrized vector inequalities. We exploit the necessary and sufficient conditions for solutions of the system to derive the Pareto frontier. All solutions of the system, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. As practical illustrations, we offer applications of the results obtained to solve bi-criteria decision-making problems of rating alternatives through pairwise comparisons and bi-criteria project management problems of project scheduling under temporal constraints.
Язык оригиналаанглийский
Число страниц1
СостояниеОпубликовано - мая 2021
СобытиеSIAM Conference on Applied Linear Algebra - Virtual Conference, New Orleans, Соединенные Штаты Америки
Продолжительность: 17 мая 202121 мая 2021


конференцияSIAM Conference on Applied Linear Algebra
Сокращенный заголовокSIAM LA21
Страна/TерриторияСоединенные Штаты Америки
ГородNew Orleans
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Предметные области Scopus

  • Теория управления и исследование операций
  • Теория оптимизации
  • Алгебра и теория чисел