Application of tropical algebra techniques in bi-objective optimization problems

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийтезисы в сборнике материалов конференциинаучнаярецензирование

Аннотация

We consider constrained bi-objective optimization problems in the framework of tropical mathematics, which focuses on the theory and applications of semirings and semifields with idempotent operations. The problems are to minimize two objectives, given as functions on vectors over an idempotent semifield (a semiring with idempotent addition and invertible multiplication), subject to constraints on the feasible solution in the form of vector inequalities. We apply a solution technique that reduces the bi-objective problems to a system of parametrized inequalities, where the parameters represent the values of the objective functions. The necessary and sufficient conditions for solutions of the system serve for evaluation of parameters to specify the Pareto frontier for the optimization problem. Given the optimal values of parameters, the solution vectors of the system are obtained to form all Pareto-optimal solutions. With this approach, we derive a complete Pareto-optimal solution of the problem in an explicit analytical form, ready for formal analysis and numerical calculations. As real-world applications, we present solutions to constrained bi-criteria problems in time-constrained project scheduling, decision making with pairwise comparisons and minimax single-facility location.
Язык оригиналаанглийский
Название основной публикацииThe 22nd Conference of the International Federation of Operational Research Societies
Подзаголовок основной публикацииProgramme Book
Страницы85
СостояниеОпубликовано - 2021
Событие22nd Conference of the International Federation of Operational Research Societies - Seoul, Республика Корея
Продолжительность: 23 авг 202127 авг 2021
Номер конференции: 22
https://www.ifors2021.kr/

конференция

конференция22nd Conference of the International Federation of Operational Research Societies
Сокращенный заголовокIFORS 2021
Страна/TерриторияРеспублика Корея
ГородSeoul
Период23/08/2127/08/21
Адрес в сети Интернет

Предметные области Scopus

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

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