Algebraic solution to bi-criteria tropical optimization problems

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Abstract

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.
Original languageEnglish
Number of pages1
StatePublished - May 2021
EventSIAM Conference on Applied Linear Algebra - Virtual Conference, New Orleans, United States
Duration: 17 May 202121 May 2021
https://www.siam.org/conferences/cm/conference/la21

Conference

ConferenceSIAM Conference on Applied Linear Algebra
Abbreviated titleSIAM LA21
Country/TerritoryUnited States
CityNew Orleans
Period17/05/2121/05/21
Internet address

Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Algebra and Number Theory

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