TY - CONF

T1 - Algebraic solution to bi-criteria tropical optimization problems

AU - Кривулин, Николай Кимович

N1 - Krivulin N. Algebraic solution to bi-criteria tropical optimization problems // SIAM Conference on Applied Linear Algebra (LA21). May 17 - 21, 2021. Virtual Conference. URL: https://meetings.siam.org/sess/dsp_talk.cfm?p=111906.

PY - 2021/5

Y1 - 2021/5

N2 - 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.

AB - 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.

UR - https://evoq-eval.siam.org/conferences/cm/conference/la21

M3 - Abstract

T2 - SIAM Conference on Applied Linear Algebra

Y2 - 17 May 2021 through 21 May 2021

ER -