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We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective…
We consider multicriteria problems of evaluating absolute ratings (scores, priorities, weights) of given alternatives for making decisions, which are compared in pairs under several criteria. Given matrices of pairwise comparisons of…
We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall scores of the alternatives. We…
We consider a decision-making problem to find absolute ratings of alternatives that are compared in pairs under multiple criteria, subject to constraints in the form of two-sided bounds on ratios between the ratings. Given matrices of…
We describe a new approach based on tropical optimization techniques to solve the problem of rating alternatives from pairwise comparison data. The problem is formulated to approximate, in the log-Chebyshev sense, pairwise comparison…
We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained…
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…
We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…
We introduce new discrete best approximation problems, formulated and solved in the framework of tropical algebra, which deals with semirings and semifields with idempotent addition. Given a set of samples, each consisting of the input and…
We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with idempotent addition and invertible multiplication). The…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition.…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
We examine a multidimensional optimisation problem in the tropical mathematics setting. The problem involves the minimisation of a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear…
We consider location problems to find the optimal sites of placement of a new facility, which minimize the maximum weighted Chebyshev or rectilinear distance to existing facilities under constraints on a feasible location domain. We examine…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…