Related papers: Using tropical optimization techniques in bi-crite…
We present a novel approach to help decision-makers efficiently identify preferred solutions from the Pareto set of a multi-objective optimization problem. Our method uses a Bayesian model to estimate the decision-maker's utility function…
The tropical semiring is an algebraic system with addition ``$\max$'' and multiplication ``$+$''. As well as in conventional algebra, linear programming in the tropical semiring has been developed. In this study, we introduce a new type of…
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is…
Real-world decision and optimization problems, often involve constraints and conflicting criteria. For example, choosing a travel method must balance speed, cost, environmental footprint, and convenience. Similarly, designing an industrial…
An algorithm to give an explicit description of all the solutions to any tropical linear system $A\odot x=B\odot x$ is presented. The given system is converted into a finite (rather small) number $p$ of pairs $(S,T)$ of classical linear…
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…
In this paper, we present methods for solving a system of linear equations, $ AX=b $, over tropical semirings. To this end, if possible, we first reduce the order of the system through some row-column analysis, and obtain a new system with…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of…
We consider the tropical analogues of a particular bilevel optimization problem studied by Dempe and Franke and suggest some methods of solving these new tropical bilevel optimization problems. In particular, it is found that the algorithm…
Many important multiple-objective decision problems can be cast within the framework of ranking under constraints and solved via a weighted bipartite matching linear program. Some of these optimization problems, such as personalized content…
The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. Previously considered criteria for evaluating proposed mechanisms…
Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
New solutions for problems in optimal scheduling of activities in a project under temporal constraints are developed in the framework of tropical algebra which deals with the theory and application of algebraic systems with idempotent…
We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto optimal solutions among a finite set of candidates for which the two objective outcomes have been observed with uncertainty (e.g.,…
We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…
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…
Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in…
When solving large-scale multiobjective optimization problems, solvers can get stuck with the memory or time limit. In such cases, one is left with no information how far is the best feasible solution, found before the optimization process…