The multi-objective simulation optimization (MOSO) problem is a nonlinear multi-objective optimization problem in which multiple simultaneous and conflicting objective functions can only be observed with stochastic error. We provide an introduction to MOSO at the advanced tutorial level, aimed at researchers and practitioners who wish to begin working in this emerging area. Our focus is … Read more
We are interested in the existence of Pareto solutions to the vector optimization problem $$\text{\rm Min}_{\,\mathbb{R}^m_+} \{f(x) \,|\, x\in \mathbb{R}^n\},$$ where $f\colon\mathbb{R}^n\to \mathbb{R}^m$ is a polynomial map. By using the {\em tangency variety} of $f$ we first construct a semi-algebraic set of dimension at most $m – 1$ containing the set of Pareto values of … Read more
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the … Read more
A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems and Bounded Knapsack … Read more
It is of crucial importance to develop risk-averse models for multicriteria decision making under uncertainty. A major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints. These problems typically involve a univariate stochastic preference relation, often based on stochastic dominance or a coherent risk measure such as conditional value-at-risk (CVaR), … Read more
We consider integer programming (IP) problems consisting of (possibly a large number of) subsystems and a small number of coupling constraints that link variables from different subsystems. Such problems are called loosely coupled or nearly decomposable. Motivated by recent developments in multiobjective programming (MOP), we develop a MOP-based decomposition algorithm to solve loosely coupled IPs. … Read more
We introduce bi-objective models for ring tree network design with a focus on network reliability within telecommunication applications. Our approaches generalize the capacitated ring tree problem (CRTP) which asks for a partially reliable topology that connects customers with different security requirements to a depot node by combined ring and tree graphs. While the CRTP aims … Read more
Geoffrion proper optimality is a widely used optimality notion in multicriteria optimization that prevents exact solutions having unbounded trade-offs. As algorithms for multicriteria optimization usually give only approximate solutions, we analyze the notion of approximate Geoffrion proper optimality. We show that in the limit, approximate Geoffrion proper optimality may converge to solutions having unbounded trade-offs. … Read more
We study conditions under which the objective functions of a multi-objective 0-1 integer linear program guarantee the existence of an ideal point, meaning the existence of a feasible solution that simultaneously minimizes all objectives. In addition, we study the complexity of recognizing whether a set of objective functions satisfies these conditions: we show that it … Read more
In recent years, the research focus in multi-objective optimization has shifted from approximating the Pareto optimal front in its entirety to identifying solutions that are well-balanced among their objectives. Proper Pareto optimality is an established concept for eliminating Pareto optimal solutions that exhibit unbounded tradeo ffs. Imposing a strict tradeo ff bound allows specifying how many units … Read more