Multiobjective memetic optimization algorithms (MMOAs) are recently applied to solve nonlinear optimization problems with conflicting objectives. An important issue in an MMOA is how to identify the relative best solutions to guide its adaptive processes. In this paper, the authors introduce a...

While a number of algorithms for multiobjective reinforcement learning have been proposed, and a small number of applications developed, there has been very little rigorous empirical evaluation of the performance and limitations of these algorithms. This paper proposes standard methods for such...

Sum of Ranking Differences is an innovative statistical method that ranks competing solutions based on a reference point. The latter might arise naturally, or can be aggregated from the data. We provide two case studies to feature both possibilities. Apportionment and districting are two...

Several decision making problems with multiple decision makers in a hierarchical decision making scenario can be best described using multilevel optimization problem. Different organizational structure adapt a hierarchical decision making system where each decision maker controls parts of the...

We provide a comprehensive overview of the literature of algorithmic approaches for multiobjective mixed‐integer and integer linear optimization problems. More precisely, we categorize and display exact methods for multiobjective linear problems with integer variables for computing the entire...

Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds...

In a single-objective setting, nonconvex quadratic problems can equivalently be reformulated as convex problems over the cone of completely positive matrices. In small dimensions this cone equals the cone of matrices which are entrywise nonnegative and positive semidefinite, so the convex...

This article is dedicated to the weight set decomposition of a multiobjective (mixed-)integer linear problem with three objectives. We propose an algorithm that returns a decomposition of the parameter set of the weighted sum scalarization by solving biobjective subproblems via Dichotomic Search...

It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of...