The most important issue in multi-objective optimization problems is to determine the Pareto points along the Pareto frontier. If the optimization problem involves multiple conflicting objectives, the results obtained from the Pareto-optimality will have the trade-off solutions that shaping the Pareto frontier. Each of these solutions lies at the boundary of the Pareto frontier, such that the i...

This paper investigates three disparate design cases where the newly developed s-Pareto frontier based concept selection paradigm is used to compare competing design concepts under a multiobjective optimization framework. The new paradigm, which was recently introduced by the authors, is based on the principle of Pareto optimality – a principle that defines an important class of optimal solutio...

In a recent publication, we presented a new multiobjective decision-making tool for use in conceptual engineering design. In the present paper, we provide important developments that support the next phase in the evolution of the tool. These developments, together with those of our previous work, provide a concept selection approach that capitalizes on the benefits of computational optimization...

Many real-world control applications, from economics to robotics, are characterized by the presence of multiple conflicting objectives. In these problems, the standard concept of optimality is replaced by Pareto–optimality and the goal is to find the Pareto frontier, a set of solutions representing different compromises among the objectives. Despite recent advances in multi–objective optimizati...

We study retrading via reopening of trading posts in a market game where the static Nash equilibria yield Pareto suboptimal allocations whenever endowments are Pareto suboptimal. We show that there are allocations on the Pareto frontier that can be approximated arbitrarily closely along some Subgame Perfect Equilibrium path of retrading. The approximation result can also be proved when traders ...

This paper is about learning a continuous approximation of the Pareto frontier in Multi–Objective Markov Decision Problems (MOMDPs). We propose a policy–based approach that exploits gradient information to generate solutions close to the Pareto ones. Differently from previous policy–gradient multi–objective algorithms, where n optimization routines are used to have n solutions, our approach per...

This paper is about learning a continuous approximation of the Pareto frontier in Multi–Objective Markov Decision Problems (MOMDPs). We propose a policy–based approach that exploits gradient information to generate solutions close to the Pareto ones. Differently from previous policy–gradient multi–objective algorithms, where n optimization routines are use to have n solutions, our approach perf...

A multiobjective optimization problem is considered in a general formulation. It is well known that the solution of the problem is not unique and represented in the objective space by a Pareto frontier. In an engineering design it can be important to provide a discrete representation of the entire Pareto surface. Meanwhile, the obtaining of a single Pareto solution may be time-consuming. Moreov...

Performance guarantees for online learning algorithms typically take the form of regret bounds, which express that the cumulative loss overhead compared to the best expert in hindsight is small. In the common case of large but structured expert sets we typically wish to keep the regret especially small compared to simple experts, at the cost of modest additional overhead compared to more comple...

We describe techniques for visualizing the Pareto optimal set that can be used if the multiobjective optimization problem considered has more than two objective functions. The techniques discussed can be applied in the framework of both MCDM and EMO approaches. First, lessons learned from methods developed for biobjective problems are considered. Then, visualization techniques for convex multio...