On the number of criteria needed to decide Pareto optimality

On the number of criteria needed to decide Pareto optimality

In this paper we address the question of how many objective functions are really needed to decide whether a given point is Pareto optimal. We prove a reduction result for the case of quasi-convex objective functions and a convex feasible set. This result states that in order to decide whether a point x in the decision space is Pareto optimal it suuces to consider at most n + 1 objectives at a t...

Pareto-optimality of Compromise Decisions Pareto-optimality of Compromise Decisions

This paper deals with the problem of existence of compromise decisions and conditions for a compromise decision to be weakly Pareto-optimal, i.e., to be a weak Pareto-maximizer, Pareto-maximizer, or strong Pareto-maximizer. The concept of compromise decision is generalized by adopting triangular norms. Further, a concept of fuzzy interval is introduced. Suucient conditions for the existence of ...

Number needed to treat (NNT); number needed to harm (NNH).

Using Pareto optimality to coordinate distributed agents

Pareto optimality is a domain-independent property that can be used to coordinate distributed engineering agents. Within a model of design called Redux, some aspects of dependency-directed backtracking can be interpreted as tracking Pareto optimality. These concepts are implemented in a framework, called Next-Link, that coordinates legacy engineering systems. This framework allows existing soft...

On the Pareto Optimality in the Context of Lipschitzian Optimization

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto–Lipschitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants. I...