We show that, in a two-period economy with uncertainty in the second period, if an allocation is Pareto optimal for a given set of beliefs and remains optimal when these beliefs are changed, then the set of optimal allocations of the two economies must actually coincide. We identify equivalence classes of beliefs giving rise to the same set of Pareto optimal allocations. Journal of Economic Lit...

This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...

In this paper we propose the multi-objective contextual bandit problem with similarity information. This problem extends the classical contextual bandit problem with similarity information by introducing multiple and possibly conflicting objectives. Since the best arm in each objective can be different given the context, learning the best arm based on a single objective can jeopardize the rewar...

The Pareto front reflects the optimal trade-offs between conflicting objectives and can be used to quantify the effect of different beam configurations on plan robustness and dose-volume histogram parameters. Therefore, our aim was to develop and implement a method to automatically approach the Pareto front in robust intensity-modulated proton therapy (IMPT) planning. Additionally, clinically r...

In design situations where a single solution must be selected, it is often desirable to present the designer with a smart Pareto set of solutions—a minimal set of nondominated solutions that sufficiently represents the tradeoff characteristics of the design space. These sets are generally created by finding many well-distributed solutions and then either filtering out the excess ones or searchi...

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranki...

In this study, a problem space genetic algorithm (PSGA) is used to solve bicriteria tool management and scheduling problems simultaneously in ¯exible manufacturing systems. The PSGA is used to generate approximately ef®cient solutions minimizing both the manufacturing cost and total weighted tardiness. This is the ®rst implementation of PSGA to solve a multiobjective optimization problem (MOP)....

An original approach to multi-objective optimization is introduced, using a message-passing algorithm to sample the Pareto set, i.e. the set of Pareto-nondominated solutions. Several heuristics are proposed and tested on a simple biobjective 3-SAT problem. The first one is based on a straightforward deformation of the Survey-Propagation (SP) equation to locally encode a Pareto trade-off. A simp...

A multi-objective evolutionary algorithm (MOEA) approach is presented in this paper. The algorithm (DFBMOEA) aims to improve convergence of Paretobased MOEAs to the true Pareto optimal set/Pareto front and remove decision maker interaction from the process. A novel distance function is used as a fitness function for MOEA. A range equalisation function and a reference vector are utilised to elim...

We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem minx∈S{(f1(x), f2(x))}, where f1 and f2 are two conflicting polynomial criteria and S ⊂ Rn is a compact basic semialgebraic set. We provide a systematic numerical scheme to approximate the Pareto curve. We start by reducing the initial problem into a scalarized po...