We extend knowledge gradient (KG) policy for the multi-objective, multi-armed bandits problem to efficiently explore the Pareto optimal arms. We consider two partial order relationships to order the mean vectors, i.e. Pareto and scalarized functions. Pareto KG finds the optimal arms using Pareto search, while the scalarizations-KG transform the multi-objective arms into one-objective arm to fin...

We study when two-member household choice behavior is compatible with Pareto optimality. We ask when an external observer of household choices, who does not know the individuals’ preferences, can rationalize the choices as being Pareto-optimal. Our main contribution is to reduce the problem of rationalization to a graph-coloring problem. As a result, we obtain simple tests for Pareto optimal ch...

In this paper, a new evolutionary technique for detecting continuous Pareto optimal sets is proposed. The technique is designed for functions of one real variable but it can be extended for several variables functions. In this approach an individual (a solution) is either a closed interval or a point. Each solution in the final population corresponds to a decision region of Pareto optimal set. ...

W propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding a maximally uniform representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling...

This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decisiontheoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory–a deductively closed set of sentences or propositions–and second for beliefs represented by an axi...

Traditionally, researchers in decision making have focused on attempting to reach Pareto Optimality using horizontal approaches, where optimality is calculated taking into account every participant at the same time. Sometimes, this may prove to be a difficult task (e.g., conflict, mistrust, no information sharing, etc.). In this paper, we explore the possibility of achieving Pareto Optimal outc...

We consider Pareto optimal matchings as a means of coping with instances of the Stable Roommates problem (SR) that do not admit a stable matching. Given an instance I of SR, we show that the problem of finding a maximum Pareto optimal matching is solvable in O( √ nα(m,n)m log n) time, where n is the number of agents and m is the total length of the preference lists in I. By contrast we prove th...

Recently, a couple of approaches have been developed that combine multiobjective optimization with direct discretization methods to approximate trajectories of optimal control problems, resulting in restricted optimization problems of high dimension. The solution set of a multiobjective optimization problem is called the Pareto set which consists of optimal compromise solutions. A common way to...

This paper investigates the influence of channel structures and channel coordination on the supplier, the retailer, and the entire supply chain n the context of two single-channel and two dual-channel supply chains. We extensively study two Pareto zone concepts: channel-adding Pareto one and contract-implementing Pareto zone. In the channel-adding Pareto zone, both the supplier and the retailer...

In many optimization problems in practice, multiple objectives have to be optimized at the same time. Some multi-objective problems are characterized by multiple connected Pareto-sets at different parts in decision space – also called equivalent Pareto-subsets. We assume that the practitioner wants to approximate all Pareto-subsets to be able to choose among various solutions with different cha...