Imprecise-reward Markov decision processes (IRMDPs) are MDPs in which the reward function is only partially specified (e.g., by some elicitation process). Recent work using minimax regret to solve IRMDPs has shown, despite their theoretical intractability, how the set of policies that are nondominated w.r.t. reward uncertainty can be exploited to accelerate regret computation. However, the numb...

In many network routing problems several conflicting objectives must be considered. Even for the bi-objective shortest path problem, generating and presenting the whole set of nondominated solutions (paths) to a decision maker, in general, is not effective because the number of these paths can be very large. Interactive procedures are adequate to overcome these drawbacks. Current et al. [1] pro...

Nondominated sorting is a fundamental combinatorial problem in multiobjective optimization and is equivalent to the longest chain problem in combinatorics and random growth models for crystals in materials science. In a previous work [SIAM J. Math. Anal., 46 (2014), pp. 603–638], we showed that nondominated sorting has a continuum limit that corresponds to solving a Hamilton–Jacobi equation. In...

The size of the nondominated set of a vector set is greatly dependent on the size of the original vector set N and the dimension of the vector M . Theoretical analysis shows that when M = O(log N) the original set has big nondominated set which may be the original set itself, and in the case M = O(log N), a classical algorithm (KLP) for finding nondominated set has complexity of KLP higher than...

Quorum-based mutual exclusion algorithms are resilient to node and communication line failures. In order to enter its critical section, a node must obtain permission from a quorum of nodes. A collection of quorums is called a coterie. The most resilient coteries are called nondominated coteries. Recently, k-coteries were proposed to be used in mutual exclusion algorithms that allow up to k entr...

Given a set of nodes in a distributed system, a coterie is a collection of subsets of the set of nodes such that any two subsets have a nonempty intersection and are not properly contained in one another. A subset of nodes in a coterie is called a quorum. Coteries may be used to implement a distributed mutual exclusion algorithm which gracefully tolerates node and communication line failures. T...

When making decisions with multiple criteria, a decision maker often thinks in terms of an aspiration point or levels of achievement for the criteria. In multiple objective mathematical programming, solution methods based on aspiration points can generate nondominated solutions using a variety of scalarizing functions. These reference point solution methods commonly use a scalarizing function t...

This paper presents an application of an evolutionary optimization algorithm for multiobjective analysis of selective withdrawal from a thermally stratified reservoir. A multiobjective particle swarm optimization (MOPSO) algorithm is used to find nondominated (Pareto) solutions when minimizing deviations from outflow water quality targets of: (i) temperature; (ii) dissolved oxygen (DO); (iii) t...

Bayesian robustness has concentrated mainly on checking sensitivity of a Bayesian analysis with respect to changes in the prior or the model. We deal here with several issues concerning robust Bayesian analysis with respect to the loss function. Stemming from foundational results, we suggest that a main computational objective would be the obtainment of the set of nondominated alternatives. We ...

This paper presents an approach to incorporate Pareto dominance into the differential evolution (DE) algorithm in order to solve optimization problems with more than one objective by using the DE algorithm. Unlike the existing proposals to extend the DE to solve multiobjective optimization problems, our algorithm uses an external archive to store nondominated solutions. In order to generate tri...