In this chapter, we present a new method for interactive multiobjective optimization, which is based on application of a logical preference model built using the Dominance-based Rough Set Approach (DRSA). The method is composed of two main stages that alternate in an interactive procedure. In the first stage, a sample of solutions from the Pareto optimal set (or from its approximation) is gener...

In this paper, the uncertain transition matrices for inhomogeneous Markov decision processes are described by use of fuzzy sets. Introducing a ν-step contractive property, called a minorization condition, for the average case, we fined a Pareto optimal policy maximizing the average expected fuzzy rewards under some partial order. The Pareto optimal policies are characterized by maximal solution...

In this paper, a Markov decision model with uncertain transition matrices, which allow a matrix to fluctuate at each step in time, is described by the use of fuzzy sets. We find a pareto optimal policy maximizing the infinite horizon fuzzy expected discounted reward over all stationary policies under some partial order. The pareto optimal policies are characterized by maximal solutions of an op...

The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this...

Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that each ag...

Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that eac...

This paper is concerned with the problem of finding a representative sample of Pareto-optimal points inmulti-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. Fir...

This paper pursues the idea of a general multiobjective optimizer that can be flexibly adapted to arbitrary user preferences— assuming that the goal is to approximate the Pareto-optimal set. It proposes the Set Preference Algorithm for Multiobjective Optimization (SPAM) the working principle of which is based on two observations: (i) current multiobjective evolutionary algorithms (MOEAs) can be...