In this paper we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower level problem of the bilevel optimization problem is convex and continuously dif...

Several interactive methods exist to identify nondominated solutions in a Multiple Objective Mixed Integer Linear Program. But what if the Decision Maker is also interested in sorting those solutions (assigning them to pre-established ordinal categories)? We propose an interactive ‘‘branch-and-bound like’’ technique to progressively build the nondominated set, combined with ELECTRE TRI method (...

Computing the nondominated set of a multiple objective mathematical program has long been a topic in multiple criteria decision making. In this paper, motivated by the desire to extend Markowitz portfolio selection to an additional linear criterion (dividends, liquidity, sustainability, etc.), we demonstrate an exact method for computing the nondominated set of a tri-criterion program that is a...

Multiobjective evolutionary algorithms (EAs) that use nondominated sorting and sharing have been criticized mainly for their: 1) ( ) computational complexity (where is the number of objectives and is the population size); 2) nonelitism approach; and 3) the need for specifying a sharing parameter. In this paper, we suggest a nondominated sorting-based multiobjective EA (MOEA), called nondominate...

In standard portfolio theory, an investor is typically taken as having one stochastic objective, to maximize the random variable of portfolio return. But in this paper, we focus on investors whose purpose is to build, more broadly, a “suitable portfolio” taking additional concerns into account. Such investors would have additional stochastic and deterministic objectives that might include liqui...

Abstract. A new algorithm for optimization problems with three objective functions is presented which computes a representation for the set of nondominated points. This representation is guaranteed to have a desired coverage error and a bound on the number of iterations needed by the algorithm to meet this coverage error is derived. Since the representation does not necessarily contain nondomin...

We propose a learning-oriented interactive algorithm for solving multicriteria linear integer programming (MCLIP) problems, considered as multicriteria decision making problems. At each iteration, the DM may partition the criteria set into at most seven classes, namely: improvement, improvement by a desired amount, deterioration, deterioration by at most a certain amount, nondeterioration, chan...

Researches in Bayesian sensitivity analysis and robustness have mainly dealt with the computation of the range of some quantities of interest when the prior distribution varies in some class. Recently, researchers’ attention turned to the loss function, mostly to the changes in posterior expected loss and optimal actions. In particular, the search for optimal actions under classes of priors and...

In this paper the effects of elitism in the Nondominated Sorting Genetic Algorithm (NSGA) are analyzed. Three different kinds of elitism: standard, clustering and Parks & Miller techniques are investigated using two test problems. For the studied problems, the Parks & Miller mechanism generated the best results. Finally, the NSGA with Parks & Miller elitism was applied to determine the nondomin...