In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates – but contradictory conclusions have been rep...

We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic MultiObjective Optimization Problem (SMOP) whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation method (SAA-N, where N is t...

Evolutionary algorithms EA have proved to be well suited for optimization prob lems with multiple objectives Due to their inherent parallelism they are able to capture a number of solutions concurrently in a single run In this report we propose a new evolutionary approach to multicriteria optimization the Strength Pareto Evolutionary Algorithm SPEA It combines various features of previous multi...

We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One o...

This paper presents a new multiobjective multicast routing algorithm (MMA) based on the Strength Pareto Evolutionary Algorithm (SPEA), which simultaneously optimizes the cost of the tree, the maximum end-to-end delay, the average delay and the maximum link utilization. In this way, a set of optimal solutions, known as Pareto set, is calculated in only one run, without a priori restrictions. Sim...

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 [5] an evolutionary algorithm for detecting continuous Pareto optimal sets has been proposed. In this paper we propose a new evolutionary elitist approach combing a non-standard solution representation and an evolutionary optimization technique. The proposed method permits detection of continuous decision regions. In our approach an individual (a solution) is either a closed interval or a po...

Is the Pareto optimality of matching mechanisms robust to the introduction of boundedly rational behavior? To address this question I define a restrictive and a permissive notion of Pareto optimality and consider the large set of hierarchical exchange mechanisms which contains serial dictatorship as well as Gale’s top trading cycles. Fix a housing problem with boundedly rational agents and a hi...

In this work, the optimization of control parameters for an active suspension system is considered. Here, two objectives – energy and comfort – play an important role. Thus, a multiobjective optimization problem is formulated which can be solved numerically with a set-oriented approach, for example. The result is the set of optimal compromises of the objectives, the so-called Pareto set. In cas...

This work studies the behavior of three elitist multiand many-objective evolutionary algorithms generating a high-resolution approximation of the Pareto optimal set. Several search-assessment indicators are defined to trace the dynamics of survival selection and measure the ability to simultaneously keep optimal solutions and discover new ones under different population sizes, set as a fraction...