This chapter reviews methods for the assessment and comparison of Pareto set approximations. Existing set quality measures from the literature are critically evaluated based on a number of orthogonal criteria, including invariance to scaling, monotonicity and computational effort. Statistical aspects of quality assessment are also considered in the chapter. Three main methods for the statistica...

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranki...

We introduce a two-stage ranking of multidimensional alternatives, including uncertain prospects as particular case, when these objects can be given a suitable matrix form. The first stage defines a ranking of rows and a ranking of columns, and the second stage ranks matrices by applying natural monotonicity conditions to these auxiliary rankings. Owing to the Debreu-Gorman theory of additive s...

Two methods for ranking of solutions of multi objective optimization problems are proposed in this paper. The methods can be used, e.g. by metaheuristics to select good solutions from a set of non dominated solutions. They are suitable for population based metaheuristics to limit the size of the population. It is shown theoretically that the ranking methods possess some interesting properties f...

We discuss a method of ranking allocations in economic environments which applies when we do not know the names or preferences of individual agents. We require that two allocations can be ranked with the knowledge only of their aggregate bundles and community indifference sets–a condition we refer to as aggregate independence. We also postulate a basic Pareto and continuity property, and a prop...

There is a variety of methods for ranking objectives in multiobjective optimization and some are difficult to define because they require information a priori (e.g. establishing weights in a weighted approach or setting the ordering in a lexicographic approach). In manyobjective optimization problems, those methods may exhibit poor diversification and intensification performance. We propose the...

This paper presents a novel adaptive multiobjective particle swarm optimization algorithm and with adaptive multi-objective particle swarm algorithm for solving objective constrained optimization problems, in which Pareto non-dominated ranking, tournament selection, crowding distance method were introduced, simultaneously the rate of crowding distance changing were integrated into the algorithm...

Two methods are presented as practical approaches to reduce the size of the Pareto optimal set of multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision-maker select solutions that reflect his/her preferences. In the second approach we used clustering techniques used in data mining, to group the data by using the k-means algori...

We propose a multi-objective evolutionary algorithm (MOEA), named the Hyper-volume Evolutionary Algorithm (HVEA). The algorithm is characterised by three components. First, individual fitness evaluation depends on the current Pareto front, specifically on the ratio of its dominated hyper-volume to the current Pareto front hyper-volume, hence giving an indication of how close the individual is t...