Giovanni Lizárraga

A Set of Test Cases for Performance Measures in Multiobjective Optimization

Comparing the performance of different evolutive multiobjective algorithms is an open problem. With time, many performance measures have been proposed. Unfortunately, the evaluations of many of these performance measures disagree with the common sense of when a multiobjective algorithm is performing better than another. In this work we present a benchmark that is helpful to check if a performance measure actually has a good behavior. Some of the most popular performance measures in literature are tested. The results are valuable for a better understanding of what performance measures are better.

IS-PAES: a constraint-handling technique based on multiobjective optimization concepts

This paper introduces a new constraint-handling method called Inverted-Shrinkable PAES (IS-PAES), which focuses the search effort of an evolutionary algorithm on specific areas of the feasible region by shrinking the constrained space of single-objective optimization problems. IS-PAES uses an adaptive grid as the original PAES (Pareto Archived Evolution Strategy). However, the adaptive grid of IS-PAES does not have the serious scalability problems of the original PAES. The proposed constraint-handling approach is validated with several examples taken from the standard literature on evolutionary optimization.

Why Unary Quality Indicators Are Not Inferior to Binary Quality Indicators

When evaluating the quality of non---dominated sets, two families of quality indicators are frequently used: unary quality indicators (UQI) and binary quality indicators (BQI). For several years, UQIs have been considered inferior to BQIs. As a result, the use of UQIs has been discouraged, even when in practice they are easier to use. In this work, we study the reasons why UQIs are considered inferior. We make a detailed analysis of the correctness of these reasons and the implicit assumptions in which they are based. The conclusion is that, contrary to what is widely believed, unary quality indicators are not inferior to binary ones.

G-indicator: an m-ary quality indicator for the evaluation of non-dominated sets

Due to the big success of the Paretos Optimality Criteria for multi-objective problems, an increasing number of algorithms that use it have been proposed. The goal of these algorithms is to find a set of non-dominated solutions that are close to the True Pareto front. As a consequence, a new problem has arisen, how can the performance of different algorithms be evaluated? In this paper, we present a novel system to evaluate m non-dominated sets, based on a few assumptions about the preferences of the decision maker. In order to evaluate the performance of our approach, we build several test cases considering different topologies of the Pareto front. The results are compared with those of another popular metric, the S-metric, showing equal or better performance.

Use of multiobjective optimization concepts to handle constraints in single-objective optimization

In this paper, we propose a new constraint-handling technique for evolutionary algorithms which is based on multiobjective optimization concepts. The approach uses Pareto dominance as its selection criterion, and it incorporates a secondary population. The new technique is compared with respect to an approach representative of the state-of-the-art in the area using a well-known benchmark for evolutionary constrained optimization. Results indicate that the proposed approach is able to match and even outperform the technique with respect to which it was compared at a lower computational cost.

Preliminary Meanline Design for Gas Turbines Using Multi-objective Optimization

Designing gas turbines is a very complex task. It is not a linear procedure but an iterative one, composed by several phases. In the initial phase, the general geometric characteristics and estimate efficiency of the turbine are determined. This phase is known as the meanline design, and it is very important because it determines the starting point for more complex analysis. In this work we use a multi--objective evolutionary algorithm to calculate the meanline design. We consider two conflicting objectives: the number of stages of the turbine, and the efficiency of the stages.

A benchmark for quality indicators in multi-objective optimization.

Comparing the performance of different evolutive Multi-Objective algorithms is an open problem. With time, many performance measures have been proposed. Unfortunately, the evaluations of many of these performance measures disagree with the common sense of when a non-dominated set is better than another. In this work we present a benchmark that is helpful to check if a performance measure actually has a good behavior. Some of the most popular performance measures in literature are tested. The results are valuable for a better understanding of what performance measures are better.

Some Demonstrations about the Cardinality of Important Sets of Non---dominated Sets

In multiobjective optimization, a very important element is thespace of objective functions, usually called Z. The set of?of all non---dominated sets that we can generatewith elements of Zis especially interesting, because itrepresent all possible output from an evolutionary multiobjectivealgorithm. In this study, we make some theoretical demonstrationsabout the cardinality of Ωand others important setsof non---dominated sets. After, we use these demonstrations toprove some theorems in the area of performance measures forevolutionary multiobjective algorithms.