Catálogo de publicaciones - libros

Deception problems are among the hardest problems to solve using ordinary genetic algorithms. Designed to simulate a high degree of epistasis, these deception problems imitate extremely difficult real world problems. [1]. Studies show that Bayesian optimization and explicit building block manipulation algorithms, like the fast messy genetic algorithm (fmGA), can help in solving these problems. This paper compares the results acquired from an extended multiobjective fast messy genetic algorithm (MOMGA-IIa), ordinary multiobjective fast messy genetic algorithm (MOMGA-II), multiobjective Bayesian optimization algorithm (mBOA), and the non-dominated sorting genetic algorithm-II (NSGA-II) when applied to three different deception problems. The extended MOMGA-II is enhanced with a new technique exploiting the fmGA’s basis function to improve partitioned searching in both the genotype and phenotype domain. The three deceptive problems studied are: interleaved minimal deceptive problem, interleaved 5-bit trap function, and interleaved 6-bit bipolar function. The unmodified MOMGA-II, by design, explicitly learns building block linkages, a requirement if an algorithm is to solve these hard deception problems. Results using the MOMGA-IIa are excellent when compared to the non-explicit building block algorithm results of both the mBOA and NSGA-II.

For the past decade, many evolutionary multi-objective optimization (EMO) methodologies have been developed and applied to find multiple Pareto-optimal solutions in a single simulation run. In this paper, we discuss three different classical generating methods, some of which were suggested even before the inception of EMO methodologies. These methods specialize in finding multiple Pareto-optimal solutions in a single simulation run. On visual comparisons of the efficient frontiers obtained for a number of two and three-objective test problems, these algorithms are evaluated with an EMO methodology. The results bring out interesting insights about the strengths and weaknesses of these approaches. Further investigations of such classical generating methodologies and their evaluation should enable researchers to design a hybrid multi-objective optimization algorithm which may be better than each individual method.

We present a new analysis of the LebMeasure algorithm for calculating hypervolume. We prove that although it is polynomial in the number of points, LebMeasure is exponential in the number of objectives in the worst case, not polynomial as has been claimed previously. This result has important implications for anyone planning to use hypervolume, either as a metric to compare optimisation algorithms, or as part of a diversity mechanism in an evolutionary algorithm.

The focus of this paper is the handling of overlapping solutions in evolutionary multiobjective optimization (EMO) algorithms. In the application of EMO algorithms to some multiobjective combinatorial optimization problems, there exit a large number of overlapping solutions in each generation. We examine the effect of removing overlapping solutions on the performance of EMO algorithms. In this paper, overlapping solutions are removed from the current population except for a single solution. We implement two removal strategies of overlapping solutions. One is the removal of overlapping solutions in the objective space. In this strategy, one solution is randomly chosen among the overlapping solutions with the same objective vector and left in the current population. The other overlapping solutions with the same objective vector are removed from the current population. As a result, each solution in the current population has a different location in the objective space. It should be noted that the overlapping solutions in the objective space are not necessary the same solution in the decision space. Thus we also examine the other strategy where the overlapping solutions in the decision space are removed from the current population except for a single solution. As a result, each solution in the current population has a different location in the decision space. The effect of removing overlapping solutions is examined through computational experiments where each removal strategy is combined into the NSGA-II algorithm.

This work focuses on the working principles, behavior, and performance of state of the art multiobjective evolutionary algorithms (MOEAs) on discrete search spaces by using MNK-Landscapes. Its motivation comes from the performance shown by NSGA-II and SPEA2 on epistatic problems, which suggest that simpler population-based multiobjective random one-bit climbers are by far superior. Adaptive evolution is a search process driven by selection, drift, mutation, and recombination over fitness landscapes. We group MOEAs features and organize our study around these four important and intertwined processes in order to understand better their effects and clarify the reasons to the poor performance shown by NSGA-II and SPEA2. This work also constitutes a valuable guide for the practitioner on how to set up its algorithm and gives useful insights on how to design more robust and efficient MOEAs.

This paper examines two repair schemes (i.e., Lamarckian and Baldwinian) through computational experiments on multiobjective 0/1 knapsack problems. First we compare Lamarckian and Baldwinian with each other. Experimental results show that the Baldwinian repair outperforms the Lamarckian repair. It is also shown that these repair schemes outperform a penalty function approach. Then we examine partial Lamarckianism where the Lamarckian repair is applied to each individual with a prespecified probability. Experimental results show that a so-called 5% rule works well. Finally partial Lamarckianism is compared with an island model with two subpopulations where each island has a different repair scheme. Experimental results show that the island model slightly outperforms the standard single-population model with the 50% partial Lamarckian repair in terms of the diversity of solutions.

This paper demonstrates how adaptive population-sizing and epsilon-dominance archiving can be combined with the Nondominated Sorted Genetic Algorithm-II (NSGAII) to enhance the algorithm’s efficiency, reliability, and ease-of-use. Four versions of the enhanced Epsilon Dominance NSGA-II (ε-NSGAII) are tested on a standard suite of evolutionary multiobjective optimization test problems. Comparative results for the four variants of the (ε-NSGAII demonstrate that adapting population size based on online changes in the epsilon dominance archive size can enhance performance. The best performing version of the (ε-NSGAII is also compared to the original NSGAII and the (εMOEA on the same suite of test problems. The performance of each algorithm is measured using three running performance metrics, two of which have been previously published, and one new metric proposed by the authors. Results of the study indicate that the new version of the NSGAII proposed in this paper demonstrates improved performance on the majority of two-objective test problems studied.

This paper studies the fuzzification of the Pareto dominance relation and its application to the design of Evolutionary Multi-Objective Optimization algorithms. A generic ranking scheme is presented that assigns dominance degrees to any set of vectors in a scale-independent, non-symmetric and set-dependent manner. Based on such a ranking scheme, the vector fitness values of a population can be replaced by the computed ranking values (representing the ”dominating strength” of an individual against all other individuals in the population) and used to perform standard single-objective genetic operators. The corresponding extension of the Standard Genetic Algorithm, so-called Fuzzy-Dominance-Driven GA (FDD-GA), will be presented as well. To verify the usefulness of such an approach, an analytic study of the Pareto-Box problem is provided, showing the characteristical parameters of a random search for the Pareto front in a unit hypercube in arbitrary dimension. The basic problem here is the loss of dominated points with increasing problem dimension, which can be successfully resolved by basing the search procedure on the fuzzy dominance degrees.

Multi-objective evolutionary algorithms (MOEAs) have proven to be a powerful tool for global optimization purposes of deterministic problem functions. Yet, in many real-world problems, uncertainty about the correctness of the system model and environmental factors does not allow to determine clear objective values. Stochastic sampling as applied in noisy EAs neglects that this so-called epistemic uncertainty is not an inherent property of the system and cannot be reduced by sampling methods. Therefore, some extensions for MOEAs to handle epistemic uncertainty in objective functions are proposed. The extensions are generic and applicable to most common MOEAs. A density measure for uncertain objectives is proposed to maintain diversity in the nondominated set. The approach is demonstrated to the reliability optimization problem, where uncertain component failure rates are usual and exhaustive tests are often not possible due to time and budget reasons.

Estimation of distribution algorithms have been shown to perform well on a wide variety of single–objective optimization problems. Here, we look at a simple – yet effective – extension of this paradigm for multi–objective optimization, called the naive ${\mathbb M}$ ID ${\mathbb E}$ A. The probabilistic model in this specific algorithm is a mixture distribution, and each component in the mixture is a univariate factorization. Mixture distributions allow for wide–spread exploration of the Pareto front thus aiding the important preservation of diversity in multi–objective optimization. Due to its simplicity, speed, and effectiveness the naive ${\mathbb M}$ ID ${\mathbb E}$ A can well serve as a baseline algorithm for multi–objective evolutionary algorithms.