Hernán E. Aguirre

Controlling dominance area of solutions and its impact on the performance of MOEAs

This work proposes a method to control the dominance area of solutions in order to induce appropriate ranking of solutions for the problem at hand, enhance selection, and improve the performance of MOEAs on combinatorial optimization problems. The proposed method can control the degree of expansion or contraction of the dominance area of solutions using a user-defined parameter S. Modifying the dominance area of solutions changes their dominance relation inducing a ranking of solutions that is different to conventional dominance. In this work we use 0/1 multiobjective knapsack problems to analyze the effects on solutions ranking caused by contracting and expanding the dominance area of solutions and its impact on the search performance of a multi-objective optimizer when the number of objectives, the size of the search space, and the complexity of the problems vary. We show that either convergence or diversity can be emphasized by contracting or expanding the dominance area. Also, we show that the optimal value of the area of dominance depends strongly on all factors analyzed here: number of objectives, size of the search space, and complexity of the problems.

Working principles, behavior, and performance of MOEAs on MNK-landscapes

This work studies the working principles, behavior, and performance of multiobjective evolutionary algorithms (MOEAs) on multiobjective epistatic fitness functions with discrete binary search spaces by using MNK-landscapes. First, we analyze the structure and some of the properties of MNK-landscapes under a multiobjective perspective by using enumeration on small landscapes. Then, we focus on the performance and behavior of MOEAs on large landscapes. We organize our study around selection, drift, mutation, and recombination, the four major and intertwined processes that drive adaptive evolution over fitness landscapes. This work clearly shows pros and cons of the main features of MOEAs, gives a valuable guide for the practitioner on how to set up his/her algorithm, enhance MOEAs, and presents useful insights on how to design more robust and efficient MOEAs.

Local dominance using polar coordinates to enhance multiobjective evolutionary algorithms

In this paper, we propose a calculation method of local dominance and enhance multiobjective evolutionary algorithms by performing a distributed search based on local dominance. In this method, we first transform all fitness vectors of individuals to polar coordinate vectors in the objective function space. Then we divide the population into several sub-populations by using declination angles. We calculate local dominance for individuals belonging to each sub-population based on the local search direction, and apply selection, recombination, and mutation to individual within each sub-population. We pick up NSGA-II and SPEA2 as two representatives of the latest generation of multiobjective evolutionary algorithms and enhance them with our model. We verify the effectiveness of the proposed method obtaining Pareto optimal solutions satisfying diversity conditions by comparing the search performance between the conventional algorithms and their enhanced versions.

Insights on properties of multiobjective MNK-landscapes

The influence of epistasis on the performance of evolutionary algorithms (EAs) is being increasingly investigated for single objective combinatorial optimization problem. Kauffmans NK-landscapes model of epistatic interactions, particularly, has been the center of several studies and is considered as a good test problem generator. However, epistasis and NK-landscapes in the context of multiobjective evolutionary algorithm (MOEAs) are almost unexplored subjects. In this work we present an extension of Kauffmans NK-landscapes model of epistatic interactions to multiobjective MNK-landscapes. MNK-landscapes present several desirable features and hold the potential of becoming an important class of scalable test problems generator for multiobjective combinatorial optimization. In order to meaningfully use MNK-landscapes as a benchmark tool we first need to understand how the parameters of the landscapes relate to multiobjective concepts. This paper is a first step towards understanding the properties of MNK-landscapes from a multiobjective standpoint.

Many-Objective Optimization by Space Partitioning and Adaptive ε-Ranking on MNK-Landscapes

This work proposes a method to search effectively on many -objective problems by instantaneously partitioning the objective space into subspaces and performing one generation of the evolutionary search in each subspace. The proposed method uses a partition strategy to define a schedule of subspace sampling, so that different regions of objective space could be emphasized at different generations. In addition, it uses an adaptive e -ranking procedure to re-rank solutions in each subspace, giving selective advantage to some of the solutions initially ranked highest in the whole objective space. Adaptation works to keep the actual number of highest ranked solutions in each subspace close to a desired number. The performance of the proposed method is verified on MNK-Landscapes. Experimental results show that convergence and diversity of the solutions found can improve remarkably on 4 ≤ M ≤ 10 objectives.

Self-controlling dominance area of solutions in evolutionary many-objective optimization

Controlling dominance area of solutions (CDAS) relaxes the concepts of Pareto dominance with an user-defined parameter S. This method enhances the search performance of dominance-based MOEA in many-objective optimization problems (MaOPs). However, to bring out desirable search performance, we have to experimentally find out S that controls dominance area appropriately. Also, there is a tendency to deteriorate the diversity of solutions obtained by CDAS when we decrease S from 0.5. To solve these problems, in this work, we propose a modification of CDAS called self-controlling dominance area of solutions (S-CDAS). In S-CDAS, the algorithm self-controls dominance area for each solution without the need of an external parameter. S-CDAS considers convergence and diversity and realizes a fine grained ranking that is different from conventional CDAS. In this work, we use many-objective 0/1 knapsack problems with m = 4 ∼ 10 objectives to verify the search performance of the proposed method. Simulation results show that SCDAS achieves well-balanced search performance on both convergence and diversity compared to conventional NSGA-II, CDAS, IBEAe+ and MSOPS.

Selection, drift, recombination, and mutation in multiobjective evolutionary algorithms on scalable MNK-Landscapes

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.

Effects of δ-Similar Elimination and Controlled Elitism in the NSGA-II Multiobjective Evolutionary Algorithm

In this paper, we propose <S-similar elimination to induce a better distribution of non-dominated solutions and distribute more fairly selection pressure among them in order to improve the search performance of multiobjective evolutionary algorithms in combinatorial optimization problems. With the proposed method similar individuals are eliminated in the process of evolution by using the distance between individuals in objective space. We investigate four eliminating methods to verify the effects of J-similar elimination and compare the search performance of enhanced NSGA-II by our method and by controlled elitism, which emphasizes the inclusion of lateral diversity.

Genetic algorithms on NK-landscapes: effects of selection, drift, mutation, and recombination

Empirical studies have shown that the overall performance of random bit climbers on NK-Landscapes is superior to the performance of some simple and enhanced GAs. Analytical studies have also lead to suggest that NK-Landscapes may not be appropriate for testing the performance of GAs. In this work we study the effect of selection, drift, mutation, and recombination on NK-Landscapes for N = 96. We take a model of generational parallel varying mutation GA (GASRM) and switch on and off its major components to emphasize each of the four processes mentioned above. We observe that using an appropriate selection pressure and postponing drift make GAs quite robust on NK-Landscapes; different to previous studies, even simple GAs with these two features perform better than a random bit climber (RBC+) for a broad range of classes of problems (K ≥ 4). We also observe that the interaction of parallel varying mutation with crossover improves further the reliability of the GA, especially for 12 12).We conclude that NK-Landscapes are useful for testing the GAs overall behavior and performance and also for testing each one of the major processes involved in a GA.

Adaptive objective space partitioning using conflict information for many-objective optimization

In a previous work we proposed a scheme for partitioning the objective space using the conflict information of the current Pareto front approximation found by an underlying multi-objective evolutionary algorithm. Since that scheme introduced additional parameters that have to be set by the user, in this paper we propose important modifications in order to automatically set those parameters. Such parameters control the number of solutions devoted to explore each objective subspace, and the number of generations to create a new partition. Our experimental results show that the new adaptive scheme performs as good as the nonadaptive scheme, and in some cases it outperforms the original scheme.