Catálogo de publicaciones - libros

In optimization studies including multi-objective optimization, the main focus is usually placed in finding the global optimum or global Pareto-optimal frontier, representing the best possible objective values. However, in practice, users may not always be interested in finding the global best solutions, particularly if these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the so-called robust solutions which are less sensitive to small changes in variables. Although robust optimization has been dealt in detail in single-objective optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find the robust optimal frontier, instead of the global Pareto-optimal front. The first procedure is a straightforward extension of a technique used for single-objective robust optimization and the second procedure is a more practical approach enabling a user to control the extent of robustness desired in a problem. To demonstrate the subtle differences between global and robust multi-objective optimization and the differences between the two robust optimization procedures, we define four test problems and show simulation results using NSGA-II. The results are useful and should encourage further studies considering robustness in multi-objective optimization.

Obtaining a well distributed non-dominated Pareto front is one of the key issues in multi-objective optimization algorithms. This paper proposes a new variant for the elitist selection operator to the NSGA-II algorithm, which promotes well distributed non-dominated fronts. The basic idea is to replace the crowding distance method by a maximin technique. The proposed technique is deployed in well known test functions and compared with the crowding distance method used in the NSGA-II algorithm. This comparison is performed in terms of achieved front solutions distribution by using distance performance indices.

In engineering and other ‘real-world’ applications, multiobjective optimization problems must frequently be tackled on a tight evaluation budget — tens or hundreds of function evaluations, rather than thousands. In this paper, we investigate two algorithms that use advanced initialization and search strategies to operate better under these conditions. The first algorithm, Bin_MSOPS, uses a binary search tree to divide up the decision space, and tries to sample from the largest empty regions near ‘fit’ solutions. The second algorithm, ParEGO, begins with solutions in a latin hypercube and updates a Gaussian processes surrogate model of the search landscape after every function evaluation, which it uses to estimate the solution of largest expected improvement. The two algorithms are tested using a benchmark suite of nine functions of two and three objectives — on a budget of only 250 function evaluations each, in total. Results indicate that the two algorithms search the space in very different ways and this can be used to understand performance differences. Both algorithms perform well but ParEGO comes out on top in seven of the nine test cases after 100 function evaluations, and on six after the first 250 evaluations.

Nearly all Multi-Objective Evolutionary Algorithms (MOEA) rely on random generation of initial population. In large and complex search spaces, this random method often leads to an initial population composed of infeasible solutions only. Hence, the task of a MOEA is not only to converge towards the Pareto-optimal front but also to guide the search towards the feasible region. This paper proposes the incorporation of a novel method for constructing initial populations into existing MOEAs based on so-called Pareto-Front-Arithmetics (PFA). We will provide experimental results from the field of embedded system synthesis that show the effectiveness of our proposed methodology.

This paper introduces a new algorithm to deal with multi-objective combinatorial and continuous problems. The algorithm is an extension of a previous one designed to deal with single objective combinatorial problems. The original purpose of the single objective version was to study in a rigorous way the properties the search graph of a particular problem needs to hold so that a randomized local search heuristic can find the optimum with high probability. The extension of these results to better understand multi-objective combinatorial problems seems to be a promising line of research. The work presented here is a first small step in this direction. A detailed description of the multi-objective version is presented along with preliminary experimental results on a well known combinatorial problem. The results show that the algorithm has the desired characteristics.

In this work the use of qualitative preferences for classifying and selecting MOEAs is introduced. The classical notions of the Analyst and the so called Prescriptive Analysis are introduced explicitly in EMO, identifying some difficulties in exploiting the results of the comparative studies performed by the current fashion. A methodology is developed that allows the analyst to translate DM’s general preferences as well as quantitative benchmarking results into a practical tool for the comparison of MOEAs, facilitating the selection of the proper method and/or parameters for the MCDM problem at hand. A comparative experimentation is performed using well known state of the art functions, allowing drawing clear conclusions about the utility of the proposed methodology. The results are useful for research, practitioners and analysts involved in benchmarking, comparative studies and prescriptive analysis for EMO.

The multiple criteria aggregation methods allow us to construct a recommendation from a set of alternatives based on the preferences of a decision maker. In some approaches, the recommendation is immediately deduced from the preferences aggregation process. When the aggregation model of preferences is based on the outranking approach, a special treatment is required, but some non-rational violations of the explicit global model of preferences could happen. In this case, the exploitation phase could then be treated as a multiobjective optimization problem. In this paper a new multiobjective evolutionary algorithm, which allows exploiting a known fuzzy outranking relation, is introduced with the purpose of constructing a recommendation for ranking problems. The performance of our algorithm is evaluated on a set of test problems. Computational results show that the multiobjective genetic algorithm-based heuristic is capable of producing high-quality recommendations.

The attainment function has been proposed as a measure of the statistical performance of stochastic multiobjective optimisers which encompasses both the quality of individual non-dominated solutions in objective space and their spread along the trade-off surface. It has also been related to results from random closed-set theory, and cast as a mean-like, first-order moment measure of the outcomes of multiobjective optimisers. In this work, the use of more informative, second-order moment measures for the evaluation and comparison of multiobjective optimiser performance is explored experimentally, with emphasis on the interpretability of the results.

This paper examines the effect of crossover operations on the performance of EMO algorithms through computational experiments on knapsack problems and flowshop scheduling problems using the NSGA-II algorithm. We focus on the relation between the performance of the NSGA-II algorithm and the similarity of recombined parent solutions. First we show the necessity of crossover operations through computational experiments with various specifications of crossover and mutation probabilities. Next we examine the relation between the performance of the NSGA-II algorithm and the similarity of recombined parent solutions. It is shown that the quality of obtained solution sets is improved by recombining similar parents. Then we examine the effect of increasing the selection pressure (i.e., increasing the tournament size) on the similarity of recombined parent solutions. An interesting observation is that the increase in the tournament size leads to the recombination of dissimilar parents, improves the diversity of solutions, and degrades the convergence performance of the NSGA-II algorithm.

This paper presents a new toolkit for creating scalable multi-objective test problems. The WFG Toolkit is flexible, allowing characteristics such as bias, multi-modality, and non-separability to be incorporated and combined as desired. A wide variety of Pareto optimal geometries are also supported, including convex, concave, mixed convex/concave, linear, degenerate, and disconnected geometries. All problems created by the WFG Toolkit are well defined, are scalable with respect to both the number of objectives and the number of parameters, and have known Pareto optimal sets. Nine benchmark multi-objective problems are suggested, including one that is both multi-modal and non-separable, an important combination of characteristics that is lacking among existing (scalable) multi-objective problems.