Catálogo de publicaciones - libros

Evolutionary Multi-objective Optimization (EMO) is ex-pected to be a powerful optimization framework for real world problems such as engineering design. Recent progress in automatic control and instrumentation provides a smart environment called Hardware In the Loop Simulation (HILS). It is available for our target application, that is, the experiment-based optimization. However, since Multi-objective Evolutionary Algorithms (MOEAs) require a large number of evaluations, it is difficult to apply it to real world problems of costly evaluation. To make experiment-based EMO using the HILS environment feasible, the most important pre-requisite is to reduce the number of necessary fitness evaluations. In the experiment-based EMO, the performance analysis of the evaluation reduction under the uncertainty such as observation noise is highly important, although the previous works assume noise-free environments. In this paper, we propose an evaluation reduction to overcome the above-mentioned problem by selecting the solution candidates by means of the estimated fitness before applying them to the real experiment in MOEAs. We call this technique Pre-selection. For the estimation of fitness, we adopt locally weighted regression. The effectiveness of the proposed method is examined by numerical experiments.

Optimization in changing environment is a challenging task, especially when multiple objectives are to be optimized simultaneously. The basic idea to address dynamic optimization problems is to utilize history information to guide future search. In this paper, two strategies for population re-initialization are introduced when a change in the environment is detected. The first strategy is to predict the new location of individuals from the location changes that have occurred in the history. The current population is then partially or completely replaced by the new individuals generated based on prediction. The second strategy is to perturb the current population with a Gaussian noise whose variance is estimated according to previous changes. The prediction based population re-initialization strategies, together with the random re-initialization method, are then compared on two bi-objective test problems. Conclusions on the different re-initialization strategies are drawn based on the preliminary empirical results.

In this paper, a new type of Multi-Objective Problems (MOPs) is introduced and formulated. The new type is an outcome of a motivation to find optimal solutions for different MOPs, which are coupled through communal components. Therefore, in such cases a multi-Multi-Objective Optimization Problem (m-MOOP) has to be considered. The solution to the m-MOOP is defined and an approach to search for it by applying an EMO algorithm sequentially is presented. This method, although not always resulting in the individual MOPs’ Pareto fronts, nevertheless gives solutions to the m-MOOP problem in hand. Several measures that allow the assessment of the introduced approach are offered. To demonstrate the approach and its applicability, academic examples as well as a "real-life," engineering example, are given.

The design of quality measures for approximations of the Pareto-optimal set is of high importance not only for the performance assessment, but also for the construction of multiobjective optimizers. Various measures have been proposed in the literature with the intention to capture different preferences of the decision maker. A quality measure that possesses a highly desirable feature is the hypervolume measure: whenever one approximation completely dominates another approximation, the hypervolume of the former will be greater than the hypervolume of the latter. Unfortunately, this measure—as any measure inducing a total order on the search space—is biased, in particular towards convex, inner portions of the objective space. Thus, an open question in this context is whether it can be modified such that other preferences such as a bias towards extreme solutions can be obtained. This paper proposes a methodology for quality measure design based on the hypervolume measure and demonstrates its usefulness for three types of preferences.

Considering external parameters during any evaluation leads to an optimization problem which has to handle several concurrent multi objective problems at once. This novel challenge, the Multiple Multi Objective Problem M-MOP, is defined and analyzed. Guidelines and metrics for the development of M-MOP optimizers are generated and exemplary demonstrated at an extended version of Deb’s NSGA-II algorithm. The relationship to the classical MOPs is highlighted and the usage of performance metrics for the M-MOP is discussed. Due to the increased number of dimensions the M-MOP represents a complex optimization task that should be settled in the optimization community.

Recent studies show that evolutionary optimizers are effective tools in solving real-world problem with complex and competing specifications. As more advanced multiobjective evolutionary optimizers (MOEO) are being designed and proposed, the issue of performance assessment has become increasingly important. While performance assessment could be done via theoretical and empirical approach, the latter is more practical and effective and has been adopted as the de facto approach in the evolutionary multiobjective optimization community. However, researches pertinent to empirical study have focused mainly on its individual components like test metrics and functions, there are limited discussions on the overall adequacy of empirical test in substantiating their statements made on the performance and behavior of the evaluated algorithm. As such, this paper aims to provide a holistic perspective towards the empirical investigation of MOEO and present a conceptual framework, which researchers could consider in the design and implementation of MOEO experimental study. This framework comprises of a structural algorithmic development plan and a general theory of adequacy in the context of evolutionary multiobjective optimization.

Multiobjective optimisation has traditionally focused on problems consisting of 2 or 3 objectives. Real-world problems often require the optimisation of a larger number of objectives. Research has shown that conclusions drawn from experimentations carried out on 2 or 3 objectives cannot be generalized for a higher number of objectives. The curse of dimensionality is a problem that faces decision makers when confronted with many objectives. Preference articulation techniques, and especially progressive preference articulation (PPA) techniques are effective methods for supporting the decision maker. In this paper, some of the most recent and most established PPA techniques are examined, and their utility for tackling -objective optimisation problems is discussed and compared from the viewpoint of the decision maker.

Pareto optimization methods are usually expected to find well-distributed approximations of Pareto fronts with basic geometry, such as smooth, convex and concave surfaces. In this contribution, test-problems are proposed for which the Pareto front is the intersection of a Lamé supersphere with the positive ℝ-orthant. Besides scalability in the number of objectives and decision variables, the proposed test problems are also scalable in a characteristic we introduce as , which is closely related to convexity/concavity, curvature and the position of knee-points of the Pareto fronts.

As a very basic bi-objective problem we propose a generalization of Schaffer’s problem. We derive closed-form expressions for the efficient sets and the Pareto fronts, which are arcs of Lamé supercircles. Adopting the bottom-up approach of test problem construction, as used for the DTLZ test-problem suite, we derive test problems of higher dimension that result in Pareto fronts of superspherical geomery.

Geometrical properties of these test-problems, such as concavity and convexity and the position of knee-points are studied. Our focus is on geometrical properties that are useful for performance assessment, such as the dominated hypervolume measure of the Pareto fronts. The use of these test problems is exemplified with a case-study using the SMS-EMOA, for which we study the distribution of solution points on different 3-D Pareto fronts.

Evolutionary algorithms have become a very popular approach for multiobjective optimization in many fields of engineering. Due to the outstanding performance of such techniques, new approaches are constantly been developed and tested to improve convergence, tackle new problems, and reduce computational cost. Recently, a new class of algorithms, based on ideas from the immune system, have begun to emerge as problem solvers in the evolutionary multiobjective optimization field. Although all these immune algorithms present unique, individual characteristics, there are some trends and common characteristics that, if explored, can lead to a better understanding of the mechanisms governing the behavior of these techniques. In this paper we propose a common framework for the description and analysis of multiobjective immune algorithms.