3,711 research outputs found
Impact of selection methods on the diversity of many-objective Pareto set approximations
Selection methods are a key component of all multi-objective and, consequently, many-objective optimisation evolutionary algorithms. They must perform two main tasks simultaneously. First of all, they must select individuals that are as close as possible to the Pareto optimal front (convergence). Second, but not less important, they must help the evolutionary approach to provide a diverse population. In this paper, we carry out a comprehensive analysis of state-of-the-art selection methods with different features aimed to determine the impact that this component has on the diversity preserved by well-known multi-objective optimisers when dealing with many-objective problems. The algorithms considered herein, which incorporate Pareto-based and indicator-based selection schemes, are analysed through their application to the Walking Fish Group (WFG) test suite taking into account an increasing number of objective functions. Algorithmic approaches are assessed via a set of performance indicators specifically proposed for measuring the diversity of a solution set, such as the Diversity Measure and the Diversity Comparison Indicator. Hyper-volume, which measures convergence in addition to diversity, is also used for comparison purposes. The experimental evaluation points out that the reference-point-based selection scheme of the Non-dominated Sorting Genetic Algorithm III (NSGA-III) and a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA-II), where the the crowding distance is replaced by the Euclidean distance, yield the best results
On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances
We consider the problem of evaluating the cumulative distribution function
(CDF) of the sum of order statistics, which serves to compute outage
probability (OP) values at the output of generalized selection combining
receivers. Generally, closed-form expressions of the CDF of the sum of order
statistics are unavailable for many practical distributions. Moreover, the
naive Monte Carlo (MC) method requires a substantial computational effort when
the probability of interest is sufficiently small. In the region of small OP
values, we propose instead two effective variance reduction techniques that
yield a reliable estimate of the CDF with small computing cost. The first
estimator, which can be viewed as an importance sampling estimator, has bounded
relative error under a certain assumption that is shown to hold for most of the
challenging distributions. An improvement of this estimator is then proposed
for the Pareto and the Weibull cases. The second is a conditional MC estimator
that achieves the bounded relative error property for the Generalized Gamma
case and the logarithmic efficiency in the Log-normal case. Finally, the
efficiency of these estimators is compared via various numerical experiments
Multiplicative Approximations, Optimal Hypervolume Distributions, and the Choice of the Reference Point
Many optimization problems arising in applications have to consider several
objective functions at the same time. Evolutionary algorithms seem to be a very
natural choice for dealing with multi-objective problems as the population of
such an algorithm can be used to represent the trade-offs with respect to the
given objective functions. In this paper, we contribute to the theoretical
understanding of evolutionary algorithms for multi-objective problems. We
consider indicator-based algorithms whose goal is to maximize the hypervolume
for a given problem by distributing {\mu} points on the Pareto front. To gain
new theoretical insights into the behavior of hypervolume-based algorithms we
compare their optimization goal to the goal of achieving an optimal
multiplicative approximation ratio. Our studies are carried out for different
Pareto front shapes of bi-objective problems. For the class of linear fronts
and a class of convex fronts, we prove that maximizing the hypervolume gives
the best possible approximation ratio when assuming that the extreme points
have to be included in both distributions of the points on the Pareto front.
Furthermore, we investigate the choice of the reference point on the
approximation behavior of hypervolume-based approaches and examine Pareto
fronts of different shapes by numerical calculations
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Decision support for build-to-order supply chain management through multiobjective optimization
This paper aims to identify the gaps in decision-making support based on
multiobjective optimization for build-to-order supply chain management (BTOSCM).
To this end, it reviews the literature available on modelling build-to-order
supply chains (BTO-SC) with the focus on adopting multiobjective optimization
(MOO) techniques as a decision support tool. The literature has been classified based
on the nature of the decisions in different part of the supply chain, and the key
decision areas across a typical BTO-SC are discussed in detail. Available software
packages suitable for supporting decision making in BTO supply chains are also
identified and their related solutions are outlined. The gap between the modelling and
optimization techniques developed in the literature and the decision support needed in
practice are highlighted and future research directions to better exploit the decision
support capabilities of MOO are proposed
Recommended from our members
Decision support for build-to-order supply chain management through multiobjective optimization
This is the post-print version of the final paper published in International Journal of Production Economics. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.This paper aims to identify the gaps in decision-making support based on multiobjective optimization (MOO) for build-to-order supply chain management (BTO-SCM). To this end, it reviews the literature available on modelling build-to-order supply chains (BTO-SC) with the focus on adopting MOO techniques as a decision support tool. The literature has been classified based on the nature of the decisions in different part of the supply chain, and the key decision areas across a typical BTO-SC are discussed in detail. Available software packages suitable for supporting decision making in BTO supply chains are also identified and their related solutions are outlined. The gap between the modelling and optimization techniques developed in the literature and the decision support needed in practice are highlighted. Future research directions to better exploit the decision support capabilities of MOO are proposed. These include: reformulation of the extant optimization models with a MOO perspective, development of decision supports for interfaces not involving manufacturers, development of scenarios around service-based objectives, development of efficient solution tools, considering the interests of each supply chain party as a separate objective to account for fair treatment of their requirements, and applying the existing methodologies on real-life data sets.Brunel Research Initiative and Enterprise Fund (BRIEF
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