2,270 research outputs found
Set-based Multiobjective Fitness Landscapes: A Preliminary Study
Fitness landscape analysis aims to understand the geometry of a given
optimization problem in order to design more efficient search algorithms.
However, there is a very little knowledge on the landscape of multiobjective
problems. In this work, following a recent proposal by Zitzler et al. (2010),
we consider multiobjective optimization as a set problem. Then, we give a
general definition of set-based multiobjective fitness landscapes. An
experimental set-based fitness landscape analysis is conducted on the
multiobjective NK-landscapes with objective correlation. The aim is to adapt
and to enhance the comprehensive design of set-based multiobjective search
approaches, motivated by an a priori analysis of the corresponding set problem
properties
Towards efficient multiobjective optimization: multiobjective statistical criterions
The use of Surrogate Based Optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, "real-world" problems often consist of multiple, conflicting objectives leading to a set of equivalent solutions (the Pareto front). The objectives are often aggregated into a single cost function to reduce the computational cost, though a better approach is to use multiobjective optimization methods to directly identify a set of Pareto-optimal solutions, which can be used by the designer to make more efficient design decisions (instead of making those decisions upfront). Most of the work in multiobjective optimization is focused on MultiObjective Evolutionary Algorithms (MOEAs). While MOEAs are well-suited to handle large, intractable design spaces, they typically require thousands of expensive simulations, which is prohibitively expensive for the problems under study. Therefore, the use of surrogate models in multiobjective optimization, denoted as MultiObjective Surrogate-Based Optimization (MOSBO), may prove to be even more worthwhile than SBO methods to expedite the optimization process. In this paper, the authors propose the Efficient Multiobjective Optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the expected improvement and probability of improvement criterions to identify the Pareto front with a minimal number of expensive simulations. The EMO algorithm is applied on multiple standard benchmark problems and compared against the well-known NSGA-II and SPEA2 multiobjective optimization methods with promising results
Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)
Recently, increasing works have proposed to drive evolutionary algorithms
using machine learning models. Usually, the performance of such model based
evolutionary algorithms is highly dependent on the training qualities of the
adopted models. Since it usually requires a certain amount of data (i.e. the
candidate solutions generated by the algorithms) for model training, the
performance deteriorates rapidly with the increase of the problem scales, due
to the curse of dimensionality. To address this issue, we propose a
multi-objective evolutionary algorithm driven by the generative adversarial
networks (GANs). At each generation of the proposed algorithm, the parent
solutions are first classified into real and fake samples to train the GANs;
then the offspring solutions are sampled by the trained GANs. Thanks to the
powerful generative ability of the GANs, our proposed algorithm is capable of
generating promising offspring solutions in high-dimensional decision space
with limited training data. The proposed algorithm is tested on 10 benchmark
problems with up to 200 decision variables. Experimental results on these test
problems demonstrate the effectiveness of the proposed algorithm
Racing Multi-Objective Selection Probabilities
In the context of Noisy Multi-Objective Optimization, dealing with
uncertainties requires the decision maker to define some preferences about how
to handle them, through some statistics (e.g., mean, median) to be used to
evaluate the qualities of the solutions, and define the corresponding Pareto
set. Approximating these statistics requires repeated samplings of the
population, drastically increasing the overall computational cost. To tackle
this issue, this paper proposes to directly estimate the probability of each
individual to be selected, using some Hoeffding races to dynamically assign the
estimation budget during the selection step. The proposed racing approach is
validated against static budget approaches with NSGA-II on noisy versions of
the ZDT benchmark functions
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