49,396 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
Bat Algorithm for Multi-objective Optimisation
Engineering optimization is typically multiobjective and multidisciplinary
with complex constraints, and the solution of such complex problems requires
efficient optimization algorithms. Recently, Xin-She Yang proposed a
bat-inspired algorithm for solving nonlinear, global optimisation problems. In
this paper, we extend this algorithm to solve multiobjective optimisation
problems. The proposed multiobjective bat algorithm (MOBA) is first validated
against a subset of test functions, and then applied to solve multiobjective
design problems such as welded beam design. Simulation results suggest that the
proposed algorithm works efficiently.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1004.417
Duality for multiobjective variational control problems with (Φ,ρ)-invexity
In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under TeX-invexity. The results generalize a number of duality results previously established for multiobjective variational control problems under other generalized convexity assumptions
Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization
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 competitive 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 weighting and aggregating the costs 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, may prove to be even more worthwhile than SBO methods to expedite the optimization of computational expensive systems. In this paper, the authors propose the efficient multiobjective optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the probability of improvement and expected improvement criteria 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, SPEA2 and SMS-EMOA multiobjective optimization methods
Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes
In multiobjective combinatorial optimization, there exists two main classes
of metaheuristics, based either on multiple aggregations, or on a dominance
relation. As in the single objective case, the structure of the search space
can explain the difficulty for multiobjective metaheuristics, and guide the
design of such methods. In this work we analyze the properties of
multiobjective combinatorial search spaces. In particular, we focus on the
features related the efficient set, and we pay a particular attention to the
correlation between objectives. Few benchmark takes such objective correlation
into account. Here, we define a general method to design multiobjective
problems with correlation. As an example, we extend the well-known
multiobjective NK-landscapes. By measuring different properties of the search
space, we show the importance of considering the objective correlation on the
design of metaheuristics.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
Combination of Evolutionary Algorithms with Experimental Design, Traditional Optimization and Machine Learning
Evolutionary algorithms alone cannot solve optimization problems very efficiently
since there are many random (not very rational) decisions in these algorithms.
Combination of evolutionary algorithms and other techniques have been proven to be an efficient optimization methodology. In this talk, I will explain the basic ideas of our three algorithms along this line (1): Orthogonal genetic algorithm
which treats crossover/mutation as an experimental design problem, (2) Multiobjective
evolutionary algorithm based on decomposition (MOEA/D) which uses decomposition techniques from traditional mathematical programming in multiobjective optimization evolutionary algorithm, and (3) Regular model based multiobjective estimation of distribution algorithms (RM-MEDA) which uses the regular property and machine learning methods for improving multiobjective evolutionary algorithms
Scalarizing Functions in Bayesian Multiobjective Optimization
Scalarizing functions have been widely used to convert a multiobjective
optimization problem into a single objective optimization problem. However,
their use in solving (computationally) expensive multi- and many-objective
optimization problems in Bayesian multiobjective optimization is scarce.
Scalarizing functions can play a crucial role on the quality and number of
evaluations required when doing the optimization. In this article, we study and
review 15 different scalarizing functions in the framework of Bayesian
multiobjective optimization and build Gaussian process models (as surrogates,
metamodels or emulators) on them. We use expected improvement as infill
criterion (or acquisition function) to update the models. In particular, we
compare different scalarizing functions and analyze their performance on
several benchmark problems with different number of objectives to be optimized.
The review and experiments on different functions provide useful insights when
using and selecting a scalarizing function when using a Bayesian multiobjective
optimization method
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