Exploring the Performance of Stochastic Multiobjective Optimisers with the Second-Order Attainment Function

Fonseca, Carlos M.; Fonseca, Viviane Grunert da; Paquete, Luís

doi:10.1007/978-3-540-31880-4_18

Cited by 47 publications

(28 citation statements)

References 12 publications

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“…Each CPF is composed of non-dominated points in the objective space. They have been considered to assess the performances of MO optimizers [33,14] under the term Random Non-dominated Point (RNP) sets: sets of random vectors in R m , non-dominated with respect to each other and with random finite cardinality (see e.g. [13]).…”

Section: Conditional Simulations For Moo: Generation Of Conditional Pmentioning

confidence: 99%

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Binois

Ginsbourger

Roustant

2015

European Journal of Operational Research

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Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto Front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian Process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob'ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob'ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

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Section: Conditional Simulations For Moo: Generation Of Conditional Pmentioning

confidence: 99%

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Binois

Ginsbourger

Roustant

2015

European Journal of Operational Research

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“…How to best analyse the distribution of RNP-sets is an ongoing research effort in multiobjective optimisation [26,28,32,33,49]. The best-known proposal is to characterise the distribution of an RNP-set in terms of the attainment function:…”

Section: A Multi-objective View Of Runtime Distributionsmentioning

confidence: 99%

Automatically improving the anytime behaviour of optimisation algorithms

López-Ibáñez

Stützle

2014

European Journal of Operational Research

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Optimisation algorithms with good anytime behaviour try to return as high-quality solutions as possible independently of the computation time allowed. Designing algorithms with good anytime behaviour is a difficult task, because performance is often evaluated subjectively, by plotting the trade-off curve between computation time and solution quality. Yet, the trade-off curve may be modelled also as a set of mutually nondominated, bi-objective points. Using this model, we propose to combine an automatic configuration tool and the hypervolume measure, which assigns a single quality measure to a nondominated set. This allows us to improve the anytime behaviour of optimisation algorithms by means of automatically finding algorithmic configurations that produce the best nondominated sets. Moreover, the recently proposed weighted hypervolume measure is used here to incorporate the decision-maker's preferences into the automatic tuning procedure. We report on the improvements reached when applying the proposed method to two relevant scenarios: (i ) the design of parameter variation strategies for MAX-MIN Ant System, and (ii ) the tuning of the anytime behaviour of SCIP, an open-source mixed integer programming solver with more than 200 parameters.

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“…. , n, are created and initialised with sentinels (lines [1][2][3][4][5][6], so that all search operations are guaranteed to return a point. Then, the first point retrieved from the queue is inserted into the corresponding X * j and into L * 1 (lines 7-10), as it must be a minimal element of J 1 .…”

Section: The Three-objective Casementioning

confidence: 99%

“…In practice, the actual outcome sets produced for the same problem vary from optimisation run to optimisation run, due to the stochastic nature of the optimisers, and may be seen as realisations of a random non-dominated point set, or RNP set [3]. Optimiser performance may then be studied through the distribution of such a random set.…”

Section: Introductionmentioning

confidence: 99%

On the Computation of the Empirical Attainment Function

Fonseca

Guerreiro

López-Ibáñez

et al. 2011

Lecture Notes in Computer Science

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Abstract. The attainment function provides a description of the location of the distribution of a random non-dominated point set. This function can be estimated from experimental data via its empirical counterpart, the empirical attainment function (EAF). However, computation of the EAF in more than two dimensions is a non-trivial task. In this article, the problem of computing the empirical attainment function is formalised, and upper and lower bounds on the corresponding number of output points are presented. In addition, efficient algorithms for the two and three-dimensional cases are proposed, and their time complexities are related to lower bounds derived for each case.

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Exploring the Performance of Stochastic Multiobjective Optimisers with the Second-Order Attainment Function

Cited by 47 publications

References 12 publications

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Automatically improving the anytime behaviour of optimisation algorithms

On the Computation of the Empirical Attainment Function

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