Hypervolume-Based DIRECT for Multi-Objective Optimisation

Wong, Cheryl Sze Yin; Al-Dujaili, Abdullah; Sundaram, Suresh

doi:10.1145/2908961.2931702

Cited by 13 publications

(11 citation statements)

References 12 publications

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“…Let us finally survey some algorithms related to the direct algorithm, although some of them make partial use of heuristics and are not, thus, fully in our scope of studying deterministic algorithms. In [1,45], the authors propose three algorithms called MO-DIRECT, derived from direct by employing either the ranks of the nondominated sorting [11], the hypervolume indicator or the nondominance (ND) concept in the objective space augmented by an extra dimension consisting of the hyperinterval radius. Several numerical performance tests have been implemented and used for measuring the capabilities of these algorithms.…”

Section: Literature Surveymentioning

confidence: 99%

“…A series of papers [5,6] discusses applications of an extension of direct to damage identification problems with a numerical comparison with MO-DIRECT [1,45]. The algorithm proposed uses a scalarization of the multiobjective optimization problem by assigning to a vector v in the objective space the rank R(v) given by the nondominated sorting.…”

Section: Literature Surveymentioning

confidence: 99%

“…Indeed, in most cases, 1. a single objective exact global algorithm is employed after the multiobjective optimization problem has been scalarized (e.g., [3,4,45]) or 2. an exact global algorithm is hybridized at some level with one or more non-deterministic principles (e.g., [4,21,42]).…”

Section: Introductionmentioning

confidence: 99%

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On the Extension of the DIRECT Algorithm to Multiple Objectives

Lovison

Miettinen

2020

J Glob Optim

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Deterministic global optimization algorithms like Piyavskii-Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce representations of the globally Pareto optimal set are usually based on heuristics. We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space. Under this light, we consider the well-known global optimization algorithm direct, analyze the available algorithms in the literature that extend direct to multiple objectives and discuss possible alternatives. In particular, we propose a novel definition for the notion of potential Pareto optimality extending the notion of potential optimality defined in direct. We also discuss its advantages and disadvantages when compared with algorithms existing in the literature.

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Section: Literature Surveymentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

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On the Extension of the DIRECT Algorithm to Multiple Objectives

Lovison

Miettinen

2020

J Glob Optim

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“…6, 7, and 8 can be seen as supplements to the empirical cumulative distribution functions (ECDFs), provided by the COCO platform by default. , MO-DIRECT-hv-rank is an extension of the DIviding RECTangles approach to multiobjective optimization [15], GA-MULTIOBJ-NSGA-II is the default Matlab implementation of the standard NSGA-II [1], and SMS-EMOA-PM is the standard SMS-EMOA variant with polynomial mutation and SBX crossover [3]. The random search will be used here as a reference algorithm to which the other three algorithms are compared to.…”

Section: A Few Examples Of Algorithm Comparisons With Arta Function Pmentioning

confidence: 99%

Quantitative Performance Assessment of Multiobjective Optimizers: The Average Runtime Attainment Function

Brockhoff¹,

Auger²,

Hansen³

et al. 2017

Lecture Notes in Computer Science

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Abstract. Numerical benchmarking of multiobjective optimization algorithms is an important task needed to understand and recommend algorithms. So far, two main approaches to assessing algorithm performance have been pursued: using set quality indicators, and the (empirical) attainment function and its higherorder moments as a generalization of empirical cumulative distributions of function values. Both approaches have their advantages but rely on the choice of a quality indicator and/or take into account only the location of the resulting solution sets and not when certain regions of the objective space are attained. In this paper, we propose the average runtime attainment function as a quantitative measure of the performance of a multiobjective algorithm. It estimates, for any point in the objective space, the expected runtime to find a solution that weakly dominates this point. After defining the average runtime attainment function and detailing the relation to the (empirical) attainment function, we illustrate how the average runtime attainment function plot displays algorithm performance (and differences in performance) for some algorithms that have been previously run on the biobjective bbob-biobj test suite of the COCO platform.

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“…At the moment, corresponding exact and global methods for multiobjective optimization have not been developed and employed to the same extent as their single objective counterparts. However, some of these methods have inspired or have been used as a component in a number of multiobjective optimization algorithms [2,3,4,5,6,7]. Nevertheless, most of them have the following characteristics:…”

mentioning

confidence: 99%

Exact extension of the DIRECT algorithm to multiple objectives

Lovison¹,

Miettinen²

2019

AIP Conference Proceedings

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The direct algorithm has been recognized as an efficient global optimization method which has few requirements of regularity and has proven to be globally convergent in general cases. direct has been an inspiration or has been used as a component for many multiobjective optimization algorithms. We propose an exact and as genuine as possible extension of the direct method for multiple objectives, providing a proof of global convergence (i.e., a guarantee that in an infinite time the algorithm becomes everywhere dense). We test the efficiency of the algorithm on a nonlinear and nonconvex vector function.

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Hypervolume-Based DIRECT for Multi-Objective Optimisation

Cited by 13 publications

References 12 publications

On the Extension of the DIRECT Algorithm to Multiple Objectives

On the Extension of the DIRECT Algorithm to Multiple Objectives

Quantitative Performance Assessment of Multiobjective Optimizers: The Average Runtime Attainment Function

Exact extension of the DIRECT algorithm to multiple objectives

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