Novel frameworks for creating robust multi-objective benchmark problems

Mirjalili, Seyedali; Lewis, Andrew

doi:10.1016/j.ins.2014.12.037

Cited by 28 publications

(9 citation statements)

References 50 publications

(74 reference statements)

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“…In addition, the proposed approach allows designing different confidence-based methods for optimisation algorithms. To benchmark the proposed technique, some of our test functions [62,63,64] and performance indicators [65] will be used.…”

Section: Contributionsmentioning

confidence: 99%

“…Although these two sets of test functions are able to provide different types of robust Pareto optimal fronts, there are other issues in robust optimisation of real problems such as discontinuous robust/global Pareto optimal fronts, convex/concave robust/global Pareto optimal fronts, and multi-modality. Therefore, we have proposed challenging test functions in [62] to fill this gap and utilize them in this study. The test functions are generated with similar frameworks to that we proposed in [62].…”

Section: Test Problemsmentioning

confidence: 99%

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Confidence-based robust optimisation using multi-objective meta-heuristics

Mirjalili

Lewis

Dong

2018

Swarm and Evolutionary Computation

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Robust optimisation refers to the process of finding optimal solutions that have the lowest sensitivity to possible perturbations. In a multi-objective search space the robust optimal solutions should have the least dispersion on all of the objectives, making it a more challenging problem than in a single-objective search space. This paper establishes a novel and cheap technique for finding robust optimal solutions called confidence-based robust multi-objective optimisation. This approach uses a novel, modified Pareto dominance operator to differentiate search agents of meta-heuristics based on both level of robustness and confidence. The proposed confidence-based Pareto dominance allows us to design different confidence-based robust optimisation variants of meta-heuristics based on different methods. As a case study, robust Multi-Objective Particle Swarm Optimisation is equipped with the proposed operator to produce Confidence-based Robust Multi-Objective Particle Swarm Optimisation. A set of specific test functions and performance indicators is employed for benchmarking the Confidence-based Robust Multi-Objective Particle Swarm Optimisation.The results show that the proposed method is able to confidently and reliably find robust optimal solutions without significant extra computational burden. The paper also considers finding robust Pareto optimal front for a marine propeller design problem to demonstrate the applicability of the approach proposed in solving computationally expensive real-world problems with unknown true robust Pareto optimal fronts.

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Section: Contributionsmentioning

confidence: 99%

Section: Test Problemsmentioning

confidence: 99%

Confidence-based robust optimisation using multi-objective meta-heuristics

Mirjalili

Lewis

Dong

2018

Swarm and Evolutionary Computation

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“…Goh et al [20] proposed five test functions called GTCO and proved that they can provide challenging and biased search space for robust multi-objective optimisation algorithms. Three frameworks have also been proposed recently that allow designers to generate robust multi-objective test problems with different levels of difficulty [32]. Shifted robust multi-objective test functions were also proposed to improve the difficulty of the current test functions [33].…”

Section: Current Robust Multi-objective Test Problemsmentioning

confidence: 99%

Hindrances for robust multi-objective test problems

Mirjalili

Lewis

2015

Applied Soft Computing

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“…Typically, in these studies, symmetric random noise is added to the decision variables [3,7,14,15,16] or the objective functions [5,9,12,18] in a bespoke way that meets the requirements for the specific uncertainties and definitions of robustness being considered. The problem that is used to benchmark every suggested algorithm is tailored to the type of uncertainty and definition of robustness considered in the study.…”

Section: Introductionmentioning

confidence: 99%

“…The problem that is used to benchmark every suggested algorithm is tailored to the type of uncertainty and definition of robustness considered in the study. For example, Deb and Gupta [3], Gaspar-Chuna et al [7] and Mirjalili and Lewis [14,15,16] considered variation in decision variables, and therefore robustness is defined as either sensitivity of the objectives to variations in decision space, or as the averaged performance over a neighbourhood of the candidate solution. The problems developed in these studies are deterministic functions that demonstrate differences between the nominal Pareto front and the 'robust' front.…”

Section: Introductionmentioning

confidence: 99%

A Toolkit for Generating Scalable Stochastic Multiobjective Test Problems

Purshouse

Giaghiozis

Fleming

2016

Proceedings of the Genetic and Evolutionary Computation Conference 2016

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Real-world optimization problems typically include uncertainties over various aspects of the problem formulation. Some existing algorithms are designed to cope with stochastic multiobjective optimization problems, but in order to benchmark them, a proper framework still needs to be established. This paper presents a novel toolkit that generates scalable, stochastic, multiobjective optimization problems. A stochastic problem is generated by transforming the objective vectors of a given deterministic test problem into random vectors. All random objective vectors are bounded by the feasible objective space, defined by the deterministic problem. Therefore, the global solution for the deterministic problem can also serve as a reference for the stochastic problem. A simple parametric distribution for the random objective vector is defined in a radial coordinate system, allowing for direct control over the dual challenges of convergence towards the true Pareto front and diversity across the front. An example for a stochastic test problem, generated by the toolkit, is provided.

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Novel frameworks for creating robust multi-objective benchmark problems

Cited by 28 publications

References 50 publications

Confidence-based robust optimisation using multi-objective meta-heuristics

Confidence-based robust optimisation using multi-objective meta-heuristics

Hindrances for robust multi-objective test problems

A Toolkit for Generating Scalable Stochastic Multiobjective Test Problems

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