Multimodal optimization using niching differential evolution with index-based neighborhoods

Epitropakis, Michael G.; Plagianakos, Vassilis P.; Vrahatis, Michael N.

doi:10.1109/cec.2012.6256480

Cited by 17 publications

(12 citation statements)

References 22 publications

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“…local optima). The algorithms developed and commonly employed for performing such optimizations are called "niching" methods, examples of which are crowding [19,20], fitness sharing [6,20,21], clearing [22], speciation [23,24] dynamic archives [25], probabilistic selection [26] and local neighbourhoods [27,28]. A full review is presented by Li et al [29].…”

Section: Introductionmentioning

confidence: 99%

Identifying Multiple Optima in Aerodynamic Design Spaces

Poole

Allen

Rendall

2018

2018 Multidisciplinary Analysis and Optimization Conference

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Parallel niching optimization algorithms are developed and applied to a multimodal aerodynamic optimization case to identify multiple optima in the design space. Previous work by the authors has presented niching optimization algorithms that use differential evolution with feasible selection as a basis that can identify multiple optima in constrained search spaces, which is necessary for aerodynamic optimization. In this paper, these algorithms are further developed for application to aerodynamic optimization by reformulating each to provide a parallel decomposition of the objective function evaluation at each iteration of the optimization process. These algorithms are tested on an analytical optimization problem. The parallel, constrained form of both local nearest-neighbourhood and local crowding are shown to be the best performing algorithms with a 99% confidence level. A variation on the AIAA ADODG case 6 multimodal wing optimization case is also studied. A multi-start gradient-based approach is used to show multimodality of the design space. The local nearest-neighbourhood-based algorithm is then applied to the aerodynamic optimization case and is able to successfully identify two minima in the design space, with one being close to the global minimum and one in a different part of the design space, which is a local minimum. * Senior Teaching Associate.

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Section: Introductionmentioning

confidence: 99%

Identifying Multiple Optima in Aerodynamic Design Spaces

Poole

Allen

Rendall

2018

2018 Multidisciplinary Analysis and Optimization Conference

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“…Further studies on the dynamics of DE [50], [51] reveal that DE individuals are inclined to cluster around either local or global optima after some iterations. A clustering tendency statistic, the H-measure, was suggested in [50] to measure the varying degrees of clustering tendency that may occur for six classical DE variants.…”

Section: B Differential Evolutionmentioning

confidence: 99%

“…The complexity of this fast niching algorithm is proved to be linear to the population size. Another approach using approximate neighborhoods is an index-based neighborhoods in DE [51], which can also substantially decrease the complexity of the niching algorithm.…”

Section: B Differential Evolutionmentioning

confidence: 99%

Seeking Multiple Solutions: An Updated Survey on Niching Methods and Their Applications

Epitropakis

Deb

et al. 2017

IEEE Trans. Evol. Computat.

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Abstract-Multi-modal optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation is an important topic which has practical relevance in problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO prolems, if equipped with specifically-designed diversity-preserving mechanisms, commonly known as niching methods. This paper provides an updated survey on niching methods. The paper first revisits the fundamental concepts about niching and its most representative schemes, then reviews the more recent development of niching methods, including novel and hybrid methods, performance measures, and benchmarks for their assessment. Furthermore, the paper surveys previous attempts on leveraging the capabilities of niching to facilitate various optimization (e.g., multi-objective and dynamic optimization) and machine learning (e.g., clustering, feature selection, and learning ensembles) tasks. A list of successful applications of niching methods to real-world problems is provided to demonstrate that niching methods are able to provide solutions that are difficult for conventional optimization methods to offer. The significant practical value of niching methods is clearly exemplified through these applications. Finally, the paper poses challenges and research questions on niching that are yet to be appropriately addressed. Providing answers to these questions is crucial before we can bring more fruitful benefits of niching to real-world problem solving.

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“…For example, Qu et al[22] developed a neighbourhood framework that was used to present new, neighbourhood-based crowding, speciation and fitness sharing DE algorithms. These were shown to outperform their non-neighbourhood counterparts.Other DE niching methods that have shown to perform well include using a dynamic archive [57], probabilistic selection [58] and local neighbourhoods [59,60]. Furthermore, an ensemble of niching methods, with dynamic selection to determine which to use, has also been successful [61].The body of work presented above on constrained optimization is solving the problem of finding the unique solution that solves a CNOP.…”

mentioning

confidence: 99%

“…Other DE niching methods that have shown to perform well include using a dynamic archive [57], probabilistic selection [58] and local neighbourhoods [59,60]. Furthermore, an ensemble of niching methods, with dynamic selection to determine which to use, has also been successful [61].…”

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confidence: 99%

Constrained niching using differential evolution

Poole

Allen

2019

Swarm and Evolutionary Computation

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The work presented here involves development and detailed investigations of niching methods for multimodal optimization of constrained functions. There is a lack of investigations in the literature on constrained multimodal optimization, hence a number of constrained niching algorithms have been developed here that leverage existing differential evolution-based niching methods with a feasibility rules-domination selection procedure. Furthermore, a suite of 18 benchmark functions has been developed and are presented in this paper; nine newly developed functions are incorporated with nine existing functions from the literature. Optimization results on these analytical functions using the constrained niching algorithms are presented, with analysis provided on the ability to locate multiple global optima, the convergence speed and constraint handling nature of the methods. The differential evolution strategy is also investigated, with SHADE and L-SHADE strategies considered. Finally, a dimensionality study also compares against the only other known constrained niching algorithm. Results indicate that all of the algorithms developed and tested generally perform well for low dimensional, low modality problems, but that local neighbourhood-based methods show the best results across the suite of functions tested. When high-dimensional problems are considered, using the L-SHADE strategy yields excellent results. An accompanying supplementary data file is provided with the manuscript.has also been successfully applied to DE [51]. The ensemble approach takes any number of constraint handling techniques and adaptively applies them to exploit the individual performance of each technique. Mezura-Montes et al.[52] investigated the effect of different mutation strategies in DE on constrained optimization. They highlighted the fact that much work in solving CNOPs using DE uses the feasibility rules of Deb [14], and as such, used this to handle the constraints.Commonly, population diversity is a requirement of EAs, such that design space exploration is achieved, with diversity decreasing through the optimization to exploit the global optimum within the space. On the other hand, while diversity is important for unimodal optimization, this is not necessarily the main driver of niching techniques. Niching requires a more careful balance of diversity to be able to locate and maintain strong and stable niches, and therefore exploit all the optima in the design space. Comprehensive reviews on niching techniques have been provided by Das et al.[53] and more recently by Li et al. [25] (the reader is particularly guided to the review of Li et al. for discussions of niching using SIAs as well as EAs), and a short review is presented here with particular attention paid to niching using EAs.One of the earliest bodies of work on maintaining population diversity, and therefore implicitly also multimodal optimization, was by de Jong [17], who introduced the classical idea of crowding. Crowding compares the fitness of close individuals and attemp...

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Multimodal optimization using niching differential evolution with index-based neighborhoods

Cited by 17 publications

References 22 publications

Identifying Multiple Optima in Aerodynamic Design Spaces

Identifying Multiple Optima in Aerodynamic Design Spaces

Seeking Multiple Solutions: An Updated Survey on Niching Methods and Their Applications

Constrained niching using differential evolution

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