MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm

Abstract

The extension of estimation of distribution algorithms (EDAs) to the multiobjective domain has led to multi-objective optimization EDAs (MOEDAs). Most MOEDAs have limited themselves to porting single-objective EDAs to the multi-objective domain. Although MOEDAs have proved to be a valid approach, the last point is an obstacle to the achievement of a significant improvement regarding "standard" multi-objective optimization evolutionary algorithms. Adapting the model-building algorithm is one way to achieve a substantial advance. Most model-building schemes used so far by EDAs employ off-the-shelf machine learning methods. However, the model-building problem has particular requirements that those methods do not meet and even evade. The focus of this paper is on the modelbuilding issue and how it has not been properly understood and addressed by most MOEDAs. We delve down into the roots of this matter and hypothesize about its causes. To gain a deeper understanding of the subject we propose a novel algorithm intended to overcome the drawbacks of current MOEDAs. This new algorithm is the multi-objective neural estimation of distribution algorithm (MONEDA). MONEDA uses a modified growing neural gas network for model-building (MB-GNG). MB-GNG is a custom-made clustering algorithm that meets the above demands. Thanks to its custom-made model-building algorithm, the preservation of elite individuals and its individual replacement scheme, MONEDA is capable of scalably B Luis Martí 123 J Glob Optim solving continuous multi-objective optimization problems. It performs better than similar algorithms in terms of a set of quality indicators and computational resource requirements.

Averaged Hausdorff Approximations of Pareto Fronts based on Multiobjective Estimation of Distribution Algorithms

“…Considering the MEDAs we deal with two well-known approaches: the naive MIDEA [18] and the multiobjective CMA-ES (MO-CMA-ES) [21]. We also include MONEDA [28] and MARTEDA [31] as they are supposed to have a better handling of diversity. The parameters of the MEDAs are summarized in Table 1.…”

“…AMS has been conjointly used with AVS in the multiobjective adapted maximum-likelihood Gaussian mixture model (MAMaLGaM-X) [27]. Similarly, the multiobjective optimization neural EDA (MONEDA) [28] embeds a custom-made model building algorithm [29] that is able to maintain diversity by correctly handling the outlier elements. This approach has been improved by the introduction of the match-based learning paradigm of adaptive resonance theory (ART) [30] leading to the multiobjective ART EDA (MARTEDA) [31].…”

Bio-inspired computation: Where we stand and what's next

“…In the early days of this area, two types of approaches were commonly adopted to cope with many-objective optimization problems: 1) to adopt or propose a preference relation that induces a finer grain order on the solutions than that induced by the Pareto dominance relation; or 2) to reduce the number of objectives of the problem during the search process or during the decision making process. Many other approaches are possible, including, for example, the use of machine learning techniques (as in MONEDA [137]), performance indicators (as in SMS-EMOA [138]), -dominance or the two-archive MOEA, which uses one archive for convergence and another for diversity [139].…”

Evolutionary multiobjective optimization: open research areas and some challenges lying ahead

“…Many other approaches are possible for tackling manyobjective problems, including, for example, the use of alternative ranking schemes (different from nondominated sorting) (see for example [54]), the use of machine learning techniques (as in MONEDA [108]), or approaches such as the two-archive MOEA, which uses one archive for convergence and another for diversity [131].…”