Multi-Objective Optimization with an Adaptive Resonance Theory-Based Estimation of Distribution Algorithm: A Comparative Study

Abstract

Abstract. The introduction of learning to the search mechanisms of optimization algorithms has been nominated as one of the viable approaches when dealing with complex optimization problems, in particular with multi-objective ones. One of the forms of carrying out this hybridization process is by using multi-objective optimization estimation of distribution algorithms (MOEDAs). However, it has been pointed out that current MOEDAs have a intrinsic shortcoming in their model-building algorithms that hamper their performance.In this work we argue that error-based learning, the class of learning most commonly used in MOEDAs is responsible for current MOEDA underachievement. We present adaptive resonance theory (ART) as a suitable learning paradigm alternative and present a novel algorithm called multi-objective ART-based EDA (MARTEDA) that uses a Gaussian ART neural network for model-building and an hypervolume-based selector as described for the HypE algorithm. In order to assert the improvement obtained by combining two cutting-edge approaches to optimization an extensive set of experiments are carried out. These experiments also test the scalability of MARTEDA as the number of objective functions increases.

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.…”

“…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].…”

Classification scheme of multi-objective Estimation of Distribution Algorithms

“…In [11] it is mentioned another way to classify EDAs, but only applied to those EDAs that involves probabilistic graphical models (PGM) in its process, never the less, there are cases in the 24 state-of-the-art algorithms, that do not involves (PGM) [6][7][8][9], so that, a new category must be added in order to include this kind of algorithms:…”

“…The complete list of algorithms and their reference is shown next: BMOA [14], DT-MEDA [15], JGBN-EDA [4], MARTEDA [9], MASO [16], MBOA [17], MEDA/D [3], MhBOA [11], MIDEA [19], mMARLEDA [20], MMEA [21], MO-CMA-ES [22], MO-COIN [23], MOEA-HCEDA [24], [8], MOHEDA [18], MONEDA [7], MO-PBIL [25], MOPED [8], MrBOA [26], P-BOA [27], RCMEDA [28], RM-MEDA [29], and VEDA [6].…”